Regulation of Contraction in Striated Muscle

A. M. Gordon, E. Homsher, M. Regnier


Ca2+ regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A7TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca2+binding sites on TnC, conformational changes resulting from Ca2+ binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca2+ binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1–2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca2+-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the “open” probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A7TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca2+ binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca2+ regulates the strong binding of M·ADP·Pi to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca2+ activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A7TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca2+]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca2+ binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. These results and conclusions suggest possible explanations for differences between skeletal and cardiac muscle regulation and delineate the paths future research may take toward a better understanding of striated muscle regulation.


A more complete understanding of the regulation of striated muscle contraction has come from the convergence of exciting new information from a number of different directions. New data have emerged about the structure of actin, the thin filament, the myosin S1 head, possible sites of actin-myosin interaction, the regulatory proteins, and the structural changes that generate filament sliding and force production (see review by Cooke, Ref. 67). Correlations have been made between the steps in the actomyosin ATPase cycle and the structural changes involved in the cross-bridge ATPase cycle, resulting in a better understanding of the activation of myosin ATPase by actin and the binding of different myosin-nucleotide states to actin (67). Structural studies have revealed changes in the thin filament that accompany activation of contraction (see Refs. 475, 507). Recent biochemical studies have better defined the steps being regulated and provided a clearer description of the possible modes of regulation (303, 455). Physiological studies now routinely use molecular techniques to better define the modes of regulation in the striated muscle cell (331,333). Finally, in vitro motility techniques combining molecular and biochemical studies along with physiological measurements of force and filament sliding offer new approaches to the study of regulation of the cross-bridge cycle in striated muscle (148, 206).

The specific questions addressed in this review are as follows.

What methods can be used to study regulation? What are their advantages and limitations?
Does Ca2+ binding to troponin (Tn) C alone regulate contraction or do strongly bound cross bridges contribute to thin filament activation? Does cross-bridge binding to actin promote additional cross-bridge binding to the thin filament? If cross-bridge binding further activates the thin filament, which cross-bridge state(s) can produce this activation?
Do the regulatory proteins merely regulate the number of cross bridges, or do they modify rate constants of the transitions between various attached states of the cross bridge? Are any of the rate constants in the actomyosin cycle controlled by thin filament regulatory proteins? Does troponin I block cross-bridge binding to one or more actin monomers in the absence of Ca2+? What factors control the tropomyosin (Tm) position on the thin filament? How flexible is Tm, and does the binding of myosin to actin vary within an A7TmTn unit?
Do regulatory proteins exert allosteric effects on the interaction between cross bridges and the thin filament?
What are the differences in the regulation of skeletal and cardiac muscle, and how can the properties of the constituent protein isoforms be accounted for by these differences?

We conclude that the major step controlled by Ca2+during activation is the strong binding of the M·ADP·Pispecies to actin with possibly some modulation by isoforms or Ca2+ of the kinetic steps in the cross-bridge cycle. Strong binding of M·ADP·Pi to actin is controlled by regulation of the effective actin concentration that varies with the fraction of time the Tm spends in an “open” position. In the absence of Ca2+, the weak electrostatic binding of myosin to actin binding sites may be blocked at some actins by TnI, but at other actins appear to be either unregulated or only poorly regulated. A major change in affinity during activation occurs subsequent to a movement of Tm that uncovers strong hydrophobic binding sites on actin by a modified steric blocking mechanism, blocking strong but not necessarily weak binding. In skeletal muscle, the movements of Tm after Ca2+ binding to TnC and the subsequent changes in Tn-Tm-actin interaction expose myosin-binding sites on actin, increasing the affinity of actin for myosin. This increased affinity allows weak binding to some actins and stronger binding to others, presumably because of the flexibility of Tm. The affinity of all actins for myosin is increased when sufficient numbers of strongly attached cross bridges displace (or stabilize the displacement of) the Tm further than occurs with Ca2+ binding alone, making still more sites available for myosin binding to actin. One factor that enhances the affinity of the actin filament for myosin, following Ca2+ binding to TnC, is a structural change in actin occasioned by allosteric actions. A second factor affecting myosin binding to actin is the distance of the myosin heads from actin binding sites, influenced by changes in interfilament spacing with sarcomere length or movement of myosin heads away from the thick filament toward the thin filament upon phosphorylation of thick filament components. This view of Ca2+ activation of the thin filament may be thought of as “analogous to the effect of a ligand that binds to a ligand-gated ion channel and cause an increase in the channel open probability” (398). This is a helpful way to conceptualize the increased probability of strong myosin binding to the thin filament, which is a result of Tm movement to increase the availability of actins for strong binding by myosin, an activated or open position. This Tm movement is in turn brought on by Ca2+ binding to TnC and by strong cross-bridge binding to actin to move Tm and/or stabilize it in this activated or open position.

The range of Tm movement over actin's surface and hence the extent of thin filament activation is controlled by Ca2+ binding to TnC and strong cross-bridge binding to actin. First, Ca2+ binding to TnC in one A7TmTn unit weakens TnI binding to actin and allows an azimuthal Tm movement in the unit exposing myosin binding sites on some or all of the seven actin monomers within the unit. Second, the TnT binding to Tm and the overlap of Tm from adjacent thin filament A7TmTn regulatory units allows coupling and propagation of Tm motion along the thin filament. The extent of this coupling, or cooperative activation, varies with the composition of the regulatory protein isoforms. Finally, cross-bridge binding contributes to activation by stabilizing the Tm/Tn unit in an activated position or allosterically modifying the actin.

The physiological studies of the regulation of force and shortening in skinned muscle fibers and filament sliding in the in vitro motility assay are the major focus of this review. The conclusions we draw from these studies are as follows.

The force-pCa relationship can be understood as a Ca2+regulation of strong cross-bridge attachment with the steep relationship between Ca2+ and force requiring cooperative activation by strongly attached cross bridges.
The rate of force redevelopment (kTR) after rapid release and restretch in skinned fibers is determined by the properties of the myosin at maximal Ca2+ activation, but at submaximal Ca2+ is best considered as a Ca2+regulation of the kinetics of activation of the thin filament. There is little evidence that either cooperativity between neighboring units along the thin filament or cooperativity of cross-bridge attachment within a regulatory unit influences kTR.
The rapid activation of contraction by step increases in [Ca2+] demonstrates that the rate of force development depends primarily on [Ca2+] and not on the initial level of force. This is consistent with conclusions from thekTR measurements that the activation rate results primarily from the kinetics of Ca2+ binding and the subsequent conformational changes of the thin filament.
Measurements of the force transient following rapid increases in [Pi] (kPi) indicate that the Pi release step and force-generating isomerization step in striated muscle exhibit little Ca2+ dependence, implying that they are not Ca2+ regulated. Therefore, the kinetic step regulated by Ca2+ is a strong cross-bridge attachment per se, before force generation.
Measurements of unloaded shortening velocity in skinned and intact muscle fibers can be understood in terms of the A. F. Huxley (215) cross-bridge model with drag from negatively strained cross bridges balancing the positive strain from force-generating cross bridges. There appears to be no intrinsic Ca2+ regulation of the cross-bridge product release steps or detachment from actin, with the main Ca2+dependence being regulation of strong cross bridges binding. However, in skinned fibers, the shortening velocity over longer distances is Ca2+ sensitive, and this may be due to a shortening-induced thin filament deactivation. There appears to be little Ca2+ dependence of the shortening velocity in intact muscle. Calcium modulates thin filament sliding speed in the in vitro motility assay, but this is probably related to limitations on the number of cross bridges interacting with the thin filament.
Strongly bound cross bridges can activate skinned fibers in the absence of Ca2+ with the steepness of the relationship between [ATP] and force depending on the muscle type, being greater in cardiac than skeletal muscle. Rigor cross bridges [e.g.,N-ethylmaleimide (NEM)-S1] do not appear to activate the thin filament directly but appear to enhance its activation by Ca2+.
Rigor cross bridges enhance Ca2+ binding to TnC, while cycling cross bridges enhance Ca2+ binding to TnC primarily in cardiac muscle, with much less effect in skeletal muscle.
During relaxation, after myoplasmic [Ca2+] has been reduced to small values, the rate of force decline during the “isometric” phase decreases with increases in the initial force level in skeletal muscle. This result provides evidence for sustained activation by strongly attached, cycling cross bridges in skeletal muscle.
During rapid shortening, the number of strongly attached cross bridges falls, which probably accounts for the shortening-induced deactivation observed in skeletal muscle.
The in vitro motility assay provides an exciting new technique for investigating the regulation of contraction. Recent experiments support the conclusion that Ca2+ regulates strong cross-bridge binding but also suggest that Ca2+ could modulate another step in the cross-bridge cycle.

Thus the regulation of cross-bridge interactions to generate force and shortening can be understood in terms of control of strong binding with possible secondary modulation of cross-bridge kinetics. Differences in kinetic rates can be understood in terms of intrinsic differences in rates of transitions between actomyosin products states and differences in regulatory protein isoforms. The effective rates of attachment and detachment of force-generating cross bridges determine differences in maximum rates. At submaximal levels of activation, kinetics are primarily controlled by the kinetics of Ca2+ binding to TnC and the related transitions of the regulatory proteins. Differences in activation properties between muscle fiber types can be understood in terms of differences between properties of the regulatory protein isoforms. The coupling between regulatory units in cardiac muscle is stronger in the absence of Ca2+, implying less flexibility of the Tm-Tn system. Also in cardiac, but not in skeletal muscle, strong cross-bridge attachment promotes Ca2+ binding, thus coupling Ca2+ binding with cycling cross-bridge attachment and force generation.


In this section we review information on the protein units responsible for regulation of contractions. This will include the thin and thick filament, the proteins forming these structures, and their interactions relevant to contractile regulation. We also discuss new information on the actin and myosin structures and the interacting surfaces between them to understand better the structural basis of regulation. Finally, we describe the cross-bridge cycle to specify the steps in this cycle being regulated.

A.  Thin Filament

The main site for Ca2+ regulation is the thin filament. Figure 1 is a diagram of the thin filament in striated muscle showing the three components: actin, Tm, and Tn with the three Tn subunits. There have been a number of reviews on the interaction between these components in regulation (77, 105, 154, 455) that can be referred to for additional details. Tobacman's review (455) contains a particularly good discussion of the proteins and their assembly into the thin filament.

Fig. 1.

A model of the molecular arrangement of troponin (Tn), tropomyosin (Tm), and actin in the skeletal muscle thin filament. The various troponin subunits are indicated [TnC (red), TnT (yellow), and TnI (green)] as they lie along the two-stranded tropomyosin shown as an α- (brown) and β-heterodimer (orange) that in turn lies along an actin (gray) strand, spanning 7 G-actin monomers. Note that adjacent tropomyosin molecules overlap head to tail with the NH2-terminal region of the highly asymmetrical TnT lying along the overlap region. The COOH-terminal region of TnT extends about one-third of the way along the tropomyosin (beyond Cys-190) and interacts with TnC and TnI, which in turn interacts with actin (see diagram in Fig. 3). (Figure courtesy of L. Smillie; adapted from S. Ebashi. Essays in Biochemistry, edited by P. N. Campbell and F. Dickens. Orlando, FL: Academic, 1974, vol. 10, p. 1–35; and C. Cohen. Sci. Am. 233: 36–45, 1975.]

1.  Actin

Actin polymerizes spontaneously to form the backbone of the thin filament, F-actin, which can be viewed as either a two-stranded long-pitch helical structure or a single short-pitch genetic helix structure. X-ray diffraction analysis of crystals of actin-DNAse I (241), actin-gelsolin (305), and actin-profilin (406) shows that actin is composed of four subdomains. These subdomains surround the binding pocket for a divalent ion (Mg2+ or Ca2+) and nucleotide (ATP or ADP). This gives a structural basis for the prominence of both divalent metals and nucleotide in the actin polymerization and thin filament structure (93). The atomic model of the F-actin filament structure was then derived from the structures of actin and X-ray diffraction patterns of oriented actin filament gels (203) and later refined (281). This model shows the larger subdomains 3 and 4 are axially located with interactions across to the subdomains 3 and 4 of the actin in the second strand; the smaller subdomains 1 and 2 are located at the periphery of the filament exposed to the solvent and available for interaction with myosin. In particular, subdomain 1 contains both the NH2 and COOH termini of actin and plays a prominent role in the interactions with myosin (see scheme 1). Each actin makes contact with four others, the preceding and following actins on the same long-pitch helix and the two actins across the filament on the other long-pitch helix (the preceding and following actins on the short-pitch helix). The model of the thin filament (203) shows that each actin uses 10 surface loops and 2 α-helices to make these interactions [see Milligan (317) for a description of these interactions]. This atomic model of the actin filament is also used to define the positioning of actin in the actin-Tm filament and the fully regulated thin filament with Tm and Tn. This is discussed in sectioniiiA under the structure of the regulated thin filament.

2.  Tm

Tm is an extended molecule ∼42 nm long formed as a homodimer or heterodimer of two α-helical chains arranged as a coiled coil. Stability of the coiled coil is produced by hydrophobic interactions between nonpolar side chains contributed by amino acids in each chain. Each chain is 284 residues long and spans 7 actin monomers on each strand of the F-actin filament. The chains are the products of at least two genes with variable expression in different muscle types, mixed α and β in fast skeletal and cardiac muscle from smaller mammals and more predominantly α,α in cardiac muscle from larger mammals (455). Neighboring Tm overlap in a head-to-tail configuration with periodicity of 38.5 nm along the thin filament.

Binding of Tm to F-actin is influenced by intrinsic interactions between Tm and actin monomers, interactions between overlapping head-to-tail regions of contiguous Tm molecules along the actin filament, and by other proteins such as Tn and myosin that greatly increase the binding. The intrinsic interactions may be through the 14 quasi-equivalent repeats of neighboring regions of charged and uncharged side chains in the amino acid sequence of Tm (304). These can be divided into two classes of alternating sites (363), providing two possible types of binding to the actin filament that are electrostatic in nature. The X-ray images of Tm decorated F-actin filaments (281) support the binding on the periphery of the F-actin filament, suggesting electrostatic binding. The tightness of this binding and flexibility of Tm on the actin may vary with the specific Tm isoforms making up the two strands. Isolated smooth muscle Tm is much more flexible than skeletal Tm with only about one-third the persistence length (55 nm compared with 150 nm, compared with the 42 nm length of Tm) (441). (Persistence length is a measure of flexural rigidity of the molecule, being the arc length along the filament at which the angle of the tangent to the arc becomes uncorrelated in three-dimensional motion, a measure of the space constant for the spread of bending along the molecule.) The flexibility of cardiac Tm in actin (A)-Tm (as measured by fluorescence anisotropy of a probe on Cys-190 on Tm) appears to be more than for skeletal Tm in A-Tm (59). The tightness of binding and flexibility may also vary along the strand because of the quasi-equivalent nature of the repeats and the intrinsic flexibility of the Tm. In fact, some of the repeats may contribute little to the actin binding affinity of Tm as their deletion affects the affinity little as long as the integral number of repeats and the coiled-coil structure of the Tm is retained (193, 263). This implies that the head-to-tail overlap between contiguous Tm provides much of the stability of the binding to F-actin. This is demonstrated by the greatly reduced affinity of Tm from which the overlap region has been deleted [the nonpolymerizable Tm of Mak and Smillie (287)]. Troponin binding extends from this overlap region to near the Tm Cys-190, one-third of the way from the COOH-terminal end of Tm toward the NH2-terminal end (Figs. 1 and 3). S1 greatly increases the binding of Tm to F-actin (53, 86), decreasing the flexibility of Tm (443) with the effect being greater for cardiac Tm than for skeletal Tm (59). Tn further stabilizes Tm binding to F-actin and provides tethering sites controlled by Ca2+through troponin with some flexibility in between (363). In fact, the largest movements of Tm in the Tm crystal occur near the COOH-terminal end (363). Movement of Tm over the surface of the thin filament brought on by Ca2+ binding to troponin and myosin S1 binding to actin are thought to be central to regulation as discussed in section iiiA .

3.  Tn

Tn is composed of three, interacting subunits each receiving its identifying letter from the first identified property: troponin C (TnC) binds Ca2+, troponin I (TnI) binds to actin and inhibits the actomyosin ATPase in a Ca2+-insensitive manner on a one-to-one basis with actin, and troponin T (TnT) links the Tn complex to Tm (158, 287). It is known that the interactions among the Tn subunits, Tm, and actin are Ca2+sensitive, allowing for Ca2+-induced conformational changes, modification of the average Tm position on the actin filament, and initiation of contraction. Figure 3 summarizes the interactions between the subunits and the changes with Ca2+.

a) tnc. TnC is the Ca2+ sensor in skeletal and cardiac muscle contractile regulation. Selective removal of TnC from skinned muscle preparations (334) prevents activation by Ca2+ (inhibiting force production) while reconstitution with native or recombinant TnC restores Ca2+-sensitive contraction. TnC has two globular regions, an NH2 terminal and COOH terminal, connected by a long central helix. Each region contains two possible Ca2+binding sites of the E-F hand, helix-coil-helix type (Fig.2). The COOH-terminal sites (III-IV) have high Ca2+ affinity (∼107M−1) and sufficient Mg2+ affinity so that under intracellular, relaxed conditions, Mg2+ is normally bound. These sites are termed structural sites because Mg2+-Ca2+ binding at these sites enhances TnC-TnI interaction and binding of TnC to the thin filament (519). The NH2-terminal sites (I-II) are the physiological Ca2+ trigger sites with lower affinity (∼105 M−1) and high selectivity of Ca2+ over Mg2+ (371). Substitution into skinned muscle fibers of recombinant TnC deficient in Ca2+ binding to these two sites renders the fiber Ca2+ insensitive (410, 418). The NH2-terminal region in cardiac TnC (the TnC isoform in both cardiac and slow skeletal muscle) contains a single Ca2+binding site (II). In this cTnC, the pentagonal bipyramidal coordination at site I is not achieved because of amino acid substitutions at three coordinating positions (leucine, alanine, and cysteine at the X, Y, and −Y positions in place of aspartic acids) (470). Elimination of Ca2+ binding to cTnC site II renders a cardiac or slow skeletal fiber insensitive to Ca2+ (375). Reengineering site I of cTnC to bind Ca2+ with site II still deficient does not restore Ca2+ sensitivity, implying that site II Ca2+binding is most critical (432).

Fig. 2.

Left: ribbon representation of the crystal structure of turkey TnC with Ca2+ (solid circles) bound to the 2 COOH-terminal binding sites. The NH2 terminal is identified, and the 8 lettered helices are colored to show their orientation. [From Herzberg and James (183).]Right: ribbon representation of rabbit fast skeletal TnC with Ca2+ (solid circles) bound at both the 2 NH2- and 2 COOH-terminal binding sites. [From Houdusse et al. (213).] The lettered helices are colored to show orientation. Note the 2-lobe structure of both TnC and long connecting helical stalk with each lobe containing two possible Ca2+binding sites formed by 4 helices organized into 2 helix-loop-helix structures. Without Ca2+ binding, the helices are orientated more parallel to one another (see the A-B and C-D helices in the turkey TnC on the left). With Ca2+ coordination, the helices are more perpendicular to one another in the so-called E-F hand configuration (see the A-B and C-D helices in the rabbit fast skeletal TnC on theright). Note that with this change, the B-C helices rotate up exposing part of the D helix of the central stalk. Herzberg et al. (184) hypothesized that this transition exposed hydrophobic residues in the D helix enhancing TnC-TnI binding. Both structures were downloaded from the Brookhaven Protein Data Bank and displayed using WebLab Viewer Pro.

The structure of TnC has been solved in a number of cases: X-ray crystallography of sTnC without (183, 428) and with Ca2+ (213) and of the NH2-terminal fragment with Ca2+(425); NMR solution structures with and without Ca2+ of NH2-terminal sTnC (130) and of sTnC (415), of cTnT (411), and of NH2-terminal human cTnC (419). TnC forms a dumbbell-like structure with the NH2- and COOH-terminal regions separated by a long central helix (Fig. 2). The four Ca2+ binding structures (3 for cardiac TnC) are composed of a helix-loop-helix region. For the COOH-terminal Ca2+ binding structures in skeletal TnC and cardiac TnC in the Ca2+-bound state, the helices flanking the binding loop are nearly perpendicular to one another forming an E-F hand structure (Fig. 2, left and right, seen most clearly in for helices A and B, C and D in the NH2-terminal of Fig. 2, right). In the apo state lacking bound Ca2+, the flanking helices are roughly parallel to one another (see the NH2-terminal region of sTnC in Fig. 2,left). In the NH2-terminal without Ca2+, this produces a closed structure whereby the B-C helices and connecting loop are folded down along the central helix. Upon Ca2+ binding in sTnC, as the B-C helices adopt a more perpendicular orientation, there is an opening of the structure, exposing hydrophobic amino acid side chains in the central helix that are thought to interact with sTnI (Fig. 2, right). Herzberg et al. (185) first proposed this model that has now been verified for sTnC.

Somewhat surprisingly, the cardiac TnC NH2-terminal structure is closed both without and with Ca2+ binding (more resembling the sTnC apo structure; Fig. 2, left) (411). In fact, there may be little change in exposed hydrophobic surface on the NH2-terminal of cTnC on Ca2+ binding (419) or the change is less favorable and not normally observed. This makes one question what drives the cTnC-cTnI interaction. Sykes et al. (276) suggest that binding of cTnC to cTnI induces the opening of the NH2-terminal of cTnC because the opening occurs with cTnC binding to a cTnI peptide. The results of fluorescence resonance energy transfer (FRET) studies of intramolecular distances in cTnC with cTnC-cTnI interaction are mixed with Putkey et al. (78), suggesting that TnC does not open with cTnI binding, whereas Cheung and coworkers (144) suggest that it does open. If after Ca2+ binding the NH2-terminal cTnC was not open and required the cTnI binding to “force” open the structure, this binding would be less favorable and the conformational change possibly slower. This could provide a major difference in sequence of events during Ca2+ regulation of cardiac muscle compared with skeletal muscle. Another difference is that the structural change, sensed by a fluorescent probe, for saturated Ca2+ binding is virtually complete for skeletal TnC, but not for cardiac TnC (84, 85) (see below). This could contribute, to some extent, to the lack of a structural change in cTnC detected by NMR upon Ca2+ binding to the NH2-terminal site II. Nevertheless, cTnC can reconstitute Ca2+-activated force when reconstituted into skinned skeletal muscle fibers, although the maximum may be less than achieved with native sTnC (63, 162, 335).

Evidence that these structural changes in sTnC with Ca2+binding occur and are important for regulation comes from studies using recombinant TnC. In these studies either a disulfide cross-link has been engineered into the molecule to prevent the opening up of the NH2-terminal structure on Ca2+ binding (156) or additional salt bridges engineered to make opening more difficult (125). In the first case, little activation is achieved with Ca2+ when this TnC is substituted for the native TnC in skeletal myofibrils, and in the latter case, much higher Ca2+ is required to achieve activation.

A number of studies have been performed on the kinetics of Ca2+ binding to TnC, isolated or in Tn. There are major differences between the skeletal and cardiac isoforms. In skeletal TnC with binding monitored either by an extrinsic fluorescent probe on TnC (233, 397) or by an intrinsic probe [Trp inserted at position 29 in a recombinant TnC (234)], Ca2+ binding to the NH2-terminal Ca2+-specific sites appears to be diffusion limited (∼108 M−1·s−1) while Ca2+ dissociation is ∼400–500 s−1. Furthermore, using quin 2 fluorescence to monitor the free [Ca2+], it was determined that the conformational change monitored by the extrinsic/intrinsic TnC fluorescence occurred almost simultaneously with the Ca2+ association/dissociation. Finally, the effective equilibrium constant for the conformational change with Ca2+ binding was high enough so that virtually all TnC with bound Ca2+ also exhibited the conformational change needed to interact with the other Tn subunits to activate. In cardiac TnC, although Ca2+ binding is probably diffusion limited (84, 85), there is a measurable delay between Ca2+ binding and the conformational change measured by an extrinsic fluorescent probe (84, 85,175) and also a delay between Ca2+dissociation and the resulting conformational change (251). Furthermore, the conformational changes for saturated Ca2+ binding are not complete, implying that even at maximum Ca2+ not all the cardiac TnC would be in the activated conformation (84, 85). This could have great significance in terms of activation for cardiac muscle and is discussed in sections iii A2 andv A.

b) tni. TnI is the subunit that holds Tn together and onto actin by binding to actin, TnC and TnT, with many of these interactions regulated by Ca2+ (Fig.3). Isolated TnI, or a positively charged inhibitory peptide from TnI (96–116 of rabbit fast skeletal TnI) (442) bind to the NH2-terminal region of actin and inhibit the binding of myosin and activation of the actomyosin ATPase in a one-to-one manner. Additional residues on skeletal TnI (140-148), which show sequence homology and positive charge similarity to the inhibitory region of sTnI 96–116 (104), appear to provide a second site of binding of sTnI to actin (463). These same sequences, potential actin binding sites, appear in two similar regions of cTnI. They also occur in a third region of both sTnI and cTnI (360), but it is not clear which of these regions are the most important functionally. This binding of TnI to actin is not responsible for inhibiting actin directly, because TnI is only present in a 1:7 ratio to actin, but it aids in anchoring the Tn complex on the thin filament in the absence of Ca2+.

Fig. 3.

Diagram indicating the effect of Ca2+ binding to TnC on the interaction between the various thin filament proteins shown in Fig. 1. A is actin, I is TnI, C is TnC, T1 is the NH2-terminal (1-158) portion of TnT, T2 is the COOH-terminal (159-259) portion of TnT, Tm is tropomyosin with the NH2 and COOH terminals indicated in the head-to-tail overlap region and the Cys-190 region indicated. Thicker lines imply stronger binding, and thinner lines imply weaker binding. The state with Ca2+ bound to the 2 NH2-terminal TnC triggering sites is shown on theright; the state without Ca2+ bound to these 2 TnC sites is shown on the left. Note that Ca2+binding to TnC enhances the TnC-TnI and TnC-TnT2 interactions and weakens the TnI-A interactions. This presumably allows the Tm to move on the surface of the actins opening up myosin binding residues (see Fig. 5). [Modified from Heeley et al. (180).]

A major step in Ca2+-mediated interaction is the Ca2+ modulation of TnI-TnC interaction. We focus on this interaction with skeletal muscle proteins and comment only briefly on the differences in cardiac TnC-TnI. There is much information on the sTnC-sTnI interaction, but no definitive structure, as crystallization of the full complex has not been achieved. Neutron diffraction studies (341) and fluorescence studies (250, 271) of the complex suggest that they associate in an extended structure. This proposed structure is not like the wrap-around structure of the TnC homologous protein calmodulin interacting with its target peptide, M-13 of myosin light-chain kinase (222, 306). It is more similar to the extended, antiparallel structure of the essential light chain interacting with the light chain-binding region of myosin S1 (379, 506). This structure is also consistent with the hypothesis that the binding of TnC to TnI occurs mainly in an antiparallel manner (104).

To date, the only X-ray crystal structure is of sTnC with the NH2-terminal fragment 1–47 of TnI bound at its COOH terminal (472). There is also an NMR structure of cTnI (33-80) with the COOH terminal of cTnC (132). This binding of TnC to TnI is dependent on the presence of Mg2+ or Ca2+ bound to sites III-IV of TnC and is thought to be the origin of the binding of TnC-TnI in relaxed muscle. TnC can be selectively removed from skinned muscle fiber preparations by chelating divalent ions in a low-ionic-strength solution rendering the fibers Ca2+insensitive (71, 519). There is a Ca2+-independent interaction of TnI with TnC, probably the central helix of TnC with the NH2-terminal helix of TnI (104). However, the important Ca2+-triggering interactions are probably between the NH2-terminal domain of TnC including the hydrophobic region, exposed upon Ca2+binding to sites I-II (47) with TnI residues 116–131 (463). Tripet et al. (463) hypothesized that this binding pulls the flanking TnI residues 96–116 and 140–148 away from their actin binding sites. The residues 96–116 of TnI could then bind to the COOH-terminal domain of TnC. This is summarized in Figure 3. More complete information on the specific interactions awaits X-ray crystallographic or NMR studies of the TnC-TnI complex.

The binding of TnI to TnC is strengthened greatly by Ca2+through specific interactions at the NH2 terminal of TnC (223). Thus Ca2+ binding to TnC may switch TnI away from multiple binding sites on actin to multiple binding sites on TnC (471). These Ca2+-dependent changes in TnC-TnI interactions weaken the binding to TnI to actin. In fact, Ca2+ abolishes the binding of isolated TnI-TnC to actin (371), and there is also much evidence for this in thin filaments during regulation. Studies using FRET between fluorescent probes on TnI and actin and TnC and TnI show clearly that Ca2+ induces a closer approximation of TnC-TnI and an increased distance between TnI and actin (138). This further supports the concept that TnI-actin binding acts as a Ca2+-sensitive anchor(s) of Tn-Tm to actin. To fully understand this Tn-Tm-actin interaction, we must describe the role of TnT.

c) tnt. TnT appears to be the structural “glue” that holds the Tn-Tm-actin complex together (Figs. 1 and 3) as it binds to Tm, TnI, TnC, and actin [see Perry (361) and Tobacman (455) for comprehensive reviews of these interactions]. In this position, it serves a number of roles in Ca2+ regulation. It acts not only to assist in binding TnC-TnI to Tm-actin and Tm to actin, but in cooperative activation of the thin filament. TnT is a highly asymmetric molecule [∼18.5 nm long for skeletal (116) and longer for cardiac TnT (455), compared with 40 nm for Tm]. The globular COOH-terminal region (TnT2) interacts with TnC, TnI, and Tm while the extended NH2-terminal region (TnT1) lies along the COOH-terminal region of Tm including the region of overlap with the neighboring Tm NH2 terminus (287,497). In this position, TnT is in a position to influence the flexibility of Tm, since the Tm overlap region is responsible for much of the affinity of Tm for actin and Tm shows its greatest flexibility in this region (363). TnT has many isoforms with a hypervariable region and a number of alternative spliced variants (30, 416). With these diverse functions, it is not surprising that different isoforms may give rise to variable properties that are just beginning to be explored. We first consider the basic interaction before speculating on the role of the variants.

The TnT interaction with TnC-TnI-Tm both increases the inhibition of actomyosin ATPase in the absence of Ca2+ and increases the stimulation in the presence of Ca2+ (104,158, 362, 373,471). The binding to TnI-TnC requires the COOH-terminal region, TnT2 (359), but the cooperative activation requires TnT1 (403). This cooperativity occurs through the interaction of TnT1 with Tm in the region where neighboring Tm overlap and possibly with actin (358). This interaction of TnT1 plus additional neighboring TnT residues with Tm and actin enhances the actomyosin ATPase compared with that for actin alone (289). TnT is also important in the binding of the Tm complex to the actin filament (358). Binding of TnT to Tm and the actin filament, occurring through TnT1, is Ca2+insensitive (358). There appears to be binding also through TnT2, but Ca2+ strengthens the TnC-TnT2 interaction thereby weakening the binding of TnT2 to Tm and actin (373). Because the NH2-terminal region of TnT2 may be inhibitory to the actomyosin ATPase (289), the Ca2+-mediated increased interaction of TnC-TnT2 may aid in activating the thin filament. This provides a second site for Ca2+ to regulate the positioning of Tm on the thin filament (in addition to the Ca2+-mediated decrease in TnI-actin binding discussed above). However, the action of Ca2+ does not cause a large decrease in the affinity of the Tm-Tn complex for actin as Wegner and Walsh (490) saw only a two- to threefold decrease and Rosenfeld and Taylor (397) a sixfold decrease in skeletal muscle. This decrease is functionally significant in skeletal muscle as Ca2+ (with Tn) increases the size of the cooperativity unit along the thin filament (297, 389). In contrast, Dahiya et al. (74) observed little change in the binding of Tn-Tm to actin with Ca2+ in cardiac muscle. This difference in properties between skeletal and cardiac muscle may play a role in the functionally important differences in regulation between the two preparations. Not surprisingly, isoforms of TnT, differing in this region of interaction of TnT2 with TnC, confer different Ca2+ sensitivities to activation of myofilament ATPase and skinned fiber tension (372).

The binding of TnT to TnI is not affected strongly by Ca2+, although there may be changes in the regions of TnI interacting with TnT (463). Modification of this interaction can modify the Ca2+ sensitivity of control of the acto-S1-ATPase by the reconstituted regulatory system (232). This is not surprising because of the multiple interactions between these regulatory subunits, several of which are regulated by Ca2+as discussed above. It was suggested by Tripet et al. (463) that one component of this interaction was due to the NH2-terminal region of TnI. Another component of this TnI-TnT2 interaction appears to involve the presence of heptad repeats in both TnI and TnT, implying that the interaction may involve α-helical coiled coils (423).

The importance of TnT as well as TnI and Tm in regulation is clearly highlighted by the mutations in these proteins that are shown to cause familial hypertrophic cardiac myopathy (21,248, 345, 361). Thus TnT through its interactions with TnC-TnI-Tm and actin helps determine the position of Tm on the thin filament and the effects of the regulatory system on actin, both important in regulation. Therefore, the differences in TnT isoforms between muscle types and during development lead to altered Ca2+ sensitivity (337, 391,402, 454, 457), enhanced activation of the ATPase (104, 157,279, 373), and possible changes in cooperativity, important functional differences in the regulation of contraction.

B.  Thick Filament

The thick filament is the bipolar polymer of the motor protein myosin that interacts with actin to produce force and sarcomere/muscle shortening. It also contains other proteins such as C, H, X, and M proteins and the large elastic protein titin. The motor protein, myosin II, is composed of two heavy chains with molecular masses of ∼200 kDa each and four light chains, two each of so-called essential and regulatory light chains (ELC and RLC, respectively), of molecular mass ∼20 kDa. The heavy chains form a parallel two-chain coiled-coil structure over most of their length except for the large, globular NH2-terminal regions, termed heads or S1 (subfragment 1). One pair of light chains bind to each S1. The coiled-coil region of the myosin, termed the myosin rod, forms filaments due to interactions between pseudo-repeats of oppositely charged amino acids in the rod regions with the molecules shifted by a regular interval along the filament of ∼14.3 nm. With this stagger, the two heads, paired S1 regions, project outward from the filament at regular intervals. In all thick filaments, these projections are helically arranged with about a 14.3-nm repeat. In vertebrate striated muscles, there is a three-stranded structure with 14.3 nm between paired S1 head projections or 43 nm between heads projecting in one direction. In the longitudinal center of the thick filament, the molecules are arranged in a head-to-tail configuration to give the whole filament a bipolar structure.

The S1 head structure projecting from the backbone of the thick filament interacts with actin to generate force and filament sliding. The structure of the S1 has been determined by Rayment et al. (379) and is shown in Figure4. The location of the S1 projections from the thick filament may depend on the nucleotide state of S1 (505). S1 heads with ADP·Piappear to lie down on the surface of the thick filament, whereas ATP and rigor heads may be more disoriented moving away from the surface (288). On the surface, the heads lie on helical ridges. This is likely an antiparallel arrangement with the paired S1 heads from one myosin projecting in opposite directions interacting with the S1 head from the next myosin, possibly in a dimer (342). Presumably any change in the S1 shape due to a change in bound nucleotide or changes in the light chains may disrupt this interaction and release the S1 head from the ordered structure on the backbone, allowing it to move toward the actin filament. This was first noticed with changes in temperature (505) but presumably also occurs with more physiological changes such as either RLC or C-protein phosphorylation (see below).

Fig. 4.

A and B: intermolecular interactions in the rigor actomyosin complex. In A, peptide backbone of two consecutive long pitch actin monomers interacting with the myosin S1 structure is shown as the peptide backbone with light chains indicated (LC). For a description of the procedures for docking the actin and S1 structures, see Milligan (317). In B, the S1 has been rotated about a vertical axis to expose the surface of contact with the actin. Residues constituting the main hydrophobic binding site are shown in blue. The region of actin to which this binds is also shown in blue on the actin structure at the left. The lysine-rich loop of the myosin S1, residues 626–647, which is absent in the X-ray structure, is shown as green spheres as are their probable electrostatic interaction sites on actin, 1–4, 24, and 25. The myosin S1 loop 404–415 and the presumed contact sites on actin (residues 324–334) are shown in purple. The secondary binding site, myosin residues 567–578 and actin 95–100 on the (n − 1)th actin are indicated in red. [Modified from Milligan (317).] C–E: G-actin monomer with shadow of Tm show position in (C) for zero Ca2+ (C), for high Ca2+(D), and for the rigor S1 bound state (E). Space-filling model of a single G-actin in the orientation shown in A with the comparable coloring to the myosin interaction sites on actin indicated in A and B. Actin residues 1–4, 24–28 are colored green; 144–148, 340–346 blue; 332–336 purple; and 93–96 red. Actin residues within the shadow of Tm in the three positions shown by Vibert et al. (475) are shown as gray. These actin residues in C and Dwere estimated from the diagrams of Vibert et al. (475) with the assistance of W. Lehman. The actin residues within the shadow of Tm in the rigor position (E) were estimated by shifting Tm 10± shift from the high Ca2+ position. Note inC in the absence of Ca2+, only the electrostatic binding sites, 1–4, 24–28, (green) are not “covered.” In the presence of high Ca2+ (D), all of the sites except the residues hydrophobic residues 332–336 (purple) are exposed. In the presence of rigor S1 binding (E), none of the indicated myosin binding sites on actin is covered. Thus, in the absence of Ca2+, only weak binding sites are exposed. In response to Ca2+ binding to TnC, Tm moves to reveal additional binding sites. With binding of S1, Tm is moved to a position exposing all the myosin binding sites. This is a static picture of Tm in fixed tissue and is not a complete picture of the dynamic Tm. The flexibility of Tm may be sufficient for it to move over the actin surface as much as from D to E just with thermal fluctuations (363).

Other proteins have been shown to play an important role in the thick filament structure, although they are not motor proteins. C protein, identified by Offer et al. (340), forms seven or eight stripes across the A band in the sarcomere shown by antibody labeling. It bundles the myosin molecules together in the filament during development (407). The X and H proteins may perform functions similar to that of C protein as the proportion of these three similar proteins varies somewhat reciprocally between different fiber types (422). The large elastic molecule titin may play a major structural role in the sarcomere contributing to the passive and possible active elasticity as well as sarcomere stability (482). The M-line proteins provide struts connecting the thick filaments together at the center of the A band in the sarcomere.

What role do these proteins of the thick filament play in regulating actin-myosin interaction in vertebrate striated muscle? We first consider the myosin light chains. For a discussion of the properties of the myosin light chains in regulation, see the reviews by Sweeney and co-workers (431, 435) and Trybus (464). In smooth muscle, phosphorylation of the RLC is essential for contraction (464). Phosphorylation of the RLC in vertebrate striated muscle is not essential for contraction, but it enhances the force and force redevelopment rate at low levels of Ca2+ activation (309, 436,437). Studies by Sweeney et al. (438) using RLC mutants demonstrated that phosphorylation was acting primarily to neutralize positively charged amino acids toward the NH2terminal of the RLC from the phosphorylatable serine. Levine et al. (272) showed that phosphorylation of the RLC affects the structure of rabbit skeletal muscle thick filaments, disordering the myosin S1 heads, presumably by moving them away from the thick filament surface toward the thin filament. Whether this disorder was caused by phosphorylation alone or by an effect on the S1 nucleotide state is not clear, but phosphorylation produced the thick filament structural change which, as discussed in sections iiiC1 andiiiC2 , promotes cross-bridge attachment and activation at lower Ca2+ levels.

In some invertebrate muscles, direct Ca2+ binding to the myosin is responsible for Ca2+ activation (446). This occurs through Ca2+ binding to the ELC with the coordination stabilized by interactions of the ELC with both the RLC and the myosin heavy chain in the light chain binding region (506). This type of binding does not occur with the vertebrate ELC, but the RLC chain of vertebrate striated muscle can bind Ca2+ and Mg2+ and probably binds Mg2+ under resting conditions (13,204). Early results suggested that this site exchanged Ca2+ for Mg2+ too slowly to be responsible for primary regulation but could modulate regulation under steady-state Ca2+ activation (13).

A modulation of thick filament structure associated with activation has been suggested by the long-recognized ∼1% increase in the repeat spacing between myosin cross bridges in the thick filament that appeared to precede force development (220,364). What role structural change plays in activation and whether it is caused by Ca2+ binding or some other event remain to be determined.

A role for Ca2+ in regulating both force and the rate of force redevelopment was suggested by the data of Metzger and Moss (312) in skinned rabbit skeletal muscle fibers. Partial extraction of the RLC both increased the force and rate constant of force redevelopment at low Ca2+ (312,356) and decreased the maximum shortening velocity at high Ca2+ (200). In contrast, Szczesna et al. (445), extracting most of the RLC using a different extraction technique, found that the extraction decreased both the force at low Ca2+ and the rate of force development. The reason for the discrepancy is not clear. Metzger and Moss (312) further suggested that the RLC inhibits cross-bridge attachment and that this inhibition was relieved by Ca2+ binding to the RLC. They also hypothesized that the effect was exerted through the RLC and not TnC, since the shift in Ca2+ sensitivity produced by elevated Mg2+could be inhibited by partial extraction of the RLC, but not by extraction of TnC (312). The effect of Mg2+ is complex, however, as they later showed that partial extraction of the RLC has opposite effects on the force-pCa relationship at high and low Mg2+. To investigate the role of Ca2+binding to the RLC, native RLC was extracted from skinned rabbit skeletal muscle fibers and replaced with a non-Ca2+ binding mutant (a recombinant chicken RLC with a point mutation decreasing Ca2+ binding). In these fibers, there was only partial reconstitution of force and Ca2+ sensitivity, the rate of force redevelopment was decreased, and the rate of relaxation was increased. This implies that the RLC is important in controlling the myosin and cross-bridge kinetics but did not provide a unique test of their hypothesis about the role of Ca2+ binding to the RLC (79).

It has been known for some time that the RLC modulates acto-myosin ATPase activity, since its extraction decreases the ATPase activity (290) and myosin light-chain composition affects the ATPase (431, 464). Therefore, changes in the RLC should affect cross-bridge binding as well as modulation of contraction. Extraction of the RLC disorders myosin head structure, moving them away from the backbone of the thick filament (273) to an even greater extent than phosphorylation of the RLC (272). Thus it is not surprising that RLC extraction can affect force (see sect. iiiC1 ) and the rate constant for force redevelopment (see sect.iiiC2 ) in a similar manner to RLC phosphorylation. In contrast, Ca2+ binding to the RLC does not appear to disorder the myosin head structure of the thick filament (272), making it unlikely that Ca2+ exerts a disordering action through the RLC.

The other proteins of the thick filament, C protein in particular, may modulate Ca2+ activation [see Winegrad (501) for a recent review]. Studies from the Moss laboratory (198-200) have shown that partial extraction of the C protein increases the Ca2+-activated force at low Ca2+ in both skeletal and cardiac preparations, much as does myosin RLC phosphorylation, and increases the speed of shortening at low Ca2+ in skeletal muscle fibers. They propose that C protein constrains the motion of the myosin heads to keep them close to the surface of the thick filament (200, 331). Extraction of C protein might then allow the myosin heads to move out toward the actin filament, increasing their effective concentration and increasing cross-bridge attachment at any Ca2+. Phosphorylation of C protein is associated with increases in cardiac contractility (170, 171), but there are results that do not support this conclusion (501). The confusion in results may originate from the difficulties in phosphorylating C protein and not other proteins that can affect regulation. There is evidence that phosphorylation of C protein in cardiac muscle increases the ATPase activity (298) by promoting movement of heads away from the surface of the thick filament (199, 331, 491). There is also a suggestion that the effects of phosphorylation of C protein have more effect on the activity of α-myosin (V1 myosin) than on β-myosin (V3 myosin) (492) and on the movement of the myosin heads away from the thick filament. They suggest that phosphorylation of C protein not only moves the myosin head away from the thick filament backbone but may order it, decreasing its flexibility (492). They hypothesize that the increased proximity to the thin filament increases the rate of myosin attachment to actin and thereby force. Furthermore, they hypothesize that the decreased flexibility increases the rate of detachment of myosin from actin and therefore could increase the speed of shortening (492). This is speculative but provides a testable model. Cardiac C protein should be able to be modified more by phosphorylation than skeletal muscle C protein because cardiac C protein has three or four phosphorylatable sites compared with only one for skeletal C protein. Thus the state of phosphorylation of C protein may modify the thick filament structure and modulate Ca2+ activation of contraction.

Finally, titin has been thought of as playing a mostly passive role in the sarcomere, keeping filaments aligned and providing passive stiffness. Recent studies have suggested that this view needs to be revised as titin may change its properties and its interaction with the other filaments in response to low levels of Ca2+ and thereby modify the properties of the resting or active sarcomere (426, 482). The importance of these changes remains to be clarified.

C.  Interaction Surfaces of Actin and Myosin

Knowledge of the structural relationships of the actin and myosin molecules has advanced rapidly with X-ray solution of their protein structures (203, 241, 378-380,417). Integration of these structures with electron micrographic (EM) reconstructions and chemical mapping suggests that four sites produce the interaction associated with contraction [see Fig. 4, based on Milligan and co-workers (317,319, 378)]. There are two sets of ionic interactions. The first involves negative charges of subdomain 1 of thenth actin from the Z line (amino acids 1–4 and 24/25) with the lysine-rich positively charged myosin 50k/20k loop (626–647), and the second involves residues 95–100 or 93–95 of subdomain 1 of the (n−1)th actin toward the Z line with myosin residues 567–578 (317). The strong binding site of rigor interaction, present at the end of the power stroke, is the interaction of a hydrophobic myosin amino acid sequence 529–558 (with contributions from 647–659) with hydrophobic actin residues 341–354 and 144–148 of the nth actin and residues 40–42 of the (n−1)th actin (data not shown). A second strong actomyosin binding site involves the unresolved structure of the myosin 404–415 loop interacting with actin 332–334 proline residues at the junction of actin subdomains 1 and 3. This is an important site because the myosin cardiac R403Q mutation is associated with the manifestations of familial hypertrophic cardiomyopathy (FHC), a reduction in the actomyosin ATPase, and an inhibition of the in vitro motility sliding speed (73,137, 439).

It has been suggested that myosin binds to actin first with the ionic binding prompting docking of actin and myosin (378). As strong binding occurs, there may be a change of the cleft between the upper and lower halves of the 50-kDa domain, which opens a passage way for the release of phosphate through the “back door” (or 50 kDa cleft side) of the nucleotide binding site (377,378, 514). The result of the cleft change is hypothesized to be conveyed to the 20-kDa region, stiffened by the ELC (379, 468), moving the end of the 20-kDa lever arm ∼7 nm (114, 378,379). As the neck region rotates, movement of Ser-243 or Arg-245 opens a pathway for Pi escape from its binding site (514). This mechanism has been called the “swinging lever arm” model of cross-bridge action (202). Recent studies have tested this idea by extending the 20-kDa level arm region by inserting repeating 20-kDa segments. These studies have shown, as predicted by the model, that the in vitro sliding speed increases in proportion to the length of the extended lever region (6, 466, 468).

D.  Cross-Bridge Cycle

The ATPase reaction mechanism that powers this swinging lever involves the reaction sequence shown in the abbreviated scheme 1 [see Cooke (67) for a review and more complete scheme]. For myosin alone, the reaction sequence is given in scheme 1 by steps 1′, 3′, and 5′. Here the rate of ATP binding to myosin and actomyosin is ∼1 × 106M−1·s−1 (for steps 1 or1′ which include the formation of a collision complex followed by isomerization to a strongly bound form of ATP), and the cleavage by myosin (step 3′) is relatively rapid, 125 s−1 at 20°C (see Table 1). For myosin alone, product release occurs first with Pirelease (at a rate-limiting value of 0.5 s−1 at 20°C) followed by the temperature-sensitive release of ADP (291). For the cross bridge and its interaction with actin, the reaction mechanism is given by the sequence of steps 1–8. This mechanism first involves rapid ATP binding to form actomyosin·ATP (AM·ATP) followed by the rapid dissociation to actin and myosin-ATP (M·ATP) in step 2.

View this table:
Table 1.

Rate constants for ATPase reaction steps from solution biochemistry (acto-S1, acto-HMM, and myofibrils) and skinned muscle fibers (rabbit psoas fibers)

Embedded Image

Next there is a fast (and reversible) cleavage of ATP on the myosin head (forming M·ADP·Pi, step 3′). At very low ionic strength (<10 mM) and high concentrations of actin, ATP is cleaved in solution by the AM complex without significant dissociation. The rate of ATP cleavage by the AM complex is >30 times slower than that by myosin alone and is the rate-limiting step for actomyosin ATPase at low ionic strength (see Table 1) (495). Furthermore, the equilibrium constant for ATP cleavage by AM·ATP is <1 (495). At physiological ionic strengths, however, the rate of dissociation of the AM·ATP complex to A and M·ATP is so rapid and complete that virtually all cleavage occurs on the dissociated myosin. Thus we omitted ATP cleavage by AM in scheme 1. The rate of Pi release from AM·ADP·Pi is >50 times faster than that from M·ADP·Pi (see Table 1). Under physiological activating conditions, there is a rapid reassociation (step 4) of actin and M·ADP·Pi forming a weakly bound A-M·ADP·Pi state that then isomerizes (step 5) to a more strongly bound AM·ADP·Pi state (a transition probably regulated by Ca2+) (see sects.iiiC2 , iiiC4 , andiiiD ). The strongly bound AM·ADP·Pi has been hypothesized to isomerize to produce force and AM**·ADP·Pi (lever arm motion, step 6) and may be stabilized in the strong binding force-exerting form by the release of Pi in step 7(75). Here we represent the force generation and Pi release as separate steps based on single fiber experiments (134, 243, 316). However, it has also been suggested that strong actin binding, force generation, and Pi release occur in the same step (202, 351, 377). Whether force generation occurs at step 6 or is contemporaneous tostep 7 (with the omission of step 6) and the formation of the strong binding state remains unresolved. Nevertheless, the transition from the weakly bound A-M·ADP·Pi to the strongly bound AM**·ADP involves a large change in free energy (350, 496) and is the transition during which force is generated. The rate of Pi release from A-M·ADP·Pi to AM**·ADP and Pi is represented in Table 1 as a combination of steps 5,6, and 7. An irreversible isomerization of the AM**·ADP state to an AM*·ADP (not shown in scheme 1 and which may be ATPase rate-limiting under isometric conditions) then occurs (414). This isomerization is followed by a rapid release of ADP (187, 449). These two steps are represented by step 8 in Table 1. Rate constants for many of these transitions have been estimated from solution biochemistry and skinned fiber studies (see Table 1). Finally, the steady-state rate of ATP hydrolysis per S1 head (k cat) under various conditions is given in Table 1.

Studies of the transient kinetics of isolated myofibrils and in single skinned muscle fibers (using caged substrates, caged products, and a fluorescent Pi binding protein) have been performed (44, 75, 76, 107,110, 142, 176,286). Results from solution biochemistry and more structured systems are in good agreement. The rates of ATP binding to AM, AM·ATP dissociation to A-M·ATP, and ATP cleavage as well as the equilibrium constant for ATP cleavage are all similar for the three preparations of actomyosin in solution, actomyosin in myofibrils and fibers (110, 111, 142,209) (Table 1). The rates of product release are more difficult to study in solution biochemistry because the rates of product release from unconstrained acto-S1 or acto-heavy meromyosin (HMM) are fast (495). In the muscle fiber, strain is applied to the cross bridge and is thought to slow the rates of product release (70, 207, 286). This conclusion follows from the fact the k catfor actomyosin in solution is greater than fivefold greater than that in fibers contracting under isometric conditions (286) (see Table 1). Even during rapid shortening in muscle fibers, the measured rates of ATP hydrolysis are approximately one-half those measured in solution. Furthermore, the rate of high-energy phosphate hydrolysis (k cat) in intact muscles is increased during shortening and is inhibited during eccentric contractions (contractions during which a contracting muscle is forcibly lengthened producing a very large force) (503). These results, together with the rapid ATP hydrolysis following its binding to actomyosin, suggest that the rate of product release in the muscle fiber is the rate-limiting step of the cross-bridge mechanism. Actomyosin interaction has been constrained in acto-S1 and myofibrillar preparations using cross-linking agents and gives results roughly comparable to those in isometrically contracting fibers (see Table 1).

The isomerization of the weak binding A-M·ADP·Pi state (formed in the rapid reassociation of actin and M·ADP·Pi) to form a more strongly bound AM·ADP·Pi state is probably the transition regulated by Ca2+ (286). This conclusion is supported by the study of muscle fiber transients produced by the photogeneration of Pi from caged Pi. These studies showed that the rate of Pi release from strongly bound AM·ADP·Pi in isometrically contracting muscle fibers at 10°C is 30 s−1 (75, 316,495). This rate is far greater than the isometric steady-state ATPase rate (1–2 s−1) and implies that the rate-limiting step, at least under isometric conditions, occurs after the release of Pi. During shortening, similar experiments show that the rate of Pi release increases to >100 s−1, implying that a step immediately before, immediately after, or the Pi-release step itself, is strain dependent (207). A comparison ofk cat to the Pi release rate is problematic because k cat is the product of the [AM·ADP·Pi] times the rate constant for Pi release. Thus the increasedk cat during shortening might be explained by an increase in the fractional occupancy AM·ADP·Pi. However, this requires an increase in the number of strongly bound cross bridges, and measurements show that during shortening the number of strongly bound cross bridges falls to approximately one-third of the isometric value (118, 239,240). Finally, the swinging-lever cross-bridge model, with a cross-bridge throw of 10 nm and a maximum shortening velocity of ∼2 muscle lengths·half-sarcomere−1·s−1 implies a duration of cross-bridge attachment of <5 ms (duration ofsteps 4–8 and 1 and 2) per ATP hydrolysis cycle.

The development of a fluorescent phosphate binding protein (FPBP), which binds Pi at rates of ∼1,000 s−1 with a Michaelis constant (K m) of <1 μM, permitted measurement of the time course of Pi release from strongly bound AM·ADP·Pi in acto-S1 solutions, myofibrils, and skinned muscle fibers (16,44, 109, 176, 177,495). In solution at low ionic strength and 10°C, the rate of Pi release from AM·ADP·Pi is in excellent agreement with the measurements in isometrically contracting muscle fibers (30 s−1) (75,495). A significant discrepancy exists in studies using the FPBP in fibers. In fibers containing the FPBP, pCa at 5, into which ATP is photogenerated, steady-state rate of Pi release is not achieved over the first 3 or 4 cross-bridge bridge turnovers, i.e., the rate of ATP hydrolysis is 3–10 times greater than that measured using enzymatic methods, freeze-clamping methods, or acto-S1 solutions in the steady state (see Table 1) (176-178). To account for the difference, the value fork −8 for at least the first four cross-bridge turnovers using FPBP must be much larger than is seen in more conventional ATPase measurements (see Table 1). Measurements of Pi release using the FPBP are made under conditions (<1 μM Pi) radically different from more physiological (Pi ∼1 mM) conditions. Efforts should be made to engineer a FPBP whose K m for Pi is in physiological or submillimolar range. In rapidly shortening fibers at 10–12°C, the steady-state rate of ATP hydrolysis is near 20 s−1 (177), whereas the Pi(75) and ADP (76) release rates exceed 100 s−1. These results suggest that for minimally strained cross bridges, the rate-limiting step for ATP hydrolysis occurs before the release of Pi itself (286). At present, there are no probes for fibers to directly monitor the weak to strong cross-bridge binding transition (A-M·ADP·Pi to AM·ADP·Pi) or for the AM**·ADP to AM·ADP isomerization limiting ADP release.

The question remains as to which of the steps in the actomyosin ATPase reaction are regulated by troponin/tropomyosin and Ca2+. Kinetic studies show that the rate-limiting step of the myosin ATPase cycle is the release of hydrolysis products (285) or an isomerization after ATP cleavage but before Pirelease, and that for actomyosin ATPase the rate-limiting step occurs after Pi release in the isometric contraction. These observations, in addition to those to be discussed, imply that the control of the muscle ATPase rate by regulatory proteins and calcium must occur between steps 4 and 5 in the mechanism shown in scheme 1, between A-M·ADP·Pi attachment and an isomerization preceding Pi release. Two hypotheses have been advanced to account for the regulation of actomyosin ATPase. The first is a steric blocking model, which postulates that through Ca2+ binding to Tn, Tm is positioned on the thin filament so that the strong binding of myosin to actin, which has been prevented in the absence of Ca2+, is now allowed. The second is a kinetic regulation model that postulates that Ca2+ binding to Tn regulates the rate of the weak to strong cross-bridge transition. Both models are discussed below, the steric blocking model in section iiia and the kinetic model in sectioniiiB .


A.  Thin Filament Structural Studies of Regulation

1.  Steric blocking

Structural studies on regulation of the actin-myosin interaction in vertebrate striated thin filaments have focused for some time on the position of Tm in controlling this interaction. As discussed in section iiA , early studies showed that Tm was located along the actin thin filament in a position to influence this interaction (322) and suggested that Tm might sterically block the interaction of myosin S1 with actin. The position of tropomyosin was identified through three-dimensional image reconstructions of electron micrographs of isolated thin filaments of actin, actin-Tm, or regulated thin filaments (see Amos, Ref. 5) and through X-ray diffraction studies of muscles or oriented thin filaments. X-ray diffraction studies (172, 219, 347), measuring changes in the intensity of the second actin layer line upon activation in whole muscle were interpreted as showing a movement of Tm on the periphery of the thin filament to a position in the groove of the actin long helix. Later studies questioned whether this change in the second actin layer line was due entirely to movement of Tm or whether there was some component due to changes in Tn position or in actin structure (see Squire and Morris, Ref. 421). The earlier investigators (172, 219, 347) hypothesized that upon activation Tm moved from a position that blocked actin and myosin interaction to one that allowed it. The binding of Ca2+ to Tn was hypothesized to initiate this movement (194), thus originated the steric blocking model of regulation. The time course of the change in the actin layer line was consistent with this hypothesis as Kress et al. (254) showed that, during the rising phase of activation, intensity increases in the second actin layer line preceded the rise in cross-bridge attachment signaled by the increase in intensity of the I(1,1) X-ray reflection or the increase in muscle force. Furthermore, because these changes occurred at sarcomere lengths at which thick and thin filament overlap was absent, they suggested that the movement was independent of the behavior of the cross bridge.

Three-dimensional image reconstructions of thin filaments using electron micrographs of fixed and negatively stained or quick-frozen specimens have confirmed and extended these studies. Early attempts at reconstructions gave differing results depending on whether S1 binding to actin was taken as tangential or “end-on” (see Amos for a review, Ref. 5). More definitive studies of frozen, hydrated filaments showed upon S1 binding that Tm moved from a position that might block S1 attachment to one in which it would not interfere with S1 binding (318). These electron micrographs set the stage for the more recent interpretations of images of regulated thin filaments with and without Ca2+ and with rigor S1 binding (see sect. iii A2).

The interpretation of both the X-ray and EM measurements (see Squire and Morris, Ref. 421) have been questioned because they do not take into consideration the presence of Tn and possible changes in its structure with Ca2+. In addition, these studies do not consider changes within actin accompanying Ca2+ or cross-bridge binding to thin filaments, and there is evidence that these changes in actin occur (see Squire and Morris, Ref. 421).

The simple, steric blocking view of regulation was called into question through later studies. Biochemical studies of regulation indicated that there may be regulation of a kinetic step rather than a regulation of binding (see sect. iiiB ). These studies also suggested that attached cross bridges might activate the thin filament [see Chalovich (55) for a review]. More recent biochemical studies (303) suggest that there may be three states of the thin filament, not just two, implying a more complex activation mechanism. Physiological studies measuring stiffness in skinned fibers at low [Ca2+] and low ionic strength implied that actin and myosin can bind even at rest (39), i.e., under conditions where the second actin layer line was not affected. Thus, if there was steric regulation, it was not absolute as some interaction occurred even without Ca2+ binding to troponin. Further impetus for additional structural studies came with the solution of the crystal structure of actin (241), enabling Lorenz et al. (282) to compute how actin monomers were arranged in the thin filament. The crystal structure of the S1 head of myosin (378) allowed for approximations of the interaction interfaces of actin and myosin referred to in sectioniiC of this review and indicated in Figure 4. Thus examination of specific actin-myosin interactions at the amino acid level could begin. This was a prerequisite for determining the position (or positions) of Tm with respect to this interaction interface.

2.  Three-state dynamic steric model

Recent X-ray diffraction studies of skinned fibers and oriented filaments and EM reconstruction studies of isolated thin filaments have shown positions of Tm supportive of a three-state [blocked, closed, and open (303)] model of thin filament regulation. This interpretation is consistent with biochemical studies discussed in section iiiB . In addition, fluorescent and electron paramagnetic resonance (EPR) studies of Tm position have provided additional information. We consider first the results of the EM and X-ray techniques. The conclusions of the EM studies and the published X-ray diffraction studies are in good agreement (201). Three-dimensional image reconstructions of electron micrographs of isolated, fixed, negatively stained thin filaments from Limulus and frog striated muscle (see Refs. 264, 265, 475) or quick-frozen filaments (507) revealed that in the absence of Ca2+, Tm occupies a position that blocks most of the potential binding sites for myosin on actin (see Fig. 4 C) (hydrophobic residues 340–346 and 144–148 colored blue, and 332–336 colored magenta). In the absence of Ca2+, the only sites available for weak electrostatic interactions with myosin are the negatively charges sites in residues 1–4 (colored green), and 93–95 (colored red) in subdomain 1 of actin (see Fig. 4 C). Binding of S1 to these sites would also direct S1 binding to additional sites on the thin filament when available. In this state, the thin filament would be in the “off” position. Further inhibition of S1 binding would occur through competition with TnI for binding to the NH2-terminal region of one to two actins in the A7TmTn structural regulatory unit. Thus there is good evidence for steric regulation of strong cross-bridge attachment by Ca2+, Tn, and Tm.

After Ca2+ binding to Tn, Vibert et al. (475) and Xu et al. (507) found that Tm moved ∼25° around on the surface of the actin filament (Fig. 4 D) from its position in the absence of Ca2+. This movement occurred with both chemically fixed and frozen-hydrated specimens (507). The Tm movement exposed several additional potential binding sites (24–28 colored green and 340–346 colored blue in subdomain 1 of actin, and 144–148 colored blue at the junction between subdomains 1 and 3 of actin), thereby promoting stronger hydrophobic binding of actin to myosin sequences 529–558 and 647–659. However, Tm continued to block myosin's access to the potential binding sites (residues 332–336 colored magenta in Fig.4 D). Tm might be stabilized in this position by electrostatic interaction between the seven pseudo-repeat sequences in Tm and actin residues located in actin subdomains 3 and 4 (281). This position could be equivalent to the McKillop and Geeves “closed” position (303) (see discussion later and in sect. iv). Upon the addition of S1, in the absence of MgATP and Ca2+, Tm appeared to move another 10° around the actin filament exposing additional myosin binding sites, specifically residues 332–336 (see Fig. 4 E). This effect was seen with two or more S1 bound per seven actin regulatory units. At lower concentrations of S1 in the absence of MgATP, they saw evidence of cooperative spread of the Tm shift along the thin filament. The shift in Tm was clear at a distance of 3 Tm from the site of rigor S1 binding, less at 7–12 Tm, and negligible at >12 Tm lengths (with 26 Tm/thin filament). This Tm position in the presence of S1 in rigor might be equivalent to the open position of McKillop and Geeves (303). Thus there is structural evidence for three activation states of the thin filament: off, partially on, and on to compare with the biochemical evidence for three activation states [blocked, closed, and open in the McKillop and Geeves nomenclature (303)]. They suggest that “full switch-on of the thin filaments by reversal of steric-blocking requires both Ca2+ and the strong binding of myosin heads, acting in sequence” (475) based on their structural studies using rigor S1 binding. Subsequent studies, using interaction of native thick and thin filaments in the presence of MgATP, found little evidence for shifting of Tm beyond the -Ca2+ position by the relatively few cycling cross bridges present in these studies (72). However, it is not known how much significant strong cross-bridge binding was present under these conditions.

Similar conclusions on activation by strongly attached, rigor cross bridges were reached by Poole et al. (367) and Lorenz et al. (281) using X-ray diffraction of skinned rabbit skeletal muscle fibers and oriented, regulated actin-Tm filaments [see Holmes (201) for a more complete discussion]. In their work, changes in the intensity of the second actin layer line were interpreted as changes in Tm position. In the absence of Ca2+, weak, electrostatic attachment could occur, but what they termed “stereospecific weak binding” could not occur. Upon Ca2+ binding to Tn, Tm, which is at a radius of 3.9 nm on the actin filament, moves by 25–30° to a position close to the position it occupies in the absence of Tn (281). Upon the attachment of rigor cross bridges at overlap of thick and thin filaments in the sarcomere, Tm was “observed” to have moved further to the “fully activated” position. These observations agree with the EM image reconstructions of Lehman et al. (475) above and suggest a three-state steric model, comparable to the three-state model of McKillop and Geeves (303) proposed from biochemical studies.

Although there seems to be equivalence between the three structural states and the three biochemical states of McKillop and Geeves (303), the agreement may be superficial. McKillop and Geeves (303) suggest that in the presence of rigor cross bridges all actin thin filament sites are in the open conformation (available to myosin for strong binding), but in the presence of high Ca2+, only ∼25% of all actin thin filament sites are in the open conformation with 75% in the closed conformation (available only for weak myosin binding). If one assumes that all actins in the A7TmTn regulatory unit are in the same conformation because of the Tm position [as do McKillop and Geeves (303)], this would imply a distribution of Tm positions in the presence of Ca2+, with 75% in the partially activated position and 25% in the rigor, fully activated position. This was not observed in the EM studies of chemically fixed filaments (475), but it is consistent with the X-ray diffraction data that measure the average Tm position. This point will be returned to in the following paragraph.

The existence of three states of Tm on the thin filament is different from the two equilibrium states for Tm binding to actin, the equilibrium determined by Ca2+ and S1 binding first suggested by Phillips et al. (363). The question is whether in fact there is a third state particularly in the absence of rigor cross bridges. The structural studies do suggest three states, but as discussed by Squire et al. (420), quoting earlier comments of Phillips et al. (363) and Cohen and Vibert (66), the thin filament is a dynamic, breathing structure. Tm has so much flexibility that it is incorrect to describe its position as fixed. Thus both the X-ray and EM images of the Tm position do not give a complete picture of the true Tm position. In the case of X-ray diffraction, the estimated Tm position would be a time-averaged one. Because the EM images are of fixed tissue, the Tm might be more likely to be fixed closer to its equilibrium position. However, the EM reconstructions are from thin filament images containing a number of A7TmTn structural units and thus average the position of Tm over a number of regulatory units. In addition, the reconstruction technique uses helical averaging with nonuniformities such as Tm-Tm overlap and Tn contributing some, but probably only a small amount to the reconstructed image (420). Thus neither the X-ray nor the EM images show the dynamics of Tm and, as such, do not give an accurate picture of regulation. The Tm position with Ca2+ binding might be particularly dynamic because the Ca2+ binding to TnC is transient and the structural changes in TnC and the other regulatory proteins as a result of Ca2+ binding may not be complete (84, 85). Thus, even if the Tm position with the maximal conformational change with Ca2+ binding was shifted by exactly the same amount as with rigor S1 binding, the time-averaged Tm position with Ca2+ binding would be between the “off” and “on” positions. The Tm position, determined by S1 rigor binding to actin, would be less dynamic because the S1 rigor binding is very tight and only very slowly reversible compared with cycling cross-bridge binding. If the average Tm position with Ca2+ bound to TnC was in fact at the position shown by Vibert et al. (475) for the fixed filaments, the thermal fluctuations of Tm observed in the crystal structure of Tm by Phillips et al. (363) (up to 0.8 nm between the middle and COOH-terminal end) would be sufficient to give an angular change greater than the angular separation between the Ca2+-bound and rigor Tm states.

The flexibility of Tm on the thin filament was shown by Szczesna and Fajer (443) to be nearly as flexible as in solution using a maleimide spin-label on Cys-190 of Tm reconstituted into fibers from which myosin, Tm, and Tn had been extracted. The mobility of the labeled domain of Tm was decreased little by binding to actin and was changed little by Tn in the presence and absence of Ca2+ but was stabilized by rigor S1 binding. Ca2+ binding to Tn increased the disorder of labeled domain, but the changes are small, indicating weak association of this Tm domain with actin. Thus, in the presence of Ca2+, Tm may be flexible enough so that at any time some of the actins in a A7TmTn regulatory unit might be in the state with all myosin binding sites on actin available (see Fig. 4 E), whereas others might be in a closed or possibly blocked state (Fig. 4,C and D). Whether this occurs or not depends on the flexibility of the Tm in association with the Tn subunits and the effects of Ca2+ binding to TnC and the binding of S1. Tm flexibility will be returned to in section iv on modeling. The data of Tregear et al. (462), showing that there are preferred target zones for myosin binding to actin in activated insect flight muscle, indicate that there within the regulatory unit there may be actins with different myosin affinities. These differences in myosin binding to actin could be because of Tm flexibility or because of constraints on myosin attachments to actin in the highly ordered sarcomeres of insect flight muscle.

To relate the structural observations to the regulation of muscle contraction, we need to know the Tm position with cycling cross bridges rather than with rigor cross bridges. The X-ray data of Kress et al. (254) show that the changes in the second actin layer line occur with muscles stretched to beyond thick and thin filament overlap and that the changes in intensity can be as large as those with filament overlap. To the extent that this layer line indicates the Tm position, this would suggest that the changes in Tm position with Ca2+ are similar to those with Ca2+ plus cycling cross bridges, but there are data from Maeda (368,369) that suggest otherwise. Thus the X-ray data do not settle the argument conclusively.

Another method of measuring the Tm position on the actin filament has been to use fluorescence probes. Lehrer and Ishii (225-227, 269), using isolated thin filaments, measured changes in fluorescence of a variety of labels on Tm (primarily on Cys-190) or changes in energy transfer between a tryptophan on actin and a probe on Tm (269) to study Tm movement. Their results imply that there is little change in the Tm position as deduced from fluorescence changes until myosin S1 binds in a rigor link. Later studies from this laboratory (12) show that Ca2+ binding does shift the Tm position in a manner consistent with the X-ray and EM results.

If in fact it is correct to interpret the EM and X-ray diffraction data in terms of three states of thin filament activation which differ in the specific actin binding sites available to myosin, these three states should correspond to three different myosin binding affinities. One would expect that the actual affinity would depend on the specific nucleotide state of the myosin and possibly also on cross-bridge strain. There would also be the question of whether a myosin once bound to the Ca2+ induced “partially on” position of Tm, could then undergo an isomerization and push the Tm out of the way to induce the more tightly bound “on” state. This has not been ruled out on energetic considerations but seems less likely to be the complete explanation because of the experiments of Swartz and co-workers (430, 516, 517) on S1 and S1·ADP binding to the overlap and nonoverlap regions in myofibrillar sarcomeres discussed in sectioniiiC6 . The different effective affinities of the actin in the three structural states are again similar to the affinities for the three blocked, closed, and open states of McKillop and Geeves (303), but again there is the lack of perfect equivalence with the partially on Ca2+-bound structural state representing a mixed biochemical state of 75% closed and 25% open.

Thus the structural studies of Tm position on the actin filaments imply three states of activation of the thin filament determined by the dynamic position of the flexible Tm. Ca2+ controls the Tm transition from allowing weak to somewhat stronger myosin binding and low or no force, but the strongest myosin binding occurs after Tm has shifted to the position where it does not block any of the myosin binding sites on actin. This shift in Tm may be caused by or stabilized by the myosin binding.

There are others (55) who interpret these changes in the thin filament in terms of an allosteric mechanism of regulation. The following evidence supports such an interpretation. The spin-label (443) and fluorescence [see Chalovich (55)] studies show changes in the thin filament or actin structure with S1 binding. In addition, biochemical studies show an enhanced S1 ATPase with the thin filament over that of actin alone in the presence of rigor S1 binding (32) that they termed “potentiation.” Others (500) observed that this was not a true potentiation since the maximum binding velocity (V max) and binding constant of the S1 ATPase were not increased with regulated filaments activated by Ca2+ and strongly attached cross bridges (NEM-S1) over that seen with actin filaments alone. What was observed was an increase in the ATPase for low S1 concentration for the regulated filaments activated by Ca2+ and cross bridges over that for actin alone (as in Fig. 5 B) without a change in the maximum ATPase. However, Tm binding alters actin structure (281), and Ca2+ binding increases thin filament flexibility (224, 512). Actin may be modified in response to Ca2+, so one clearly cannot treat the regulatory proteins as purely modifying the binding of S1 to actin alone. One must also consider the possibility of direct interaction of Tm with S1. S1 increases the binding of Tm to actin either by some direct interaction or an effect mediated through actin. In addition, there could be changes in actin brought on by Ca2+ binding to Tn and interactions through Tm or strongly attached cross bridges through Tn-Tm. Thus, in addition to the shift of Tm and changes in myosin binding surface, one must consider strongly the possibilities of molecular changes in actin. The movement of Tm in response to Ca2+ binding and cross-bridge attachment is the major structural change and is the focus of the analysis presented in this review. Following the suggestion that thin filament activation is analogous to the ability of a ligand to increase the open probability of a ligand-gated channel (398), it could be said that the Tm movement leads to an increased probability of actin sites being open to strong binding by myosin.

B.  Biochemical Studies of Regulation

The biochemical studies of regulation have been well reviewed by Chalovich (55) and Tobacman (455). Two important conclusions come from these studies, with supporting evidence reviewed by Chalovich (55). The first is that Ca2+ regulates actomyosin ATPase by controlling a kinetic transition (specifically the rate of the transition of the cross-bridge binding to actin from a weak to a strong binding form) and not by controlling the binding of myosin to actin per se. The second is that the strong binding of myosin to actin can modulate this transition through its effect on the thin filament. The first conclusion (that the rate of the weak to strong transition is regulated) originated with the observation that at low ionic strength (18 mM) in the presence of regulatory proteins, [Ca2+] regulated the acto-S1 ATPase rate with the expected hyperbolic relationship between regulated actin concentration and ATPase rate. However, over this same range of actin concentration, there was no change in the fraction of S1 bound to actin (at 1 μM S1 and 100 μM actin, ∼50% of the S1 bound to actin/Tm/Tn in the absence and presence of Ca2+), suggesting that myosin binding to actin was not being regulated by Ca2+ (57). This observation could not be explained by the simple steric blocking model (that Ca2+ controls access of the cross bridge to the thin filament in a switchlike on or off mechanism) because the steric blocking model would predict that the ATPase rate would be proportional to the fraction of S1 bound to actin. The model for the actomyosin ATPase reaction mechanism at that time involved S1·ADP·Pi binding to actin to form the weakly bound A-S1·ADP·Pi followed by the release of Pito create a strongly bound A-S1·ADP state. Furthermore, because the rate of ADP release to form the A-S1 state and the binding of ATP and dissociation of the A-S1·ATP to A and S1·ATP are very fast, the only conclusion consistent with these data was that Tn/Tm controlled the rate of the transition from the weakly bound A-S1·ADP·Pi state to the strongly bound A-S1·ADP state. With this understanding of the steps involved, it was hypothesized that Ca2+ regulated the phosphate release rate (which was thought to be the weak to strong cross-bridge transition) (56, 57). Thus there was “kinetic” regulation of the actomyosin ATPase by Ca2+(55). Tests of this model using caged Pi to generate phosphate transients showed that the processes associated with force production and Pi release are little, if at all, affected by [Ca2+] (316, 479) (see sect. iiiC4 ). However, if additional steps exist between the weakly bound AM·ADP·Pi and strongly bound AM·ADP complex, then regulation of their equilibrium or rate constants could also produce the observed behavior. Supporting evidence for kinetic regulation came at the same time from skinned muscle fiber data demonstrating that the rate of force development (k TR) increases with [Ca2+] while the original steric blocking model predicted an independence ofk TR from [Ca2+] (35) (see sect. iiiC2 for other interpretations of this data). The kinetic model holds that the Ca2+ binding to Tn allows the thin filament to undergo a transition that is affected by strong cross-bridge binding. A second aspect of this model is that the strong cross-bridge binding turns on the thin filament in a graded, cooperative fashion.

Many studies have pointed to a role for strong binding of myosin to the regulated skeletal thin filaments in regulating myosin binding and actin-activated ATPase activity. The studies of Trybus and Taylor (465) and Greene and Eisenberg (160) showed that binding of S1 or S1·ADP to regulated actin was highly cooperative in the absence of Ca2+ but that the cooperativity decreased greatly in the presence of Ca2+. Both discussed this effect in terms of the regulated filament being switched to an “active” or on state of increased S1 affinity. The change in fluorescence of a fluorophore attached to TnI (159, 465) or Tm (269) monitors changes in the thin filament structure thought to be associated with this increased affinity. These changes occurred when about one-half of the actin binding sites were occupied with S1 (or S1·ADP). Thus the strong binding rigor S1 or S1·ADP was hypothesized to switch the actins in the regulated unit of the thin filament from a low to a high affinity for S1. Weaker binding forms of S1 (S1·ATP, S1·ADP·Pi, orN,N′-p-phenylenedimaleimide (pPDM)-S1] do not have this effect (56; see also Chalovich, Ref. 55).

Similar studies on activation of S1 ATPase by regulated actin came to similar conclusions. They are inherently more difficult to interpret because of the need to have some MgATP to measure acto-S1 ATPase activity. The studies of Bremel and Weber (32), investigating ATPase of S1 and regulated filaments in the presence of low MgATP, demonstrated that even in the absence of Ca2+, strong S1 rigorlike binding activates the ATPase. The stoichiometry of this activation was similar to the switching of the regulated thin filament from low to high myosin affinity discussed above, ∼50% of actin sites occupied (31). This work was supported by many other studies that demonstrate activation of the ATPase by strong-binding S1 species such as NEM-S1 (161) but little activation by weaker binding forms such as pPDM-S1 (161). This seemed to imply that strongly bound cross bridges, in addition to enhancing the binding of myosin to the regulated filament in the absence of Ca2+, also enhanced the ATPase activity. In the presence of Ca2+ and a low S1-to-actin ratio, the addition of strong binding S1 (NEM-S1) to regulated acto-S1 increases the ATPase activity. The regulated acto-S1 has a higher V max than in the presence of Ca2+ alone, but the V max does not exceed that observed using unregulated actin for a given S1 concentration under their low ionic strength conditions (500). This implies that when the ratio of S1 to actin is small, Ca2+ cannot completely activate the regulated filament and that adding strong-binding NEM-S1 enhances the ATPase for a given S1-to-actin ratio. With NEM-S1, there is no increase in the ATPase V max over that seen with actin alone or regulated plus Ca2+ and high S1 concentration so there is not a true “potentiation.” What occurs is that the relative affinity of actin for S1 is enhanced by the presence of the regulatory proteins plus Ca2+ and NEM-S1. The increased affinity will increase the activation for a fixed S1 concentration in biochemical studies or in the filament lattice in the fiber. Two questions then arise: 1) Do long-lasting, strong-binding states exist in the fiber? 2) Does the occupancy of actin binding sites by myosin in the fiber approach that required for activation in the biochemical studies? These questions are discussed in sectioniiiC1 .

The studies of Lehrer and Morris (270) of the S1 ATPase activity in the presence of skeletal actin, actin-Tm, actin-Tm-Tn ±Ca2+ as a function the [S1] have served as a model for the role of strong cross-bridge activation of the thin filament during normal cross-bridge cycling. Their studies were interpreted as showing that, compared with S1 ATPase with actin alone, the ATPase activity with actin-Tm-Tn +Ca2+ was inhibited at low [S1] and potentiated at high [S1]. Thus, during cross-bridge cycling, it was assumed that even in the presence of Ca2+, a sufficient number of S1 cross bridges must be strongly bound to move the Tm to a position where the actin in the regulated filament could bind freely to S1 and activate the ATPase. Figure5 A illustrates the S1 ATPase as a function of the [S1] (for [S1] >50% of the [actin]) for a number of different types of actin filaments. As can be seen, the ATPase for S1 with actin-Tm-Tn-Ca2+ is always greater than for actin alone for all [S1] showing no inhibition. In contrast, their Figure 3 shows it always below the curve for all [S1] (not shown here). In Figure 5 A (their Fig. 1), there are no data points for [S1] below 50% of [actin]. In fact, the ATPase activity/S1 with regulated filaments plus Ca2+ appears to be constant up to [S1] = [actin] above which it increases. This is very similar to the ATPase data for the cardiac regulatory proteins measured by Tobacman (46) shown in Figure 5 B. The data of Tobacman (46) are particularly significant because they are taken at very low [S1], <0.02 of the [actin]. Over the range of [S1] up to 3–4 S1/7 actins (∼50%), the ATPase/S1 is constant. Above this, the ATPase/S1 is higher, which could be called potentiation, but in fact, the change is not in theV max, but in the apparent binding constant, the S1 binding. Because the ATPase/S1 is constant down to very low [S1], there is no cooperative activation by strong binding cross bridges required for actin-activated S1 ATPase of regulated thin filaments. There are sufficient actin sites available in the actin-Tm-Tn unit in the presence of Ca2+ for S1 to bind and go through the cross-bridge cycle without the participation of any neighbors. If there were a requirement for the participation of neighbors, then the ATPase/S1 would not be constant but would depend on [S1]. Above 3–4 S1/7 actin, there is an apparent potentiation. This implies that Ca2+ binding is sufficient to activate for low S1 but that cooperative binding of S1 can further activate at higher [S1]. This is discussed in section iii, A,B, and C1, in the context of what occurs physiologically in the sarcomere. The behavior seen in Figure5 B with one ATPase/S1 seen below a particular [S1] and a higher ATPase/S1 above this [S1] is what would be expected of the McKillop and Geeves (303) model (discussed next). In their model, a fraction of the actin sites would be in the open configuration for strong S1 binding in the presence of Ca2+, but even more would be open in the presence of strongly bound neighboring S1.

Fig. 5.

Effect of Tm, Tn, and Ca2+ on the S1 ATPase measured as a function of [S1] using isolated skeletal (A) or cardiac (B) proteins. A: S1 ATPase with actin alone (+A), with actin-tropomyosin (+ATm), with actin, tropomyosin, and troponin ±Ca2+ (+ATmTn-Ca2+ and +ATmTn−Ca2+). The ATPase is expressed as the absolute amount (in nmol) of ATP hydrolyzed per second corrected for the amount hydrolyzed by S1 alone. Note that the ATPase of S1 with the regulated ATmTn filaments without Ca2+ (0.5 mM EGTA) is lower than the ATPase with actin alone, indicating that the filaments are regulated. With Ca2+, the S1 ATPase with regulated actin, ATmTn, depends on the S1 concentration being slightly above that for actin alone up to an S1 concentration of ∼4 μM but increasing more steeply above that S1 concentration. In these experiments, there was 3.2 μM F-actin, 0.79 μM Tm, 0.77 μM Tn, 0.05 M NaCl, 5 mM Mg2+, and 0.05 mM Ca2+, pH 7.9, at 23°C. Thus the S1 ATPase rate for regulated actin + Ca2+ is enhanced over that for F-actin alone at any S1 concentration and is cooperatively increased for an S1 concentration approximately equal to the F-actin concentration used. However, the saturating maximum binding velocity (V max) is the same as that for F-actin alone so that there is no potentiation ofV max (500). [From Lehrer and Geeves (267), with data from Lehrer and Morris (270).] B: ATPase for skeletal S1 with cardiac regulated filaments in the presence of Ca2+ (pCa 4.8) as a function of [S1] is shown. ATPase is expressed as the change in [MgATP] per second (in μM). Note that as [S1] is increased from a very low value up to ∼3 μM, the ATPase increases linearly, but that above 3 μM the ATPase also increases linearly, but at a higher rate. ATPase is enhanced by increased [S1] in the presence of the regulatory proteins and Ca2+. The conditions for their experiment were 20 mM imidazole (pH 7.3), 3.5 mM MgCl2, 7 mM KCl, 5 μM skeletal F-actin, 1.5 μM cardiac Tm, 1 μM cardiac Tn, and 25°C. [From Butters et al. (46).]

Many of the recent biochemical studies and models of regulation have come from Geeves and colleagues (133, 136,179, 297, 303). These studies evaluated both the kinetics of and steady-state binding of S1 to regulated thin filaments. Light scattering was used to measure total (weak + strong) S1 binding and fluorescence of pyrene labeled actin to measure strong binding of S1 to actin. Furthermore, Geeves and Lehrer (136) combined studies of myosin binding to the regulated filament with measurements of changes in Tm position on actin (indicating thin filament activation) using pyrene-labeled Tm (226). Their studies show that the binding of actin to myosin occurs in at least two steps; the formation of what they term an “A state” consisting of actin weakly bound to an S1 having a strongly bound nucleotide, followed by an “R state” with actin strongly bound to an S1 with a weakly bound nucleotide. Isomerization of the A state to form the R state is required to accelerate the S1 ATPase and generate force in muscle [see Geeves (133) for a review]. Using equilibrium binding and kinetic measurements of binding of S1 to regulated thin filaments, McKillop and Geeves (303) proposed a three-state model for activation of the thin filament. In this model, the thin filament could occupy a blocked state that is unable to bind S1, a closed state that can only bind S1 relatively weakly (the A state) or an open state in which S1 can bind and undergo the isomerization to the more strongly bound R state. They further characterized the Ca2+ and ionic strength dependence of the equilibrium constants for the various thin filament and myosin binding states (179,303). In more recent studies, they have extended this analysis to include cooperative activation of the thin filament using labeled Tm (136, 297). In the presence of Ca2+, the cooperative unit appears to extend for more than 7 actins, up to 14 indicating more flexibility of Tm in regulation expansion of the cooperative unit with loosened binding of Tn to actin. These studies are discussed in more detail in section iv, describing models of regulation, but provide a good framework for discussing the physiological studies.

In summary, it is difficult to establish from the biochemical studies alone whether Ca2+ is regulating strong attachment in a steric manner or regulating a kinetic step. A major problem is that solution biochemistry measures only ATPase rates and binding of long-lived cross-bridge states. The following sections will conclude from fiber studies and in vitro motility assays that the main step regulated is strong cross-bridge attachment, but that there also may be some regulation of cross-bridge kinetics.

C.  Physiological Studies on Muscle Fibers

The control of contraction is studied in muscle fibers whose organized sarcomeric structure allows measurement of physiological variables such as force, the rate of force development, and shortening. Although biochemical studies are needed to define the possible molecular interactions, they must be reconciled with the results of muscle fiber studies where there are geometric and mechanical constraints imposed on the relationships between the proteins within the sarcomere. The sarcomeric structure can either limit or enhance interactions depending on whether the geometry separates or brings the interactants together and whether one or several of these interactions are dependent on strain. Early studies using intact muscle cells demonstrated the importance of Ca2+ in the activation of contraction [see Ebashi and Endo (87) for a review], but more detailed understanding of the mechanism of regulation commenced with studies of skinned muscle preparations first described by Natori (338). Skinning muscle fibers allow control of the intracellular environment, free of the sarcolemmal barrier, and allows physiological tests of models of control arising from biochemical studies. They also allow exchange or partial replacement of some of the regulatory proteins [TnC, TnI, TnT, and MRLC; see Moss (331)] to examine roles of protein isoforms in regulation and to test models of molecular interactions during regulation. Furthermore, they allow measurement of Ca2+ binding through changes in structural labels (fluorescence or EPR) on regulatory proteins (TnC, TnI) exchanged into skinned preparations or through measurements of 45Ca binding. Findings from these physiological studies are discussed along with their implications for regulation of contraction.

The central measurement for studying regulation in the skinned fiber has been steady-state force as a function of [Ca2+] because it is relatively easy and assesses how Ca2+controls force-generating cross-bridge attachment under a variety of experimental conditions. A secondary measure has been muscle fiber stiffness assessed either with rapid length changes, steps, ramps, or sinusoids. This stiffness measurement provides information about the fraction of cross bridges attached when properly corrected for filament compliance and nonuniform sarcomeric properties. By varying the rate of change of length, information can be obtained about the rate of attachment and detachment of cross bridges in both resting and active muscle. Using this technique, Brenner et al. (39) concluded that in both the relaxed and active muscle cross bridges can attach and detach rapidly. At low [Ca2+], low ionic strength, and low temperatures, 65–90% of cross bridges are attached (39). This decreases to just a few percent at more physiological ionic strengths and temperatures. Such cross bridges have high rates of attachment/detachment and very weak binding and generate no active force, but are detected by stiffness measurements.

Before discussing the results of physiological studies of contractile regulation, we first consider the constraint imposed by the sarcomeric structure on the number of actins with which myosin can interact. A simple calculation derives the appropriate numbers given the density of thick filaments (500/μm2), the number of myosins/half thick filament (300), the ratio of thin to thick filaments (2), the overlap of thin and thick filaments (0.75 μm/h), and the number of actins per 38-nm thin filament repeat (14, 7/Tm).1 This calculation implies that in rigor (assuming attachment of all cross bridges), one S1 head binds per 1.8 actin monomers, or 3.9 S1 heads per A7TmTn regulatory unit. Steric considerations suggest that in isometric contractions not all S1 heads can bind. Measurements suggest that 20–40% of all S1 heads bind to the thin filament during a maximal isometric contraction (67, 280). If so, only 0.75–1.5 S1 heads are bound per regulatory unit under fully activated isometric conditions. During unloaded shortening, when the number of attached and cycling cross bridges falls to less than one-third of the isometric number [assuming stiffness is proportional to the number of attached cross bridges (117,240)], only 1 S1 can be attached for every 15–30 actins, ∼1 S1 for every 2+ regulatory units. This number also assumes that both S1 heads of a myosin molecule can attach at the same time. If only one S1 per myosin can attach, these numbers will all be decreased by a factor of two. These numbers should be remembered when discussing cooperative activation by attached cross bridges during isometric and unloaded shortening contractions.

As discussed in section iiiB , a major question from the biochemical studies is whether the number of force-generating cross bridges or the kinetics of the transitions between cross-bridge states are controlled by Ca2+. To answer this question, the physiological studies must include kinetic measurements investigating how Ca2+ controls steady-state shortening and the pre-steady-state kinetics of force development. Control of shortening is discussed in sectioniiiC5 . Several techniques are now available to study Ca2+ regulation of pre-steady-state kinetics. These involve mechanical or chemical perturbations of the skinned fiber and observations of the kinetics of the return to steady state. Some time ago, Brenner (34, 35) devised a clever mechanical procedure for detaching most of the strongly attached cross bridges and studying the rate constant for reattachment and tension redevelopment. This method and its implications for regulation are discussed in section iiiC2 . A more recent and powerful approach involves rapid chemical changes in skinned fibers by the use of “caged” compounds that are diffused into the skinned fibers in an inactive form and released rapidly to an active form by photolysis of the caged compound. This approach has been used to produce step changes in Ca2+, a Ca2+ chelator, Pi, MgATP, and MgADP (209, 283). We discuss, in sections iiiC3 ,iiiC4 , and iiiC8 , the results of the first three of these techniques and the implications of the pre-steady-state kinetics for the mechanism of regulation of contraction.

1.  Control of isometric force: force-pCa relationship

The initiation of isometric force by elevated Ca2+ in a skinned muscle fiber was an early demonstration that Ca2+activates contraction (87, 181,338). The steady-state relationship between [Ca2+] and force was shown to be steeper than that expected if force was just proportional to Ca2+ binding (181, 237). This relationship was first fit by Donaldson and Kerrick (83) with the Hill equation (189), F = F0[Ca2+]n /(Kn + [Ca2+]n ) (originally used to describe the binding of O2 to hemoglobin). This has become the equation of choice to fit these data. In this equation, the size of the Hill coefficient n, often calledn H, is related to the number of interacting sites. For muscle, such an association has not been shown, but the equation is widely used to characterize the relationship between Ca2+ and force. In this form, K is the [Ca2+] producing half-maximum force, here called the Ca2+ sensitivity. Because most investigators use pCa = −log10[Ca2+], the form of the Hill equation often used to fit the data isF=F0[1+10n(pCa1/2pCa)] The pCa1/2 gives a measure of the [Ca2+] required to activate the muscle, the Ca2+ sensitivity of activation, but is not necessarily a direct measure of the Ca2+ affinity of the Ca2+ binding sites giving rise to activation, as discussed below. The pCa1/2 also varies greatly with conditions.

The Hill n H gives a measure of the cooperativity of Ca2+ activation. If Ca2+binding to a single site controls force in a one-to-one basis, thenn = 1. If as in skeletal TnC, Ca2+ binds to two sites, n can be up to 1.2 (155) if the sites are independent, and binding to both sites is required for activation. For control of isometric force, n is always >1, varying from ∼2 to 5–6 in skeletal and cardiac muscle (23, 24). The value of n depends on the experimental conditions and how the data are analyzed. If force data from a number of fibers are averaged at each pCa and then the average force is plotted versus pCa, differences in Ca2+sensitivity between fibers can result in an apparently lowern for the ensemble than for any individual fiber. It is better to fit the Hill equation to the data from each fiber and average the resultant Hill n H and pCa1/2 values. With such a steep force-pCa curve, small changes in conditions can produce large changes inn H. Thus care should be taken in interpreting changes in n H. Some investigators (see Moss, Ref. 331) find that a single Hill equation does not fit the data because the slope of the curve may be greater for low [Ca2+] than for high [Ca2+] so that two Hill equations give a better fit to the data. However, most investigators find that the data are adequately fit by a single Hill equation (23, 513).

a) factors affecting ca2+ sensitivity. A number of diverse factors are known to increase the Ca2+sensitivity (i.e., decrease pCa1/2) of the force-pCa relationship [see Yates (513) for an extensive review and Table 2]. These include increases in pH (81, 102, 396) or sarcomere length (101, 103); decreases in ionic strength (113, 146, 247,452), lattice spacing (294, 296,300), Pi (315), MgATP (141), and [Mg2+] (82,83); phosphorylation of the myosin RLC (309,437); or addition of NEM-S1 (429) or MgADP (128, 195). The effect of lattice spacing on Ca2+ sensitivity poses problems in many of the studies of the force-Ca2+ relationship, since force generation per se can decrease the lattice spacing (43). Some researchers minimize changes by preshrinking the lattice to the in vivo spacing with 4% dextran T-500 (296).

View this table:
Table 2.

Factors increasing Ca2+ sensitivity of activation of contraction

The factors listed in Table 2 alter activation by different mechanisms. For example, changes in pH (100, 348,396) and changes in ions such as K+(113) alter Ca2+ binding to TnC. Elevated [Mg2+] does not appear to alter the force-pCa curve by direct competition with Ca2+ for binding to TnC because sites I and II have very low affinity for Mg2+(371), and Mg2+ does not shift the fluorescence of a probe on TnC incorporated into the thin filament upon Ca2+ binding to these sites (513,520). However, Mg2+ may modify interactions within the thin filament regulatory proteins (513). Decreases in sarcomere length and increases in lattice spacing decrease Ca2+ binding in cardiac (196) but not skeletal muscle (124, 357) even though in skeletal muscle, Ca2+ sensitivity still varies with sarcomere length. Thus some of these effects are explained by changes in Ca2+ binding, but others apparently operate through different mechanisms. Increases in sarcomere length, decreases in lattice spacing, and phosphorylation of the myosin RLC (272) all either decrease the distance between the filaments or decrease the distance from the myosin S1 to actin. Decreases in interfilament distances could affect the Donnan potentials at the surfaces of the filaments and possibly the effective [Ca2+] because of the 2+ charge on Ca2+(96). This does not seem to be important in the skinned fiber measurements because the fluorescence of a probe on TnC sensitive to Ca2+ binding, exchanged into skinned skeletal muscle fibers, demonstrates the same fluorescence-pCa relationship at long and short sarcomere lengths (shorter and longer interfilament separations) (163). The sarcomere length, lattice spacing, and myosin RLC phosphorylation effects on Ca2+ sensitivity would more likely result from an increased effective myosin [S1], increased S1 binding to actin, and force production for a given level of Ca2+ binding. Similarly, decreases in ionic strength, MgATP, and Pi; increases in MgADP; or substituting 2-deoxy-ATP (dATP) for ATP (383) will also increase the myosin binding to actin and thus the cross-bridge attachment and force for a given level of activation. In the case of dATP, both force and stiffness are enhanced at all submaximal pCa for skeletal and cardiac muscle, but only in cardiac muscle are the maximum force and stiffness enhanced (384). This suggests an additional action of strong cross-bridge attachment accompanying enhanced Ca2+ sensitivity.

Another effect of increases in strong cross-bridge attachment will be to increase the activating effect of strongly attached cross bridges within the individual regulatory unit and in neighboring regulatory units. This is described in section iiiB and later under factors that control n H. This increased activation by strongly attached cross bridges will result in additional cross bridges attached for a given Ca2+concentration, an apparent increase in Ca2+ sensitivity. Thus changes in Ca2+ sensitivity can be understood in terms of changes either in Ca2+ binding and the resulting increase in the open probability of actin for myosin binding or in the binding of myosin S1 to actin at a given level of Ca2+activation of the thin filament.

In addition to direct effects on TnC Ca2+ binding or myosin-actin interaction, Ca2+ sensitivity can be modified through changes in the other Tn subunits. Phosphorylation of TnI in cardiac muscle at the two NH2-terminal Ser sites (Ser-22 and -23) decreases Ca2+ sensitivity by decreasing Ca2+ binding to the Tn complex (395) through modulation of the TnC-TnI interaction (278). Changes in TnT also have major effects on Ca2+ sensitivity during development or in pathological conditions such as FHC as discussed in the TnT part of section iiA . Because of TnT's role as a glue holding the regulatory complex together (interacting with Tm, TnI, and TnC), it is not surprising that changes in TnT will affect the ease of movement Tm in response to Ca2+ binding and to myosin cross-bridge attachment.

b) the steepness of the force-pca relationship. The steepness of the force-pCa relationship (n H) provides information about the departure from independent activation of the force-generating units or about the interaction between units in the thin filament. This will be termed cooperative activation of the thin filament. Skinned skeletal and cardiac muscle measurements have yieldedn H values as large as 6 (23,25), implying great cooperativity. In addition, these values may underestimate actual/real cooperativity due to sarcomere shortening or the methods used to average the data. Possible sources for cooperativity include the following: 1) coupling between Ca2+ binding at the two NH2-terminal sites on skeletal TnC; 2) coupling between Ca2+ binding sites along the thin filament; 3) cross bridge-induced increase in Ca2+ binding in that regulatory unit or neighboring regulatory units; and 4) cross bridge-induced movement of Tm to activate the thin filament in a direct or allosteric manner in that regulatory unit and neighboring regulatory units.

The first possible source of cooperativity involves Ca2+binding to each TnC. In fast skeletal muscle, where there are two NH2-terminal low-affinity Ca2+ binding sites, n H could be as great as 1.2 (155) due to this cooperativity, and less in cardiac muscle whose TnC has only one functional Ca2+ trigger site. However, n H is very much greater than 1.2 in both skeletal and cardiac muscle so that this is not the major source of cooperativity for skeletal muscle. Substitution of skeletal TnC for cardiac TnC in cardiac preparations increasesn H (11), supporting the idea that some cooperativity exists within the NH2-terminal sites of skeletal TnC.

A second source of cooperativity is coupling between Ca2+binding sites along the thin filament, i.e., calcium binding to one site enhances Ca2+ binding to adjacent Tn sites along the thin filament. This coupling could occur through head-to-tail interactions between neighboring Tm. Fluorescent probe studies have demonstrated that there is some cooperativity in Ca2+binding along the thin filament (n H of up to 1.5) (155, 163, 459), but this is not sufficient to completely account for the highn H values. Partial extraction of TnC greatly decreases n H (26,334), implying that cooperativity along the thin filament is important, but this does not necessarily indicate that this cooperativity is through Ca2+ binding. Extracting TnC leaves TnI attached to actin and the remaining Tn-Tm complex in place. Brandt et al. (26) suggested that since they could see changes in n H with as little as one TnC extracted per thin filament, there was cooperative interaction of all the Tn along the thin filament. In contrast, the results of Moss et al. (332) suggest that the activating unit is about three A7TmTn units long, since maximum Ca2+-independent tension was achieved when only one-third of the Tn along the whole thin filament was extracted. This is a somewhat artificial estimate, since removing Tn affects both Tm binding to actin and its interactions in the thin filament (see sect. iiA ). Further evidence of the cooperativity between neighboring Tn comes from the studies of Tobacman and co-workers (46). They measured the ATPase activity of S1 using maximally Ca2+-activated cardiac thin filaments made from mixtures of the wild-type cTnC and a cardiac TnC mutant (CMBII) (375) lacking Ca2+ binding at the single NH2-terminal Ca2+ trigger site. The ATPase for a fixed S1-to-actin ratio increased in a curvilinear (quadratic) manner with the fraction of functional Ca2+binding units at high [Ca2+]. They interpreted this to mean that adjacent TnC must bind Ca2+ to allow S1 to bind and hydrolyze ATP in the presence of these regulated actin filaments. Moss et al. (334) observed a similar curvilinear relationship between total TnC and force during maximal Ca2+ activation in skinned skeletal fibers with partially extracted TnC. However, in that study, the TnI-TnT subunits of Tn were still present along the thin filament, which could affect the cooperativity. Recently, Regnier et al. (387) and Morris et al. (328) extracted native TnC from skinned skeletal fibers and replaced it with mixtures of native TnC and a mutant TnC unable to bind Ca2+ to the regulatory site(s). They found the relationship between force and number of activatable units (i.e., the fraction of native TnC in the mixture of native and mutant TnC) at high Ca2+ is approximately linear. It is not clear whether the difference between this linear relationship and the curvilinear relationship of Butters et al. (46) is due to the differences between skeletal and cardiac thin filament regulation or to differences in the experimental techniques used. The implication is that Ca2+ binding to adjacent Tn sites may be more important for complete activation in cardiac muscle than in skeletal muscle.

A third possible source of cooperativity is the effect of strongly bound cross bridges, acting through Tm and Tn, to increase Ca2+ binding to the thin filament and thereby increase activation. There is good evidence that this occurs in the presence of rigor cross bridges in both skeletal (32, 50,122) and cardiac muscle (196). However, the important physiological question is whether strongly bound, cycling cross bridges affect Ca2+ binding to TnC. There is good evidence that Ca2+ binding to TnC is increased by strongly bound, cycling cross bridges in cardiac muscle (196), but not in actively contracting skeletal muscle (124). In cardiac muscle, Tobacman and co-workers (46) suggested that Ca2+ binding to one TnC facilitates the binding of S1 to an actin in the same unit, which in turn facilitates Ca2+ binding to the next TnC to “turn on” that unit. There is no compelling evidence for such a phenomenon in skeletal muscle, but there is some evidence that cycling cross bridges may affect the TnC structure in skeletal thin filaments (4,163, 275), although this effect is probably small (292). Thus this form of cooperative activation may be important in cardiac muscle but most likely does not play a large role in skeletal muscle activation. This point is considered again in section iiiC9 on shortening-induced deactivation.

A fourth possible source of cooperativity is a direct activation of the thin filament by strongly attached cross bridges, independent of a change in Ca2+ binding. As discussed in sectioniv, strongly attached cross bridges may enhance the binding of cross bridges to that unit or to neighboring actin-Tm units in an allosteric or a graded manner. This mechanism may facilitate additional cross-bridge attachment subsequent to Ca2+binding to Tn and Tm movement (see sect. iiiA ). Additional discussion of activation by strong cross-bridge binding is found in section iiiC6 . Rigor cross bridges activate skinned skeletal fibers (393) and skinned skeletal and cardiac muscle preparations (307). Furthermore, strongly bound noncycling cross-bridge attachments (NEM-S1) can activate the ATPase activity of S1 and regulated thin filament in biochemical preparations (20,500) and enhance the Ca2+ sensitivity of contraction in skinned muscle preparations (429) (see sect. iiiB1 ). In the presence of NEM-S1, then H for Ca2+ activation is greatly diminished, decreasing the cooperative feedback of the endogenous cross bridges (429). However, under physiological conditions, the rigor state is short lived, and noncycling cross bridges do not exist. The important question, therefore, is can cross-bridge states, other than the rigor state, cooperatively activate muscle? As discussed in sectioniiiC6 , cross bridges attached in the AM·ADP state may activate the thin filament. As discussed in sectioniiiB , cycling cross bridges increase the S1 ATPase of Ca2+-activated isolated thin filaments (155) (Fig. 5). In addition, then H for the Ca2+ dependence of the S1 ATPase with regulated filaments is greater than that for TnC structural changes (155). In skinned fibers, then H for force is much greater than then H for TnC structural changes [fluorescent probes (4, 163, 292)]. Both results indicate that there is greater cooperativity in activation than can be accounted for from Ca2+ binding to TnC. Thus the cooperativity must occur by a mechanism other than enhanced Ca2+ binding. Furthermore, procedures that decrease strong cross-bridge attachment and force, such as treatment with 2,3-butanedione-2-monoxime (BDM), N-phenylmaleimide (NPM), or mutant TnC species with low Ca2+ binding, decrease Ca2+ sensitivity and n H. Thus cooperative activation by cycling cross bridges contributes to activation in both skeletal and cardiac muscle but may be more significant in cardiac muscle because the activation due to Ca2+ binding may be less complete, as discussed in sectionivA .

The above discussion has focused primarily on data from skinned fibers, where the [Ca2+] is controlled with buffers and the steady-state force-pCa relationship measured. The steady-state force-pCa relationship has also been measured in intact cardiac and skeletal muscle preparations, monitoring intracellular [Ca2+] with Ca2+ indicators and achieving relatively steady electrical activation using a variety of techniques. This was first accomplished in cardiac muscle (515), yielding high n H values often greater than those observed in otherwise similar skinned muscle preparation (131). In these studies, there was no control of sarcomere length or lattice spacing so that shortening during activation could influence the observed Ca2+ sensitivity (see discussion in section iiiC9 ). Similarly largen H values have been obtained for intact skeletal muscle fibers (324, 493) equal to the highest reported values for skinned skeletal muscle fibers. There are uncertainties about the measurements in intact fibers such as the calibration of the intracellular Ca2+ indicators, the assumptions of a steady state of force and [Ca2+], and the effects of sarcomere shortening on Ca2+ sensitivity. Nevertheless, it is clear that cooperative mechanisms of Ca2+ activation are also present in intact skeletal and cardiac muscle cells.

In summary, cooperative activation varies with muscle type and is likely related to differences in regulatory protein isoforms and myosins. In cardiac muscle, the evidence shows that cooperative, increased Ca2+ binding caused by myosin attachment to the thin filament is important for thin filament activation. This cooperativity may be through the mechanism suggested by Tobacman and co-workers (46), whereby the binding of Ca2+ to a cardiac TnC allows myosin attachment in one regulatory unit which, in turn, increases Ca2+ affinity of the nearest TnC along the thin filament. In skeletal muscle, cooperative activation appears to be more through the strongly attached, cycling cross bridges in one regulatory unit, through Tm movement or an allosteric mechanism, increasing cross-bridge attachment in neighboring units without significantly enhancing Ca2+ binding to TnC. For both cardiac and skeletal muscle however, Ca2+ binds to TnC to begin the activation process and allow cross-bridge attachment. These strongly attached cross bridges can enhance activation through additional movement of Tm to open up more strong myosin binding sites on actin or through an allosteric mechanism (see section iv on modeling). This gives rise to the steep force-pCa relationship. Thus the measured force-pCa relationships in skeletal and cardiac muscle support this two-step activation scheme proposed by Vibert et al. (475) and McKillop and Geeves (303).

2.  Control of force redevelopment: force-kTR relationship

In the previous section we concluded that Ca2+ binding to TnC, through Tn-Tm, controlled steady-state force by controlling the initial cross-bridge attachment. Moreover, strong cross-bridge binding promotes additional cross-bridge binding in skeletal muscle and possibly cardiac muscle. Strong cross-bridge binding does strengthen Ca2+ binding in cardiac muscle, providing further activation. As discussed above, an important, unanswered question is whether control of contraction occurs via regulation of the number of force-generating cross bridges or the kinetics of the transitions between cross-bridge states. To gain additional insight, the effects of [Ca2+] on cross-bridge kinetics must be measured. In this section we discuss Ca2+ control of the pre-steady-state kinetics of force. In subsequent sections, we consider other physiological measures of contractile regulation.

In 1986, Brenner and Eisenberg (40) developed a clever mechanical procedure for estimating the rate constant of cross-bridge attachment and force generation. In this technique, a single skinned muscle fiber, generating steady-state isometric force at a particular pCa, is allowed to shorten for a brief period under unloaded conditions. The muscle fiber is then restretched to its original sarcomere length (see Fig.6 A). In this technique, force always redevelops at the same length, eliminating any sarcomere length dependence of force production. It is assumed that the unloaded shortening and the rapid restretch detaches most of the strongly bound cross bridges, forcing most cross bridges into weakly bound states. After the rapid restretch of the fiber, the rate of force redevelopment monitors the approach to the isometric steady-state distribution of force-generating cross bridges (35). The assumption that the period of rapid shortening detaches attached cross bridges is justified by the greatly reduced stiffness andI 1,1/I 1,0 X-ray equatorial reflection ratio (33) observed during this maneuver. A further reduction in the number of strongly attached cross bridges during the rapid restretch was also suggested by the fact that the force and stiffness immediately after restretch often fall to very low values. However, in many cases, the force immediately following the restretch does not fall to the resting level but has a value of up to 50% of isometric force (see Fig. 6 A) (45). This value may represent the force produced by the stretch of cross bridges that rapidly reattach just before the restretch. Finally, it is assumed that the release and restretch do not affect thin filament activation. Evidence supporting this assumption comes from fluorescent probe studies of TnI incorporated into skinned skeletal muscle fibers (41). This is discussed further in sectioniiiC9 on shortening-induced deactivation.

Fig. 6.

Measurement of the rate constant for force redevelopment (k TR) (A), as a function of the steady-state force level (B), and the correlation of maximum k TR and maximum unloaded shortening velocity for different muscles and different conditions (C).A: protocol for measuring k TR, a plot of force vs. time, is shown. After force has reached a steady state at different pCa values (indicated on right), the fiber is shortened by ∼20% of the fiber length (L f) at a rate of 4L f/s for ∼50 ms and restretched to the original length. The rate constant for force redevelopment is estimated from the time to half-maximum redeveloped force. Note how the rate of force redevelopment slows with increased pCa (decreased Ca2+). B: rate constantk TR, determined as in A as the average of a number of fibers, is plotted as a function of the relative steady-state force at each pCa. Note the lack of change ink TR with increased force at low force (low Ca2+) and the rapid increase with elevated Ca2+for forces >50% of maximum. C: maximumk TR (s−1) is plotted as a function of maximum unloaded shortening velocity [in muscle lengths (ML)/s for different muscles and different conditions]. Triangles are data from rabbit or rat soleus muscles; circles are data from rabbit psoas muscles; open circle is datum from psoas at 10°C in deoxy-ATP (381). Unloaded shortening velocity (V u) was computed from values measured at 10 or 15°C in soleus and psoas muscles and extrapolated to 5, 10, 15, or 20°C using a Q10 of 2.5 (503). The solid line is a least-squares linear regression line to the data (r 2 = 0.93). [Data from Brenner (35), Metzger and Moss (310,311), Millar and Homsher (316), and Regnier and Homsher (381).]

After the shortening/restretch procedure, force rises following a single exponential time course to ∼95% of the isometric force when the sarcomere length of the central part of the fiber is held constant by length feedback (34, 309). The rate constant for tension redevelopment is termedk TR. In studies without sarcomere length control (63, 429),k TR is reduced somewhat (∼30%), and there is often a small departure from a single exponential at high [Ca2+]. In the latter case, a rate constant is calculated from the time to redevelop one-half of the maximum force (63, 309). Brenner (34) showed that the k TR- pCa relationship is usually shifted to the right of the force-pCa relationship, indicating a difference in the Ca2+ sensitivity of the steady-state force and k TR.k TR is often plotted as a function of the steady-state force at each [Ca2+] (see Fig.6 B), to isolate control of k TRthrough the number of force-generating cross bridges (presumably proportional to force) from control of the kinetics of cross-bridge cycling. The shape of the k TR-force relationship and the maximum k TR rate vary greatly among different muscles. When the maximumk TR is plotted against the unloaded shortening velocity (V u) for a number of muscles and different conditions, there is a roughly linear relationship over a 10-fold range of shortening velocities (see Fig.6 C). Given the linear relationship between shortening velocity and actomyosin ATPase (15), this result implies that k TR is directly related to the steady-state cross-bridge turnover rate. Increasing the cross-bridge cycling rate by substituting 2-deoxy-ATP for ATP as the contractile substrate increases the maximumk TR, while decreasing the cycling rate by lowering the [ATP] decreases the maximumk TR (383). In faster mammalian skeletal fibers, k TR increases up to 15 times with increasing force ([Ca2+]) and is concaved upward (see Fig. 6 B). It was shown first by Brenner (35) that, in rabbit psoas skinned muscle fibers, thek TR-force relationship is highly curvilinear, increasing from ∼1–1.5 s−1 at low force to 4–5 s−1 at maximum force at 5°C, and increasing from ∼2 s−1 to 15 s−1 at 15°C. Subsequently, this same sort of curvilinear relationship was seen by other workers in the same rabbit psoas fibers (309, 437), in mammalian slow-twitch (type I) fibers (310), in frog myofibrils (23), and in cardiac trabeculae (344, 504). The main differences are in the absolute magnitude of the minimum and maximum rates and the shape of the k TR-force relationship. In slower mammalian skeletal fibers, maximal k TR is slower and the increase in k TR with increasing force is much less (310). In cardiac cells,k TR increases less with [Ca2+] than in skeletal muscles (166,344, 504). Additionally, increasing [Pi] reduces force but increasesk TR in skeletal muscle (386,476), but depresses both force andk TR in cardiac muscle (448). Thus the relationship is a complex one, but important because it gives information about the pre-steady-state kinetics.

In his initial papers on k TR measurements, Brenner (see Ref. 36 for an excellent review of this subject) interpreted force redevelopment following the release and restretch of muscle as the transition of cross bridges from the weak to the strongly bound force-generating state. Because cross bridges can attach weakly to the thin filament in the absence of Ca2+, Brenner et al. (42) concluded (as discussed in sect.iiiA ) that the original steric blocking mechanism (172, 219, 347) is not strictly correct. Furthermore, although only 5–10% of the cross bridges are weakly attached at any one time at the ionic strength conditions existing in resting muscle cells (42,404, 405), all the cross bridges could potentially make the weak to strong transition to generate force (since they all would be in rapid equilibrium with the weak-binding state). Thus Brenner (35) suggested that Ca2+controls this transition between the weak and strongly bound states. To describe the transition from the weakly attached to strongly attached, force-exerting state, Brenner (35) used the A. F. Huxley (215) formalism as modified by Kushmerick and Krasner (259) with an attachment rate constantf app and detachment rate constantg app (see actomyosin ATPase diagram, scheme 1). The subscript “apparent” is used because both rate constants combine the rate constants of a number of steps in the actin-myosin ATPase cycle involving attachment to actin, various actin-myosin nucleotide states, and detachment. From measurement of the ATPase rate and stiffness of the fiber as a function of pCa (and force), Brenner and Eisenberg (40) estimated the absolute values off app and g app. He concluded that g app was not a function of [Ca2+] but that f app was. Subsequent investigators using this model have come to similar conclusions (310, 437).

The important question is what aspect of the weakly to strongly bound transition does Ca2+ control? There are two competing hypotheses. The one possibility is that Ca2+ affects a kinetic parameter of the power stroke of the attached cross bridge and thereby influences the transition from weak to strong attachment. This would be a true Ca2+ regulation of cross-bridge kinetics. A second is that Ca2+ affects the kinetics of thin filament activation through the kinetics of Ca2+binding to Tn and the subsequent conformational changes in the thin filament that allows strong cross-bridge binding with no effects on the power stroke per se. Both are consistent with the initial studies of Brenner (35).

In the first hypothesis, the direct effect of Ca2+ on the cross-bridge power stroke could be through a Ca2+dependence of one of the steps in the ATPase cycle such as Pi release (57). However, as discussed in section iiiC4 , the force-generating and Pi release steps exhibit little or no dependence on Ca2+ (316, 386,479). Still, a direct effect on the myosin cross-bridge could result from Ca2+ binding to the myosin RLC as suggested by Metzger and Moss (312). As discussed in section iiB , the RLC has a Ca2+ binding site which, under resting intracellular [Mg2+] conditions, would be saturated with Mg2+. Evidence for RLC control of contraction was provided by Metzger and Moss (312), who showed that removal of the RLC results in a small enhancement of k TR, at any level of Ca2+ activation. These studies imply that the RLC influences the magnitude of k TR but probably not its Ca2+ dependence. That Ca2+binding to the RLC is not necessary for maximumk TR is demonstrated by the observation that a maximum k TR can be achieved even in the absence of Ca2+ when an oxidized cardiac TnC (aTnC) is substituted for the native sTnC (167). aTnC activates skeletal muscle in the absence of Ca2+ when substituted for native sTnC. This demonstrates that the Ca2+ activation ofk TR is through the thin filament, not the myosin directly (63). Finally, in vitro motility measurements of the sliding speed of unregulated F-actin filaments, propelled by rabbit skeletal HMM with a full complement of light chains, show that the speed is independent of Ca2+(148, 206). These observations suggest that Ca2+ is not directly regulating myosin in vertebrate skeletal and cardiac muscle.

The second hypothesis is that the Ca2+ or force dependence of k TR is exerted through effects on thin filament activation. This hypothesis was first stated explicitly by Landesberg and Seidman (261) but was implied earlier by Brenner (35). Landesberg and Seidman (261) (see sect. iv) showed that a nonlineark TR-force curve (34) (Fig.6 B) could be obtained using a simple model that couples the kinetics of Ca2+ binding to TnC to the kinetics of cross-bridge transitions between weakly and strongly bound, force-generating states (see Fig. 8). The rate constants for the cross-bridge transitions, f app andg app, do not depend on Ca2+ but must be the same order of magnitude or much smaller than the rate of thin filament activation. The rate of Ca2+ binding to the thin filament is high at saturating Ca2+, but low at low [Ca2+], since the binding rate is proportional to [Ca2+]. Furthermore, even if the binding rate is high, in this model Ca2+ binding to TnC regulates the rate of transition into the force-generating state because the overall rate of force development is a product of the probability of the thin filament being activated {[Ca2+]*K eq/(1 − [Ca2+]*K eq) in a simple model with a single Ca2+ binding site} andf app (see Hancock et al., Ref. 165). Support for this kind of model is convincing and comes from experiments (shown in Fig. 8 B and described also in sect. iv) in which the kinetics and affinity of Ca2+ binding to TnC are changed using drugs or TnC isoform substitution. Calmidazolium, which decreases the rate of Ca2+ dissociation from TnC [3- to 4-fold in solution (234)], has no effect on maximalk TR but increasesk TR at low levels of Ca2+(385), as predicted by this model (383). Substituting aTnC (for native TnC) gives the maximumk TR independent of Ca2+(63). Substitution of an NH2-terminal deletion mutant of skeletal TnC, which has a greatly increased rate of Ca2+ dissociation from TnC [2- to 3-fold in solution for native TnC (392)], shifts the force-pCa by ∼0.55–0.77 pCa units and causes similar shifts in thek TR-pCa relationship (58,388) but has little or no effect on thek TR-force relationship. These studies indicate that Ca2+ activation of the thin filament can be a major factor determining the k TR-force relationship, along with the kinetics of the cross-bridge attachment/detachment.

In recent studies, Moss and co-workers (301) have shown that changes in sarcomere length shift thek TR-force relationship such that during submaximal activation k TR is elevated at longer sarcomere lengths. McDonald et al. (301) demonstrated that most of this effect was due to the decrease in filament lattice spacing that accompanied the increased sarcomere length. The force for submaximal Ca2+ is also enhanced by decreasing the distance that the myosin head has to reach out to attach to actin (294, 300). Both of these results could be explained by an increase in f app as the effective myosin concentration near actin binding sites is increased.

If the k TR-force relationship is determined by the Ca2+ activation of the thin filament along with the kinetics of cross-bridge attachment/detachment, we need to question what role cooperative thin filament activation by strongly attached cross bridges. The basic shape of this curve for skeletal muscle concaved upward, increasing steeply with force (and thus strong cross-bridge attachment) for forces >60% open probability (P o) (Fig. 6 B) suggests that cooperative activation depending on force/cross-bridge attachment may be important. The Landesberg and Seidman (261) model shows that this shape can be achieved without cooperative activation by strongly attached cross bridges, but does not rule it out. If it were present, it would involve activation of the thin filament by strongly attached cross bridges acting through movement of Tm (sect.iiiA ) or allosterically through actin, which would facilitate attachment of additional cross bridges either in that regulatory unit or neighboring units (see sect.iii C1 b). Perhaps when enough force-generating cross bridges are attached, the rate of strong attachment by additional cross bridges would be increased. Such positive feedback cannot be invoked where the curve is flat (165) or even sloped in the opposite direction in high Pi in cardiac muscle (448). The most compelling evidence that activation by strongly attached cross bridges can play a role in the k TR-force relationship is the data of Swartz and Moss (429) who showed that adding noncycling strongly attached cross bridges (NEM-S1) can enhance the k TR to the maximum value at low levels of Ca2+. At these levels of NEM-S1, there was neither activation of force in the absence of Ca2+ nor decreased force at maximal Ca2+. However, this result does not establish a role for cycling cross bridges in determining thek TR-force relationship in unmodified skinned fibers.

If strongly attached cross bridges contribute to enhancing the redevelopment of force, the cooperativity must be within a regulatory unit and not due to interactions between neighboring units. Metzger and Moss (311) partially extracted the TnC to decrease the effect of strongly attached cross bridges to activate neighboring units (28, 307; see sects. iiiC1 andiiiC6 ). They found that partial extraction of TnC, which decreased greatly the Hill n Hslope of the force-pCa relationship and the maximal force, had no effect on either maximum or submaximum k TR. These studies have been extended, in skinned fast skeletal fibers reconstituted with the mixtures of cardiac TnC and the cardiac TnC mutant lacking Ca2+ binding at site II (CMBII) (328); the results show that maximumk TR was little affected by mixtures that reduced maximum force to 20% of control maximum force (Fmax). Similar studies in skeletal muscle fibers gave similar results. Mixtures of native/wild-type sTnC and mutant sTnC (deficient in Ca2+ binding to sites I and II) were reconstituted into skinned skeletal muscle fibers and found to affect maximal k TR little, even at 10% of control Fmax (387).

Further evidence that there does not need to be cooperative activation between neighboring units comes from the aTnC studies (oxidized cTnC which activates in the absence of Ca2+; see above) (63). Full activation of k TRwas achieved by extraction of native TnC and substitution with sufficient aTnC to activate only 20% of the maximum force in the absence of Ca2+. This implied that neighboring regulatory units did not have to be activated to achieve maximumk TR. Of course, activation by aTnC is different from that achieved by normal Ca2+ binding to TnC in that Ca2+ binding is reversible and the structural change from Ca2+ binding may not be complete.

Therefore, it seems that the k TR-force relationship is not determined by cooperative activation between neighboring thin filament regulatory units, and thus the thin filament unit controlling k TR cannot be much larger than the basic A7TmTn regulatory unit.

The role of cooperative activation within a regulatory unit remains unclear; however, evidence from the k TRmeasurement itself (34) suggests that cooperative activation by strongly attached cross bridges, even within one regulatory unit, is not required for redevelopment of force. Because the release-restretch procedure should leave few strongly attached cross bridges, if they required for cooperative activation, then a few strongly attached cross bridges must form before others could attach. This would result in a lag in the rise of force during redevelopment. However, such a lag has not been observed.

In conclusion, the dependence of k TR, the rate constant for force redevelopment after the shortening and restretch protocol, on activation and force is best explained at this time by changes in activation of the thin filament and changes in the rate of strong cross-bridge attachment as a result of additional thin filament activation. There is probably little influence of cooperativity between regulatory units along the thin filament onk TR, but possibly some influence of cooperative activation by strongly attached cross bridges within each regulatory unit.

3.  Pre-steady-state kinetics of Ca2+ activation (kCa)

Another technique for investigating pre-steady-state cross-bridge kinetics is the use of rapid step changes in [Ca2+]. In intact fibers, electrical stimulation causes rapid Ca2+ release from the sarcoplasmic reticulum across the whole muscle cell because of the rapid inward conduction of the electrical signal by the muscle transverse tubule system. This produces nearly synchronous release of Ca2+ across the muscle cell. A technique to achieve rapid, synchronous activation in skinned fibers is the rapid release of Ca2+ from a chelator whose affinity for Ca2+ declines greatly upon photolysis, a so-called caged Ca2+. The chelator should be selective for binding Ca2+ over Mg2+, with a large change in Ca2+ affinity upon photolysis elevating [Ca2+] from 10−7 to 10−5 M in the fiber within fractions of a millisecond. Several compounds satisfy these criteria with variable success. The first group, the Nitr series, developed by Tsien and colleagues (1), is 1,2-bis(2-aminophenoxy)ethane-N,N,N′,N′-tetraacetic acid-related compounds. They are highly selective for Ca2+ over Mg2+ but have low quantum efficiency so that relatively intense radiation is required to release sufficient Ca2+ for maximal activation. The second calcium chelator, DM Nitrophen (an EDTA derivative), developed by Kaplan and Ellis-Davies (242), has a high affinity for both Ca2+ and Mg2+, a higher quantum efficiency, and undergoes a large affinity change upon photolysis. The third, nitrophenyl EGTA (NP EGTA), also developed by Ellis-Davies and Kaplan (98, 99), selectively binds Ca2+ over Mg2+, has a higher quantum efficiency, and has a large change in affinity upon photolysis. However, because unphotolyzed NP EGTA has such a high affinity for Ca2+, any unphotolyzed NP EGTA after photolysis binds Ca2+ that has just been released. This produces a transient spike in [Ca2+] upon photolysis of some of NP EGTA complexed with Ca2+ rather than the desired step increase. This behavior must be considered in interpreting the results (99).

Several studies used these compounds to investigate the pre-steady-state kinetics of regulation of contraction by Ca2+. These include studies by Wahr and Rall (478), Araujo and Walker (7), Ashley et al. (10) and Patel et al. (356) in skeletal muscle, and by Araujo and Walker (7) and Palmer and Kentish (344) in cardiac muscle. Wahr and Rall's (478) study in skinned frog skeletal muscle (478) using DM Nitrophen and Nitr-5 is the most comprehensive. They found that the rise in force resulting from laser photolytic release of Ca2+ could be described by two exponentials, a fast initial rise followed by a slower approach to the maximum isometric force. The fast rise almost matched the rapid rise in an intact fiber stimulated electrically at the same temperature. The slower rise may stem from sarcomeric nonuniformities in the fiber, as the experiments did not use sarcomere length control, but it could also be a property of activation. The slow rise is not seen in the intact fiber and was not caused by the particular caged compound, as it was seen with both Nitr-5 and DM Nitrophen. We will call the fast rate constant k Ca. Their measuredk Ca increased with increasing final [Ca2+] and increasing final steady-state force and produced a k Ca-force relationship similar to the k TR-force relationship shown for skinned rabbit skeletal muscle in Figure 6 B. The value ofk Ca at maximal Ca2+ activation did not depend on the initial force level and varied by increasing the preflash [Ca2+] or by decreasing force to <40% of maximum by either partial extraction of TnC or pretreating the fiber with 0.2 mM vanadate during activation.

In similar experiments using rabbit psoas skinned skeletal muscle fibers, Araujo and Walker (7) observed a single rate constant for the force increase after flash activation in Nitr-5, Nitr-7, or NP EGTA. Working at a higher temperature (15°C rather than 10°C), they found a similar increasing relationship between the final steady force and k Ca, withk Ca increasing from ∼1 to 16 s−1 from low to maximum force. Measurements ofk TR under similar conditions showed an increase from ∼2 to 22 s−1 over the same force range (309). Thus the k TR andk Ca values were similar under comparable conditions. Because Araujo and Walker's equipment (7) was limited to releasing only enough Ca2+ to partially activate the fiber, it was necessary to photolyze caged Ca2+ in solutions of elevated [Ca2+] to achieve final forces over the full range of fiber activation. For final Ca2+ levels that gave maximum force, they observed that thek Ca had little dependence on the initial force level. Unfortunately, their method of varying the initial force level results in final Ca2+ levels that also vary so that while final force was maximum for all Ca2+ activations, the final Ca2+ was not. Wahr and Rall (478) found that k Ca did not depend on the initial force, on the number of force-generating cross bridges attached at the time of activation, or on the final force, but only on the final [Ca2+]. This suggested that they were studying the rate constant of Ca2+ activation of the thin filament. Patel et al. (356) also found that k Cadid not depend on the final force when force was varied by TnC extraction, but k Ca did depend on the final [Ca2+]. Furthermore, Araujo and Walker (7) and Patel et al. (356) found that a decrease in [Mg2+] increased the k Ca, more at low-intermediate force levels and less at higher force. The origin of the Mg2+ effect was unclear and could be due to an effect on TnC, on Tm binding, or on the myosin RLC. Patel et al. (356) attributed the effect to the RLC because partial extraction of the RLC decreased the Ca2+ dependence of thek Ca. As discussed in sectioniiiC2 and later in section iv, the RLC extraction may directly affect cross-bridge kinetics, and not Ca2+ regulation. Ashley et al. (10) also found that k Ca (they actually measured the half-life) increased with the final [Ca2+] and final steady force in frog skeletal muscle, but unlike the data of Wahr and Rall (478) and Araujo and Walker (7), they found that k Ca saturated at higher [Ca2+]. This difference may be due to variations in data analysis or experimental conditions.

The studies in cardiac muscle gave similar results. Araujo and Walker (7) observed that k Ca in skinned rat ventricular myocytes increased from 1 to 4 s−1as force was increased from low to near maximum. This is slightly lower than the 4–10 s−1 range ofk TR values reported by the same laboratory under comparable conditions for skinned rat ventricular trabeculae (504). As in their skeletal muscle data,k Ca was independent of the initial force level. Palmer and Kentish (344) measuredk Ca, k TR, and the rate constant for relaxation (sect. iiiC8 ) in both rat and guinea pig cardiac muscle. Rat cardiac muscle has much faster cross-bridge kinetics than guinea pig cardiac muscle (473), but the Ca2+ sensitivity is similar (344). In both preparations,k Ca increased with increasing [Ca2+] and final force, and maximumk Ca at 22°C was about the same as the maximum k TR and rate of relaxation for that tissue. In the case of guinea pig myocardium, thek TR varied less with force than for rat myocardium. The relative values of maximumk Ca, k TR, and rate constant of relaxation for the two muscles varied with the actomyosin ATPase rate of the myosin from that tissue, suggesting that these maximum rates are determined by the cross-bridge cycling rates.

The conclusions of these studies are that the rate constants fork Ca and relaxation vary with the final [Ca2+] and vary little with the initial or final force level per se. Thus there is little evidence that strongly attached cross bridges play any role in the kinetics of Ca2+activation measured by k Ca. However, although the slower rate observed by Wahr and Rall (478) at higher force levels might be due to nonuniformities of sarcomeres during contraction, it could also be caused by cooperative activation by strong attached cross bridges. However, there is little evidence that interactions between neighboring regulatory units play an important role in activation, as extraction of TnC had little effect on the maximal rate (356, 478); thus any cooperativity would need to be within a regulatory unit. The TnC extraction experiments need to be expanded to include substitution of TnC lacking NH2-terminal Ca2+ binding to strengthen these conclusions. Thus the kinetics of activation, measured from the primary rate constant k Ca, appear to be dominated by activation through Ca2+ binding to TnC.

The observation that the k Ca does not appear to saturate (7, 478; but see Ashley et al., Ref. 10) suggests that it may not be determined solely by the rate of Ca2+binding to TnC and the resulting conformational change in TnC and interaction with TnI (see Refs. 84, 85, 175, 397). The rate of the conformational change in TnC with Ca2+ should saturate. However, it is not clear that the investigators increased the final [Ca2+] sufficiently to test for true saturation. In any case, the data fit well with the simple modeling of activation used to describe the k TR-force relationship (165; see sect. iv) whereby Ca2+ regulates thin filament activation and not cross-bridge kinetics.

The same conclusions can be drawn for the studies on cardiac muscle. Comparison of the k Ca andk TR rates indicates that the maximums are similar for the same tissue at the same temperature, but the dependence on force may be different. The data for guinea pig cardiac muscle show less dependence of k TR on force thank Ca on force. As shown by the modeling of Hancock et al. (165), this is possible if strong cross-bridge attachment increases Ca2+ binding to TnC. Thus the k Ca data support the conclusions that Ca2+ regulates strong attachment of cross bridges and has little or no direct effect on cross-bridge kinetics, and there is little cooperative activation by strongly attached cross bridges to determine the initial rate of force development.

4.  Kinetics of force relaxation with step increases in Pi (kPi)

Subsequent to M·ADP·Pi cross-bridge binding to actin, the products of hydrolysis are released in an ordered fashion, i.e., Pi first, followed by ADP (286). Studies of the kinetics of isolated actin and myosin in solution (or soluble fragments of myosin, HMM or S-1) have shown that the release of Pi from newly formed AM·ADP·Pi is rapid (36 s−1 at 10°C and 77 s−1 at 20°C) (495) compared with the steady-state ATPase rate (2–3 and 12–22 s−1, respectively) (see Table 1). The release of ADP in these unconstrained cross bridges is >200 s−1(412, 450). In solution, there is no strain on the actomyosin interaction of the AM·ADP·Pi complex. However, in muscles contracting under isometric, loaded isotonic or eccentric conditions, there are relatively large positive forces applied to the cross bridge, and in this case, the release of Pi and ADP are significantly slowed. This conclusion is based on measurements of muscle mechanics (76,186), the time course of ATP hydrolysis of muscles contracting under these conditions (110,111), and the time course of Pi formation and release using a Pi monitoring system (176,177) (see Table 1). Likewise, in rapidly shortening muscle, even though the rate of ATP hydrolysis is faster than that seen in the isometric case, cross bridges still bear force and the rate of product release is slower (<20 s−1) than that seen in isolated unloaded proteins (205, 209,258). Studies of the free energy change associated with product release have shown that a large amount of free energy is released when Pi dissociates from the AM·ADP·Pi system (ca. −40 kJ/mol depending on the [Pi]). It was suggested that the release of Pi is directly associated with the power stroke itself (351, 378, 379,496). Furthermore, it has been shown in numerous studies that the force exerted by an isometrically contracting skeletal muscle is inhibited as the intracellular [Pi] increases (69, 76, 186, 246,295, 316, 350,370). Over 10 years ago Pate and Cooke (350) reported that the isometric force declines linearly with the log [Pi]. This result could be interpreted to mean that the power stroke (that portion of the cross-bridge cycle that generates force and/or shortening) is produced by the dissociation of Pi; i.e., Pi release and force generation are synchronous events. In their kinetic studies, Chalovich et al. (57) found that calcium regulation of contraction could be explained if Ca2+ regulated either the rate of Pi release from the AM·ADP·Pi complex or a rapid equilibrium step before the release. This interpretation is consistent with the fact that at 10–15°C, as the [Pi] in the fiber is increased, k TR increases above its value of ∼15 s−1 at <1 mM Pi and increases asymptotically three- to fourfold as [Pi] is increased to 30 mM (313, 386,476).

If the release of Pi from the cross bridge is directly coupled to the power stroke, then the photogeneration of [Pi] from caged Pi in the filament lattice during isometric contraction should produce an exponential decline in force whose rate should increase linearly with [Pi]. Tests of this hypothesis have shown that the rate of the tension decline increases as [Pi] is increased (8,75, 315, 479). However, plots of the rate of the Pi transient,k Pi, are not linearly dependent on [Pi] but exhibit saturation kinetics. These experiments were most simply interpreted as showing that before the release of Pi, a cross bridge undergoes a force-generating isomerization from a nonforce exerting AM·ADP·Pi state to one, AM*·ADP·Pi, which exerts force (75, 316). This force-generating isomerization is followed closely by the release of Pi. A similar conclusion has been reached independently in sinusoidal analysis studies of force (244, 245) and in pressure-jump studies of contracting skeletal muscle fibers (119, 120) at various [Pi]. These groups suggested that during the normal cross-bridge cycle, immediately after the force-generating isomerization, Pi was released from the AM*·ADP·Pi state in a rapid equilibrium reaction, which, because of its large free energy change, shifts the cross-bridge distribution toward those exerting force and thus stabilizes the force-exerting cross bridges. A simple modification of the Huxley (75) model of the cross bridge is able to account for the observed behavior. The rate of the force-generating isomerization under isometric conditions (at 10°C) is ∼30 s−1 at 1 mM Pi, nearly twice as fast as the k TR measured in the same fiber under the same conditions. This implies that the two measurements are not observing the same transition (315,386). Luo et al. (284) offered another interpretation of the caged Pi studies. They argued that the force-generating step should be much faster than that observed and correctly pointed out that significant compliance in the fiber system would slow the observed k Picompared with that actually occurring at the level of the cross bridge. However, the behavior of the tension transient according to their hypothesis, even with the added compliance, would exhibit multiexponential behavior, which was not observed. Furthermore, if Pi release is directly coupled to force generation, isometric force should decline linearly with log [Pi] as reported by Pate and Cooke (350). If the force generation occurs in a step immediately preceding the release of Pi, the decline in force will exhibit an S-shaped relation with log [Pi]. The data in Millar and Homsher (315) suggest such behavior. Additional experiments are needed to resolve this question.

In slow-twitch muscle fibers, photogeneration of Piproduces an exponential fall in force similar to that observed in fast skeletal muscle (316). The amplitude of the Pitransient is smaller than in fast-twitch skeletal muscle (in agreement with the effects of [Pi] on force, Ref. 316), but k Pi is >10 fold slower (1 s−1). The Pi release may actually be the rate-limiting step in the ATPase cycle under isometric contractions. This result is consistent with the linear relationship between k Pi and [Pi] in slow-twitch muscle fibers (K = 3,100 M−1·s−1), although the concentrations of Pi used in that study were not raised to an extent to test for saturation kinetics. Similar conclusions were reached in sinusoidal oscillation studies in skinned slow muscle fibers (481) where the [Pi] was raised high enough (>10 mM) to observe saturation kinetics of the process associated with the power stroke. Comparable results have been obtained in skinned cardiac muscle cells, although k Pi is somewhat greater than in rabbit soleus fibers (8).

If the release of Pi from the cross bridge is directly associated with the power stroke and is controlled by the calcium concentration, then muscle fibers activated to various degrees should exhibit a Pi transient rate constant that decreases as [Ca2+] is reduced. This hypothesis was tested by Millar and Homsher (315) and Regnier et al. (386) using photogeneration of [Pi] from caged Piin isometrically contracting muscle fibers at various [Ca2+]. They found no significant change ink Pi with pCa, even thoughk TR was dramatically reduced at low [Ca2+]. Thus they concluded that Ca2+ must control a step that occurs before the force-generating isomerization. Walker et al. (479), working at a higher temperature and using a slightly different caged Pimolecule, found a small but significant [Ca2+] dependence of k Pi (a 2.5-fold change as force was reduced to <10% of that observed at full activation). They suggested that their k Pi data could be explained by a dependence of the rate constant of the force-generating isomerization on pCa. They too found much more marked effects of pCa onk TR than onk Pi. Although the model they used accounted for the effects on k Pi, it could not explain the k TR data. Additional experiments by Regnier et al. (386) concluded that to account for the variation of k TR andk Pi as force was changed by changes in Pi, BDM, or [Ca2+], the Ca2+control must occur on a process before the force-generating step. The controlled step presumably involves Ca2+ regulation of a weakly to strongly bound cross-bridge transition. Pressure-jump studies (120) have also found that the transients thought to be associated with Pi release are independent of pCa.

Araujo and Walker (8) have also measuredk Pi in cardiac muscle. They report that as [Ca2+] is reduced,k Pi falls slightly (declining by 50% when the force is reduced by 80%), implying a modulation ofk Pi by [Ca2+] greater than that seen in skeletal muscle. There are at least two possible explanations for this difference. The first is that indeed Ca2+ may modulate the kinetics of a step in the cross-bridge cycle in cardiac muscle. It would be interesting to compare the modulation of k Pi with the [Ca2+] dependence of k TR andk Ca observed in cardiac muscle under similar conditions. The second possibility is that the rate-limiting process in the cardiac cross-bridge cycle is different from that of skeletal muscle.

In summary, available data from measurements of Pitransients, pressure-jump studies, and force oscillation measurements suggest that Pi release from AM·ADP·Pi follows the power stroke and is coupled to it. Data from studies of these parameters at different [Ca2+] indicate that [Ca2+] exerts either a minor effect or no effect on the rate of the power stroke and Pi release step per se.

5.  Regulation of unloaded shortening velocity

a) studies on intact muscle fibers. I) Measurement of unloaded shortening velocity. A measure of a muscle's ability to shorten against various loads, its shortening velocity (v), varies inversely with the load (P). This relationship is given by Hill's classic equation (188)(P+a)v=b(PoP) where Po is the isometric force and a andb are constants in units of Po and muscle lengths/s, respectively. Typical values for frog skeletal muscle at 0°C are 0.25 Po and 0.33 l o/s (l o is usually reported as the sarcomere length of the muscle at maximal overlap or total muscle length at maximal sarcomere overlap). When the force against which the muscle shortens is zero (unloaded), the equation reduces tovmax=bPo/a and thereforevmax=1.32lo/s where v max is the “unloaded shortening velocity.” To avoid confusion with enzymatic rates, we designate the unloaded shortening velocity in fibers asV u. Originally,V u was measured by extrapolation to zero load from a series of measurements of the shortening velocities obtained at various afterloads (188). In 1979, Edman (91) introduced a simple method for estimatingV u. In a tetanically stimulated muscle fiber after isometric force reached a steady state, he rapidly released the muscle fiber by stepping one end toward the other a distance sufficient to reduce to force to zero (allowing the fiber to become “slack”). During this release, force falls to zero and, when the slack is taken up by sarcomere shortening, force begins to rise at the new shorter isometric length. The time taken to begin force redevelopment after the release is called the “slack time.” The greater the distance released, the greater the slack time. Plots of the distance released against the slack time in fully activated fibers are linear, and the slope of this line estimates the unloaded shortening velocity (see Fig. 7). We will call this estimate of unloaded shortening velocity V oto distinguish it from V u, measured by extrapolation. The unloaded shortening velocity values estimated by the two techniques are not different (91, 239).

Fig. 7.

Protocol for measurement of unloaded shortening velocity using the slack test (91) for two pCa values, 4.5 and 6.0.Inset: protocol with fiber length and force vs. time records at each pCa value. In each record at the given pCa, the fiber was quickly released a distance Δx at time 0, and the time required for force to begin redeveloping (slack taken up in the fiber) was measured (indicated by numbered arrows). For the pCa 6 data, records are shown at higher force sensitivity. In the graph, the length change (Δx) is plotted against the duration of time required for the unloaded shortening to take up the slack, force to begin to redevelop. The numbered data points 1,2, and 3 are for pCa 4.5 and 4,5, and 6 are for pCa 6.0. The slope of this line is the unloaded shortening velocity. Note that at shorter distances of shortening, the velocity (slope) is independent of Ca2+, but that at shortenings >10%, the unloaded shortening velocity for pCa 6.0 is substantially slower than at pCa 4.5. [From Moss (330).]

II) The effect of filament overlap on shortening velocity. The unloaded shortening velocity is much less affected by the extent of thin and thick filament overlap than is the isometric force (92, 147). When measured in intact skeletal muscle fibers within the range of sarcomere lengths from 1.7 to 2.7 μm (where significant resting force begins to develop in single skeletal muscle fibers), V o is independent of sarcomere length (91). At sarcomere lengths <1.7 μm,V o declines (91). These results compare favorably with measurements ofV u during controlled releases (147). Furthermore, V u is independent of the extent of thick and thin filament overlap from 2.2 to 3.1 μm sarcomere lengths (91, 147). In this range, the thick and thin filament overlap ranges from 0.75 μm/half-sarcomere (100% or optimal overlap) to 0.30. This important finding demonstrates that the unloaded shortening velocity in the intact, maximally activated muscle fiber is independent of the number of cross bridges pulling on the thin filament (when that number is varied from 40 to 100% of those available). Unfortunately, measurements of V u andV o are not available at sarcomere lengths greater than ∼3.1 μm, where filament overlap is <40% of optimal. This is because passive tension (passive recoil of elastic elements) beyond 3.1 μm is large and contributes to the apparent shortening velocity, complicating the analysis. At sarcomere lengths <1.7 μm,V o decreases markedly.

III) The effect of temperature on shortening velocity. Measurement of V u in living muscle fibers over the temperature range of 10–25°C has shown a Q10 of 2–2.5, implying that it is limited by a process with an activation energy of 40–60 kJ (54, 91,376). V o and/orV u have been measured in a variety of muscles where shortening velocity varies by more than a factor of 104. In all these muscles, V uis roughly proportional to the actin-activated S1/HMM/myosin ATPase rate for myosin from that muscle (15). Thus, with the assumption that the step size of myosin head per ATP is the same for these various muscles, this implies that the rate of the power stroke (that part of the cross-bridge cycle during which force and/or displacement of the thin filament occurs) is proportional to the maximal ATPase rate, both in the unloaded condition. However, this does not mean that the power stroke itself is the rate-limiting step of the cross-bridge ATPase cycle. These results suggest that maximal shortening velocity is dependent on the cross-bridge cycling rate and is independent of the number of cross bridges pulling on the thin filament.

IV) What limits shortening velocity? Is the unloaded velocity limited by 1) the intrinsic viscous drag on the filaments, 2) the drag from attached cross bridges,3) cytoskeletal elements that resist sliding, 4) the number of active cross bridges, or 5) other factors? Each of these separate factors is discussed below.

A) Viscous drag. During sarcomere shortening atV o, viscous drag is produced as the thin filaments slide past the thick filament through the cytosol. Both theoretical and experimental evaluations have shown that the drag offered by such sliding is very small (61,214, 216). Solving the equation for the axial viscous drag/half-thick filament/two thin filaments sliding at 6 μm/s, Fd (214) gives 1.4 × 10−14 N/half-thick filament/2 thin filaments. If 300 S1 heads are available to attach /half-thick filament (see sect.iiiC ) and 40% (67,280) attach and exert 2 pN force/cross bridge during an isometric contraction (112, 320), then the active positive force exerted by a thick filament is 2.4 × 10−10 N. Thus the force needed to overcome viscous drag atV o is <0.01% of the force the cross bridges can exert. The power required to overcome thin filament viscous drag is the Fd × V o (1.4 10−14 N/thick filament/half-sarcomere × 6 × 10−6 m·half-sarcomere−1·s−1) is 8.4 × 10−20 W. This is <0.004% of the cross-bridge power output of 2.5 × 10−15 W produced by ATP splitting per half-thick filament (assuming an ATPase rate by the cross bridges of 5 cycle/s, 3 × 102 cross bridges/h; change in ATP free energy = −50 kJ/mol, and 50% efficiency). Thus viscous drag of sliding thin filaments should not limit shortening velocity.

B) Structural or cytoskeletal factors may limit shortening. At sarcomere lengths <1.7 μm, energy is dissipated in deforming both the sarcomere and thick filament structures as well as changing filament separation. For sarcomere lengths of 1.7–3.1 μm, other factors limit V o, and there are two major sources of energy dissipation. As a fiber shortens, the filament lattice expands (97), and this expansion may be resisted by cytoskeletal links between myofibrils and attachments to the muscle basement membrane. This resistance is probably very small because between sarcomere lengths of 1.7 and 2.5 μm in skeletal muscle there is negligible restoring force exerted during relaxation to return the muscle to its initial sarcomere length. Alternatively, it may be that M·ADP·Pi cross bridges rapidly attach and detach from the thin filament and so constitute a resistive force (37). Careful studies of the passive force exerted by such cross bridges during rapid stretches of relaxed muscle have shown that such forces are miniscule (190). It may be that such attachments (as well as other cytoskeletal forces) do constitute a significant force during shortening. However, there is no compelling evidence for such forces, so this hypothesis remains to be tested.

C) Resistive drag produced by strongly attached cross bridges. A. F. Huxley (215) suggested that the drag from the attached cross bridges opposes thin filament sliding and limits V o. He imagined that cross bridges, driven by thermal energy, oscillate axially on the thick filament about an equilibrium position at x = 0. As they oscillate toward the Z line (at x > 0), they could attach in a conformation from which they would exert positive force acting to pull the thin filament toward the M line. With the assumption of a cross-bridge stiffness k (∼5 × 10−4 N/m) (143, 349, 354), an initial cross-bridge attachment to actin on the Z-line side of the cross-bridge equilibrium position would generate a force κ·x. During muscle shortening, attached thin filaments slide toward the center of the sarcomere (x→0), the attached cross-bridge heads move toward their equilibrium position and attached cross-bridge force decreases. At its equilibrium position, cross-bridge force equals zero, and the work done by the cross bridge moving from its attachment point, x nm from the equilibrium position, will be (κ·x2 )/2. As thick and thin filament sliding (shortening) continues, the attached cross-bridge is dragged passed its equilibrium position into a negative force-bearing region where force is −κ·x. A. F. Huxley (215) hypothesized that the accumulation of attached cross bridges in the negative force-bearing region produces a force opposing continued sliding. When the force exerted by “negatively” strained cross bridges is equal and opposite to the force exerted by cross bridges generating positive force, the sliding velocity reaches its maximum steady-state velocity,V u. Thus the detachment rate of the cross bridges in the negatively strained region (x < 0) limits unloaded shortening velocity. This view is supported by the independence of V o on thick and thin filament overlap at sarcomere lengths greater than 2.2 μm. Further interventions that slow cross-bridge detachment from the thin filament (e.g., increasing [ADP] or decreasing [ATP]) decreaseV o (62, 68,70, 108, 382). The effects of [ATP] and [ADP] are predicted by several strain-dependent models (94, 351).

Josephson and Edman (236) presented evidence supporting the idea that the drag, imposed by negatively strained cross bridges, limits V o. They measuredV o early in a tetanus (in the first 30 ms after the beginning of stimulation before tension had risen to 30% of maximal), during the plateau of the tetanus, and during relaxation from the tetanus. At first glance, A. F. Huxley's (215) view of V o would seem to imply thatV o would be the same at each point in the tetanus. However, Josephson and Edman (236) found that at the start of the titanic stimulation, V owas ∼30% greater than that seen during the plateau of the tetanus. Furthermore, during the initial stages of relaxation from the tetanus,V o fell to values significantly less than those during the tetanic plateau. Josephson and Edman (236) argued that such behavior was predicted by Huxley's model (215). They noted that at the beginning of a tetanus, before tension has reached the plateau, cross bridges attach and exert force. If shortening begins before a steady state of attached positively strained cross bridges is attained, then as cross bridges are dragged into the negatively strained region, even more cross bridges will be attaching in the positively strained region. Thus, at early times during titanic contraction, the rate of attachment of positively strained cross bridges (from x = 0 tox) will exceed the rate of formation of negatively strained cross bridges and unloaded shortening velocity will be high. If, however, shortening begins during the plateau of the tetanus, the negatively strained and positively strained cross bridges will be balanced and, consequently, V o will be constant and independent of activation. During relaxation, as calcium concentration drops, the rate of formation of positively strained cross bridges declines, and the rate of entry of cross bridges into the positively strained state lags behind the rate of entry of cross bridges into the negatively strained state, resulting in a slowerV o than that observed during the tetanus plateau. Josephson and Edman (236) showed that a modification of A. F. Huxley's equations (215) accurately accounted for their experimental observations.

V) Effect of cross-bridge numbers on thin filament shortening velocity. With the assumption that during the cross-bridge throw d (of 10 nm), a cross bridge generates positive force during the power stroke at rapid speeds for a timet s (of 5 ms), and that the maximum ATPase rate is k cat (8 s−1 at 10°C) (382), the equation relatingV o to the number of attached cross bridges (N) (467) isVo=d/ts×[1(1ts×kcat)N] Solution of this equation for various numbers of cross bridges attached to the thin filament shows that, to produce shortening at 0.95 of the maximum velocity (1.9 μm/s), 73 actin monomers per thin filament (27% of those in a thin filament at optimal sarcomere overlap) must be bound to cross bridges that are pulling. Similarly, 17 cross bridges must be bound per thin filament (6% of those in a thin filament at optimal sarcomere length) to generate a speed of ∼0.5V o, and 7 cross bridges must be bound per thin filament (3% of available actin monomers) to generate a speed of 0.25V o. In sectioniiiC1 we estimated that during shortening atV o at maximum activation, one cross bridge was attached and propelling the thin filament per 11–26 actin monomers. This implies that at V o, only three to eight cross bridges are pulling each thin filament toward the center of the sarcomere. If there are 1,000 thin filaments rigidly attached to the Z line in each myofibril, 3,000–8,000 cross bridges produce the Z-line movement at full activation, and the shortening velocity will be 2 μm·half-sarcomere−1·s−1. Even at 10% activation, the number of attached cross bridges per Z line in each myofibril would be at least 300 cross bridges, more than enough to reach V o. This analysis is valid only if the attachment of thin filaments to the Z line is rigid and moves as a single unit. In summary, the evidence in intact skeletal muscle fibers supports the conclusion that the unloaded shortening velocity is independent of the number of attached cross bridges but is probably limited by the intrinsic drag from attached cross bridges.

VI) Calcium regulation of unloaded shortening velocity. If calcium regulates contraction by controlling only the rate of entry into the force-generating portion of the cross-bridge cycle, then steady-state V o should be independent of the extent of muscle activation. This conclusion assumes that even if the cross-bridge throw in the power stroke is only 5–10 nm, there are enough cross bridges pulling on the thin filament to ensure that it is constantly moving (see above). Edman (91) tested the idea that V ois independent of activation in single living muscle fibers by grading the intracellular [Ca2+] with sodium dantrolene inhibition of Ca2+ release from the sarcoplasmic reticulum. Using the slack test and releasing the muscle by <9% of the initial length, Edman (91) found that, when the isometric force is reduced to as low as 10% of maximum by exposure of the fiber to sodium dantrolene, V o was within 10% of its value at full activation. Although the result seems compelling, dantrolene treatment may not uniformly inhibit the release of calcium over the fiber cross section, i.e., it may inhibit calcium release more in the outer fiber annulus than the inner core. If so, force may be reduced to zero in the outer annulus but is normal in a core region experiencing maximal Ca2+ activation. In such a case, the fiber force would be reduced but V o would be unchanged. Thus experiments should be directed at examining the [Ca2+] profile throughout the fiber in the presence of dantrolene (474). As discussed in sectioniiiC9 , data exist suggesting that rapid shortening itself may deactivate the fiber (90), possibly through the detachment of strongly attached cross bridges influencing either Ca2+ binding to the thin filament or direct activation of the thin filament. The data of Vandenboom et al. (469) suggest that at maximal calcium activation, although the shortening may influence the rate of force development, it does not affect V o, which in living fibers is not greatly sensitive to the level of activation.

b) effect of [ca2+ ] on unloaded shortening velocity in skinned muscle fibers. The use of skinned muscle fibers permits variation of parameters not easily altered in the intact fiber, such as [Ca2+] and the TnC isoform. Moreover, both the force and the unloaded shortening velocity exhibited by skinned muscle fibers are similar to those measured in the intact fiber (238). The effect of a reduction of [Ca2+] on unloaded shortening in skinned fibers appears to differ from that observed with reduction of thick and thin filament overlap in intact fibers. In the slack test measurements ofV o at reduced or submaximal [Ca2+], plots of the distance released against the slack time interval no longer form a single straight line (see Fig. 7) and are better characterized by the sum of two straight lines. For releases <6–8% of l o (60–80 nm/h), plots of the distance released versus slack time have a single slope, the unloaded shortening velocity of phase 1, V o 1 which is independent of [Ca2+]. At submaximal Ca2+and releases of >8% (phase 2), plots of distance released versus slack time exhibit a reduced slope, V o 2, indicative of a reduced unloaded shortening velocity compared withV o 1. PlotsV o 1 and V o 2as a function of the relative isometric force, P/Po, varied by changing [Ca2+], show very different behavior.V o 1 decreases only slightly as Ca2+ is decreased until P/Po has fallen to <20% of maximal, but then falls precipitously as Ca2+ is decreased further. V o 2, on the other hand, decreases linearly with the decline in P/Po. Thus, at a pCa producing a P/Po of 0.5,V o 1 is ∼0.9 of the maximalV o, whereasV o 2 is 0.5 of maximalV o. The behavior ofV o 2 is different from that seen in the intact fiber where V o is independent of P/Po values down to 0.4, when force is decreased by decreasing filament overlap. However, V o 1(at submaximal pCa) behaves in a manner similar toV o in the fiber whose overlap is reduced. How closely they correspond cannot be stated, since there is no unambiguous data at thick and thin filament overlap <40% of optimal in the fully active fiber. The similarity betweenV o in intact fibers andV o 1 in skinned fibers is supported also by the data discussed above of Edman (91), suggesting thatV o in intact fibers may depend little on the level of Ca2+ activation.

The behavior of V o 2 has no analogy in the fully active fiber contracting at reduced overlap. However, Edman (91) and Vandenboom et al. (469) measurements used slack test releases of 9% or less. This means that the releases were not large enough to produce the V o 2result seen in skinned muscle fibers. Thus there may be no discrepancy between intact and skinned muscle fibers vis á vis the calcium dependence of V o. As discussed in sectioniiiD , measurement of in vitro motility sliding speed, V f, reveals thatV f changes little with reductions in [Ca2+] until pCa is raised to 6.5. At still greater pCa,V f declines toward zero. Thus regulated thin filaments in the in vitro motility assay using fast muscle myosin behave in a fashion comparable to V o 1, and not like V o 2. Possible explanations for the effects of [Ca2+] onV o 1 and V o 2include the trivial (the skinned fiber is a poor model for the behavior of the living fiber) and the significant: 1) a reduction in [Ca2+] reduces the rate of the cross-bridge power stroke, 2) a reduction in [Ca2+] reduces the rate of cross-bridge detachment from the thin filament during shortening, or 3) a reduction in [Ca2+], along with shortening per se, reduces the rate of cross-bridge formation or the rate of cross-bridge detachment.

These hypotheses have been tested using several approaches. The activation of the thin filament, independent of [Ca2+], can be altered by removal of TnC (334) or replacement of TnC with a mutant cardiac TnC, CBMII (327). This mutant TnC can be substituted for TnC in the fiber but does not bind Ca2+ at the NH2-terminal Ca2+binding trigger site and thus is not activated by Ca2+. Variation of relative isometric force, P/Po, at saturating [Ca2+] indicates that P/Po is inversely proportional to the amount of TnC removed or replacement by the CBMII (328). The behavior of V oafter TnC removal or replacement by CBMII is similar to that seen when [Ca2+] is varied in the control skinned muscle fiber. As the isometric force declines, V o 1 is little affected until force is reduced to <20% of maximal whileV o 2 declines in direct proportion to the reduction in relative isometric force. These latter results suggest that the calcium-dependent changes inV o 2 are a consequence of regulatory protein interaction with the structural arrangement of the contractile proteins in the muscle fiber. The constancy ofV o 1, even when force decreases, significantly suggests that the rate of cross-bridge attachment and detachment are largely unaffected by the extent of thin filament activation. For displacements of <80 nm/h, the rate of cross-bridge attachment, detachment, and the size of the power stroke are unaffected by thin filament activation. Thus the first phase of unloaded shortening velocity (V o 1) is largely independent of the effects of [Ca2+], thin filament activation, or the number of thick and thin filament interactions. The behavior of V o 1 is similar to the behavior of the regulated thin filament sliding speed as pCa is varied and/or CBMII content of the thin filament is varied. The behavior of the in vitro unloaded, regulated thin filament sliding speed in the in vitro motility assay, V f, under reduced [Ca2+] or increased thin filament CBMII can be accounted for by changes in the number of cross bridges pulling on the thin filament (148, 206). The similarity of V o 1 and the in vitro motility behavior thus invite similar explanations.

The behavior of V o 2 is, however, different from what is seen for V f in the in vitro motility assay and must involve a different explanation. In the above experiments, pCa was constant and saturating. BecauseV o 2 decreases as the proportion of CBMII bound to the thin filament increases (i.e., as the extent of thin filament activation was reduced) at saturating pCa, changes inV o 2 cannot be the result of a Ca2+-mediated change in binding to Tn or a regulatory light chain. These changes are more related to the number of cross bridges bound to the thin filament and remain to be explained.

Recently, similar experiments have been done in fast rabbit psoas fibers reconstituted with mixtures of skeletal TnC and the skeletal non-Ca2+-binding TnC mutant [sTnC(D27A, D63)] (Regnier, unpublished observations). The results of these experiments suggest that, as the number of activatable Tn units is decreased, a reduction in unloaded shortening velocity can occur during maximal Ca2+ activation (pCa 4) even at shorter length steps (i.e.,V o 1), with no additional slowing (V o 2) at longer length steps. The discrepancy between these results and those with CBMII may result from differences between cardiac and skeletal forms of TnC. Further study is needed to determine if this is so.

Moss (330) has suggested that cross bridges attached to thin filaments can remain attached and be dragged long distances (60–80 nm) past their equilibrium position before they are forcibly detached, and thus produce a drag that slows the muscle shortening velocity. This was suggested to occur particularly as attached cross bridges, sliding along the partially activated thin filament, found a region of the filament that was in the “off” state and got “stuck.” This hypothesized effect would be exacerbated by the reduction of the extent of thin filament activation. However, ifV o is 5 μm·h−1·s−1, this hypothesis requires that the cross bridge remains attached for up to 16 ms (80 nm·5 μm−1·h−1·s−1) as opposed to the 1–3 ms usually supposed in the Huxley model (215). Furthermore, this hypothesis requires that, over short ranges of cross-bridge travel (−2 to +5 nm), the cross-bridge stiffness would be 5 × 10−4 N/m; however, for deflections from the equilibrium position between −2 and −80 nm, the stiffness would have to be >100 times less to account forV o 1. The stiffness would then need to increase again markedly at distances >80 nm. These requirements seem unrealistic.

Another possibility is that during rapid shortening the thin filament is deactivated by the rapid detachment of cross bridges. Iwamoto (230) found that at submaximal activation, during a repetitive series of rapid shortenings at velocities nearV o followed by quick restretches to the initial muscle length, there is a progressive slowing of shortening velocity. In other words, the V o 1 phase of shortening is lost and the V o 2 phase predominates. The data also showed that a 300-ms period of isometric contraction must be interposed between releases to reverse this inhibition. During rapid shortening at saturating pCa, the stiffness of the muscle fiber decreases by nearly 60%, indicating that the number of attached cross bridges is markedly reduced. At saturating Ca2+, enough cross bridges are attached to forestall significant deactivation of the thin filament. However, during shortening near V o and submaximal [Ca2+], the number of attached cross bridges (which promote thin filament activation) may fall below a level required for full activation of the thin filament. A thin filament deactivation could manifest itself in two ways: 1) an increase in the rate of cross-bridge detachment, or 2) a decrease in the rate of cross-bridge attachment. Either effect would result in a reduced number of cross bridges attached and interacting with the thin filament. If the rate of cross-bridge detachment increased, the unloaded shortening velocity would increase (because the number of negative force-generating cross bridges would decrease). On the other hand, if the rate of cross-bridge attachment decreased, the unloaded shortening velocity would decrease in a fashion similar to that described by Josephson and Edman (236) during relaxation from a tetanus.

A paradoxical aspect of the reduction inV o 2 at low [Ca2+] is the effect of added Pi. Metzger (308) found that at submaximal levels of [Ca2+] there is an inhibition ofV o 2, but the addition of 10–30 mM Pi returns V o 2 toward control values of V o. This behavior seems inconsistent with the changes in V o 2arising from structural constraints on the shortening velocity (an imposed load other than that arising from the cross bridges themselves) because it implies that such a restraint is Pi dependent. One explanation for this behavior is that an elevated [Pi] reduces the fraction of AM·ADP cross bridges by increasing the fraction of cross bridges in the AM·ADP·Pi, a weakly bound cross bridge. If such a Pi binding is stronger to negatively strained cross bridges than positively strained cross bridges, then the drag force will be reduced and velocity of shortening would increase. If true, at saturating calcium, addition of Pi would increaseV o beyond that of control. The data (308, 353) on this point are equivocal. In summary, the unloaded shortening velocity of muscle can be altered by many variables; the size of the cross-bridge throw, the duration of the cross-bridge duty cycle (the time the cross bridges stay attached to the thin filament per ATP hydrolysis cycle), the number of cross bridges interacting with the thin filament, the temperature, and both the rate of cross-bridge attachment (at least transiently) and detachment. The effects of Ca2+ on theV o seem explicable by changes in the rate of cross-bridge attachment, which in turn are set by the extent of the access of the cross bridge to the thin filament.

6.  Activation by strong cross-bridge attachment

As was discussed in section iiiC1 , strongly attached cross bridges are involved in activating the thin filament during muscle contraction. There is also significant experimental evidence that strongly attached myosin cross bridges can activate contraction in skinned muscle fibers in the absence of Ca2+. Reuben et al. (393) first showed that decreasing the concentration of MgATP in the absence of Ca2+ could produce force in skinned crayfish muscle fibers. Further decreases in [MgATP] resulted in a decrease in force so that the MgATP-force relationship was biphasic. This was the skinned fiber equivalent of the increased ATPase activity observed in myofibril preparations by Bremel and Weber (32) and the biphasic MgATP-ATPase relationship seen under similar conditions. The interpretation of these results was that in the absence of Ca2+ and presence of low MgATP, rigor (AM) cross bridges and possibly AM·ADP cross bridges (453) (see next page) bound to and activated the thin filaments in a cooperative manner. The binding of a strongly bound rigor cross bridge presumably displaced Tm and allowed the binding of S1·ADP·Pi cross bridges to actin, activating the ATPase and generating force. At very low MgATP levels, there were insufficient numbers of S1·ADP·Picross bridges to produce force or ATPase activity. These data indicate that the same mechanism exists for the control of force in skinned fibers and for the control of ATPase activity in simpler myofibril preparations. In skinned rabbit psoas muscle fibers, Brandt et al. (28) demonstrated that the relationship between force and decreased MgATP {increased pMgATP (log10[MgATP])} was very steep and could be fitted by a Hill equation (equation in sect.iiiC1 ) with a n H of ∼5 and pMgATP1/2 (pMgATP at which the force had increased to one-half of the maximum value) of ∼4.6 (2.5 × 10−5 M). The maximum force was only ∼70% of the maximal Ca2+-activated force so that under these conditions activation by decreased MgATP was not maximal. It was previously shown that partial activation with Ca2+ decreased then H observed with force obtained by decreasing [MgATP] (27), implying some interaction between Ca2+ and rigor cross bridges in thin filament activation. Furthermore, Brandt et al. (28) showed that at least part of the activation by rigor cross bridges was due to a spread of activation along the thin filament between A7TmTn regulatory units (Tm movement), since extraction of most of the TnC decreased n H to ∼2. The assumption was that extraction of TnC disrupts the coupling of Tm movement between regulatory units. This is expected since in the absence of TnC, TnI remains bound to actin, thus effectively anchoring the regulatory complex to the thin filament every seven actins (297). TnC extraction also decreases the slope of the force-pCa relationship in skinned skeletal muscle fibers (26, 334), presumably for the same reason. Complete extraction of TnC decreases the maximum force at low MgATP (“rigor force”) in the absence of Ca2+ by only ∼25%, implying that the maximum rigor force depends less on coupling between units and more on activation within one unit (28).

In later comparative studies, Metzger (307) confirmed these results for fast and slow skeletal muscle fibers but showed that the n H was slightly larger for slow fibers. Additionally, he found that the n H was much greater for cardiac myocytes, ∼15 rather than ∼5, implying a highly cooperative activation by cross bridges. Furthermore, he showed [as did Brandt et al. (28)] that extraction of TnC (to ∼10% of the normal TnC estimated by the decline of maximal Ca2+-activated force to 10% of control) decreased then H with decreasing MgATP in the absence of Ca2+ for all muscle types, reducing all to nearly the same value, ∼4. [Although this number is higher than that measured by Brandt et al. (28), variations between labs may not be highly significant because determining the exactn H is very sensitive to the technique used.] These results imply that, in the absence of Ca2+, rigor cross bridges in one regulatory unit can displace the Tm of neighboring units more easily in cardiac muscle than in skeletal muscle. There are several possible explanations for this. 1) In cardiac muscle, Tm may be less well anchored to the thin filament through TnI, TnC, and TnT in the absence of Ca2+. Cardiac Tm is less well anchored to actin in the absence of Tn (59). 2) Cardiac Tm is less flexible so that neighboring Tm are more strongly coupled. The evidence suggests the opposite (59). 3) Rigor binding could be stronger in cardiac muscle. The last explanation is not likely as evidenced by Metzger's data (307) showing that then H from each fiber type becomes similar after extraction of TnC. The simplest interpretation is that the extraction of TnC reduces the ability of cross bridges to activate more than just one A7TnTm unit, resulting in no coupling between neighboring units along the thin filament. In other words, full TnC extraction might show the relationship for rigor activation within a single regulatory unit (although one cannot rule out interactions across the thin filament, as there are Tm on both sides).

The above discussion has assumed that it is the rigor (AM) cross bridge that provides activation in the absence of Ca2+. There is excellent evidence that a strong binding AM·ADP cross bridge can also activate. Increased MgADP increases the skinned fiber Ca2+sensitivity (128, 195) and increased MgADP increases tension in the absence of Ca2+(128). As discussed in sectioniiiC , MgADP increases S1 binding to regulated actin filaments in a cooperative manner (160), and discussed later in this section, MgADP increases S1 binding to thin filaments in myofibrils in the absence of Ca2+(516). In fact, much of the force in skinned fibers at low MgATP in the absence of Ca2+ may be attributed to the activation by AM·ADP cross bridges (453). The relative population of the various cross-bridge states is strain sensitive so that the proportion of AM and AM·ADP cross bridges will vary as discussed in section iiD . The data clearly support that the rigor binding of S1 in the total absence of ATP can shift the Tm to an apparent activating state, as discussed in sectioniiiA , which is consistent with activation by rigor S1. Thus one must consider both AM and AM·ADP cross bridges in activation by strongly attached cross bridges. We do not try to distinguish the relative contribution in this section and generally imply both when we refer to activation by rigor cross bridges.

Under these conditions of maximal TnC extraction, then H and relative force provide information about the number of force-generating cross bridges activated by each rigor cross bridge or how many rigor cross bridges are need to activate one force-generating cross bridge. Comparing these results in different fiber types with and without TnC extraction could also provide information about the number of rigor units per A7TmTn needed to activate that unit and the extent of the cooperative spread of activation along the thin filament. However, the exact relationship depends on the model used. Complications in the modeling arise because [MgATP] may affect both the cross-bridge attachment time and the force/cross bridge, and the interpretation also depends critically on the specific model of activation (29, 31). Brandt et al. (28) developed a concerted-transition [Monod-Changeaux-Wyman (321)] model to describe these data, but their model assumed that the thin filament normally activates as a unit, and this has been disputed (50, 332) (see sect. iiiC1 ). In addition, their model predicts that if cycling cross bridges can activate the thin filament, the muscle will not relax (29). These intriguing data await more complete modeling.

In summary, the results of decreasing [MgATP] studies clearly show that rigor cross bridges can activate the thin filament and that the activation within one regulatory unit can spread along the thin filament. Furthermore, it appears that spread along the thin filament in the absence of Ca2+ occurs more readily in cardiac muscle than in skeletal muscle, presumably because of a greater ease of Tm movement. Finally, it should be pointed out that this activation by rigorlike cross bridges is due to activation by long-lived cross bridges, whereas under more physiological MgATP concentrations, cycling cross bridges are much more short-lived.

Further evidence for activation by strongly bound cross bridges comes from the activation produced by a strongly bound myosin analog, NEM-S1 (429). As discussed in sectionsiiiB and iiiC1 , NEM-S1 was used extensively in biochemical experiments because it bound strongly to and dissociated slowly from actin and maximally Ca2+-activated regulated thin filaments (500). Swartz and Moss (429) diffused NEM-modified S1 into skinned muscle fibers and found that high concentrations decreased the maximum Ca2+-activated force (presumably because NEM-S1 can displace endogenous cross bridges), whereas lower concentrations of NEM-S1 increased force at low levels of Ca2+ and decreased the n H of the force-pCa relationship without decreasing maximum force. Although there is some question about the speed of NEM-S1 diffusion into skinned muscle fibers (253), Swartz and Moss (429) observed clear effects of NEM-S1, implying that it was not a limitation in their experiments. Furthermore, at low Ca2+, NEM-S1 increasedk TR to virtually its maximum value, indicating that these strongly attached cross bridges enhanced the effects of Ca2+ in activating muscle fibers. In doing so, they decreased the cooperative activation of force by cycling cross bridges, since the steepness of the force-pCa relationship was decreased. Surprisingly, NEM-S1 did not activate skeletal muscle or cardiac muscle in the absence of Ca2+ (115), as it does the acto-S1 ATPase of S1 with regulated actin filaments (161). Thus NEM-S1 provides additional evidence that strongly bound cross bridges can assist Ca2+ activation of skinned muscle fibers. The effect of NEM-S1 to decrease then H of the force-pCa relationship can be understood if it partially moved Tm, but not enough to allow attachment of cycling cross bridges in an A7TmTn unit. In this partially shifted state, Tm could be moved sufficiently by Ca2+ binding to TnC to bring about full activation of that regulatory unit. Thus the increase in force after Ca2+binding is not highly cooperative in the presence of NEM-S1.

The studies described above used force as the measure of the level of activation. Another measure of activation is the amount of myosin bound to the thin filament in the sarcomere. This was used to great advantage with isolated filaments by Greene and Eisenberg (160) and has now been done using fluorescently labeled S1 in myofibrils with intact sarcomeric structure by Swartz and colleagues (430,516, 517). In these studies, the binding of fluorescently labeled S1 to the thin filament was compared in the region of cross-bridge overlap and nonoverlap with the thick filament. This was done as a function of Ca2+ and [S1] under rigor (430) or ADP conditions (516,517), enabling them to assess the effect on thin filament activation. In both rigor and S1·ADP conditions, and at high Ca2+ and very low added S1 (<1 nM), S1 bound about four times more to the overlap region than the nonoverlap region. As the added [S1] was increased in both the presence and absence of Ca2+, the binding of S1 to the nonoverlap region increased in a highly cooperative manner. This occurred particularly in the absence of Ca2+, saturating at a value consistent with binding to all available sites. As expected, S1·ADP bound somewhat more weakly than S1 in rigor, but not by as much as would be predicted from the relative affinities of the strong binding complex estimated by McKillop and Geeves (303). Thus, in the nonoverlap region, where there was no competition from endogenous cross bridges, the binding of added S1 or S1·ADP to the thin filament was nearly four times less than in the overlap region, even in the presence of high [Ca2+]. Importantly, maximum activation as measured by S1 binding did not occur with high Ca2+ alone. At high Ca2+, endogenous rigor or ADP cross bridges in the overlap region increased the binding of added S1 or S1·ADP to the thin filaments in that region over that seen in the nonoverlap region. This supports the conclusion that endogenous strongly attached cross bridges in the sarcomeric structure can provide additional activation (cross-bridge binding) of the thin filament above that provided by Ca2+ alone.

The increased S1 rigor or S1·ADP binding in the overlap region with high Ca2+ and low added S1 can be understood well from the model of thin filament activation from McKillop and Geeves (303), derived from their studies on isolated filaments. In their model, as discussed in section iiiA2 , there would be a distribution of blocked, closed, and open actins on the thin filament that is dependent on Ca2+ and strong S1 binding. In the presence of low added S1 and high Ca2+, the McKillop and Geeves model (303) predicts that 20–25% of the actins in the nonoverlap region would be in the open state compared with 100% of the actins in the overlap region. This is because of the presence or absence of the endogenous cross bridges in the rigor or ADP nucleotide state. The ratio of open actins in the overlap/nonoverlap regions would be ∼4, which was similar to the ratio of S1 or S1·ADP binding between the two regions that they observed at low added S1. Thus the data of Swartz and co-workers (430,516, 517) are supportive of the Geeves model at low [S1], but the data need to be fit over the whole range of added S1 or S1·ADP, as well as ±Ca2+, to conclude that the data are well described by the model.

The above data appear to make less likely a model of activation where high [Ca2+] or strong cross bridges shift Tm such that all actins in a regulatory unit have the same myosin affinity. With this model in the presence of low added S1 and high Ca2+, the ratio of S1 binding in the overlap/nonoverlap regions would be equal to the increased cross-bridge affinity from Tm movement resulting from endogenous cross-bridge binding in the overlap region. This increase in affinity should depend on the nucleotide state of the S1 (rigor or ADP). Although this appears less likely because of the studies of Swartz and co-workers (430,516, 517), the available data cannot entirely eliminate this possibility. In conclusion, these studies in myofibrils with intact sarcomere structure support the idea that there is a distribution in states in the thin filament with weaker and stronger S1 binding. Additionally, the data support the idea that binding of endogenous rigor or ADP cross bridges in the intact sarcomere can shift the cross-bridge distribution to stronger binding. Finally, the above data support the conclusion that Ca2+ alone can stimulate strong binding of S1 to the thin filament but that additional binding can occur in the presence of endogenous rigor or ADP cross bridges.

7.  Ca2+ binding and TnC structural changes in fibers

Because Ca2+ activates contraction in skinned muscle preparations, a quantitative assessment in this preparation of Ca2+ binding and the conformational changes in TnC and other regulatory proteins leading to activation are crucial. There have been numerous direct studies of Ca2+ binding including45Ca binding studies and electron-probe X-ray microanalysis of Ca2+ binding in the sarcomere under a number of different conditions. There have also been indirect studies of Ca2+ binding using fluorescent or EPR probes on TnC to sense local structural changes in TnC again under various cross-bridge and activation conditions. These studies show a strong coupling between rigor cross-bridge attachment, enhanced Ca2+ binding, and TnC structural changes in all muscles as in myofibrils (32). However, the coupling between cycling cross bridges and Ca2+ binding/TnC structural changes appears to differ between muscle types. Studies indicate a strong coupling in cardiac muscle (168, 197), whereas similar but less decisive changes are observed in fast and slow skeletal muscles (124, 292,483). These data are reviewed next.

Direct measures of Ca2+ binding (45Ca) by Fuchs and co-workers (122-124, 196) in various muscle types, and Pan and Solaro (346) in cardiac muscle, have shown clearly that Ca2+ binding at the NH2-terminal Ca2+ binding sites is associated with activation in these muscles. Fuchs and co-workers have shown that rigor cross bridges enhance Ca2+ binding in both skeletal (122) and cardiac (196) muscles. In contrast, inhibition of cycling cross bridges byV i or extensive muscle shortening (decreased sarcomere lengths) decreases 45Ca2+binding in cardiac muscle preparations (197), but not in either fast (124) or slow (483) mammalian skeletal muscle preparations. This latter point is particularly significant because cardiac and slow skeletal muscle share the same TnC and myosin isoforms (231, 413,498, 510) and both show decreasing Ca2+ sensitivity with decreasing sarcomere lengths. In further support that differences exist between skeletal and cardiac muscle, Wang and Fuchs (484) observed that osmotic compression of the fiber lattice enhances Ca2+ sensitivity (pCa1/2) of force in both fast skeletal and cardiac muscle but enhances 45Ca2+ binding (at a given pCa) only in cardiac muscle. The lack of a sarcomere length effect on Ca2+ binding to TnC in fast skeletal muscle was verified by Patel et al. (357) using a very different technique. Cantino et al. (50) confirmed the enhanced Ca2+ binding to TnC with rigor cross bridges in fast skeletal muscle and demonstrated this enhanced binding was in the region of overlap in the sarcomere, with little extension along the nonoverlapped portion of the thin filaments. Cantino et al. (51) also showed that when fibers were stretched to beyond overlap of thick and thin filaments, Ca2+ binding along skeletal muscle thin filaments was uniform and increased with increasing Ca2+. Thus direct measures of Ca2+binding show that rigor cross bridges enhance Ca2+ binding, but the effects of cycling cross bridges are less certain and appear to depend on the muscle type.

Studies of the relationship between Ca2+ binding and TnC structural changes, using fluorescent or EPR probes bound to TnC, have produced similar results in some laboratories but differing results in others. In every study, rigor cross bridges have caused structural changes in TnC (4, 153, 163,168, 275, 292, 374) and produce activation in every muscle tested. This is in excellent agreement with the 45Ca studies. However, the change in TnC structure with cycling cross bridges in skinned cardiac muscle preparations depends to some extent on the location of the probe (293, 374). The results for cycling cross bridges in skeletal muscle also depend somewhat on the laboratory and technique used. Results of early studies (4,163, 323) suggest that cycling cross bridges in skeletal fibers produced the largest structural change in TnC when TnC was labeled with 5-dimethylamino-1-napthalenyl sulfonylaziridine (DANZ) at Met-25. This result came from comparisons of fluorescence in the presence of Ca2+ and ATP at maximum filament overlap versus the fluorescence in the absence of overlap (sarcomere length >4.0 μm). The increased fluorescence at full overlap was interpreted as an effect of the cycling cross bridges. All these studies found little effect of added Pi on the fluorescence, despite substantial inhibition of force. In subsequent studies using fluorescent probes sensitive to either TnC orientation or local environment, inhibition of force by either stretching the fiber to 3.6 μm or addition of BDM or AlF4 , demonstrated little influence of force or strong cross-bridge attachment on TnC structure at maximal Ca2+ (292). The differences between this latter study and the others include the use of techniques to minimize sarcomere shortening, the use of both environmentally sensitive and orientation-sensitive probes, and the use of dextran to minimize changes in lattice spacing during activation. In another study using EPR, Li and Fajer (275) demonstrated only a small change in TnC structure with force inhibition by AlF4 . Thus the effect of cycling cross bridges on the skeletal TnC structure may be small. This could be because cycling cross bridges have, in fact, little effect on TnC structure in skeletal muscle or because the fraction of attached cross bridges is much smaller during cycling than in rigor.

A more indirect measure of Ca2+ binding has been the increase in sarcoplasmic free [Ca2+] seen with a step decrease in length of isometrically contracting cardiac muscle (3) and barnacle muscle (149,394) during the declining phase of the Ca2+transient during a twitch. These investigators interpreted the increased [Ca2+] as being released from TnC subsequent to a decreased Ca2+ affinity resulting from the detachment of cross bridges accompanying the shortening step. This implied that active cross bridges enhanced Ca2+ binding to TnC in cardiac and barnacle muscle. Support for this hypothesis came from the studies of Gordon and Ridgway (150, 151), Kurihara et al. (257), and Allen and Kentish (2) and the modeling studies of Gordon and Ridgway (152). In the latter studies (measuring [Ca2+] using aequorin), the change in Ca2+affinity of TnC for a given force level was estimated. This was done by assuming the increased [Ca2+] measured with the shortening step was proportional to the TnC-bound Ca2+, and calculating the relative affinity from the observed increased [Ca2+] and the measured free [Ca2+]. These data resulted in a calculated TnC Ca2+ affinity that increased steeply as a function of the force (152). It also demonstrated that, during transient stimulation, the time course of Ca2+ bound to TnC bound was intermediate between free [Ca2+] and force. During the rise in free [Ca2+] and force, the increase in bound Ca2+lagged the rise in Ca2+ and led to the rise in force. During relaxation, the decrease in bound Ca2+ occurred after the decline in free [Ca2+] but before the decline in force. The calculated Ca2+ affinity as a function of force could then be used to calculate the force resulting from the bound Ca2+ using a simple activation model and assuming that the effect of force/cross-bridge attachment on the TnC Ca2+ affinity was through a change in the dissociation rate of Ca2+ from TnC (152). These results again suggest that cycling cross-bridge attachment in cardiac and barnacle muscle increase Ca2+ binding to TnC. The result in cardiac muscle is similar to the 45Ca2+ results discussed above (197) and the fluorescent probe results (168).

In contrast to the direct, steady-state measure of Ca2+binding using 45Ca2+ in skeletal muscle showing little effect of cycling cross bridges (124), there are indirect measures of Ca2+ binding using length changes that demonstrate some effect of cycling cross bridges to enhance Ca2+ binding to TnC. Cannell (49) and later Caputo et al. (52) and Vandenboom et al. (469) showed there was a transient increase in free Ca2+ during nonuniform relaxation from tetanic stimulation in skeletal muscle. At this time during relaxation, many sarcomeres are shortening rapidly while others are lengthening (65,218). The rapid shortening is accompanied by cross-bridge detachment and extra Ca2+, presumably dissociated from TnC because of decreased Ca2+ affinity. In addition, Caputo et al. (52) showed increased Ca2+ accompanying a shortening ramp during the initial phase of relaxation from tetanic stimulation, but not during the force plateau. Later, Vandenboom et al. (469) showed that if the shortening were rapid enough and large enough (close toV u and >10%l o, respectively) during the plateau, they could observe extra Ca2+ during shortening and decreased Ca2+ during the subsequent force redevelopment. This implies there is some effect of cycling cross bridges on Ca2+ binding to TnC in skeletal muscle, but the effect may be smaller than in mammalian cardiac muscle or barnacle muscle. These indirect techniques suffer from uncertainties in calibrating the [Ca2+] signal, relating free [Ca2+] to TnC-bound Ca2+, and calculating the effects of the other Ca2+ buffers, so it is difficult to compare results between tissues and calculate actual changes in TnC Ca2+ affinity. It could be that Ca2+ binding to TnC site II is more affected by strong cross-bridge attachment than binding to site I (cardiac TnC and barnacle TnC have only site II Ca2+binding, skeletal TnC has both site I and site II Ca2+binding) (325). If this were the case, Fuchs and Wang (124) might have had a more difficult time observing changes in total Ca2+ binding. This cannot completely account for the difference between the effect of cycling cross bridges on 45Ca2+ binding to skeletal and cardiac muscle TnC, since force-dependent Ca2+ binding is not observed in slow skeletal muscle fibers, even though it contains the cardiac TnC isoform with Ca2+ binding only at site II. However, there may be other variations in the regulatory protein interactions that enhance the effect in cardiac muscle. Finally, another contrast between the 45Ca2+ binding measurements and the indirect measures using changes in free [Ca2+] is that the former are steady-state measurements and the latter are transient measurements. If the change in TnC Ca2+ affinity were only transient, it would only be detected by latter techniques. In any case, the data suggest the differences may be quantitative, rather than qualitative, and that Ca2+ binding to TnC serves to initiate contraction but is not the only step in regulation.

To more fully understand regulation, one must follow structural changes in the other components of the regulatory system occurring during activation. This can be done using skinned fibers where the native proteins can be exchanged for fluorescent or EPR-labeled proteins. With the available techniques for exchanging various components of the regulatory system, additional studies are clearly possible (TnT exchange) (173, 174). The protein that has been the most difficult to exchange is Tm. Studies where Tm has been exchanged involve digestion and repolymerization of actin, followed by incorporation of Tn and labeled Tm (127,129). These new techniques are required to provide this important information.

In summary, studies of Ca2+ binding and TnC structural changes indicate a strong coupling of these changes with attachment of cycling cross bridges in cardiac muscle, but less coupling in skeletal muscle. The possible role of these differences in Ca2+activation is discussed in section v.

8.  Control of relaxation

The kinetics of relaxation from force can also provide information about the mechanism of activation. The most well-defined condition for studying relaxation in intact fibers is relaxation from an isometric tetanic contraction. Under this condition, the kinetics of cross-bridge detachment and cross bridge-induced activation by cooperative mechanisms are complicated by contemporaneous processes. These other processes involve changes in intracellular [Ca2+] via uptake by the sarcoplasmic reticulum, binding to high affinity Ca2+ binding proteins such as parvalbumin, and dissociation from Tn changing Ca2+activation as well as by changes in cross bridges through reattachment. There have been a number of studies of the relaxation process, but most have investigated the decrease in [Ca2+], whereas few have studied the mechanism of thin filament relaxation. A major experimental problem in studying relaxation is that large sarcomere nonuniformity can develop that contributes to the observed mechanical relaxation. Over 25 years ago, Cleworth and Edman (65) and Huxley and Simmons (217, 218) showed that during relaxation there were large changes in sarcomere spacing within fibers even when the total muscle length was held constant. The end sarcomeres relaxed first and were stretched as the central sarcomeres shortened. These processes were exacerbated after force had declined linearly by ∼20–30%, producing a shoulder in the force curve as force in the shortening sarcomeres declined rapidly. This means that in the first phase of relaxation sarcomeres are under nearly isometric conditions, whereas in the second phase they are clearly not. Huxley and Simmons (218) showed that when the length of the central region of a single muscle fiber is controlled, the initial linear phase of relaxation and the shoulder are prolonged. This phase is more characteristic of isometric relaxation. The rate of decline in force during this phase is so slow (<1 s−1 at 4°C, Ref.218) that there may not be simply cross-bridge detachment, there may be some reattachment as well. This complexity in analyzing relaxation due to sarcomere nonuniformity occurs in both intact and skinned fibers.

As outlined in sections iiA andiiiA , the Tm position is a major factor determining the attachment of cross bridges. Thus it is important to know Tm position during relaxation. A comparison of the time course of force relaxation and Tm movement in intact fibers was made by Kress et al. (254) using X-ray diffraction (discussed in sect.iiiA1 ). This study showed that Tm movement during relaxation, as measured by the change in intensity of the second actin layer line, declined faster than force. However, if the amplitude rather than the intensity of the second actin layer line were plotted (which would be a better measure of Tm movement if thin filaments were not activated as units, but in segments), the amplitude would decline at the same rate as force. This would be consistent with Tm moving back toward the relaxed position as force declined and with the rate-limiting step in relaxation being the net dissociation of cross bridges. Their data also suggested that some thin filament activation was being maintained by cross-bridge reattachment because the intensity of the second actin layer line (possible Tm movement) declined earlier if relaxation occurred at a long sarcomere length where there was little thick and thin filament overlap. Furthermore, the change in intensity of the second actin layer line during stimulation was not significantly different at this longer sarcomere length with no filament overlap than the intensity at sarcomere lengths with full overlap, implying the change in Tm position during activation was similar with and without cross bridges. These data are consistent with cycling cross bridges holding Tm in an activating position or attached cross bridges enhancing Ca2+ binding, while delaying the dissociation of Ca2+ and return of Tm from the Ca2+-activated position during relaxation. There is support for both hypotheses and reason to suggest they may be coupled (see sects.iiiA2 , iiiB ,iiiC1 , iiiC7 , andiv). Another possibility is that the return of Tm to its resting position can in some way accelerate cross-bridge dissociation. However, there is little support for such a mechanism at this time.

If strongly attached cross bridges activate in a positive-feedback manner, then how does the muscle ever relax? Of course, this will depend on the extent of the feedback, but in any case, relaxation is accelerated by the nonuniformity in sarcomere length. These nonuniformities bring about a rapid relaxation when still active sarcomeres can shorten rapidly because sarcomeres in series lose activation and can be readily stretched. These nonuniformities are less important in cardiac muscle because of the larger internal stiffness (256).

Skinned fibers offer some advantages in studying the mechanisms of thin filament relaxation. The [Ca2+] can be decreased rapidly using caged Ca2+ chelators such as diazo-2, and the sarcomere length can be controlled to minimize nonuniformities along the fiber. Furthermore, the steady-state force level before relaxation can be varied to test for the contribution of attached cross bridges on the relaxation rate. If attached cross bridges sustain activation, one would expect that at higher initial force levels there would be slower relaxation, if either cross-bridge reattachment or a reduced tendency for Tm to “push” the cross bridges off occurs.

There have been several studies using the diazo-2 technique to rapidly chelate Ca2+ and initiate relaxation in skinned skeletal and cardiac muscle preparations. In skeletal muscle, the time course of relaxation of force is similar to intact preparations, a linear phase to a shoulder and a rapid phase that can be characterized with two exponential functions (355, 477). Because of the nonuniformity issue discussed above, only the initial linear phase gives reliable information about relaxation in skeletal muscle. Additionally, the Ca2+ affinity of diazo-2 does not increase enough with photolysis to bring about complete relaxation of a fiber from maximal Ca2+ activation, but the level of the initial force can be varied. In skeletal muscle, the rate of this initial phase of relaxation is slower the higher the Ca2+level and force when relaxation is initiated (355,477). This effect also occurs when techniques (38) are used that partially stabilize the sarcomeres (477). Even with this technique, the slower phase of relaxation was always more abbreviated in the skinned fiber preparation than in intact fibers, indicating more nonuniformity of sarcomeres during relaxation in the skinned preparation (477). This makes one cautious in interpreting the results from skinned fiber studies, none of which uses sarcomere length control. Slowing of relaxation also occurs with added NEM-S1 (355) or added ADP (9), indicating that strong cross bridges influence the relaxation rate. Finally, in a very small, myofibrillar preparation where myofibrillar [Ca2+] was decreased very rapidly, the rate of relaxation during the linear, more “isometric,” phase of relaxation decreased with the initial level of force (339). Taken together with the results of Kress et al. (254), all these observations are evidence that cycling or strongly attached cross bridges prolong activation (by their positive feedback to activate the thin filament) and thus allow reattachment of cross bridges. The data support a direct role of cross bridges in feedback activation in skeletal muscle, since Ca2+ bound to Tn declines more slowly than does free Ca2+ during relaxation but faster than force (152). Additionally, in skeletal muscle, Ca2+ binding to TnC does not show a strong dependence on cross-bridge attachment (124) (see sect.iiiC7 ), although a dependence may exist (as discussed in sect. iiiC7 ; Refs. 49, 52, 469).

In cardiac muscle, studies of relaxation using diazo-2 also have not used sarcomere control, but this may be less important since sarcomere nonuniformities are reduced due to the increased sarcomeric stiffness from passive elements. In three studies (343,344, 518), the rate constants for the decline of force did not depend on the initial force level. This implies there is either no effect of cross bridges to slow relaxation in cardiac muscle (as there appears to be in skeletal muscle) or that the effect of cross bridges saturates at very low levels of attachment. This would be consistent with Tm moving more readily in cardiac muscle (see sect.iiiC6 ). However, because strong cross-bridge attachment promotes Ca2+ binding to TnC in cardiac muscle (see sect. iiiC7 ), one might expect higher forces to promote Ca2+ binding, continued thin filament activation, and slower relaxation if substantial reattachment of cross bridges occurred during relaxation. That this does not occur suggests that relaxation is determined more by the kinetics of cross-bridge detachment than by reattachment. This was most clearly demonstrated in the study of Palmer and Kentish (344). They found that the rate of relaxation was nearly equal to the respective maximumk TR and k Ca for rat and guinea pig cardiac muscle, whereas the maximum ATPase of the two animals differed due to their respective cardiac myosin isoforms. The kinetics of relaxation in skeletal and cardiac muscle point out major differences in activation between these two tissues, with cooperative activation by cross bridges playing a more direct role at higher force levels in skeletal muscle, but perhaps a less direct role in cardiac muscle (440). In cardiac muscle, strongly attached cross bridges enhance Ca2+ binding to TnC and thereby promote continued activation (discussed in sect.iiiC7 ). As Ca2+ activation falls during relaxation in cardiac muscle, both the Ca2+activation and strong cross-bridge attachment would decline with a rate equal to the sum of the apparent rate constants for strong cross-bridge attachment and detachment,f app and g app. This sum would be approximately equal to the maximumk TR and k Ca(see discussion of model in sects. iiiC2 andiv). Thus, in cardiac muscle, strong cross-bridge binding, Ca2+ binding, and activation are more tightly coupled than in skeletal muscle.

9.  Shortening-induced deactivation

An important aspect in the study of contractile regulation is the question of whether the mechanical perturbations themselves affect regulation. For some time it has been recognized that, in both skeletal and cardiac muscle, shortening and/or stretch alter contractions [see Edman (89) for a review]. In a definitive study, Edman (90) described the effect of a shortening step to decrease subsequent force development either in a twitch or series of twitches, a phenomenon he called “shortening-induced deactivation.” In subsequent studies, this shortening-induced deactivation has been demonstrated for steady-state force and the rate of force redevelopment and, more recently, for shortening velocity.

The main effect of shortening initially described (90) was that the force developed subsequent to a shortening step was less than the isometric force developed at the shorter length. Because of the effect of sarcomere length on isometric force, Edman (90) was careful to operate at sarcomere lengths where the maximum isometric force varied little with length. Edman (90) demonstrated that the deficit in force due to shortening increases with the distance shortened, is present even if the shortening occurs after activation but before force develops, disappears with time (about one second) as stimulation continues, and is independent of the load during shortening (loads from 0 to 1/3Po). On the other hand, the amount of force deficit and shortening-induced deactivation depends on the level of Ca2+ activation, decreasing as Ca2+activation approaches maximal (88). It also depends on sarcomere length but with the same dependence as the maximum force (88).

Shortening-induced deactivation was also shown to decrease the rate of force redevelopment subsequent to a shortening step (88,469). As was the case for the force deficit described above, the deficit in the rate of force redevelopment after shortening depends on the level of Ca2+ activation, decreasing as the Ca2+ activation approaches maximum (95). Furthermore, it depends on the level of force at the time of shortening, decreasing the smaller the initial force (469).

In contrast, there appears to be little effect of shortening-induced deactivation on the unloaded shortening velocity, at least in the intact fiber (88,469). In skinned fibers, it has been postulated to be responsible for the slowing of shortening at submaximal Ca2+ during longer length steps (230) (see sect. iiiC5 on control of the shortening velocity).

There are several possible mechanisms for this deactivation as pointed out by Ridgway and Gordon (394). The first is that shortening enhances relaxation because cross-bridge detachment rates are faster when the fiber is shortening than when it is held isometric (217, 218). The second is that shortening-induced detachment of cross bridges releases Ca2+ bound to TnC by changing the Ca2+ affinity of TnC (32, 394). This feedback effect of strongly attached cross bridges to enhance Ca2+ binding is discussed in section iiic7 . The third mechanism is that shortening-induced detachment of strongly attached cross bridges removes the cooperative activation or maintenance of activation of the thin filament by strongly attached cross bridges (32, 394). As suggested by Edman (90), there may be other explanations involving long-lasting structural changes in the myofilaments.

The question is which of these mechanisms is relevant. The first only applies to relaxation and will not be considered further. The effects of strongly attached cross bridges to enhance both Ca2+binding and thin filament activation directly (through stabilizing Tm in the activating position) may be important in mediating shortening-induced deactivation. There is strong evidence that decreases in Ca2+ affinity of TnC occur with detachment of cross bridges accompanying muscle shortening as discussed in sectioniiiC7 . Ekelund and Edman (95) suggested this mechanism and it was supported by the observations of Ridgway and Gordon (394) and Gordon and Ridgway (150), who measured the increase in intracellular Ca2+ accompanying shortening steps in activated, aequorin-injected barnacle single muscle fibers. Recent studies by Vandenboom et al. (469) verified the extra intracellular Ca2+ on shortening in frog single muscle fibers and the correlation of the changes with deactivation. The problem with these studies is the inability to determine whether the decrease in bound Ca2+ is the cause of the shortening-induced deactivation or the result of the decrease in thin filament activation by strongly attached cross bridges. In other words, is the decline in TnC-bound Ca2+ (signaled by the rise in free Ca2+) directly responsible for the decrease in thin filament activation and force seen with continued stimulation or is it only secondary to changes in activation by strongly attached cross bridges? The only quantitative measurement of changes in bound Ca2+ in skeletal muscle indicates that bound Ca2+ does not change significantly with shortening (124). This would imply the extra Ca2+ seen with shortening (by isotopic or aequorin techniques) is probably a result of, not the cause of, the change in thin filament activation.

The data support the hypothesis that shortening-induced deactivation of the thin filament results from a reduction of strongly attached cross bridges. This is consistent with the deactivation dependence on extent of shortening (89) and the level of force before the shortening. The smaller deactivation at higher levels of Ca2+ is consistent with either explanation. Decreases in Ca2+ affinity upon shortening would change Ca2+binding little at saturating Ca2+. In like manner, decreases in strongly attached cross bridges upon shortening would have less of an effect at maximal activation when cross-bridge attachment is at a maximum. In addition, release and restretch experiments in barnacle muscle (Ridgway and Gordon, unpublished data) indicate that substantial extra Ca2+ can be observed with no change in force. Recent observations on the effect of shortening on thin filament activation using a fluorescent probe on TnI show that there is a small decrease in activation accompanying a shortening step from which the thin filament recovers quickly (41). It is not clear that this change is sufficient to explain the deactivation seen in all cases. Finally, as discussed in sectioniiiC5 , the slowing of the unloaded shortening velocity with extended shortening at submaximal Ca2+activation is also most consistent with deactivation via a decrease in the number of strongly attached cross bridges, resulting in a reduction of thin filament activation [see discussion of Iwamoto's results (230) in sect. iiiC5 ]. The slowing of unloaded shortening velocity with extended shortening at submaximal activation is also seen when using a non-Ca2+-requiring activator, aTnC (see sect. iiiC2 ). This is consistent with the deactivation not being tied to Ca2+binding but to decreased strong cross-bridge attachment. More experiments with Ca2+-insensitive activation with conditions like aTnC and direct measures of thin filament activation are needed to determine definitively the cause of shortening-induced deactivation.

There are significant physiological implications of shortening-induced deactivation that must be considered. In the mechanical measurements discussed in this review, the two that are most likely to be affected are measurements ofk TR and shortening velocity. In thek TR measurements, a large shortening step is followed sometime later by a restretch to the original length. This should put the muscle back to initial conditions where activation is determined by Ca2+ binding and the initial steps in activation before strong cross-bridge attachment. Thus the effect of shortening-induced deactivation on the normalk TR measurement is to make the result less dependent on the conditions at the time of the length changes and more characteristic of the initial activation process. However, very short periods of shortening or not restretching the fiber to detach cross bridges could yield variable conditions of strong cross-bridge activation due to shortening-induced deactivation and make the results more difficult to interpret. Second, as discussed above, the shortening velocity in fibers and the early phases of shortening in skinned fibers are little affected by shortening-induced deactivation, but the later phases at submaximal Ca2+activation may be. If Iwamoto's hypothesis is correct (230), this could account for the slowing seen during the later phases of shortening. Thus the effect of shortening-induced deactivation must be considered in understanding the mechanical performance of skeletal and cardiac muscle following muscle shortening. Furthermore, the existence of this deactivation supports the role of strongly attached cross bridges in sustaining activation at high levels of force in skeletal muscle.

D.  Regulation of Reconstituted Thin Filaments in In Vitro Motility Assays

The in vitro motility assay is a powerful approach for examination of the mechanical sequelae of structural alteration of the regulatory proteins [see Sugi (427) for a recent review]. Currently, myosin, HMM, or S1 are bound to a surface coated with nitrocellulose or dichloromethylsilane. Thin filaments, usually labeled with rhodamine phalloidin (RhPh), are then applied to the surface where they bind to the motor proteins. On addition of MgATP, the filaments slide over the surface at speeds (V f) comparable, but not identical to, speeds at which thin filaments slide past thick filaments in the intact or skinned muscle fiber (<0.75V u). It is generally assumed that the motion of the thin filament is unrestrained by drag produced by the solution (see sect. iiiC5 ) or interaction of the filament with the surface. The power of this assay stems from the specificity with which chemical and genetically modified proteins can be substituted in the assay and correlated with effects on mechanical behavior. Recently, motility assays have been used to measure isometric force produced when thin filaments, attached to flexible microneedles (249, 468) or to glass beads held in optical traps (112, 485), are brought into contact with the surface. These approaches have made examination of mechanical behavior of single or small arrays of contractile proteins a reality. Studies of myocytes transfected with mutant proteins (400,433, 488, 494) or muscles from transgenic animals (299, 314) are superior in that the filament geometric lattice is retained and the protein is in an environment more like that in the living animal. However, in vitro motility assays offer experimental simplicity and speed for evaluation of mechanistic changes consequent to protein structural changes and are likely to be a useful approach for screening mutations for years to come. Recently, Ishiwata and colleagues (127,129) have developed an approach in which thin filaments in skinned muscle fibers are enzymatically digested (by gelsolin) and then reconstituted using actin and regulatory proteins. Although this approach has exciting potential, it has not been successfully applied to skeletal muscle, and the formation of the thin filaments and the length and uniformity of the reconstituted thin have yet to be successfully controlled.

1.  Limitations of the in vitro motility assay

Several limitations of in vitro motility system should be considered when interpreting motility data. The most serious problem is one of geometry. Myosin heads bound to the motility surface are randomly oriented. Thus the measurements cannot be used to directly estimate the force exerted or the cross-bridge throw size because the orientation of the motor(s) with respect to the thin filament orientation is indeterminate. To alleviate this problem, Sellers and Kachar (409) and Yamada et al. (508) measured thin filament sliding along isolated molluscan thick filaments. They found that thin filaments slide along the thick filaments at a speed comparable to those of the intact muscle. The movement of the thin filaments toward the center of the thick filament is ∼10-fold faster than that away from the center of the thick filament. The use of clam thick filaments would preclude the ability to use myosin mutations and restricts the calcium concentration used in thin filament regulation studies, since the activation of the molluscan thick filaments is [Ca2+] dependent. Attempts to create oriented filaments from isolated myosin have been problematic. Toyoshima et al. (461) bound myosin to thin filaments in the absence of ATP and applied the decorated thin filaments to the motility surface, supposing that the actin filament would orient myosin binding to the surface. Their studies, however, indicated that the myosin that bound was not oriented. Recently, in an effort to orient the myosin head, Yamada and Wakabayashi (509) made thick filaments from myosin and Ishijima et al. (228) made thick filament copolymers of myosin rods and intact myosin at different ratios. In the latter case (228), “thick filaments” were 5–8 μm long and some were as wide as 0.2 μm at their center. Thin filament sliding speeds of 9–10 μm/s toward the center of the copolymer and ∼2.5 μm/s for speeds sliding away from the center of the copolymer were observed, similar to those observed by Sellers and Kachar (409) and Yamada et al. (508). However, structural evidence showing that copolymers were structurally polarized at the cross-bridge level was not presented. Furthermore, measurement of force exerted on thin filaments attached to microneedles by these thick filaments fell by only 50% for a 20-fold reduction in myosin head content per unit length of the copolymer. Additional work should be directed toward production of oriented myosin heads for motility assays.

The V f observed in the motility assays of unregulated thin filaments is less (by 30–40%) than that seen in muscle fibers at temperatures at which the two can be compared (10–20°C) (6, 211). In addition to the myosin head orientation problem, this behavior could stem from the presence of inactive or enzymatically damaged myosin S1 heads (255), differences in ionic strength (211), structural differences between the fiber or motility assay, or the lack of regulatory proteins on the thin filament. The addition of regulatory proteins produces significant increases in thin filament sliding speed. Sellers and co-workers (48) have reported a 30% increase in sliding speed of small smooth muscle myosin-coated beads sliding over Nitella actin cables exposed to Tm and a 10-fold increase in speed of thin filaments with Tm bound propelled over surfaces coated by Limulus myosin. Gordon et al. (148) find that the unloaded unregulated thin filament sliding speed increases from 5 to 6.5–8 μm/s (30–60%) when skeletal Tm/Tn are bound to thin filaments at pCa 5, while Marston and co-workers (17) also found that skeletal Tn enhanced the speed of actin-skeletal Tm filaments by 21%. Others (208) find that cardiac regulatory proteins produce a 30% increase in thin filament sliding speed at pCa 5. Marston and co-workers (18) reported no change in thin filament sliding speed when skeletal Tm was bound to actin filaments, but an ∼40% increase in thin filament sliding speed when smooth muscle Tm binds to actin filaments. The small effects of Tm alone are not dependent on the presence of Ca2+ (145). Thus regulatory proteins in the presence of Ca2+ potentiate thin filament V f. It could be argued that binding of regulatory proteins stiffen the thin filaments (compared with unregulated F-actin) and thus increaseV f. However, the difference in thin filament persistence length (a measure of filament stiffness) in the presence and absence of regulatory proteins is too small to make a significant change in V f(224). These results imply that regulatory proteins allosterically modify the actin structure and its interaction with myosin. In addition, when myosin is oriented and thin filaments contain Tm/Tn, V f may approachV u.

Significant changes in the thin filament sliding speed are produced by isoforms of myosin (408) and different types of enzymatic preparations of myosin (HMM and S1) (460). Rabbit skeletal HMM is often used because myosin produces fragmentation and erratic movement of thin filaments. Other groups find that rabbit myosin propels thin filaments at high speeds [e.g., 8 μm/s at 22°C (169) and 8.6 μm/s at 27°C (229)]. S1 can propel thin filaments but does so at a speed 50% of that seen using HMM (460). The reason for this decrease is probably an ineffective binding of the S1 to the motility surface. It has been shown that attachment of the tail of the myosin to the surface by antibodies directed to the S2 or S2-LMM region can significantly increase V f (502).

Another limiting condition for motility studies is the fact that the actin, Tm, and Tn concentrations must be dilute. The actin concentration in the motility assay is usually ∼8–50 nM. Higher concentrations reduce the contrast between the filament and background. Although RhPh stabilizes thin filament structure, actin mutants may alter actin structure so that binding of RhPh is not strong enough to stabilize the actin filaments at very dilute actin concentrations. The Tm and Tn concentration must be sufficient to ensure saturation of the reconstituted filaments, but not so great that filaments bundle.

Finally, too often the methods of data selection and analysis of thin filament movement are not described. For all analyses, selection criteria, definition of what constitutes a filament, how the frame to frame speeds are determined, the length of time filament movement is monitored, how frequently the movement is sampled, and how sliding speeds are calculated should be described. This is needed because the recorded speeds depend on the method of speed measurement. Sampling at too low a rate truncates the filament path and underestimatesV f. If one samples at too great a rate, sampling error of the speed increases and can render mean speeds meaningless. The presence of noise (arc wander, vibration of the microscope stage with respect to the image plane, photobleaching, and weak binding to the motility surface) contribute significantly to movement noise and make slowly or nonmoving objects appear to move, when automated data analysis systems are used. Finally, motility fields can vary from one part of the coverslip to the next. Consequently, it is wise to sample from multiple fields to produce estimates representing the population as a whole. Although there are some limitations to the in vitro measurements, with proper attention to detail, reliable results can be obtained.

2.  Characteristics of thin filament movement over motility surfaces

Thin filaments move over a motility surface at similar speeds over a wide range of HMM densities, but V f is proportional to the HMM ATPase for a variety of myosin isoforms (408). Many reports of thin filament motility use surfaces equilibrated with myosin solutions containing 100–500 μg/ml yielding a surface density of 1,500–2,500 HMM molecules/μm2(17, 18, 20, 121,148, 164, 169, 206,211, 279, 401,408). Reduction of the HMM concentration to 20–30 μg/ml produces little change in unregulated thin filament sliding speed, suggesting S1 head density is sufficient to ensure continual movement of the thin filament. This behavior is reminiscent of the independence of V u on sarcomere length between sarcomere lengths of 1.7 and 3.1 μm. When the surface is equilibrated with <20 μg/ml HMM, V f is reduced, suggesting that there are an insufficient number of heads available to ensure continual movement. Another well-documented behavior is the independence of thin filament sliding speed for thin filament lengths above ∼1 μm (467). This result suggests that beyond this filament length, enough heads are attached at any time to give continuous movement. In addition, it could mean that a non-cross-bridge viscous drag force proportional to thin filament length exists or that both the drag force and propelling force acting on the thin filament are proportional to thin filament length. Because calculations of solution viscosity render the former possibility unlikely, the latter possibility is more probable. This would be the case if the drag force were dependent on the number of cross bridges interacting with the S1 heads, as in the Huxley view of unloaded sliding speed (215).

When the [ATP] is reduced or the [ADP] is increased, the rate of cross-bridge dissociation from the thin filament is reduced andV f falls in a manner reminiscent of the behavior of V u in skinned muscle fibers (211, 486). Also greatly elevated nonionic solute concentrations decrease V f in a manner similar to decreases in V u in skinned muscle fibers (61). Finally, Bing et al. (17) have suggested that the nitrocellulose surface (as compared with a surface of dichloromethylsilane) produces a drag on the thin filament that slows the thin filament movement. This suggestion is inconsistent with the data obtained from nitrocellulose surfaces described above. It is also inconsistent with the fact that when regulated thin filaments attached to microneedles are dragged over an HMM covered surface at pCa 9, the displacement of the microneedle is imperceptible (208). Thus the drag force is <2% of the force exerted on thin filaments by HMM in isometric conditions at pCa 5. In conclusion, factors that control the sliding speed in the in vitro motility assay appear to be similar to those in skinned muscle fibers (see sect. iiiC5 ).

3.  Early studies of regulation of thin filaments sliding in the in vitro motility assay

Early reports of the sliding speed of regulated thin filaments indicated that regulation occurred in an on or off (step function) fashion seemingly predicted by Huxley's view ofV o (215). At pCa >5.7 (212) or >6.1 (169), thin filaments bound to a motility surface but did not move. However, when pCa was lowered further to 5.6 or 6.0, respectively, regulated thin filaments began to move a maximum speed. A recent study by Sata et al. (401) confirmed these observations using rabbit skeletal actin and cardiac regulatory proteins. Unfortunately, these studies did not define the methods used to quantitate filament movement or selection and did not specify the protein constituency of filaments (actin:Tm:Tn). Fraser and Marston (121) successfully addressed some of these issues by varying the amount of regulatory proteins attached to the thin filaments and by randomly selecting filaments for analysis before observing their movement and quantitating the number of filaments moving and their average speed. They also concluded that calcium regulation was an “all-or-none” process. However, their data showed that at as [Ca2+] fell from 3 × 10−5to 1 × 10−9 M, sliding speed fell progressively from 5.2 ± 1.0 to 3.3 ± 0.8 μm/s. Furthermore, at 1 × 10−9 M, a [Ca2+] at which isometric force is zero, and the muscle does not actively shorten, 20% of the thin filaments were still moving at a speed equivalent to that of naked actin. In their experiments, Fraser and Marston (121) used motility solutions containing <100 nM [Tn] and no added Tm. This is probably too little free Tm/Tn to produce complete regulation of the thin filaments. Given the binding of Tm and Tn to thin filaments (455), ∼100 nM of each will be required to saturate the thin filament in the motility assay.

4.  Effects of pCa on regulated thin filament sliding speed and force development

Recent experiments using fully regulated thin filaments in the in vitro motility assay utilized cardiac or skeletal regulatory proteins (148, 206). These two studies took care to ensure that the thin filaments were completely regulated by including 80–100 nM Tm and 100 nM Tn in the motility and wash solutions. Furthermore, the two studies used an automated motion analysis system allowing mapping and analysis of the movement of large numbers of thin filaments. In these studies, the movement of each filament's centroid was followed for 2 s or more, and the number of moving and nonmoving filaments was determined. The results of these two sets of experiments are similar both in the conclusions and the absolute values. The thin filament movement over motility surfaces was measured at various pCa values ranging from 4.5 to 9. Each group measured the fraction of thin filaments moving and the average speed of the moving filaments at each ionic strength. The two groups studied motility at different pH values [7.4 and 7.0 for Homsher et al. (206) and Gordon et al. (148), respectively] so one expects a shift in the Ca2+ sensitivity (∼0.8 pCa units), but they also used different regulatory proteins, cardiac and skeletal, which should also affect the shift. Gordon et al. (148) also measured isometric force in skinned muscle fibers in parallel experiments. Table 3 summarizes the results of each group. The primary conclusions are as following.

View this table:
Table 3.

Effects of pCa on regulated thin filament sliding speed and force development

1) At pCa 9, few, if any, filaments move, whereas at pCa 4.5–5, 80–90% of the thin filaments move at maximal speed. Thus complete regulation of thin filament movement is obtained.

2) Both the speed of moving filaments and the fraction of filaments moving can be fit by an equation of the formy=ymax/[1+10n(pCapCa50)] where y represents either the filament speed or fraction of moving filaments; y max is the maximum sliding speed, V f, or maximum fraction of moving filaments, fmax; n is the Hill coefficient; and pCa50 is the value of pCa at which the value of y is half-maximal.

3) The sliding speed is not very cooperative (n< 2.2), while the number of sliding filaments generally exhibited greater cooperativity.

4) When comparable plots of the force-pCa curve were made using either skinned muscle fibers contracting under the same conditions as the motility assay (148) or using microneedles with single regulated thin filaments attached in motility assays (208), both groups found the pCa50 for the force-pCa curves to be 0.4–0.8 pCa units smaller than the speed-pCa curves. These data suggest that as the calcium concentration is reduced the force declines before any change in speed is observed.

Table 3 shows that although the absolute values obtained using cardiac or skeletal regulatory proteins are not identical (different pH values and regulatory proteins were used), the behavior is qualitatively similar and very different from the earlier studies (169, 212, 401). Both groups examined the relationship between sliding speed of thin filaments with and without regulatory proteins. Gordon et al. (148) found that the unloaded sliding speed of thin filaments with regulatory proteins was 30–50% greater than for F-actin alone at the same ionic strength. Homsher et al. (206) found that cardiac regulatory proteins had little effect on the maximal sliding speeds, although in later studies they (208, 279) observed a 10–30% increase. Both groups concluded that that relatively few cross bridges are needed to make the filaments move but that significant numbers are needed to propel the filaments at maximal speed. Because force decreases significantly at pCa values at which speed is unaffected, control of contraction is primarily exerted by controlling the numbers of attached and cycling cross bridges rather than controlling the rate or size of the cross-bridge throw in the cross-bridge cycle. The modified steric blocking hypothesis of Vibert et al. (475) and McKillop and Geeves (303) is consistent with this conclusion. In the absence of Ca2+, the Tm is in a position (blocked) that allows weak cross-bridge attachment but not strong cross-bridge attachment. In the presence of Ca2+, Tm oscillates between a position that allows weak attachment and access to some of the strong binding positions (closed) and a position that allows access to all of the weak and strong binding sites (open). As Ca2+ is reduced, the fraction of actin sites occupied by cross bridges will decrease, and with it force, but enough cross bridges can attach to ensure that the filament slides at maximal speed. Model calculations suggest that if >20% of the cross bridges are attaching and cycling, then the thin filament will move at near (>95%) maximal speed (206). However, as the percentage falls, the sliding speed should fall in a fashion that depends on the assumed duty cycle time and strong binding time for myosin (467) (see discussion of shortening velocity in sect. iiiC5 ).

LaMadrid et al. (260) have, however, reported that the speed-pCa curve for moving filaments depends little on the filament length and thus may be relatively independent of the total number of S1 heads interacting with a thin filament. One interpretation of this observation is that [Ca2+] may modulate the cross-bridge power stroke or dissociation rates as well as the controlling strong cross-bridge attachment. A possible problem with this interpretation is that the motion of the filaments may be erratic. As filaments slide, most undergo periods of time when the leading edge moves more slowly than the trailing length so that the filament tends to fold. A few hundred milliseconds later, the leading edge accelerates and straightens the folded sections of the thin filament. Monitoring the movement of the filament centroid smooths such deceleration and acceleration changes in speed of segments of the filaments. Thus centroid monitoring blurs such changes and produces a slowedV f. This analysis-dependent blurring of filament movement is similar to the reduction in filament sliding speed seen when the HMM density on the surface of the motility assay system is reduced. An important test of this interpretation is measurement of the persistence length of thin filaments moving over various motor densities. The hypothesis predicts that the lower the motor density, the smaller the persistence length.

5.  Activation of thin filaments by attached cross bridges

Under some conditions, the thin filament sliding speed does depend on the number of cross bridges productively interacting with the thin filament, demonstrating that strongly bound cross bridges can activate the thin filament. Bobkov et al. (20) examined the effect of modification of the SH1 by NEM orN-(1-oxyl-2,2,6,6-tetramethl-4-piperidinyl)iodacetamide (IASL) on the regulated thin filament sliding speed at pCa 5. They found that SH1-modified HMM bound to the motility surface without unmodified HMM could not translocate thin filaments. NEM-S1 binds to actin very strongly and IASL-S1 binds to actin ∼10 times more strongly than S1 in the presence of ATP. When the density of HMM on the motility surface was reduced (reducing the [HMM] in the labeling solution from 400 to 60 μg/ml to 40 μg/ml), the regulated thin filament sliding speed fell from 5.3 μm/s (87%) to 4.9 μm/s (64%), to 2 μm/s (9%), respectively (values in parentheses indicate the percentage of smoothly moving filaments). However, if 1 μM IASL-S1 was added to the motility solution (to bind to the regulated thin filaments, but not to the motility surface), the filament sliding speeds decreased little with declining [HMM] being 4.8 μm/s (95%), 4.9 μm/s (85%), and 4.0 μm/s (75%) at the corresponding [HMM] densities. Similar results were obtained on adding NEM-S1 to the motility solution. Thus cross bridges (IASL-S1) strongly bound to regulated F-actin (and not to the motility surface) can activate the thin filament, perhaps stabilizing the Tm in the open position and cooperatively exposing actin binding sites to surface-bound HMM on either side of the IASL-S1-bound head. This result agrees with the work of Williams et al. (500) and Schwartz and Moss (429) on the thin filament activation effects of SH1 modified S1.

6.  Genetic modification of tnc and its effects on thin filament sliding speed and force

Thin filaments can be reconstituted with native Tm and Tn whose TnC subunit has been modified so that it is unable to bind Ca2+. Cardiac TnC has only one regulatory calcium-binding site, and mutation of a coordinating carboxyl group (D65A) renders TnC unable to bind Ca2+ (375). The cTn containing D65A is designated CBMII-Tn (221,375). Skeletal TnC has two calcium NH2-terminal or regulatory calcium binding sites that can be modified by point mutations (D27A and D63A) so that neither of its regulatory Ca2+ binding sites can be activated (444). Skeletal Tn containing sTnC with these mutations is called xxsTn (387) (see sect.iiiC1 ). The effects of varying the ratio of cTn to CMBII cTn or sTn to xxsTn on motility assays of regulated thin filament V f and skinned muscle fiberV u have been studied by Morris and co-workers (208, 210, 327) and by Chase and co-workers (277, 387), respectively. Their strategy was to examine how thin filament inactivation at constant saturating pCa affects the unloaded sliding speed, force, and k TR. The results of both groups are similar. First, as the fraction of CBMIITn or xxsTn bound to the thin filament increases, the thin filament sliding speed in the in vitro motility assay does not change significantly until the fraction is greater than ∼0.7. This result implies that the unloaded sliding speed is largely independent of the number of cross bridges interacting with the thin filaments. This contrasts with the effects of these mutants on force and k TR discussed in sections iii C1 and iii C2, respectively. Isometric force exerted by single muscle fibers in which the mutant Tn has replaced the native Tn decreases nearly in direct proportion to the extent of native Tn replacement whilek TR is largely independent of the amount of mutant Tn incorporated. As noted in sectioniii C2, these data suggest that the maximumk TR is not strongly influenced by “near neighbor” cooperativity between neighboring A7TmTn units.

7.  Modification of actin, Tm, and Tn residues and their effect on regulation

Recent studies of the sequelae of modification of amino acid residues of actin, Tm, and TnT have provided additional insights into the mechanism of regulation. These mutations produce a variety of effects on the acto-S1 ATPase, force, V f, and calcium sensitivity in both motility assays and muscle fibers (see Table 4). Studies in this area have been stimulated by the fact that specific dominant negative mutations in thick (myosin) and thin (actin, Tm, and TnT) filament proteins are associated with the expression of FHC. This disease manifests itself by a hypertrophy of the myocardium in the absence of increased load and is followed by sudden cardiac arrest. The disease is frequently undetected until the patient has a heart attack. Thick filament FHC mutations produce a significant and uniform hypertrophy of the myocardium with few clinical symptoms and a variable frequency of sudden death. The FHC TnT mutations usually exhibit a mild hypertrophy but a high incidence of sudden death at an early age (447). The implication of many studies of the thin filament FHC mutant proteins is that point mutations and/or deletions of single amino acid residues markedly alter the nature of the interaction between actin and myosin. Thus Tm and TnT mutations appear to affect steps within the cross-bridge power stroke.

View this table:
Table 4.

Effect of mutant thin filament proteins on actomyosin interaction

Marston and co-workers (18) expressed an actin mutation (E93K) and examined its effect on in vitro motility. They hypothesized that the negatively charged actin residue E93 repels negatively charged portions of Tm and thus holds Tm in the on state. If true, conversion of the negatively charged residue to a positively charged residue (K93) would attract Tm to K93 and hold Tm in the off or blocked position. Their tests of this hypothesis showed that the E93K mutant actin had no significant effect on the thin filament sliding speed in the absence of Tm but reduced sliding speed by ∼35% and the number of sliding filaments by ∼60% in the presence of skeletal Tm. This effect could be reversed by addition of NEM-S1. They suggest that electrostatic charge on the actin surface of domain 2 plays a role in controlling the access of the cross bridge to strong binding sites on the actin surface. Binding of smooth muscle Tm to E93K actin reducedV f by ∼40%, whereas smooth muscle Tm addition to wild-type actin increasedV f by ∼35%. This result is consistent with the effects of smooth muscle Tm on the ATPase of F-actin-Tm (268). These results supported conclusions drawn using sTm, but also imply that smooth Tm may also modify the rate of detachment of the cross bridge from the thin filament.

Lorenz et al. (281) have identified six putative sites on the actin surface (primarily in actin domains 3 and 4) whose electrostatic interaction with Tm may control its position on, and the activation of, the thin filament by calcium. One of these sites, the 309–320 loop in actin domain 3, contains four charged residues. Two actin mutants E311A/R312A (139) and K315A/R312A (252) within this region have been examined. Mutations at 311/312 produce no changes in regulated actomyosin ATPase, binding of the regulatory proteins to the thin filament, or maximalV f of regulated thin filaments, but it did reduce the [Ca2+] at which V fwas half-maximal. Mutations at 315/316 markedly reduced the regulated actomyosin ATPase and weakened the binding of Ca2+ to the regulatory proteins. These data suggest that either the modification of the Tm position or an allosteric effect on the actin structure alters the interaction of S1 with the thin filament and supports the view that these sites are important in the regulation of contraction.

Three mutations of the Tm molecule, V95A, D175N, and E180G, are associated with the presence of FHC (345,456). Each produces significant changes inV f in motility assays (see Table 4). Studies of skinned slow muscle fibers of patients containing D175N Tm revealed no significant changes in maximal isometric force orV u, but there was a significant reduction in the [Ca2+] at which the isometric force was half-maximal (22). The D175N Tm mutation is close to a putative TnT-1 binding region, and it may be that its interaction with TnT in the regulated system is responsible for the change in calcium sensitivity. Like the smooth muscle Tm data above, the alteredV f seen in these mutant Tm suggests that Tm modifies a step in the cross-bridge power stroke perhaps an increased rate of cross-bridge release from the thin filament.

Striated muscle Tm spans seven actin monomers and contains a corresponding number of quasi-repeat sequences, each having a putative actin-binding motif. These quasi-repeat sequences are hypothesized to be important in the positioning of Tm over the actin surface and in the regulation of cross-bridge interaction (281). Tobacman and co-workers (262,263) have explored the importance of these quasi-repeat sequences in the regulation of cross-bridge function by expressing a series of mutant Tm having two or more internal quasi-repeat sequences deleted from their structure (262, 263). In each case, repeat sequences 1 and 7 were retained because their overlap allows formation of a continuous Tm strand on the thin filament. Incorporation of deletion mutants, D234, D34, D345, and D456 (corresponding to deletion of amino acid residues, Q47-A166, N89-A166, N89-E208, D124-E234, respectively) and Tn onto thin filaments completely inhibited Ca2+-activated ATPase and V f. Incorporation of deletion mutant D23 (deletion of Q47-E124) had no effect on Ca2+ activation of acto-S1 ATPase but did produce a significant inhibition (to 60%) of V f. None of these deletions had a significant effect on Tm binding to the thin filament in the absence or presence of Tn or in the presence or absence of [Ca2+]. However, the presence of myosin increases the binding of Tm to actin by ∼1,000-fold. Deletion mutants D234, D34, D345, and D456 reduce this binding by >100-fold. These results suggest that myosin binding induces a conformational change in actin which determines the azimuthal positioning and binding of Tm to the actin filament. Deletions of quasi-repeating sequences 4, 5, and 6 are important in promoting this binding and the associated allosteric changes in actin structure greatly alter processes in the power stroke (262).

The effects of TnT mutations associated with the presence of FHC (345, 487) have been studied with respect to Ca2+ binding to Tn, binding of Tn to the thin filament, acto-S1 ATPase activity, in vitro sliding speed and isometric force exerted on regulated thin filaments and in muscle fibers. The effects of these mutations are summarized in Table 4.

In general, the results observed using biochemical and in vitro motility studies are consistent with the behavior of skinned muscle fibers from transgenic animals expressing the mutant TnT. These studies showed that the effects of the mutant proteins on contractile function do not correspond to any single stereotypic etiology. Four of the mutant FHC proteins increase V u orV f, and three inhibit maximal isometric force. Two exhibit an increased Ca2+-activated regulated acto-S1 ATPase and one markedly inhibits Ca2+-activated regulated acto-S1 ATPase. Three of the FHC mutant TnT alter calcium sensitivity. One (I79N) expressing the latter change is particularly interesting. At a pH >7.1, there is no change in the calcium sensitivity, but at pH values <7.1 or less, there is a reduction in the [Ca2+] at which the filament is half-maximally activated. Changes in regulated acto-S1 ATPase, unloaded thin filament sliding speed, or isometric force, caused by TnT mutations, imply that TnT directly affects a transition between strongly attached cross-bridge states and argue for allosteric effects on the thin filament. Changes in Ca2+ sensitivity could be accomplished by changes in accessibility of the cross bridge to actin's interacting surface.

Sweeney et al. (434) transfected quail myotubes with DNA coding for TnT mutations associated with FHC (I79N, R92E, and DE160). The myotubes overexpress the protein and incorporate it into the regulatory proteins. There is no evidence of a significant histological alterations or defects in the myotubes (433). Sweeney et al. (434) measured the force-pCa curve and unloaded shortening velocity of skinned myotubes containing one of three FHC mutant TnT. The results are summarized in Table 4 along with comparable data where available from in vitro motility assays and acto-S1 ATPaseV max measurements. The results are in good agreement with the data from in vitro motility assays and support the idea that regulatory proteins can modulate the cross-bridge kinetics of the strongly bound state in a fashion separate from their ability to control the attachment of cross bridges to the thin filament. Thus the in vitro motility studies support the conclusion that [Ca2+] regulates strong cross-bridge attachment to the thin filament and modulates a kinetic step in the cross-bridge cycle.


Models of Ca2+ regulation of contraction have been categorized on the basis of the method used to formulate the model, from structural to biochemical to physiological. We are nearing a time when these approaches can be integrated. In sectioniii A, we discussed the thin filament structural changes following Ca2+ binding, leading first to the steric blocking model and more recently to a revised model with at least three positions for Tm on actin (blocked, closed, and open). These positions correspond to 1) blocking of all but weak, electrostatic binding sites for myosin on actin; 2) blocking of only some hydrophobic binding sites; and 3) exposing of virtually all myosin binding sites on actin, respectively (475, 507).

Biochemical models of regulation in the 1970s focused on the effects of Ca2+ binding to Tn and the regulation of the actin-Tm interaction by Ca2+ binding and strong myosin binding [see Tobacman (455) for a detailed discussion of this work]. These studies culminated in the detailed descriptions of the interactions between the regulatory proteins discussed in sectioniiA . They provided a more complete understanding of the factors that may affect Tm position on the thin filament and changes in the actin filament during activation. The models of this activation evolved from studies over the last two decades (discussed in sect. iii B) on the cooperative binding of myosin to the regulated filament. These models have been mainly allosteric models of regulation [see Tobacman (455) for a detailed discussion]. By this it is meant that Ca2+ binding or strong myosin binding changes the structure of the thin filament so that myosin binding at another site is enhanced. In these models, the thin filament is switched between a weak and strong myosin binding state with the equilibrium determined by strongly attached cross bridges and Ca2+ binding. This model assumes that the two states correspond to the thin filament being in either an off or on conformation. The first formulation of this model was by Hill et al. (191) and was based on the studies of the cooperative binding of myosin to the regulated filament (160,465, 499). The results were interpreted in terms of myosin binding to a A7TmTn-regulated unit with interaction between neighboring units. The assumption was that the entire regulated unit was switched from a weak to strong binding state. The equilibrium between the on and off forms was determined by strong cross-bridge and Ca2+ binding to that unit and neighboring units. The model was simple, mathematically precise, and fit the data. Studies of the regulation of actomyosin ATPase (161) ruled out a more complex model with Tm occupying more states (192) on the basis of their binding data. Their studies indicated that the binding of Ca2+ activated the ATPase activity to only 10–20% of maximal and that full activation required strong cross-bridge attachment. Lehrer and Morris (270) reached a similar conclusion. Furthermore, Williams et al. (500) found that at low [S1], rigorlike cross bridges (NEM-modified S1) could increase the ATPase activity of S1 with regulated filaments by increasing theV max over that observed with Ca2+ alone, but the V max in the presence of NEM-S1 was not different from that observed using unregulated F-actin filaments. They also found that the actin concentration required to activate the ATPase was much less than that for binding, implying a different rate-limiting step for the ATPase and binding. However, this model of Hill et al. (191) was not consistent with the structural studies of the thin filament (see sect. iii A) which found that Ca2+caused a major movement of Tm (475). Finally, there were discrepancies between the experimental data and the predictions for the kinetics of S1 binding to the regulated thin filament in the presence and absence of Ca2+ (465; see the model of Geeves and co-workers, next paragraph).

More recently, Geeves and co-workers (135,179, 302, 303) proposed a detailed model with three states for the thin filament and two-step myosin binding to actin. The two steps of myosin binding to actin were applicable to any nucleotide state of myosin and involved first a weaker binding followed by an isomerization to stronger binding. The three states of the thin filament they termed blocked, closed, and open (analogous to terms describing the English shop of blocked with gate locked for overnight security, closed with door shut as at tea time or during lunch break, or open for business). In the blocked state, there is no myosin binding, not even weak binding. In the closed state, there is only weak myosin binding. In the open state, myosin could bind weakly in any nucleotide state and then isomerize to the strong-binding, force-producing configuration. The equilibrium constants for the two myosin binding states depend on the nucleotide state. The equilibrium constants for the transitions of the thin filament from blocked to closed and closed to open are a function of Ca2+ with the blocked to closed transition having a Hill coefficient of 1.8 (179) using fast skeletal muscle regulatory proteins and 1.36 using cardiac regulatory proteins (390). The blocked to closed transition loses its Ca2+ sensitivity at ionic strengths below ∼50 mM at 2 mM [Mg2+] but retains it at 5 mM [Mg2+] (297). There was cooperativity within the A7TmTn regulatory unit but no cooperativity between neighboring units as in the Hill et al. (191) model, because it was not required to explain the original data. The authors adduced other data that the cooperative unit is larger than the seven actin units (136) and have now expanded the model to include cooperativity between neighboring units (297). In their new data, the cooperative unit is not an integral multiple of 7 actins, being greater than 7 but less than 14. The implication is that where neighboring Tm overlap, the Tm are coupled and move together and that in between overlap regions the Tm would be flexible so that the different actins spanned by one Tm would not all be equivalent. This is an important point to which we will return.

The Geeves model accounts for the highly cooperative binding of myosin nucleotide to regulated actin. Introducing the blocked state circumvents the major problem of the Hill et al. (191) model: the discrepancy between the kinetic studies of S1 binding to regulated filaments in the presence and absence of Ca2+(465). In those studies, in the presence of Ca2+, S1 bound to the regulated filament with the same time course as binding to actin in the absence of regulatory proteins. In the absence of Ca2+, there was a lag in binding unless the regulated filament was incubated with 3 S1/A7TmTn unit. This result suggested that in the presence of Ca2+, >90% of the regulated filaments were in the on state, although the equilibrium binding data had suggested that only 20% were in the on state. Introducing a blocked state alleviated this problem and gave good fits to both the equilibrium and kinetic binding data.

This model conforms to structural studies showing three thin filament states (366, 475) (see sect.iii A). It also corresponds to the conclusion from structural studies that, although Ca2+ binding shifted the Tm to expose most of the myosin binding residues on actin, Tm movement to expose all the myosin binding sites on actin required strongly attached cross bridges. Thus Ca2+ binding by itself could not fully activate the thin filament. The Geeves model has received broad acceptance for its simplicity, agreement with the structural and biochemical data, and quantitative development.

Despite this broad acceptance, there are some problems with this model. First, there may be more than two steps in myosin binding to actin. Geeves and Lehrer (136) could detect only total binding (through light scattering) or strong binding (through pyrene fluorescence) (136). The interaction surfaces shown in Figure 4 raise the possibility that there are potentially three different strengths of binding, if in fact they represent actual equilibrium positions of Tm. If Tm is quite flexible (as discussed above and also below in the third alternative), then there may be a much broader range of binding affinities available, particularly considering other nucleotide states of the myosin. Second, the strong binding studies only included more strongly bound nucleotide forms and did not include those most likely involved in the initial myosin binding, S1·ADP·Pi. This may be why the blocked state was considered truly blocked, even to weak binding. Lehrer (266) has suggested that blocked state is produced by TnI binding to actin in the absence of Ca2+ to block S1 attachment as an alternative to a Tm-blocked state. Because TnI does not span seven actins, this is a less likely alternative. Third, the three structural states discussed in sectioniii A and the blocked, closed, and open states do not match up exactly. For example, in the presence of Ca2+, McKillop and Geeves (303) found that 20% of the regulatory units were in the open state, yet the structural studies show no open actins with Tm still covering some of the myosin binding sites on all actins (Fig. 4). A number of interpretations are possible.1) The Tm position is an average one so that at any time, 20% of the A7TmTn regulatory units are actually in the fully open state with all myosin binding sites on actin available while the other regulatory units are in a more closed state. This does not seem likely, since the position of the Tm is well defined (but see Squire and Morris, Ref. 421). 2) If Tm is very flexible, then within one regulatory unit such flexibility could remove much of the discrepancy with the structural studies. Within one unit A7TmTn, a flexible Tm in the presence of Ca2+might allow one to two actins in the open configuration and five or six in the closed configuration (or 3 actins in a A14Tm2Tn2 “unit”) and be consistent with the structural, biochemical, and physiological data for skeletal muscle. As discussed above, Tm may be so flexible that it could move about its equilibrium position to open up all myosin-binding sites on 20% of the actins at any one time. If this occurs within one unit, the state of each actin must be defined. It may be that strong attachment of S1 stabilizes Tm in the fully deflected position with all actin sites open. 3) Myosin binding to the actin sites available in the presence of Ca2+ provides the initial binding from which the isomerization of myosin aids in “pushing” the Tm into the fully deflected position, the fully open state. The data of Swartz and co-workers (430,517) on S1 binding to myofibrils argues against this latter interpretation because their data would require that both the closed and open states of actin would have the same relative affinity for rigor S1 and S1·ADP. Thus Geeves and co-workers (268, 297) view Tm flexibility as central to the understanding of regulation. Furthermore, there is evidence of preferred actins for cross-bridge attachment during activation (462) that also argues against treating all actins in a regulatory unit as equivalent. If so, a model with only three actin binding states may need revision.

Lehrer (266) proposed a modified version of the two-state cooperative/allosteric model that differed from the Geeves model in not having a fully blocked state of the thin filament. Again, it was allosteric because strong binding of myosin at one place on the thin filament cooperatively enhanced the binding of myosin at another site. Lehrer (266) hypothesized that Ca2+ does not cause the transition from a blocked to a closed state by movement of Tm but causes TnI movement that allows weak binding of myosin to the thin filament from which the myosin can isomerize to the strong binding form. Once in the strong binding form, the myosin produces force and further activates the thin filament for binding of other myosins through the movement of Tm. Although there is strong evidence that TnI can block myosin binding to actin on a one-to-one basis (442) (see sect.ii A) in the absence of Tm, and that TnI may bind to two actins (463), there is little evidence that this inhibition of myosin binding extends to the neighboring actins in the seven actin unit because of the presence of TnI alone and not because of the blocking position of Tm. Again, as in the Geeves model, there are only two proposed types of myosin binding, which reflect the limitations of the techniques used to assess binding. Of course in the structured sarcomere, strained myosin cross bridges could have a continuum of binding states. Li and Fajer (274) suggest additional thin filament states are needed to account for the responses of EPR probes on TnC to Ca2+ binding and various cross-bridge states, so one may consider more complex models.

In an alternative model of regulation, Tobacman (455) suggests that Ca2+ binding activates the thin filament but that strong cross-bridge binding further activates the thin filament. This would give rise to the potentiated state described by Bremel et al. (31). As pointed out by Tobacman (455), the actin filament and myosin alone are all that is required for movement and force in the in vitro motility assay. The presence of regulatory proteins can bring about an increase in speed in the in vitro motility assay (148) and the ATPase activity for a given actin concentration by increasing theK ATPase of regulated actin over actin in the S1-actin ATPase assay (500). However, the maximum ATPase activity given by the V max of S1 and regulated thin filaments plus Ca2+ in the presence of strongly attached myosin (NEM-S1) is no different from that for actin alone (500). Thus this is not good evidence for a truly potentiated state with higher V max. An enhanced K ATPase for actin activation of the ATPase with cardiac regulatory proteins and Ca2+ is also suggested by Tobacman and co-workers' ATPase data (46) (Fig. 5 B). These data show that the cardiac thin filament could activate the ATPase of S1 at very low [S1], but a ratio of ≥4 S1/7 actin is required to achieve a higher ATPase rate/S1. This could imply a cooperative activation/allosteric system for the thin filament, but only at S1-to-actin ratios higher than those found in the sarcomere. On the other hand, during isometric contractions, the strongly bound time of cross bridges in the sarcomere is undoubtedly much longer than in the completely unloaded condition of actin-myosin in the test tube. Unloaded shortening conditions in the fiber may be more like the conditions seen for actin-myosin in the test tube (see the discussion in the beginning of sect.iii C). This alternative suggestion from Tobacman (455) has not been developed to the quantitative model stage for testing. Furthermore, Tobacman (455) suggested that not all actins in the regulatory unit are necessarily equivalent (discussed above); that makes further experimental information necessary to formulate a more complete model of regulation from the biochemical data. The model of McKillop and Geeves (303) seems like a reasonable starting point for the refinement, by including the possibility of different activation properties for the various actins in the regulatory unit.

The physiological models differ from the biochemical models in that the output is force and shortening (as opposed to ATPase), and the proteins are constrained both in concentration and arrangement within the sarcomere. This constraint in the sarcomere results in strained cross bridges during contractions, which modifies at least some of the rate constants, changing the cross-bridge kinetics and substantially altering the duration of cross-bridge attachment. These differences can have a profound influence on the Ca2+ regulation. The first quantitative model of Ca2+ regulation was that of Julian (237), who hypothesized that Ca2+increased the attachment rate constant (f) of the original Huxley (215) cross-bridge model. This was challenged by Podolsky and Teichholz (365) on the basis that they did not find a [Ca2+] dependence of maximum shortening velocity, launching a debate on this point (see sect.iii C5). They hypothesized that regulation occurred via recruitment of cross bridges rather than regulation of cross-bridge kinetics. This debate on regulation by recruitment of cross bridges versus regulation of cross-bridge kinetics continues (see Brenner, Ref. 36) and is discussed at length in sectioniii C2.

Many recent models describing Ca2+ control of tension generation rely on the formulation of Brenner (34), which was derived from his studies on the control of the rate of tension redevelopment (k TR) in skinned muscle fibers. As discussed in section iii C2, this technique was used to measure how Ca2+ controlled the transition of cross bridges from weak binding to strong, force-generating states. He then described this transition along the lines first suggested by Kushmerick and Krasner (259). This involved using the Huxley (215) model with two apparent rates, f app andg app, which lumps the rate constants for all steps in the actomyosin ATPase cycle related to cross-bridge attachment to force generation and detachment from force-generating states, respectively. As described in sectioniii C2, he measuredk TR, force, stiffness, and ATPase as a function of Ca2+ and found thatk TR and force data could be fit iff app is a function of [Ca2+]. The question in this formulation is how Ca2+ regulatesf app. It leads to two hypotheses: control of a force-generating kinetic step in the actomyosin ATPase cycle or control of thin filament activation. Control of thin filament activation is included in the f app as defined by Brenner (34), but as will be shown below, for clearer understanding of the mechanisms involved one needs to know if the two possibilities can be experimentally distinguished.

Ca2+ control of a kinetic step in the actomyosin cycle was concluded from many biochemical studies [see Chalovich (55) discussed above] and provided an attractive hypothesis for tying together both biochemical and physiological data. However, measurements in skinned fibers using caged compounds, pressure-jumps, and sinusoidal length changes have shown little if any Ca2+ regulation of any of the observable steps, such as Pi release (see sect. iii C4). Thus the skinned fiber data do not support Ca2+ regulation of a kinetic step by strongly attached cross bridges, and subsequent models have centered on Ca2+ regulation of thin filament activation and strong cross-bridge attachment. We discuss two types of models of this regulation: direct Ca2+ regulation through Tn/Tm using the simple A7TmTn regulatory unit and cooperative activation through strong cross-bridge attachment in one unit or interaction between A7TmTn units along the thin filament.

An example of a simple Ca2+ activation model is that of Landesberg and Sideman (261), discussed in sectioniii C2. In this model (diagrammed in Fig.8 A), Ca2+ binding to Tn can activate a simple regulatory unit so that weakly attached cross bridges can transition to strong, force-generating cross bridges with attachment and detachment rate constants off app andg app, respectively. The model allows strong cross bridges to remain attached even when Ca2+dissociates from Tn (state 4). However, from this state, cross bridges dissociate with a g app rate constant, and reattachment is negligible. With no Ca2+ dependence of the apparent rate constants for cross bridges, Ca2+ acts only through binding to Tn to activate the thin filament. This simple model can fit thek TR data for fast skeletal muscle as described in section iii C2 with reasonable values for the various rate constants (383,388) (see legend to Fig. 8). This includes the effects of factors that modify cross-bridge kinetics (383) and Ca2+ binding to TnC (385, 388). This is illustrated in Figure 8, B and C, where experimental data are compared with model calculations for three conditions affecting thin filament activation: 1) Ca2+-independent activation (aTnC) as well as 2) decreased and 3) increased Ca2+ dissociation rate from TnC (calmidazolium and the NH2-terminal deletion mutant of TnC), respectively. The model also provided a ready explanation for the variety of shapes observed for thek TR-force curves in different muscles and different temperatures. However, this model does not fit the force-pCa relationship, because it lacks cooperative feedback. Landesberg and Sideman (261) added feedback from force-bearing cross bridges to Ca2+ binding to TnC to obtain both a steeper force-pCa relationship and a fit to the force-sarcomere length relationship. There is good evidence that cycling cross bridges enhance Ca2+ binding in cardiac muscle, but there is much less evidence in skeletal muscle (see sect.iii C7). Thus, although this type of feedback has some relevance for cardiac muscle, it is probably not the mechanism that makes the force-pCa relationship cooperative in skeletal muscle (see sect. iii C7). Additionally, the model is incomplete because it cannot describe how strongly attached, noncycling cross bridges can activate the thin filament, as discussed in sections iii C1 andiii C6. Therefore, the model needs to be expanded to more completely explain the activation of skinned muscle preparations including more complex behaviors such as thek Ca (see sect.iii C3), thek Pi (see sect.iii C4), and the increase ink TR with increasing [Pi] (see sect. iii C2).

Fig. 8.

Left: 4-state model of activation, separating thin filament Ca2+ activation kinetics from cross-bridge attachment/detachment kinetics. The 4 states are distinguished by the absence or presence of Ca2+ binding to TnC to activate a A7TmTn unit and by weak/no binding or strong, force-generating cross-bridge binding to actin. Ca2+ is bound in states 2 and 3 and dissociated instates 1 and 4. Ca2+ binding tostate 1, with association/dissociation rate constantsk on/k off, produces the activated thin filament state 2. Strong, force-generating cross-bridge attachment can occur to the activated thin filament actins in state 2 to produce force and shortening with attachment rate constantf app and detachment rate constantg app. Ca2+ can dissociate (with a k on /k off which is usually assumed to be the same ask on/k off) from the activated thin filament with the cross bridge strongly attached (state 3) in the transition to state 4. Fromstate 4, the cross bridge can detach to state 1with rate constant g app with negligible reattachment. [Modified from Regnier et al. (388), Landesberg and Seidman (261), and Hancock et al. (165).] Right: comparison of predictions and experiment k TR-force data for 3 different manipulations that affect the kinetics of thin filament activation. Experimental data points are shown with theoretical lines from the model. a: Experimental data are for substitution of aTnC for some of the endogenous TnC (oxidized cTnC which activates in the absence of Ca2+). Parameters used in the modeling are as follows: f app = 17 s−1; g app =g app = 1.5 s−1;f app = 0,k on =k on = 0–144 s−1(k on varied by changing [Ca2+]); and k off =k off = 10 s−1for control fibers, 3.5 s−1 for calmidazolium (CDZ), and <0.3 s−1 for aTnC. [Data from Chase et al. (63) (•) for the addition of 10 μM CDZ (which slows the Ca2+ dissociation rate from TnC); data from Regnier et al. (385) (○) and for control fibers with endogenous TnC before the addition of CDZ (•).] b: Experimental data are for substitution in rabbit psoas skinned muscle fibers of an NH2-terminal deletion mutant chicken skeletal TnC (NHdel) in which the Ca2+ dissociation rate is greatly increased (▿). Control fibers have wild-type chicken skeletal TnC (WT) substituted for the endogenous rabbit TnC (•). Parameters used in the modeling are as follows; f app = 17 s−1; g app =g app = 1.5 s−1;f app = 0;k on =k on = 0–200 s−1(k on varied by changing [Ca2+]); k off =k off = 10 s−1for control fibers (wild type) and 70 s−1for fibers with NHdel TnC (NHdel). [Data from Regnier et al. (388).]

To explain the steepness of the force-pCa relationship in skeletal muscle requires, in addition to direct Ca2+ activation, cooperative activation of the thin filament by cycling cross bridges. Campbell (48) introduced a model that does this. In its most general form, this model expanded the four-state model of Landesberg and Seidman (261) to a six-state model including separate Ca2+ binding and thin filament activation steps, as well as the cross-bridge attachment/detachment steps with their apparent rate constants. Campbell (48) suggested two feedback pathways: one from the force-generating states to the Ca2+ binding rate constants and a second from force-generating states to the rate constants for the transition of the thin filament into the activated state. Calculations, using a simplified version of the model with feedback from force-producing states to thin filament activation, showed that the model could produce a typical k Ca-force relationship. It also produced the two-phase force-pCa curve seen by Moss (331), but not the single-phase force-pCa curve seen by others (23) (see sect.iii C1). An interesting feature of this feedback is a slow build-up of force to its maximal level. This slow build-up occurs because feedback enhances the final force level so that the force “chases” this final level, which is constantly rising because of the feedback. Thus feedback steepens the force-pCa relationship and slowsk Ca at lower levels of activation. Although Campbell did not model the force redevelopment rate constant,k TR, his formulation does produce a typical k TR-force relationship, as in Figure 6. This model also provides a ready mechanism by which strongly attached, noncycling cross bridges can activate the thin filament. However, the shape of the k TR-force curve in Campbell's model is dependent on cooperative activation. As discussed in section iii C1, cooperative activation is required to explain the force-pCa relationship but may not be required to explain the k TRrelationship (see sect. iii C2). Furthermore, the Campbell (48) model only considers cooperativity within the single A7TmTn regulatory unit and does not consider cooperativity along the thin filament, which steepens the force-pCa relationship (387).

The model of Dobrunz et al. (80) is an example of a model that includes cooperativity along the thin filament. This model has similarities to Campbell's six-state model, with a thin filament regulatory unit with or without Ca2+ binding, an activated thin filament regulatory unit with or without Ca2+ binding, and a regulatory unit with attached force-generating cross bridge(s). They assume rapid equilibria between the states and coupling between neighboring activated regulatory units that increases the equilibrium between active and inactive units depending on whether one or both neighboring units are active. They found that they needed to consider interactions between only 9 units/thin filament (rather than all 26 units) for their calculated parameters to be independent of the number of units. Although this model was designed to calculate the steady-state force-pCa relationship, it includes a formalism that could potentially be used for calculating transient behavior. The introduction of many parameters fit in the modeling means that uniqueness of fit is a problem until more parameters can be independently measured. The model demonstrates an approach that could be used for a more complete model incorporating the known mechanisms of activation and measured parameters to explain both steady-state and transient behavior.

In the models discussed thus far, the cross-bridge ATPase cycle (scheme 1, see sect. iiiD ) is described simply by f app andg app (see discussion in sect.iii C2 and earlier in this section). A more complete model of regulation should include rates for individual cross-bridge transitions that have been measured in fibers and in solution (see sect. iii C). Such a model was proposed by Regnier et al. (386), based on their observations on the effects of Pi, BDM, and Ca2+ on k TR,k Pi, force, and stiffness in skinned skeletal muscle fibers. They concluded that Ca2+controls strong cross-bridge binding, specifically a weak-to-strong binding step preceding force generation and Pirelease. They were able to obtain reasonable fits to thek TR andk Pi data using values of the rate constants that they measured, which are similar to those shown in Table 1. They could account for Ca2+ regulation of force through control of the weak-to-strong cross-bridge binding transition. However, because they did not include a cooperative activation by strongly bound cross bridges, there was no steep dependence of force on [Ca2+]. Similar models relating the ATPase cycle to force generation have been proposed by Kawai and Zhao (245) and Wahr et al. (476). Thus, rather than using the lumped rate constantsf app and g app(Fig. 8, left), a more complete model of regulation needs to include Ca2+ and strong cross-bridge control of the thin filament and a more detailed cross-bridge kinetic scheme.

In summary, the individual models mentioned above are each able to describe specific aspects of thin filament activation and regulation of cross-bridge binding by Ca2+ for which they were intended. However, none of these models has been able to provide a completely satisfying picture. The ideal model would incorporate a more complete description of the thin filament activation process and the chemomechanical states associated with cross-bridge cycling. This would include Ca2+ activation of the thin filament and cooperative activation by strong cross bridges both within individual A7TmTn regulatory units, which may be more flexible in size and between units along the thin filament, to describe steady-state and transient behavior. The beginning of a more comprehensive approach to modeling including the coupling between neighboring units is the cellular automaton approach of Zou and Phillips (521), but this needs to be developed further to account for all of the biochemical, structural, and physiological data discussed here. Considering the flexibility of Tm, it may be necessary to consider the different states (open, closed, blocked) and the open probability of individual actins and to include more detailed descriptions of the three-dimensional nature of individual thin and thick filaments. Finally, a kinetic description of these processes and the interactions between thin filament regulatory proteins and cross bridges is essential to describe a realistic mechanism by which Ca2+ controls dynamic processes like the rate of force development and shortening in muscle.


A.  Conclusions

Ca2+ regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament to regulate the open probability of actin, which regulates strong cross-bridge binding to actin and may influence cross-bridge detachment kinetics. Thus the focus of the review has been regulation of the thin filament. Data have been summarized from structural, biochemical, physiological, and in vitro motility studies.

As discussed in sections ii andiii A, the position of Tm on the thin filament determines the interaction of myosin with actin, whether the actin is open to myosin binding, and whether the binding will be weak (electrostatic) or stronger (hydrophobic interactions). However, depending on the Tm isoform and the Tn subunits that interact with Tm, the Tm may be quite flexible so that, although it spans seven actins, the availability of myosin binding sites on these (and neighboring) actins may vary. Biochemically these binding sites may be characterized as blocked, closed, or open depending on the strength of the myosin binding and whether the myosin can isomerize to a strongly bound, force-generating state. In the blocked state, TnI binding to actin may itself block one, two, or more actins per A7TmTn regulatory unit. The position of Tm and TnI on the actin filament is determined by 1) the occupancy of regulatory Ca2+ binding sites on Tn, 2) conformational changes resulting from Ca2+ binding, and 3) changes in the interactions of Tn, Tm, and actin and as well as by myosin S1 binding to actin. Ca2+ binding to TnC enhances TnC-TnI interaction, pulling TnI away from its binding sites on one to two of the actins in the basic A7TmTn structural regulatory unit. The reduced TnI affinity for actin allows increased Tm movement and exposes actin binding sites previously blocked by Tm. The coupling of adjacent Tm by an overlap region can result in movement of the adjacent Tm and exposure of some of their associated actins. The movement of Tm is also affected by interactions with TnT and TnT's interactions with TnC-TnI that are modulated by Ca2+. TnT can increase the coupling between neighboring Tm and, by its interaction with as much as 40% of the length of Tm, may influence the flexibility of individual Tm. Because this implies there will be variations in the position of Tm on individual actins, it means that variation of TnT isoforms may give rise to differences with respect to the properties of fractionally activated Tn-Tm. This suggests a potentially high degree of variability in Ca2+ activation depending on the specific protein isoforms.

Ca2+ activation and Tm movement exposes myosin binding sites on some fraction of the actins so that they are available for myosin attachment and isomerization to strong-binding, force-producing states. Evidence from structural studies on skeletal muscle proteins supports the idea that strong binding of skeletal myosin to these sites promotes additional Tm movement, stabilizes Tm in the open position, and provides cooperative activation of additional actins in the A7TmTn structural regulatory unit and possibly of additional actins in neighboring regulatory units.

These structural and biochemical findings support physiological observations of steady-state and transient mechanical behavior discussed in section iii. The conclusions from these physiological studies and the section in which the data are discussed are as follows.

The regulated step in the actomyosin ATPase cycle is the strong binding of myosin to actin (see sect. iii, B,C1, C2, C3, and C5). There is also some evidence from the in vitro motility studies (see sect.iiiD) that there is modulation of another kinetic step in the cross-bridge cycle, possibly cross-bridge detachment, but probably not the Pi release step (see sect. iiiC4).
Ca2+ binding to Tn results in Tm movement and uncovers sites on actin to which myosin can bind, isomerize to strong binding states, and produce force and muscle shortening.
The initial rate of force development depends mostly on the level of activation of the thin filament by Ca2+, and on the myosin kinetic properties, but depends little on the initial force level (see sect. iii, B and C1C3).
A small number of strongly attached cross bridges within an A7TmTn regulatory unit (number still to be determined) can activate the unit's actins and perhaps those in neighboring units so that additional myosins can bind, isomerize to strongly bound states, and produce force (see sect. iii, C1,C6, C8, and C9).
Cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force (see sect.iii, C1 and C6) but does not affect the rate of force development (see sect.iiiC2).
Strongly attached cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner (see sect.iiiC8).
Strongly attached, cycling cross bridges can enhance Ca2+binding to cardiac TnC but influence skeletal TnC to a lesser extent (see sect. iiiC7).

Differences have been noted in regulation between vertebrate skeletal and cardiac muscle. Compared with fast skeletal muscle, cardiac muscle exhibits the following: 1) a decreased steepness of the force-pCa curve (see sect.iii C1); 2) less effect of the initial level of force on the relaxation rate; 3) less dependence of k TR on Ca2+;4) more cooperativity between neighboring units during rigor cross-bridge activation in the absence of Ca2+;5) more feedback between cycling cross bridges and Ca2+ binding to cTnC; and 6) unique regulatory protein isoforms including TnC, TnI, TnT, Tm, myosin, and some structural proteins, although there are some equivalents between slow skeletal muscle and some cardiac cells in TnC and myosin.

Presumably, these properties are caused by the differences in protein isoforms in these two muscle tissues, since the sarcomere structure is so similar. The feedback between cycling cross-bridge attachment and Ca2+ binding to cTnC (5) implies a strong coupling between S1 binding to actin, Tm movement, and TnT-TnI-TnC interactions in cardiac muscle. Ca2+ binding does not produce the large structural change in the NH2terminal of cTnC as occurs in skeletal TnC (84,85, 411). The binding of cTnI to cTnC appears to promote the open cTnC structure associated with Ca2+binding, enhanced Ca2+ binding, and activation (276). Dissociation of cTnI from actin by Tm-TnT coupling and stronger binding to cTnC in the absence of Ca2+ may be facilitated in cardiac muscle as would be implied by the greater cooperativity between neighboring regulatory units in rigor activation in the absence of Ca2+(4, 307). Thus strong cross-bridge attachment in cardiac muscle and Ca2+ binding to cTnC might be coupled through Tm-TnT-TnI. It is not because of the properties of cTnC alone because slow-twitch muscle (with cTnc) does not show this effect of cross-bridge attachment (483). The enhanced coupling of Tm movement to TnC might occur if cardiac Tm-Tn were less flexible than skeletal Tm with strong cross-bridge binding (60) or because of interactions of Tm with cTnT. A stiffer Tm-TnT connection would be more likely to transmit to TnC the effect of cross bridges binding to actin, which in turn shift or stabilize Tm. A tighter coupling between Ca2+ binding to TnC and cycling cross bridges could reduce the cooperative activation by strongly attached cross bridges separate from their effect to enhance Ca2+ binding. This would lead to reduced cooperativity during relaxation (2) and possibly a reduction in Ca2+ dependence ofk TR (3) (see sect.iii C2).

A shallower force-pCa curve (1) for cardiac muscle is due in part to the Tn isoform. In cardiac muscle reconstituted with filaments made from skeletal or cardiac Tn and Tm in various permutations, the increased steepness of the force-pCa curve follows the skeletal Tn isoform, and not the skeletal Tm isoform (126). Although other Tn subunits may contribute to this difference in cooperative activation, some is attributable to the properties of TnC alone since with TnC exchanges, the steeper curve follows the skeletal TnC (11). The shallower force-pCa curve associated with cTnC could result in small part from having just one functional NH2-terminal Ca2+ binding site but probably mainly from the lack of a one-to-one coupling between Ca2+ binding and conformational change in cTnC (84, 85). This makes cTnC more dependent on binding to cTnI to achieve this conformational change. With Ca2+ binding at just one TnC, the shift in Tm would be less likely to bring actins in the A7TmTn regulatory unit into the open configuration for strong myosin binding and force generation. Thus cardiac muscle would not be fully active at maximal Ca2+ as observed (384) and would be more dependent on activation by strongly attached cross bridges or anything that would promote the cTnC-cTnI interaction. This would make cardiac muscle more sensitive to conditions that influenced strong cross-bridge attachment such as sarcomere length (filament lattice) (294, 300), augmentation or inhibition of cycling cross-bridge attachment (383,384), or phosphorylation of myosin RLC (272) or C protein (501).

The above summary of possible reasons for differences in properties between cardiac-skeletal is somewhat speculative, but it suggests a number of lines of investigation that should be pursued.

B.  Future Research Directions

As detailed in this review, an enormous amount of information is now available on Ca2+ activation of the thin filament in striated muscle, and the general concepts are now clearer. A detailed mathematical model is still needed that quantitatively explains the physiological behavior of skeletal and cardiac muscle. Before this occurs, additional information is required. There are a number of areas that are clearly important directions for future investigations that have been suggested by the material reviewed here. Some of these are discussed below.

The flexibility of Tm and the possible variability of activation of individual actins have been suggested as important issues to be investigated. The role of TnT in stabilizing Tm and the role that various TnT isoforms play in determining the properties of regulation are worth considering. One of the consequences of flexible Tm is the possibility that all actins are not equivalent. A test of this idea will require better techniques for assessing changes at different actins in the A7TmTn unit, possibly through X-ray and imaging techniques or through using mutant Tm or actins.

More information is needed on the detailed interactions between the regulatory proteins and the variations produced by different isoforms. Such studies cannot be done just with isolated proteins but must include studies in skinned muscle fibers and in vitro motility assays, in which the interaction with all the neighboring proteins in an ordered system can be assessed. This will necessitate development of additional techniques for probing interactions in skinned fibers. Our understanding of regulation has already benefited from the ability to introduce labeled or mutant proteins into skinned fibers, cultured myocytes, transgenic animals, or filaments in the in vitro motility system. This should allow both probing of protein interaction and better testing of models of regulation.

Although we conclude that the major site of Ca2+ regulation is in regulating strong myosin binding to actin, there is evidence from the in vitro motility assay that modulation of cross-bridge kinetics, possibly of cross-bridge detachment, can occur particularly with different TnT or Tm isoforms. It is not clear whether this modulation is due to differences in interaction between Tm and myosin or due to changes in actin, which affect its interaction with myosin. In this review we have not stressed the role of actin, as less is known about it, but evidence is strong (106) that actin is much more than a passive element in the contraction and regulation processes. Further investigation must be done on these issues before we have a complete understanding of regulation.

In addition to Ca2+ binding to activate the thin filament, the evidence supports a role for strongly attached cross bridges in attaining full force development, particularly in cardiac muscle. A quantitative model is needed to describe in a testable manner the roles of direct Ca2+ activation and cooperative activation by strongly attached cross bridges in muscle fibers. This will require experimental measures of thin filament activation in fibers by measuring Tm position using fluorescent or spin labels or other techniques. It will also require improved techniques to specify strong cross-bridge attachment in fibers, possibly by incorporating pyrene labels on the actin in addition to the presently used stiffness measurements.

In the in vitro motility system, there is a need to study oriented cross-bridge heads, either using long native thick filaments, polymerized thick filaments, or nano-fabrication techniques. Finally, the field is ready for single cross-bridge head measurements using optical traps to study the Ca2+dependency of strongly attached cross-bridge transitions. Although some single molecule techniques have been worked out, there are problems distinguishing between weak and strong cross-bridge attachment. Pyrene labeling of actin may be used to assess strong attachment, or measurements of the stiffness of attachment may yield the required information.

This is an exciting time to be studying the problem of regulation of contraction because of the amazing proliferation of new techniques and preparations. These technological and scientific advances offer the hope that a more complete understanding of the crucial question of the mechanism of the regulation of striated muscle contraction can be achieved in the near future.


We acknowledge the assistance of many individuals in writing this review. Larry Smillie and Ron Milligan prepared excellent figures for us and provided important discussions. Bill Lehman provided valuable advice in preparing a figure summarizing some of their work. Others (Rick Moss, Sam Lehrer, and Larry Tobacman) gave us permission to use figures from their studies. Mike Geeves shared with us an important manuscript before it was published and was generous with his time explaining his ideas and models. Discussions with Larry Tobacman were particularly helpful. Lee Sweeney shared with us results from his studies before they were published. We appreciated the editing of the manuscript and useful comments by Don Martyn and P. Bryant Chase and the careful reading and comments of Emilie Warner. We are particularly appreciative of the assistance with the manuscript, figures, and references of Martha Mathiason who provided important computer support. Denise Nishioka also assisted greatly with the references and figure scanning. Finally, we gratefully acknowledge the patience, support, encouragement, and indulgence of Della Gordon, Dianne Homsher (remembering Alexandra), and Julie Regnier in the long process of writing this review.

This work was supported in part by National Institutes of Health Grants HL-52558, NS-08384 (to A. M. Gordon), AR-30988 (to E. Homsher), and HL-61683 (to M. Regnier).


  • Address for reprint requests and other correspondence: A. M. Gordon, Dept. of Physiology and Biophysics, Univ. of Washington, Box 357290, Seattle, WA 98195-7290 (E-mail:amg{at}

  • 1 Electron microscopic and X-ray diffraction studies show that myosin molecules are arranged in groups of three every 14.3 nm along the thick filament. Each half thick filament has 0.75 μm [(1.65 μm/thick filament− 0.15 μm bare zone)/2] of cross bridges/half-sarcomere so that there are 52 crowns of myosin molecules/half-sarcomere. Thus ∼300 S1 cross bridges per half thick filament may attach to the thin filaments. In skeletal muscle fibers, there are ∼500 thick filaments/μm2 of myofibril. Thus maximally 1.5 × 105 cross bridges can form per half-sarcomere for each square micron of cross-sectional area. At maximal overlap, there is 0.75 μm thin filament overlap per half-sarcomere/thin filament. Each thin filament contains 14 actin molecules/38-nm thin filament length or 370 actin molecules/μm thin filament. Thus 280 actin molecules are available for attachment per thin filament per half-sarcomere at maximal overlap. There are 2 thin filaments per thick filament or 1,000 thin filaments/μm2 muscle. Consequently, per half-sarcomere, there are 2.8 × 105 actin molecules/μm2. If maximally 1.5 × 105cross bridges · h−1 · μm−2 can form, one S1 head will be bound for every 1.8 G-actin molecules. If only 20–40% of all S1 heads are bound to the thin filaments during maximal isometric contraction (67), there will be 1.5–3.0 S1 heads bound for every 38 nm of a single actin strand, i.e., maximally 0.75–1.5 S1 heads bound/regulated strand that has 7 actin molecules available. During rapid, unloaded shortening, the total number of cross bridges attached and cycling at any one time falls to less than one-third of the number attached in the isometric case (assuming stiffness is proportional to the number of cross bridges attached, Refs. 117, 118, 240). This corresponds to one S1 attached every 15–30 G-actin monomeres, or one S1 head per two plus regulatory units.