PHYSIOLOGICAL REVIEWS   Vol. 78 No. 2 April 1998, pp. 359-391
Copyright ©1998 by the American Physiological Society

The Filament Lattice of Striated Muscle

BARRY M. MILLMAN

Biophysics Interdepartmental Group, Physics Department, University of Guelph, Guelph, Ontario, Canada

I. INTRODUCTION
II. STRUCTURE OF THE A-BAND LATTICE
    A. X-Ray Diffraction From the Filament Lattice
    B. Density Across the A-Band Lattice
    C. Backbone Structures
    D. Z-Line and I-Band Lattice
III. A-BAND LATTICE OF INTACT MUSCLE
    A. Lattice Spacings
    B. Changes With Sarcomere Length
    C. Changes With Osmotic Shrinking or Swelling
    D. Spacing Changes During Contraction
    E. Intensity Changes During Contraction
    F. Effects of Length Changes During Contraction
IV. A-BAND LATTICE OF SKINNED MUSCLE
    A. Preparation of Skinned Muscle Fibers
    B. Control of Lattice Dimensions by Osmotic Agents
    C. Effects of Changes in Sarcomere Length
    D. Filament Charges
    E. Changes in Lattice Spacing With Physiological State
V. CONTRACTILE FORCE AS A FUNCTION OF LATTICE SPACING
    A. Intact Muscle and Fibers
    B. Skinned Muscle Fibers
VI. LATTICE EFFECTS IN OTHER STRIATED MUSCLES
    A. Vertebrate Heart Muscle
    B. Invertebrate Striated Muscle
VII. FORCES STABILIZING THE A-BAND LATTICE
    A. Electrostatic Forces
    B. Effects of pH on Lattice Spacing
    C. Effects of Ionic Strength on the Lattice
    D. Van Der Waals Forces
    E. Entropic Forces
    F. Intrafibrillar Structural Forces
    G. Extracellular Structural Components
    H. Cross-Bridge Forces
    I. Radial Forces in the A Band of Intact Muscle
VIII. CONCLUSIONS
REFERENCES

	ABSTRACT

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Millman, Barry M. The Filament Lattice of Striated Muscle. Physiol. Rev. 78: 359-391, 1998.  The filament lattice of striated muscle is an overlapping hexagonal array of thick and thin filaments within which muscle contraction takes place. Its structure can be studied by electron microscopy or X-ray diffraction. With the latter technique, structural changes can be monitored during contraction and other physiological conditions. The lattice of intact muscle fibers can change size through osmotic swelling or shrinking or by changing the sarcomere length of the muscle. Similarly, muscle fibers that have been chemically or mechanically skinned can be compressed with bathing solutions containing very large inert polymeric molecules. The effects of lattice change on muscle contraction in vertebrate skeletal and cardiac muscle and in invertebrate striated muscle are reviewed. The force developed, the speed of shortening, and stiffness are compared with structural changes occurring within the lattice. Radial forces between the filaments in the lattice, which can include electrostatic, Van der Waals, entropic, structural, and cross bridge, are assessed for their contributions to lattice stability and to the contraction process.

	I. INTRODUCTION

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Striated muscle is a well-ordered and efficient machine for converting chemical energy into physical work. The details of the molecular mechanisms that drive the muscle machine are still poorly understood, although the recent determinations of atomic structures for the main components of the contractile machinery: actin and myosin S1 (118, 153, 241), will advance our understanding of the molecular process. This review examines the structure of striated muscle at the level of the filaments and the filament lattice: the hexagonal array of thick and thin filaments within the muscle's longitudinal unit or sarcomere. The relation between lattice structure and the mechanical behavior of muscle are discussed, along with those changes in the lattice that occur as the muscle changes its physiological state. Structural and functional observations are linked, so far as possible, to the physical processes and forces that act between filaments in the muscle lattice.

The viewpoint of the author is that of a physicist who has worked for many years on the macromolecular structure and physiological function of various types of muscles (intact, skinned, vertebrate, invertebrate, striated, and smooth) and who has a particular interest in explaining structural and mechanical data in terms of basic physical mechanisms. Many previous reviews in this area have tended to discuss contraction either from the structural perspective (e.g., Refs. 99, 131, 136, 258) or from the biochemical/physiological perspective (e.g., Refs. 28, 76, 227). Here, I attempt to deal with a limited aspect of structure, the filament lattice, and relate relevent physiological and biochemical observations to this structure. I am not aware of a previous review with this particular emphasis, although lattice effects have been considered in several previous reviews (108, 129, 131, 258, 278).

The contractile apparatus of striated muscle, so called because of its transversely banded structure, has the sarcomere as its basic unit. Alternating I bands (isotropic) and A bands (anisotropic) are seen in the light or electron microscope (Fig. 1). The A band of the sarcomere is a double, overlapping, hexagonal array of thick filaments (mostly myosin) and thin filaments (actin plus the regulating proteins: troponin and tropomyosin) (Fig. 2). Only thin filaments are found in the I band. A Z line divides the I band, usually taken as the edge of the sarcomere, and M lines divide the A band and hold the thick filaments together.

View larger version (72K): [in this window] [in a new window]   FIG. 1.   Electron micrograph of longitudinal section of freeze-substituted, relaxed rabbit psoas muscle. Sarcomere shows A band, I band, H band, M line, and Z line. Scale bar, 100 nm. [Micrograph courtesy of C. J. Hawkins and B. M. Bennett. Prepared as in Millman (111).]

View larger version (117K): [in this window] [in a new window]   FIG. 2.   Electron micrographs of transverse sections of A band from freeze-substituted rabbit psoas muscle, relaxed (A) and in rigor (B), prepared as in Figure 1. In each micrograph, top fibrils are from region of thick and thin filament overlap; bottom fibrils are from nonoverlap region that contains only thick filaments. Unit cell of filament lattice is outlined on A. Scale bars, 100 nm. (Micrographs courtesy of C. J. Hawkins and P. M. Bennett.)

The filament lattice (Figs. 2 and 3A) was first observed by low-angle X-ray diffraction (125, 127) and later by electron microscopy (100, 126, 128). The two types of filament and their arrangement in a regular overlapping fashion provided one of the most important pieces of evidence that led to the formulation of the sliding filament model for muscle contraction (124, 137).

View larger version (22K): [in this window] [in a new window]   FIG. 3.   A: diagram of filament lattice of vertebrate striated muscle in overlap region of sarcomere, showing unit cell of filament lattice (dotted lines) along with 1,0 (d10) and 1,1 (d11) lattice planes (solid and dashed lines, respectively). Thick filaments are represented by a solid circle with an outer circle for "cross-bridge" region; thin filaments are represented by a smaller solid circle. Arrows indicate h and k axes. B: diagram showing first 8 orders of equatorial X-ray diffraction pattern from vertebrate striated muscle hexagonal A-band lattice. Central rectangle is backstop to absorb "straight-through" X-ray beam at center of pattern. Numbers below each reflection are (h, k) indexes, corresponding to crystallographic planes for that reflection.

X-ray diffraction patterns from living muscle in the relaxed state were obtained in the 1950s and early 1960s (61, 125, 127) and in the contracting state in the later 1960s (59, 60, 134, 135). These showed changes in lattice spacing as the muscle length was changed and changes in the intensities of the primary equatorial reflections during the shift from the relaxed to the contracting or rigor state (Fig. 4). These observations led H. E. Huxley (130) to propose the "swinging cross-bridge" model for the contraction process.

View larger version (19K): [in this window] [in a new window]   FIG. 4.   Densitometer traces of equatorial X-ray diffraction pattern from intact frog sartorius muscle taken in 3 steady states: relaxed (A), isometric tetanic contraction (C), and rigor (E). B, D, and F are same patterns with background subtracted. Dashed lines are original data; solid lines are fitted curves; dotted lines are background. All data were taken with a single, Ni-coated glass mirror using an Elliott rotating-anode X-ray generator. Exposure times: A and E, 120 s; C, 65 s. [From Li (169).]

Much of the early history has been reviewed by H. E. Huxley in his Croonian lecture (131). A detailed review of the interpretation of the X-ray diffraction patterns from vertebrate striated muscle has been written by Haselgrove and Rodger (108) and Squire (258). A more general review of the application of X-ray diffraction techniques to muscle was written by Wray and Holmes (289), and Squire's book (258) includes a detailed discussion of X-ray diffraction methods and results. Recent X-ray diffraction studies on fish muscle have been summarized by Harford and Squire (104).

Since about 1970, there has been considerable effort directed at time-resolved studies of the changes that occur in X-ray diffraction patterns of muscle during the contraction process utilizing the very high X-ray intensities available from synchrotrons and electron storage rings. The time courses of intensity changes in the two strongest reflections were determined with a time resolution of 1-5 ms during isometric and isotonic contractions, as well as during stretches and releases during both contraction and relaxation (14, 52, 92, 140, 164, 277). A full interpretation, in terms of the contraction process, has still not been made for many of the changes observed. Time-resolved studies have been reviewed by H. E. Huxley and Faruqi (136) and synchrotron studies on muscle by Wakabayashi and Amemiya (278).

Recent studies (e.g., Refs. 41, 299) have emphasized the use of single fiber preparations which, because of their small size, require much longer exposures to the X-ray beam. The loss in terms of exposure time and signal-to-noise ratio is compensated for by a decrease in variability of the sample and rapid diffusion times for solutes in the bathing solution.

Much of the study of contraction mechanisms over the last decade has used preparations from which the external membrane has been removed. These preparations are usually of three types: 1) glycerol-extracted muscles that have been stored for either long (several weeks) or short (few days) periods in saline/glycerol mixtures (245, 247), 2) chemically skinned muscles in which the membranes have been removed or rendered inactive with detergent (26, 63, 178, 220), and 3) mechanically skinned single fibers from which the external membrane has been removed by physical stripping (185, 223, 224, 235). Such preparations have enabled the behavior of the contractile apparatus and the lattice to be studied when the composition of the interfilament fluid is varied, contraction is induced by ATP, or the lattice is compressed by large, inert polymers (72, 178, 220). Some of these studies have been directed at measuring and deciphering the forces that stabilize the filament lattice (e.g., Refs. 33, 186, 199, 218).

In this review, discussion centers on specific aspects of the filament lattice of intact and skinned striated muscles: 1) the changes in lattice spacing that occur when the lattice is subjected to osmotic compressive forces; 2) the effects of sarcomere length, pH, and ionic strength on the lattice; 3) the structural changes that occur when a resting muscle shifts into contraction or rigor; 4) the changes in physiological behavior of a muscle (force, shortening speed, stiffness) when the lattice changes size; and 5) the forces that stabilize the lattice along with the changes in these forces during contraction and rigor.

	II. STRUCTURE OF THE A-BAND LATTICE

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The filament lattice can be viewed directly from electron microscope transverse sections (Fig. 2), but preparation for such micrographs requires fixation, staining, and dehydration of the sample, procedures which can cause considerable distortion to the lattice structures. The filament lattice shrinks during preparation for electron microscopy (Table 2), and filament diameters measured from transverse electron micrographs are consistently smaller than those measured from negatively stained, isolated filaments, where less shrinkage takes place (cf. Refs. 128, 158). Recently, freeze substitution techniques have reduced the effects of preparative procedures, but even here, the sample must be viewed in a vacuum, and dehydration damage, although reduced, is still present (Table 2).

Alternatively, the lattice can be viewed in the living and even contracting state by low-angle X-ray diffraction.¹ In an X-ray diffraction experiment, a sharply focused or collimated beam of X-rays (e.g., 0.1 mm in diameter) is passed through a muscle sample ~1 mm thick, and the diffraction pattern is observed as a series of spots or lines on photographic film or an electronic detector placed a suitable distance away. In the case of laboratory X-ray generators, this distance is usually 20-50 cm; with synchrotrons, it is typically 1-5 m. In fibrous samples such as muscle, the axis of the diffraction pattern parallel to the fiber axis is referred to as the meridian; the perpendicular axis is the equator. Equatorial reflections are those that lie along the equator and originate (mostly) from the filament lattice (see Fig. 3B). In the case of the equatorial diffraction pattern, the lattice is viewed in its axial projection, i.e., as if all the density along the length of a sarcomere were projected onto a single transverse plane. Specific spots are observed in the equatorial diffraction pattern that correspond to Bragg reflections from planes through the unit cell of the lattice (Fig. 3). The separation of the X-ray reflections in the diffraction pattern gives a measure of lattice dimensions. Specifically, the distance of the 1,0 reflection from the center of the X-ray pattern (S) enables the separation of the 1,0 planes (d₁₀; see Fig. 3 and Table 1) to be calculated using the Bragg relationship, which, for the small angles involved, reduces to

(1)

where  is the distance from the muscle to the detector (or film) and  is the wavelength of the X-radiation used (e.g., 0.154 nm for copper K radiation). The spacings of other planes formed by the lattice are geometrically related to d₁₀ (e.g., d₁₁ = d₁₀ / , d₂₀ = d₁₀/2). In general, for a hexagonal lattice where h and k are integers, indexes for the crystal directions in the plane (see Fig. 3).

X-ray diffraction experiments can yield two types of information. As well as lattice dimensions or the spacing between filaments (see sect. IIA), the electron density across the unit cell can be calculated from the reflection intensities. In particular, the electron density projected axially along the sarcomere can be calculated by Fourier transformation of the equatorial X-ray diffraction pattern (Fig. 5). Because diffraction spots (or reflections) are waves, in addition to the amplitude, each has a phase which can vary between 0 and 360°. Fourier amplitudes are obtained directly as the square root of intensities of the diffraction reflections. Phases, however, need to be derived from other considerations, e.g., known aspects of the structure, structural symmetry, changes during swelling and shrinking, or the fitting of structural models to the observed electron density. Details of phase determination methods are beyond the scope of this review but can be found in more specialized X-ray diffraction references (e.g., Ref. 258).

View larger version (151K): [in this window] [in a new window]   FIG. 5.   Electron density diagrams for filament lattice calculated using intensity data from Li (169) for frog sartorius muscle at rest (A-E) and during an isometric tetanus (F). Thick filaments are centered at corners of hexagonal unit cell (see Fig. 3). Shadings represent contours of equal electron density difference: gray on white, positive density; light on dark, negative density. A: first 2 orders with phasing ++ (107). B: first 5 orders with phasing +++ (109, 145). C: first 5 orders with phasing ++++ (299, 104, 105). D: first 8 orders with phasing +++ [from electron micrographs (111, 117)]. E: first 8 orders from relaxed muscle with phasing +++++ (169). F: first 8 orders from contracting muscle with phasing +++++ (169).

Because X-ray diffraction patterns can be obtained from "living" muscle, the dimensions of the filament lattice can be determined accurately from the spacings of reflections in the pattern. In principle, filament diameters can be measured from transverse electron density diagrams, but such determinations are limited in practice by resolution limits and the fact that phases must be determined indirectly. At low resolution, the filament lattice structure is centrosymmetric, meaning that phases for each reflection can only be 0 or 180° (usually designated + or , respectively). The centrosymmetric condition is probably appropriate over the range of equatorial reflections observed in practice and discussed here.

The resolution of an electron density diagram will be a function of the number of diffraction orders (or reflections) used in the reconstruction. In general, resolution will be proportional to the inverse of the maximum lattice spacing observed. Thus, for a lattice with d₁₀ of ~40 nm, as in frog or rabbit skeletal muscle (Table 1), two orders of diffraction will give a resolution of ~23 nm (Fig. 5A), five orders will give a resolution of ~13 nm (Fig. 5, B and C), and eight orders will give a resolution of ~10 nm (Fig. 5, D-F).

Analyses of the diffraction patterns from frog, rabbit, and fish skeletal muscles (104, 145, 299) along with models of the lattice (103, 145, 259, 297) have reduced the possible phase combinations for the first five equatorial reflections (1,0, 1,1, 2,0, 2,1, and 3,0) to either +++ (Fig. 5B) (109, 145) or ++++ (Fig. 5C) (102, 104, 303). In most situations, the difference in electron density calculated from the two phasings is small, since the 2,1 reflection is weak. Both phasing combinations show clearly defined thick and thin filaments, with a more diffuse density between the filaments corresponding to the region containing myosin heads or heavy meromyosin (HMM) S1, the projections from the thick filaments (Fig. 5, B and C). In relaxed muscle, the major differences between the two phasing combinations lie in the thin filament density and the positioning of the diffuse material. Neither combination can be completely accepted at this time, but the +++, first proposed by Haselgrove et al. (109), gives slightly smaller residuals and is probably the preferred phasing for relaxed frog and rabbit skeletal muscle. However, the same phasing may not apply to all vertebrate muscles under all conditions; fish muscle, which has a larger lattice spacing (Table 1) (103), and muscle in rigor may have the ++++ phasing (303).

Phases for the orders beyond the 3,0 (i.e., 22, 31, 40, and 41) are still uncertain. There can be substantial intensity in these orders; thus they will have a significant effect on the electron density distribution across the lattice (cf. Fig. 5, D and E) (169).

Equatorial phases and amplitudes have also been determined from freeze-substituted electron micrographs and used to calculate transverse lattice density diagrams (Fig. 5D) (111, 117, 272). These data differ from X-ray diffraction determinations, particularly the amplitudes which are lower than those observed by X-ray diffraction, possibly because of preparative effects mentioned in section IIA. Electron microscopy may, however, turn out to be a valuable method for determining the phases.

Early interference microscope studies, in which the actin, myosin, tropomyosin, and troponin were removed by solutions with high salt concentration, showed that material remained in the sarcomere linking the Z lines together (101, 138). Recently this "backbone" material has been associated with the proteins titin (or connectin) and nebulin (182, 282). Some electron micrographs have shown filamentous material linking the ends of thick filaments to the Z line, linking thin filaments together across the H zone, or linking thick and thin filaments together (11, 179, 238).

It now appears clear that there are additional structures that provide a backbone to the sarcomere and that probably control the positions and lengths of the thick and thin filaments (121). These structures may also provide much of the muscle's resting tension (120, 177, 179). The detailed structure, location, and arrangement of these structures have yet to be determined, but they must contribute to the density across the filament lattice (271, 281).

Reflections from another lattice, formed from thin filaments in the Z line and the I band (near the Z line), are also seen in equatorial X-ray diffraction patterns from the muscle sarcomere (60, 102, 146, 301). The most prominent order is the first (d_z), which lies between the 1,0 and 1,1 reflections from the A band, at a spacing corresponding to ~25 nm (Fig. 4B). A second order may overlie the 2,0 reflection (102) or may be seen as a diffuse reflection appearing at a spacing of ~1.6 times d_z (146). This "extra" spacing lies between the expected spacing for a square lattice (1.41 times d₁₀; found in intact muscle in normal Ringer solution) and an hexagonal lattice (1.73 times d₁₀; found in swollen and shrunken intact muscles and in skinned muscle), suggesting that I-band diffraction may arise, at least in part, from thin filaments as they shift from a (small) square structure in the Z line to an hexagonal packing in the A band (102, 146). Except at extreme lattice swelling or shrinking, the Z/I lattice swells (or shrinks) proportionately to the A-band lattice (60, 146, 301).

As a result of limited resolution in the X-ray cameras, some measurements of 1,1 intensities (I₁₁) and of the intensity ratio (I₁₁/I₁₀) may have included intensity in I₁₁ , which properly belonged to the Z-line reflection. The intensity of the Z-line reflection (I_z) tends to increase with sarcomere length (249, 250), and part of the observed increase in I₁₁/I₁₀ with sarcomere length may be an artifact. Such an effect may also explain the unexpected observation of changes in the relative spacings of the 1,1 and 1,0 reflections as the sarcomere length is changed (251). Most recent experiments have avoided this problem because of better resolution in the diffraction pattern.

	III. A-BAND LATTICE OF INTACT MUSCLE

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The center-to-center distance between thick filaments in intact frog and rabbit skeletal muscles is normally ~43 nm (corresponding to a d₁₀ of ~37 nm) (Table 1). The spacing is larger in fish muscle (Table 1) (103) and is much larger in many invertebrate striated muscles (Table 5).

Lattice dimensions measured from transverse electron micrographs are always smaller than those measured by X-ray diffraction (Table 2) because of shrinkage that occurs during the preparation of the specimens. This shrinkage occurs mostly in the interfilament spaces during the dehydration process, although some shrinkage also occurs in the filaments as shown by the difference in filament diameters when measured from sections, as compared with negatively stained, isolated filaments (cf. Refs. 129, 158). The amount of the lattice shrinkage, normally 10-20% (Table 2), suggests that the filament lattice as seen in electron micrographs often corresponds to the lattice when maximally compressed osmotically.

Because X-ray diffraction apparatus is often not available or convenient to use in conjunction with physiological experiments, several authors have used measurements of fiber diameter to estimate changes in lattice spacings (72, 97, 197, 199, 248). Although fiber diameter and lattice spacing are related qualitatively, there is generally not a direct proportionality between them under all conditions (186, 298; Fig. 3). In either highly swollen or highly compressed intact muscle fibers (and probably skinned fibers as well), the fiber diameter changes more than the filament lattice, implying a greater swelling of the extrafibrillar spaces. In the spacing range from that in normal Ringer solution down to ~20% compression, fiber diameter provides a reasonable estimate for lattice changes (156). Below 20% compression, however, little lattice shrinkage is seen in vertebrate skeletal muscles. The swelling or shrinking of extrafibrillar spaces is thus greater than that of the lattice outside this range. This consideration is particularly relevant in analyses from electron micrographs, where the filament lattice may shrink during preparation below the range where fiber diameter is proportional to lattice spacing.

In the earliest low-angle X-ray diffraction study of the filament lattice, Huxley (125) noted a decrease in the lattice spacing as relaxed muscle was stretched. Elliott et al. (61) later showed that in living relaxed muscle this decrease in lattice spacing was inversely related to the square root of the length of the muscle sarcomere, showing that the volume of the A-band lattice remained constant. For most skeletal muscles, this volume (defined as 2/ times d₁₀² times sarcomere length) is ~4 × 10³ µm³/sarcomere (Table 1). The constancy of the lattice volume is observed over a wide range of sarcomere lengths (Fig. 6). If, however, the lattice spacing is decreased below a d₁₀ of ~27 nm by either stretching or through osmotic compression, constant volume behavior may no longer be observed (107, 219, 246). Furthermore, there is a tendency for the volume of the lattice to decrease over an extended period of time for reasons that are probably associated with the transport of ions across the sarcolemma membrane (60, 185, 219).

View larger version (13K): [in this window] [in a new window]   FIG. 6.   1/(d10)2 as a function of sarcomere length in living, relaxed frog semitendinosus muscle (B. M. Millman and G. F. Elliott, unpublished data). Straight line corresponds to a constant lattice volume of 3.75 × 103 µm3 [(2/)(d10)2(sarcomere length)].

As sarcomere length changes in relaxed muscle, there are changes observed in the intensities of the 1,0 and 1,1 reflections in the equatorial X-ray diffraction pattern; the intensity ratio I₁₀/I₁₁ increases with sarcomere length (3, 61, 107, 129). The change in intensity ratio as sarcomere length changes is a result of small changes in the intensity of the 1,0 reflection: I₁₀ (an increase up to 2.3 µm, a decrease beyond 2.5 µm) coupled with a large decrease in I₁₁ as the relaxed muscle is stretched (249). These changes are believed to be because of increased lateral disorder of the thin filaments as the sarcomere length is increased (61).

Because muscle fibers are enclosed by a membrane that limits the passage of ions, one would expect that a muscle fiber would behave as an osmometer. Experiments in which the diameter or volume of frog skeletal muscle fiber was measured as a function of the osmolarity of the external solution showed that, within a considerable range of osmolarities, muscle fibers behave as good osmometers, swelling when the external osmolarity is reduced and shrinking when it is increased (23, 47, 244, 248). These experiments indicated an osmotically inactive volume (i.e., solid matter and nonexchangable water) in the fiber between of 25 and 40%.

The direct effect of changing osmolarity on the filament lattice spacing was first investigated by Rome (246) using toad sartorius muscles. She varied the ionic concentration of the external solution and found a linear relationship between lattice volume and the inverse of ionic concentration over the range from 0.6 to 2.0 times normal concentration (Fig. 7), indicating that the muscle fiber does behave as an osmometer. Extrapolation of her line to infinite concentration gave an inactive lattice volume of 38% (Fig. 7, dotted line).

View larger version (15K): [in this window] [in a new window]   FIG. 7.   Lattice volume as a function of (osmolarity)1 for living, relaxed amphibian skeletal muscle. Points are averaged data from references. Lines are least-squares fits. Intercepts give inactive volume. Open circles/solid line, frog sartorius (219); solid circles/dashed line, frog semitendinosus (219); triangles/dotted line, toad sartorius (246).

Similar experiments with frog sartorius and semitendinosus muscles in which the osmolarity of the external solution was increased by adding glucose, sucrose, or physiological ions up to a final osmolarity of 2.7 times normal osmolarity (245 mM) (219) showed that the lattice could not be shrunk below ~45% of normal volume, presumably because at that point the filaments were fully pressed up against one another. Avoiding extreme parts of the curve, a linear relationship was found between lattice volume and 1/osmolarity over most of the range which, when extrapolated to infinite osmolarity, gave an osmotically inactive volume of ~30% (Fig. 7). More recent experiments (143, 169, 285) have yielded very similar results. The osmotically inactive lattice volume of 30% is surprisingly close to the value for the whole fiber and probably represents 20-25% protein with a small amount of water bound to the filamentous structures.

When intact frog muscle contracts in normal Ringer solution, there is little or no change in the lattice spacing (60, 107, 134). When the lattice is shrunk in hyperosmotic solutions, however, contraction causes the lattice to swell by ~4%; in hyposmotic solutions, on the other hand, contraction causes the lattice to shrink by a very small amount (~0.5%) (Fig. 8) (169, 221, 285; T. C. Irving, Q. Li, B. Williams, and B. M. Millman, unpublished data). These changes on contraction are either too large (hypersomotic solutions) or in the wrong direction (hyposmotic solutions) to be explained by internal changes in sarcomere length. Because the total volume within an intact muscle fiber should remain constant during short contractions, changes in lattice volume imply a shift of sarcoplasm between the A band and other parts of the fibril, possibly accompanied by longitudinal shape changes in the sarcomere.

View larger version (15K): [in this window] [in a new window]   FIG. 8.   Lattice spacing from intact frog sartorius muscle as a function of external osmolarity. Open circles and lines, relaxed; solid circles, isometric (tetanic) contraction. Correction for small spacing changes resulting from decrease in sarcomere length (because of series elasticity) will slightly increase lattice spacing for contracting muscle (by ~1%). Arrow indicates in vivo osmolarity that equals 245 mosM. [Data averaged from Li (169); Williams (285); and T. C. Irving and B. M. Millman, unpublished data.]

Changes that are qualitatively similar have been observed in frog single fibers during tension rise in a tetanus (16, 91). In normal Ringer and hypertonic solutions, only small changes in spacing were seen upon contraction, whereas greater lattice shrinkage was observed in hyposmotic solution as compared with whole muscle. Some of the changes were transitory, and the differences between whole muscle and intact fibers may be explained, at least in part, through a larger series compliance in fibers and additional volume constraints in whole muscle.

Lattice spacing has been found to change over time in a complex fashion that appears to be related to time from dissection, number, and frequency of contractions, temperature, and the ionic state (and pH) of the sarcoplasm. Over a very long series of twitch contractions (lasting up to 24 h), Elliott et al. (60) found a 2-3% decrease in the resting lattice spacing. On the other hand, a lattice expansion that can be two to three times the previously observed decrease has been observed in shorter contraction series (221, 240, 285). Some lattice effects reported during contraction may be caused in part by "fatigue" or changes in the internal pH of the muscle, particularly during the lengthy experiments required to obtain detailed diffraction patterns. Rapp et al. (240) have calculated that the lattice increases by 0.024 nm/twitch during a series of contractions and suggest that this increase is caused by the "production of osmotically active material by mechanical activity."

When a muscle shifts from the relaxed state into rigor, there is a dramatic change in the intensities of the 1,0 and 1,1 reflections; in relaxed muscle, the 1,0 reflection is always stronger than the 1,1, whereas in rigor, the 1,1 is much stronger than the 1,0 (cf. Fig. 4, B and F) (127, 129).

A similar, although smaller change in relative intensities is observed when a living, relaxed muscle contracts (cf. Fig. 4, B and D). Basic changes in equatorial X-ray diffraction patterns during contraction were observed by Elliott et al. (59, 60), Haselgrove and Huxley (107), Podolsky et al. (237), Sugi et al. (264, 265), Matsubara and colleagues (193, 292), and Vazina et al. (277). These have been discussed in Huxley and Faruqi (136), a review that also contains a good basic discussion of the relevent X-ray diffraction apparatus and techniques. Although there is little or no change in lattice spacing when an intact muscle contracts isometrically, there are large changes in the intensities of the 1,0 and 1,1 reflections. The I₁₀ value decreases by a factor of ~2, whereas I₁₁ increases by a similar factor, leading to a large decrease in the intensity ratio I₁₀/I₁₁ (Figs. 4, B and D, and 9). These intensity changes have been interpreted as resulting from the attachment of myosin cross bridges to actin filaments, and I₁₀/I₁₁ has frequently been used as a quantitative measure for the fraction of cross bridges attached to the thin filaments (e.g., Refs. 32, 192, 237, 300). It should be noted, however, that low-angle X-ray diffraction data in general and I₁₀/I₁₁ in particular depend on specific models (174, 175) and can only indicate that mass has moved to (or from) the vicinity of the thin filament. Whether actual actin-myosin "binding" has occurred cannot be established from X-ray diffraction data (except at atomic resolution); other data (e.g., biochemical or physiological) are necessary to establish actual binding or "attachment."

View larger version (18K): [in this window] [in a new window]   FIG. 9.   Intensities of 1,0 and 1,1 reflections, along with their intensity ratio, for frog sartorius muscle as a function of isometric force. Force developed in contractures with different concentrations of caffeine (1.25-2 mM). [Points are averaged from data in Figs. 3 and 4 of Yu et al. (300).]

Although intensity changes have usually been interpreted as indicating a shift of mass from the region of the thick filaments to that of the thin filaments, other interpretations, such as an azimuthal shift in cross-bridge position (i.e., a mass shift around the thick filament in the plane perpendicular to the fiber axis), can also explain the observation (174). More recent data, which include more diffraction orders along with a clearer separation of the Z-line reflection from the 1,1 reflection (see sect. IID), suggest that a combination of radial and azimuthal shifts in the position of HMM S1 probably occurs when a muscle contracts or shifts into rigor (see Fig. 5) (34, 102, 104, 145, 299).

With the use of the intensity data for relaxed and contracting muscle along with the +++ phasing for the first five equatorial diffraction orders, electron density diagrams suggest that the shift from the relaxed to the contracting state involves a radial shift in myosin head (HMM S1) position of ~1 nm toward the thin filaments along with some average reorientation of the heads from the 1,0 planes (where they tend to point toward adjacent thick filaments) to the 1,1 planes (where they tend to point toward the thin filaments) (see Fig. 5) (34, 102, 143, 170, 303).

With the development of more intense X-ray sources and more efficient detecting systems, it has become possible to study changes in structure during the course of a contraction and during stretches and releases by dividing a contraction into a series of time intervals or "time slices" (see Ref. 136). Most of these studies have been done using frog skeletal muscle at low temperatures (0-5°C). Early studies (reviewed in Ref. 136) showed 1) that during an isometric contraction, the time course of changes in equatorial intensities (I₁₀ and I₁₁) were ahead of tension rise (by ~10 ms) (132, 277); 2) during relaxation, equatorial intensity changes showed two components, one with a time course similar to that of tension and the other delayed by ~7 s with respect to tension (292); 3) equatorial intensities were unchanged (from isometric values) during shortening under all but very light loads [<10% maximum isometric force (P_o)], in which case the intensity ratio moved toward the resting value (133, 237); 4) equatorial intensities showed little change when the muscle was stretched or released during contraction (5, 264, 265, 294); and 5) at very long sarcomere lengths where there is no filament overlap and only the 1,0 reflection is seen, I₁₀ does not change when the muscle is activated (133). These results indicate that filament overlap is necessary for cross-bridge changes and that these changes are largely independent of mechanical changes to the muscle during activation, with the exception of rapid shortening, which shifts the cross bridges toward the resting configuration.

In the years since the Huxley and Faruqi review (136), the use of synchrotron radiation and the steady improvement of apparatus and techniques (see Ref. 278) have enabled the earlier findings to be refined and extended. In particular, the size of the time slices has been reduced ~10-fold, enabling time slices as small as 0.2 ms to be achieved (141). Studies have been extended to other muscles such as fish skeletal muscle (104) and to single (frog) fibers (40, 41, 92). The earlier findings have, by and large, been confirmed, but further details have emerged on structural changes during the rise of isometric tension and during stretches or releases.

The rise of tension in an isometric contraction is always preceded by changes in the intensities of the 1,0 and 1,1 equatorial X-ray reflections as described above. In frog muscle, these intensity changes precede tension rise by 10-50 ms (24, 41, 164, 278) and are accompanied by a parallel increase in axial stiffness (14, 41). In fish muscle, while I₁₁ leads tension changes by ~15 ms, I₁₀ leads tension by only ~5 ms (104). In all cases, however, the data indicate that cross bridges shift to the vicinity of the actin filaments ~15 ms before tension is developed and that this mass shift is accompanied by an increase in stiffness (105).

As found in earlier studies, when a contracting muscle is stretched, released, or shortens isotonically, changes in equatorial intensities are small unless the shortening is very fast. Some small changes have been observed, but quantitative evaluation of these is difficult because of several factors that can affect the X-ray intensities during a length change. Intensities need correction for changes in the amount of tissue in the X-ray beam, the degree of lattice or filament disorder, and changes in lattice spacing because of constant lattice volume as the saromere length changes (see Refs. 291, 296). Slow stretches during contraction in which force increased greatly or isotonic stretches at loads well above isometric give little or no change in I₁₀/I₁₁ , indicating that despite a large increase in force, there was no marked change in cross-bridge orientation or the number of cross bridges during these stretches (270). Changes in lattice size in intact muscle can mostly be explained through the constant lattice volume unless there is osmotic compression (see sect. IIIC). Small decreases have been observed in I₁₁ when a contracting muscle is stretched (possibly because of a decrease in thin filament ordering), with little or no change in I₁₀ and opposite effects observed when a contracting muscle is released, but the effects on the intensity ratio are masked by variability in I₁₀ (4, 270, 295, 296). Isotonic releases to zero load give a substantial drop in both I₁₀ and I₁₁, whereas release to small loads (e.g., 0.2P_o) gives much smaller intensity decreases (92). Small (1%) sinusoidal length changes during tetanic contraction in frog muscle cause oscillating changes in tension and equatorial intensities; large increases in tension are accompanied by moderate (~15%) decreases in I₁₁ and small increases in I₁₀ (280).

The common conclusion from all these studies is that during a contraction, there is little change in the mass associated with the thin filaments, even when there are large changes in the force being developed or the load being lifted. The exception is the case of rapid shortening under very small loads when the equatorial intensities shift toward resting values, but the equatorial intensities during a contraction always remain closer to isometric values than resting ones.

These results demonstrate, as noted earlier, that the location of cross bridges near thin filaments does not necessarily mean that they are actively "bound" or involved in force production. Yagi and Takemori (295) have suggested that the positioning of cross bridges near the thin filaments may be the result of electrostatic forces between myosin heads and the thick and thin filaments. Some such cross bridges may be "weakly bound," in some "precontracting" state of the cross-bridge cycle (17, 30, 35, 65, 139) (see sect. VIIC).

	IV. A-BAND LATTICE OF SKINNED MUSCLE

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The technique for mechanically skinning frog fibers was developed by Natori (223, 224), introduced to North America by Podolsky (235), and was first used for X-ray diffraction studies by Matsubara and Elliott (185). Since then, it has been used by several other groups (e.g., Refs. 83, 96, 98, 186, 273). In these preparations, a single fiber is isolated and then the cell membrane, along with associated structures, is peeled back along the length of the fiber to expose interior structures to the external solution. Because the membrane barrier is gone, water, ions, and other soluble molecules or particles can diffuse freely into the fiber. As the fiber is skinned, the fiber and the filament lattice expand by 10-20% as a result of removal of the osmotic and structural constraints (72, 185). The original lattice dimensions can be restored by adding large inert molecules, which cannot penetrate the lattice, to the external bathing solution (72, 186) (see sect. IVB).

An alternative to mechanical skinning is chemical skinning in which a small amount of a suitable detergent or similar agent (Triton, Saponin, Brij) is added to the bathing solution so as to dissolve or damage the muscle's cell membrane. This can be done either with intact muscle or muscle bundles (e.g., Refs. 145, 178, 220) or with single fibers (e.g., Refs. 36, 191, 204, 260, 269, 302, 305). Detergent normally removes only membrane material, leaving other structural components in place (115). In some procedures, structural components have been removed through enzymatic degradation (114). Various improvements in skinning procedures have resulted in preparations giving data of high quality and reproducibility (26, 71, 162, 254). As in the case of mechanical skinning, the lattice swells upon removal of the membrane and can be returned to normal dimensions through addition of an osmotic agent (36, 204). Diffusion to the center of the skinned preparation will depend on sample size. In large skinned muscle preparations, diffusion to the center of the tissue may take an hour or more, but diffusion in single fibers is relatively fast (a few seconds) (273).

Glycerol extraction (21, 48, 226, 245, 267, 268) can be considered as a special case of chemical skinning. In these preparations, the muscle is placed in an ionic solution containing glycerol for a period of several weeks at a low temperature (20°C), during which time the cell membrane is dissolved or degraded. The advantage of these preparations is that a sizable amount of tissue can be stored for extraction and used over a period of several weeks. After extraction, the muscle is in the rigor state, but it can be relaxed, particularly in the case of single fibers or small fiber bundles, with a suitable ATP-containing solution (247). In practice, for repeatable results using glycerol-extracted preparations, it is usually necessary that the extraction process be carefully controlled and the period over which these preparations are stored and used be limited (142, 247).

A variation on the glycerol-extraction procedure involves osmotically shocking the tissue by shifting it several times between a glycerol solution and a salt solution over a 24-h period before extraction (247). This procedure improves and speeds up the extraction process, often enabling preparations to be used after only 24 h of extraction.

Glycerol extraction can also be used in combination with a small amount of detergent to speed up membrane degradation (26, 115). These modified procedures, along with other modifications noted above, usually produce much improved relaxed preparations that are ideally suited for physiological experiments.

Another method of preparing skinned muscle samples is by freeze drying (150, 152, 261). Stiffness measurements and equatorial X-ray diffraction results from freeze-dried fibers are comparable to those obtained from other skinned preparations in activated, relaxed, and rigor states (149).

A recently developed technique, flash photolysis of caged ATP and other high-energy compounds, has extended the use of skinned preparations to time-resolved studies. With the use of this technique, such compounds can be fully diffused into the muscle lattice and then instantaneously "activated" by a laser flash, thus initiating chemical reactions sychronously across the muscle (75, 79-81).

In all the skinned preparations described above, lattice size is not controlled by the fiber membrane but is a function of the solution (e.g., pH and ionic strength), the sarcomere length, and physical constraints on the lattice such as M lines and cross bridges. The lattice size (or volume) can be controlled by adding inert, uncharged, nonpenetrating osmotic agents to the bathing solution. The most commonly used agents are dextran or polyvinylpyrrolidone (PVP) with molecular weights >100,000 (e.g. Fig. 10) (72, 178, 186, 220). Solutions with 3-6% of these agents are sufficient to shrink the lattice of skinned muscle fibers back to their original size; greater concentrations cause the lattice to shrink further.

View larger version (13K): [in this window] [in a new window]   FIG. 10.   Lattice spacing as a function of applied osmotic pressure in skinned frog sartorius muscle, when relaxed () and in rigor (). [Data from Millman and Irving (215).]

The osmotic solutions described above can be used to apply a specific force or pressure on the filament lattice and thereby provide a tool for measuring interfilament forces within the lattice (33, 197-199, 218, 275, 290). This "osmotic stress" technique was first applied to lipid bilayer systems (168) and has since been extended to a wide variety of gel-like systems formed from biological molecules or within tissues (211, 231). Through this technique, osmotic pressures equal to several atmospheres can be directly applied to the filament lattice (218, 220).

Whereas the size of the lattice in intact muscle is chiefly controlled by an osmotic balance across the fiber membrane, in skinned muscle no such barrier exists, and forces between filaments in the lattice provide the major control on lattice size (for full discussion, see sect. VII). Within the lattice of the relaxed sarcomere, electrostatic forces between the negatively charged filaments will be one factor determining lattice size (218, 263). At very small or very large lattice spacings, steric interference of the filaments themselves or limitations in the extension of structural elements such as M lines, will control lattice size (186, 198, 215). In contracting or rigor conditions, there will be a radial component of cross-bridge force that will add to the electrostatic and structural forces (32, 186, 253, 290), and the electrostatic and structural forces may themselves be modified by changes in the physiological state of the muscle (215).

In intact muscle, most of the lattice effects related to sarcomere length are a result of the cell (fiber) membrane and its (osmotic) control of fiber volume. Under most physiological conditions, the lattice volume (cross-sectional area times sarcomere length) is constant (see sect. IIIB). When the membrane constraints are removed in skinned muscle, however, there is nothing to keep the lattice at a constant volume, and lattice spacing will be determined by other factors. There will be a balance between repulsive and attractive forces in the lattice and between the filaments. In the relaxed muscle, there will be repulsive electrostatic and attractive van der Waals forces (53, 218), along with structural components such as M lines, Z lines, and scaffolding structures that can exert forces that will limit both swelling and shrinking (115, 185). Physical contact of the filaments (or steric hindrance) will provide a lower limit to the lattice spacing.

In the absence of osmotic compression, Rome (245, 246) concluded that lattice spacing in glycerol-extracted rabbit psoas muscle is determined chiefly by electrostatic forces. However, there are problems, particularly in the case of ionic strength effects (36, 246). Recent comparisons with electrostatic calculations indicate that, although some effects consistent with electrostatic forces are observed, the lattice spacing cannot be calculated simply from a model of smooth, incompressible cylinders (filaments) in an ionic solution (215, 218). The specific forces stabilizing the lattice and their contributions in different physiological states are discussed in section VII.

Under physiological conditions (pH 7-8, ionic strength = 100-200 mM), both thick and thin filaments are negatively charged (53). Elliott (55, 56) has developed a technique in which microelectrodes are used to measure Donnan potentials in the sarcomere, and these Donnan potentials can be used to calculate the fixed charge in the A and I bands of a sarcomere. With the knowledge of the size of the lattice and the filament composition, the charge per unit length of filament can be calculated (42, 57, 225). Filament charges for several muscles under relaxed and rigor conditions are shown in Table 3.

Donnan potentials measured from glycerol-extracted rabbit psoas muscle showed no change with sarcomere length, implying that the A-band and I-band potentials are similar (225). Different A-band and I-band potentials were, however, measured from chemically skinned rat semitendinosus muscle (21).

There are changes in filament charge as the ionic strength is changed. In rigor muscle, as ionic strength drops from 180 to 19 mM, the thick filament charge falls by a factor of ~2. In relaxed sarcomeres and on the thin filaments, however, changes with ionic strength are much smaller (21). As expected, the (negative) charge on the filaments decreases with decreasing pH until, at the isoelectric point (pH ~5), it is zero and becomes positive as the pH decreases further (57, 225).

The charges on actin, myosin, and myosin subfragments were determined similarly, in the presence and absence of ATP, using microelectrode measurements in gels of purified protein or subfragment (19, 44). Data relevent to physiological conditions are shown in Table 4. Note that all molecular charges are negative. Discrepancies between measured and calculated charges (e.g., tropomyosin) may indicate the binding of small ions.

The lattice spacing changes when a skinned muscle shifts from relaxation to rigor (Fig. 10). As in the case of intact muscle (Fig. 8), the direction and amount of the change depend on the externally applied pressure (186, 199, 210, 215, 220). If there is no (osmotic) compression, the lattice spacing decreases by ~10% to about the same spacing as before removal of the membrane. If, on the other hand, the lattice has been substantially shrunken through osmotic compression, the lattice swells when it goes into rigor. At an applied osmotic pressure of ~2 kPa, sufficient to shrink the lattice close to its in vivo spacing (see Table 1), the lattice spacing does not change. These results indicate that (rigor) cross bridges resist both swelling and shrinking of the lattice away from an intermediate spacing, which is normally close to the in vivo spacing (186, 210, 215). It should be noted, however, that in vivo spacings can vary from muscle to muscle and from experiment to experiment (Table 1) for reasons that are not clear.

Similar results are obtained when a skinned muscle shifts from the relaxed to the activated state. In mouse toe muscle (191) and rabbit psoas muscle (32, 33, 256, 290), contraction causes lattice shrinking when there is no applied pressure but a swelling when the lattice is substantially shrunken. Again, no change is observed at an intermediate spacing that is usually near the in vivo spacing (see sect. VIIH).

	V. CONTRACTILE FORCE AS A FUNCTION OF LATTICE SPACING

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As the filament lattice shrinks in hypertonic solutions, decreasing the interfilament spacing, P_o decreases, until it is near zero when the fiber (or lattice) volume is reduced by ~50% (Fig. 11). The effects of hypertonicity on tension during forced lengthening and release imply a direct impairment of the force-generating processes (234). As the lattice swells in hypotonic solutions, there is a small increase in isometric force followed by a decrease (Fig. 11). It is the reduction in lattice spacing that causes force to decrease, not the pressure itself, since huge hydrostatic pressures can be applied to a muscle and cause only small effects on contractile force (67). Moreover, when the lattice is swollen or shrunken osmotically, the optimal sarcomere length for isometric force development increases or decreases, respectively, so as to keep the surface-to-surface separation of the thick and thin filaments at an optimal distance of 10-12 nm (corresponding to a d₁₀ between 37 and 39 nm, close to d₁₀ in vivo, 36-37.5 nm, Table 1) (13; see also Ref. 31). It appears that in intact muscle (and in skinned muscle as well; see sect. VB) there is an "equilibrium" spacing for force development, which is usually close to the spacing in vivo (39). When either an intact or a skinned, swollen or shrunken muscle contracts, the filament lattice tends to shrink or expand, respectively, to bring the lattice toward this equilibrium spacing. The in vivo spacing appears also to be where the isometric tension-to-ATPase hydrolysis ratio (a measure of "tension cost") is lowest in skinned skeletal muscle (see comment by R. E. Godt in Ref. 196).

View larger version (18K): [in this window] [in a new window]   FIG. 11.   Maximum isometric force as a function of external osmolarity in various amphibian muscles. Intact frog sartorius: open circles, T. C. Irving, Q. Li, B. M. Williams, and B. M. Millman, unpublished data; solid circles, Ref. 122. Intact toad sartorius: open triangles, Ref. 106; solid triangles, Ref. 18. Frog tibialis anterior single fibers: open squares, Ref. 180. Frog semitendinosus single fibers, solid squares, Ref. 93. Frog extensor longus digiti IV fiber bundles, open diamonds, Ref. 85. Arrow indicates in vivo osmolarity of 245 mosM.

The lattice spacing in intact muscle can also be decreased by increasing the sarcomere length (61). In this case as well, isometric force decreases with the decrease in lattice spacing as sarcomere length increases (13, 39, 51). When sarcomere length increases, however, both lattice spacing and filament overlap decrease, both of which will contribute to a decrease in developed force. In this situation, the major factor causing contractile force to decrease appears to be the decrease in filament overlap that causes a proportional decrease in isometric force (87).

Osmotic compression of intact muscle has two effects: it brings the filaments closer together, and it increases the ionic concentrations within the sarcomere. Because the effect of hypertonic solutions on P_o is very similar in tetanic contractions and in caffeine contractures, Gordon and Godt (85) concluded that osmotic compression affects contractile tension directly rather than through excitation-contraction coupling (see also Ref. 234). Furthermore, because the reduction in isometric tension in intact muscle matches the reduction in calcium-activated tension in skinned muscle fibers when the (internal) ionic strength is the same, increased ionic strength appears to be the major reason for reduced isometric tension in osmotically compressed intact muscle fibers (86).

The situation is more complex in the case of shortening speed. Increasing sarcomere length does not affect unloaded shortening speed (V_max) for sarcomere lengths between 1.85 and 3.15 µm, but it does reduce shortening speed under load (50, 88). Decreasing the lattice spacing osmotically, however, decreases both loaded and unloaded shortening speed (Fig. 12).

View larger version (16K): [in this window] [in a new window]   FIG. 12.   Maximum shortening speed as a function of osmolarity in single fibers from frog semitendinosus and tibialis muscles. Open circles, Ref. 51; solid circles, Refs. 94, 95, 97. Arrow indicates in vivo osmolarity of 245 mosM.

Osmotic compression using sucrose decreases both P_o and V_max , whereas compression using increased concentrations of permeant ions (e.g., KCl), which raise the ionic concentration without shrinking the lattice, causes a decrease in P_o but no change in V_max . From this, Gulati and Babu (95) conclude that a decreased filament separation reduces V_max but has little effect on P_o , confirming that the reduction in P_o is a result of the increased ionic concentration as the fiber shrinks. In contrast to the effects of sarcomere length on isometric force, increasing sarcomere length of frog single fibers from 1.8 to 3.0 µm causes little change in unloaded shortening speed (49, 87). Thus there are problems relating to the effects of sarcomere length on contraction that can only be resolved through experiments on skinned muscle fibers (see Ref. 205).

View larger version (25K): [in this window] [in a new window]   FIG. 13.   Isometric force as a function of lattice spacing (solid squares) or fiber width in various skinned muscle fibers. Frog semitendinosus: small open circles, Ref. 73; large open circles, Ref. 273; open triangles, Ref. 96. Rat soleus: solid diamonds, Ref. 204. Rat superficial vastus lateralis: solid circles, Ref. 204. Glycerol-extracted rabbit psoas: solid triangles, Ref. 66; solid squares, Refs. 156, 305; open diamonds, Ref. 1. Rabbit soleus: open squares, Ref. 163.

The stiffness of both resting and contracting muscle is increased by lattice compression. There is a substantial increase in the tension during a controlled stretch of resting frog muscle when the lattice is osmotically shrunk (116, 167). Hill explained this effect through (extra) links between filaments. Several suggestions for such additional "bridges" have been made over the years (11, 179, 238). Simmons (257) observed small amounts of sarcomere shortening in fully overlapped frog single fibers as the osmolarity of the external solution was increased by addition of NaCl, suggesting the formation of a small number of additional cross bridges during lattice shrinking.

Some of the problems associated with intact muscle fibers, particularly control of the ionic strength, can be avoided by using skinned preparations. In skinned fibers, the internal solution can be controlled directly. As well, the lattice can easily be shrunk by osmotic stress (see sect. IVB). Much data on skinned muscle have accumulated over the last two decades, but only the general effects of changes in lattice spacing on the physiological behavior of the muscle are discussed here. The effects of external conditions (e.g., pH and ionic strength) on force development and shortening or on the biochemical processes involved have been reviewed elsewhere (28, 29, 76, 78, 255).

In skinned muscle, as the filament lattice or fiber diameter shrinks, isometric force first increases, then decreases (200) (see Fig. 13). The amount of fiber shrinking required to reduce force to zero is ~50% (Fig. 13) and may be species dependent, possibly because of a difference in the proportion of extrafibrillar space in different muscle preparations. When the swelling that occurs upon skinning is taken into account, the relationship between force and lattice spacing is qualitatively similar to that in intact muscle. In both cases, maximal force is developed close to the in vivo spacing (see Table 1).

The V_max value also decreases with lattice shrinking of skinned muscle in a manner similar to the decrease in intact muscle (Fig. 14). At the same time, stiffness increases with decreasing lattice spacing (1, 83, 151, 155, 196).

View larger version (19K): [in this window] [in a new window]   FIG. 14.   Maximum shortening speed as a function of fiber width in various skinned muscle fibers. Frog semitendinosus: open circles, Ref. 273; open triangles, Ref. 77. Rat soleus: solid diamonds, Ref. 204. Rat superficial vastus lateralis: solid circles, Ref. 204. Glycerol-extracted rabbit psoas: solid triangles, Ref. 66.

Changes in mechanical performance as the lattice shrinks or swells have been interpreted by different authors according to frictional/viscous mechanisms (83, 116, 273), changes in cross-bridge geometry, (163), changes in biochemical reaction rates (305), cross-bridge making/breaking rates (96), or in the case of intact fibers, changes in ionic strength (12, 51, 85, 86).

The stiffness increase in both intact and skinned fibers has been related to an increase in "frictional" forces between thick and thin filaments, possibly resulting from additional bridges linking adjacent thick and thin filaments (83, 116, 163). Although it is possible that the increase in stiffness and the changes in V_max that have been observed after lattice shrinkage are related to some such bridging structures, it seems more likely that they represent a frictional effect resulting from the increased closeness and contact of the filaments with each other (see Refs. 94, 95).

A decrease in force and velocity as the lattice shrinks may also be related to changes in ATPase activity, which decreases as the lattice spacing decreases (305). Calcium sensitivity (as measured by a shift in the P_o vs. calcium concentration curve) increases at longer sarcomere lengths (62, 181, 262). Modest osmotic compression also increases calcium sensitivity (up to about the in vivo spacing), but further osmotic compression causes a decrease in calcium sensitivity (73). The decrease in lattice spacing at long sarcomere lengths appears to be the primary cause of the increased calcium sensitivity (69, 73). It should be noted, however, that modest osmotic pressure (e.g., that produced by 5% dextran) has opposite effects on P_o and V_max . At a fixed calcium concentration below full activation, 5% dextran causes an increase in P_o but a decrease in V_max (206). This observation probably reflects the opposite effects of lattice swelling (i.e., reduced osmolarity) on P_o and V_max in intact muscle fibers (cf. Figs. 11 and 12) and of modest lattice compression (toward the in vivo spacing) in skinned fibers (cf. Figs. 13 and 14). The decrease in V_max may indicate a slowing of cross-bridge detachment during lattice compression due to a partial blocking position of tropomyosin (206).

Recently, Adhikari and Fajer (1) studied myosin head (cross-bridge) motions by electron paramagnetic resonance (EPR) in relaxed, rigor, and contracting rabbit psoas muscle under various extents of osmotic compression. For osmotic compression up to ~65% of the (uncompressed) skinned fiber diameter (i.e., with 0 to 12% dextran), only small changes were observed in isometric force and axial stiffness, but EPR rotational correlation times increased threefold, suggesting a modest change in average cross-bridge orientation and motion. Compression between 65 and 50% (using up to 20% dextran) caused isometric tension to fall to zero and stiffness to rise sharply in relaxed muscle, but to fall from a high value to near the resting value in contracting muscle. Over the full range of compression, the rigor stiffness remained high, close to the maximum observed in the contracting case. The EPR correlation times for both relaxed and contracting muscle increased sharply at higher dextran concentrations, but osmotic compression had no effect on the EPR signal in rigor muscle. These data were interpreted as indicating that cross-bridge motion can be significantly restricted during lattice compression (down to 65%) without affecting isometric force development or stiffness, but that further lattice compression results in inhibition of force development, increase in stiffness, and severe restriction of cross-bridge motions as found in rigor muscle.

Although all striated muscles appear to show similar physiological effects from lattice shrinking, it may be a mistake to assume that the causes are the same in each case. Ionic strength or pH may give rise to a compounding of various factors. Further specific experiments are required to clarify the basic causes.

	VI. LATTICE EFFECTS IN OTHER STRIATED MUSCLES

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The structure and the protein composition of vertebrate heart muscle are very similar to that of vertebrate skeletal muscle (154, 229). X-ray diffraction patterns (reviewed in Ref. 184) have been obtained from the papillary and trabecular muscles of a variety of mammalian species and are basically similar to those of skeletal muscle. Heart muscle contains substantial amounts of collagen as shown by the characteristic meridional diffraction pattern based on a 64-nm periodicity (189).

The filament lattice of heart muscle is the same as in skeletal muscle, and it gives rise to the usual equatorial reflections that can be observed out to the 3,0 reflection in the quiescent state (187, 189, 190). In intact muscle, the 1,0 spacing at 2.2 µm is 37 nm, essentially the same as in most vertebrate skeletal muscles (Table 1). Although heart muscle is restricted to a small range of sarcomere lengths (1.9-2.5 µm), probably because of the collagen present, the lattice maintains a constant volume over this range of 3.5 × 10³ µm³ (189), similar to that of amphibian skeletal muscle (Table 1).

The 1,0 and 1,1 intensities in heart muscle are also similar to those in skeletal muscle; I₁₀/I₁₁ is ~3 in quiescent (relaxed) muscle and 0.4 in rigor (187). During cyclic contraction (or beating) in perfused dog papillary muscle at 37°C, I₁₀/I₁₁ oscillates between ~1.7 and 0.7, decreasing as tension rises and vice versa (193) [similar results (unpublished) have been obtained by A. Hamilton and B. M. Millman using isolated cat papillary muscle]. Because the intensity ratios during cycling are always greater than the quiescent ratio, this implies that some cross bridges are always in the region of the thin filaments, even in the diastolic part of the cycle.

Moderate osmotic compression (up to ~10%) affects isometric force development in skinned preparations similarly to intact muscle, causing an increase in force; greater compression causes decreased force (283). Changes in isometric forces are correlated with changes in calcium sensitivity, which varies with both sarcomere length and osmotic compression (64, 283). A decrease in filament separation is probably the primary cause of the increase in calcium sensitivity (69). The resulting length dependence of cardiac activation may largely explain the relationship between myocardial force development and ventricular filling pressure known as the Frank-Starling relationship (see Ref. 166).

Chemically skinned rat papillary muscle was studied by Matsubara et al. (188). It develops tension when calcium activated, much as does skeletal muscle. Heart muscle differs from skeletal muscle, however, in the calcium level at which the equatorial intensities change. Calcium activation causes I₁₀ to drop and I₁₁ to rise at a pCa of ~6, whereas force development requires a pCa of 0.5 higher. This indicates that a significant number of cross bridges are in the vicinity of the thin filaments without producing tension at low calcium concentration, possibly a state similar to the weakly bound cross bridges observed with skeletal muscle in low ionic strength solutions (36) (see sect. VIIC).

Invertebrate striated muscles tend to show more variation in structure (and function) than vertebrate striated muscles. Most thick filaments from invertebrate muscle are thicker because the protein paramyosin is present in their cores in addition to myosin (see Refs. 209, 258, 287). Thick filament lengths range from ~1.7 µm in scallop striated adductor muscle to ~10 µm in barnacle depressor muscle (Table 5). The striated scallop adductor, which has filament and sarcomere lengths similar to those of vertebrate striated muscle (213), also has physiological behavior closest to that of frog sartorius muscle (123, 209, 239).

All the invertebrate striated muscles mentioned above have thick filaments arranged in an hexagonal lattice with thin filaments between the thick, but the number and positions of the thin filaments vary (Fig. 15). In insect flight (112, 243) and crayfish abdominal muscle (293), there are 3 thin filaments for every thick filament arranged in dyad positions (one thin filament between each pair of thick filaments; see Fig. 15, A and C), whereas in scallop adductor (213), crustacean leg muscle (6, 293), Limulus telson muscle (45), and barnacle muscle (70), there are 12 thin filaments around each thick filament (a 6:1 ratio) arranged as in Figure 15, B or D. In the former type of lattice (3:1, thin to thick), the 2,0 reflection is much stronger than the 1,1 reflection so that the 1,0 and 2,0 reflections dominate the equatorial pattern. In crustacean muscles, the equatorial X-ray diffraction pattern contains strong reflections out to the 4,1 order, which have been analyzed by Fourier synthesis to show thick filaments with a low-density or hollow interior (279, 293). The equatorial and layer-line X-ray diffraction pattern from insect flight muscle in rigor has been analyzed in conjunction with cross-bridge modeling (119), but this muscle shows no evidence of hollow thick filaments. (Occasional electron microscope images show a low-density region in the center of some thick filaments, but this is likely because stain has not penetrated to the center of the thick filament.)

View larger version (19K): [in this window] [in a new window]   FIG. 15.   A-band filament lattices in invertebrate muscles. A: insect flight muscle (207). B: scallop striated adductor muscle (213). C: crayfish abdominal muscle (293). D: crayfish and crab leg muscle (6, 293).

Despite the variations in lattice structure in different invertebrate striated muscles and their difference from vertebrate striated and heart muscle, the nature of lattice changes and their effect on contraction are remarkably similar in all vertebrate and invertebrate striated muscles.

Early X-ray diffraction studies on both vertebrate and invertebrate muscle have been reviewed by Miller and Tregear (208), and their review includes a discussion of the insect lattice and equatorial reflections under relaxed, rigor, and activated states, including the case of oscillating calcium-activated muscle. During the course of forced oscillations of glycerol-extracted Lethocerus (water bug) flight muscle, the equatorial reflections change in much the same way as in vertebrate muscle (I₁₀ decreases in rigor while I₂₀ increases), indicating that 10-20% of the cross bridges are close to (attached to?) the thin filaments during the cycle, the actual number oscillating with the tension change with a slight delay (10). The changes in insect flight muscle (and other invertebrate striated muscles as well) suggest that the contractile processes involved are similar to those of vertebrate striated muscles.

In those invertebrate striated muscles examined to date (crayfish leg, Ref. 6; scallop, Ref. 213; barnacle depressor, Ref. 70), the filament lattice of the intact muscle shows a constant-volume behavior when the sarcomere is lengthened similar to that observed in vertebrate striated muscle. Both lattice spacing and lattice volume in invertebrate muscle are larger than in vertebrate muscle (Table 5).

Like vertebrate muscle (246), when invertebrate muscle is skinned, the lattice swells and no longer shows constant volume behavior (crayfish leg, Ref. 9; barnacle depressor, Ref. 70). The skinned muscle lattice will shrink osmotically with dextran (scallop adductor, Ref. 214; crab leg, Ref. 176). As in vertebrate striated muscle, when rigor is induced in a swollen, skinned fiber, the lattice shrinks, whereas the lattice swells in osmotically compressed fibers (8). When isometric force, developed in response to calcium activation, was measured in skinned crayfish leg muscle fibers with increasing amounts of dextran in the bathing solution, the force increased as the lattice shrank to somewhat less than the original spacing (d₁₀ reduced from ~60 to 40 nm) and then fell to zero as the lattice shrank further (to 30 nm) (7).

Filament charges have been measured in crayfish muscle by microelectrode techniques and, as in the case of vertebrate muscle (see sect. IVD), it appears that electrostatic forces are the primary repulsive forces stabilizing the filament lattice in relaxed invertebrate muscle (2).

	VII. FORCES STABILIZING THE A-BAND LATTICE

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The stability and size of the A-band filament lattice are a result of a balance between several types of forces, acting either between the filaments or on the outside of the muscle fibers or fibrils. Maughan and Godt (198) found that changes in diameter of mechanically skinned frog semitendinosus muscle fibers over a range of applied osmotic pressures could be approximated by a combination of elastic, entropic, electrostatic, and compressive forces. Other forces, e.g., structural (186) and van der Waals (38, 53, 218), have also been associated with the filament lattice. The various forces that may be involved are described below, and the overall role of each is assessed under different physiological conditions.

In muscle sarcomeres under normal physiological conditions, both thick and thin filaments carry a net negative charge, which will give rise to a repulsive electrostatic force between the filaments (53). Long-range electrostatic forces between the filaments will be governed by the filament diameters and charge (a function of solution pH), along with the ionic strength of the solution around the filaments, which will tend to shield the charges (218).

Long-range electrostatic force (or pressure) can be calculated, based on solutions to the Poisson-Boltzmann equation (38, 53, 218), and can be compared with lattice pressure measured directly by the osmotic stress technique (see sect. IVB). Such comparisons support the existence of a significant electrostatic component to the radial forces in the relaxed, contracting and rigor lattices.

Calculations of electrostatic forces between adjacent pairs of thick filaments, adjacent pairs of thin filaments, and adjacent thick and thin filaments demonstrate that at shorter sarcomere lengths, thick-thin filament forces dominate (218). But as the sarcomere length increases to the point of nonoverlap between thick and thin filaments, thick-thick and thin-thin filament forces take over. Because electrostatic forces between nonadjacent filaments are very much smaller than those between adjacent filaments, the former can be neglected in the calculations of lattice forces (218). Electrostatic calculations predict a slow decrease in lattice spacing as sarcomere length is increased until at some point, just before filament overlap ceases (at 3.6 µm), a greater decrease in spacing is predicted.

Data from osmotic stress experiments on relaxed muscle are, in general, consistent with electrostatic calculations (see Figs. 16 and 17). As sarcomere length in skinned muscles is increased, the lattice spacing decreases gradually until, at ~3 µm, a much more rapid spacing decrease is observed (256; B. M. Millman and G. F. Elliott, unpublished data). When lattice spacings at full overlap and nonoverlap are compared over a wide range of osmotic compressions, the spacing differences (d_10 short  d_10 long) range between 5 and 8 nm, close to those predicted from electrostatic calculations (215; Fig. 7). It should be noted, however, that cytoskeletal and extrafibrillar components can limit lattice swelling, particularly in chemically skinned muscle fibers (115), and that the contribution of such passive components to radial forces may vary with sarcomere length.

View larger version (16K): [in this window] [in a new window]   FIG. 16.   Lattice spacing as a function of applied osmotic pressure in chemically skinned frog sartorius muscle in relaxing solution. Solid circles, pH 5.5; open circles, pH 7.0; open triangles, pH 8.5 (Irving and Millman, unpublished data). Lines are electrostatic pressures calculated as in Reference 218 for an ionic strength of 114 mM, thick and thin filament diameters of 26 and 9.5 nm, thin filament charge of 12 electrons/nm, and thick filament charge of 1 (dotted line), 10 (solid line), and 100 electrons/nm (dashed line).

View larger version (18K): [in this window] [in a new window]   FIG. 17.   Lattice spacing as a function of applied osmotic pressure in chemically skinned frog sartorius muscle in relaxing solution at the following ionic strengths: 114 mM (open circles), 38 mM (solid circles), and 24 mM (open triangles). Lines are electrostatic pressure calculated as in solid line of Fig. 16 for appropriate ionic strength. [Data from Irving (142).]

The relationship between externally applied osmotic pressure and lattice spacing is in agreement, at least qualitatively, with changes predicted from calculation of electrostatic pressure as filament charge (pH) or ionic strength are varied (see sect. VII, B and C). These data indicate that electrostatic forces between filaments are one of the factors determining lattice spacing, except perhaps at extreme lattice spacings.

Electrostatic forces (both long and short range) may, of course, play an important role in the attachment of cross bridges to the thin filaments. Given the recent crystallographic determination of the atomic structures of myosin S1 (241) and actin (153), this aspect can now be explored along with the specific effects of such forces on the filament lattice (46, 113, 295).

Decreasing the pH of the solution around the filament lattice down to the isoelectric point (pH <5), particularly at long sarcomere lengths where thick-thin filament interaction is minimized, will decrease the charge on the filaments, reduce electrostatic repulsion, and tend to cause the lattice or fiber to shrink; increasing the pH, and thus the filament charge, will increase electrostatic repulsion and tend to cause the lattice and fiber to swell (142, 198, 211, 220, 236, 246). As pH is further reduced below the isoelectric point, the lattice tends to swell (57, 142, 246).

Changes in lattice spacing as pH is varied are in qualitative agreement with changes in electrostatic pressure, calulated for changes in filament charge (Fig. 16). This has been found in relaxed frog muscle (142, 195, 211, 215, 276) and rabbit psoas muscle in rigor (195, 220, 245). It has also been found in frog muscle in rigor and relaxed rabbit psoas muscle (144, 216; B. M. Millman and T. C. Irving, unpublished data). The magnitude of the changes observed, however, suggests that pH may also cause a swelling of the thick filament charge diameter as pH is increased (211).

An increase in ionic strength will increase the ionic shielding of filament charges and tend to cause a decrease in lattice spacing. At an ionic strength of about one molar, the shielding effect will saturate, and no significant further lattice shrinking is normally expected for ionic strengths above one molar (218). A decrease in ionic strength will reduce ionic shielding, increase electrostatic repulsion, and tend to cause lattice swelling.

The effect of changes in ionic strength on the filament lattice is more complex than those of pH. In rabbit psoas muscle in rigor, either glycerol extracted or skinned, the lattice shrinks with increasing ionic strength up to ~100 mM (246; Millman and Irving, unpublished data). When electrostatic pressure was calculated and compared with data from osmotic stress experiments on rabbit psoas in rigor, there was reasonable agreement (218, 220). In rigor solutions with ionic strengths >100 mM, however, the lattice in rabbit muscle expands (216, 246) or does not change (36), contrary to electrostatic predictions. Similar swelling behavior, which is independent of the monovalent cation used to increase ionic strength, is seen with fiber diameter (228), but the fiber swells much more than the filament lattice. Because thick (myosin) filaments are known to dissolve in high-salt solutions (100, 110) but remain in the region of the A band (203), it is probable that the observed lattice/fiber expansion in high ionic strength is a result of swelling of the thick filaments followed by their dissolution. At ionic strengths where the myosin filaments are completely dissolved, a thin-filament lattice is observed with a spacing that appears to be determined by entropic (osmotic) forces between myosin molecules that are in solution (G. Offer, P. Knight, W. Gilmore, B. Millman, and B. Nickel, unpublished data).

The situation in relaxed muscle appears even more confusing. Relaxed, chemically skinned frog sartorius muscle shrinks as the ionic strength is increased from 24 to 114 mM as expected for an electrostatic system (142), and observed lattice changes during osmotic stress experiments are consistent with calculated electrostatic pressure curves (Fig. 17). On the other hand, the width of relaxed mechanically skinned frog fibers increases as the ionic strength rises from 100 to 280 mM (198). Overall, it appears that as ionic strength is increased from a few to several hundred millimolar, the filament lattice first shrinks as electrostatic repulsion is reduced through an increase in ionic shielding and then increases as the thick filaments come apart. The position for minimum spacing probably varies somewhat with the particular muscle and ionic conditions, but generally lies close to 100 mM (see Ref. 246; Fig. 2).

In the case of skinned rabbit psoas muscle in relaxing solution, the filament lattice shrinks as ionic strength is decreased from 200 to 20 mM (36, 232), even at long sarcomere lengths where there is no filament overlap (33). The net charge on the thick filaments is reduced (by ~25%) as ionic strength is decreased to 20 mM (21), but this reduction cannot explain the observed lattice changes. The situation may be complicated by a shift in the position of or charge distribution on the myosin head (or cross bridge) as ionic strength falls. At low temperatures (5-20°C) and an ionic strength of ~20 mM, skinned rabbit psoas muscle shows a small increase in stiffness (30) and a change in the 1,0 and 1,1 equatorial reflection intensities in the same direction, but with a magnitude different from that observed when muscle moves from rest to either contracting or rigor states (34, 36, 194). This state, referred to as weakly bound cross bridges, is thought to represent an intermediate cross-bridge state in the normal contraction cycle (27, 35, 161).

In skeletal muscle from frog (142, 291) and fish (260), much smaller changes in equatorial intensities have been observed when ionic strength is lowered at low temperatures (5-10°C). Furthermore, ramp stretches of skinned, single fibers from frog muscle in low ionic strength solutions at 15°C show no evidence for weakly binding bridges (15). It is important to note that the temperatures used in the frog and fish studies are within normal body temperatures for these species, whereas the temperature used in the rabbit muscle experiments is 15-30°C below the normal body temperature for rabbits (260). It is still not clear whether or not weakly bound cross bridges are found in most muscles in the physiological state, but they do, at least, provide an interesting tool for studying the cross-bridge cycle.

The above results clearly show that ionic strength affects much more than electrostatic forces or filament charges. Changes in ionic strength may modify the structure of the myosin filament as a whole, or the charge on individual heads whether they are forming cross bridges or not. It has also been suggested that the cytoskeletal network, which can limit lattice spacing at longer sarcomere lengths, may itself be sensitive to ionic strength (33). We still have much to learn about the role of ionic strength on the filament lattice, but the results do not require another mechanism for setting lattice spacing in relaxed muscle beyond a balance between repulsive electrostatic forces (plus contact forces at small spacings) and attractive or constraining forces from structural components in or outside the fibril.

Van der Waals, or London forces, are molecular attractive forces resulting from dipole interactions and extending over a few tens of nanometers (147, 230). They have been proposed as the attractive force that limits swelling of the lattice when there is no other restraining force (37, 53, 218). Experiments on simpler gels systems (tobacco mosaic virus, Refs. 217, 218; cornea, Ref. 58) along with force calculations on the muscle lattice indicate that van der Waals forces are too small, relative to thermal (kT) forces, to limit swelling at physiological temperatures. They can be, however, a contributing factor to lattice stability (211).

A repulsive or swelling force is produced from the thermal motion (~kT) of particles or molecules in the sarcoplasm (198). If the internal osmolarity is greater than that of the external bathing solution, there will be a net swelling pressure within the lattice. This effect may be important in situations where large molecules, with a large osmotic contribution, are constrained to the sarcoplasm inside the lattice. An example is the case of myosin molecules, dissolved from thick filaments but held within the lattice by attachment to actin filaments, a situation that can occur with skinned (rabbit) muscle in rigor at high ionic strength (see sect. VIIC).

Entopic pressure can be calculated as the difference in osmotic concentration times kT, where k is the Boltzmann constant (1.38 × 10²³ J/K) and T is absolute temperature.

The major structure that restrains the A-band lattice is the M line, which holds the thick filaments together at their centers. The structure of this region in vertebrate striated muscle has been described in detail (173, 258), but its quantitative contribution to radial forces is unknown. One would expect, however, that the M line acts to limit swelling and possibly shrinking of the lattice beyond the normal range of physiological solutions.

Similarly, the Z line will tend to constrain swelling and shrinking at the center of the I band, but its contribution to A-band stability is probably minor. As discussed in section IID, there is a distinct Z-line reflection seen in the equatorial X-ray diffraction pattern, by means of which Z-line swelling and shrinking can be monitored. Over most of the "normal" physiological range, the Z-line lattice changes in proportion to the A band, but at extreme swelling or shrinking, the I-band spacing changes less than the A-band spacing (146), thus tending to constrain swelling in the I band and at the ends of the A band.

If the thin filaments from the A-band hexagonal lattice and from the Z-line square lattice occupy the same cross-sectional area, the Z-line spacing would equal d₁₀/3^1/4 = d₁₀/1.316. In practice, over a wide range of solution osmolarities, the Z-line spacing is smaller than this (~d₁₀/1.41-1.45) (146). This means that under hydrated conditions, the sarcomere should have a bowed appearance, being wider in the A bands than at the Z lines. This effect is seen occasionally in electron micrographs (22, 284). Most electron micrographs, however, show the sarcomere as having a uniform cylindrical shape, probably because of lateral A-band shrinkage during preparation (see sect. IIA).

Other structural constraints within the filament lattice can arise from the backbone structure of the sarcomere (see sect. IIC). The precise form of the backbone structures is at present unclear, and calculations of their contribution to radial forces have yet to be attempted. Because none of the individual components can be measured specifically, their contributions to radial lattice forces have been grouped together and considered as a single force.

Another approach to the structural forces was used by Maughan and Godt (198), who considered an elastic component of force resulting from entropic changes associated with configurational changes of the protein network in the sarcomere. Comparison of their calculated forces with measured passive tension gave qualitative, but not quantitative, agreement.

There are two major components to the extracellular force: the cell membrane and the nonmembranous sarcolemma structures, such as collagen and elastin. The cell membrane, as discussed in sect. III, A and C, is the major factor in determining lattice spacing in intact muscle, but its effect will be absent in skinned muscle. The sarcolemmal components are normally removed in mechanically skinned fibers. In chemically skinned fibers, they may be present in whole or part, depending on the specific extraction procedures (115). Higuchi (114) showed that lattice swelling, particularly at long sarcomere lengths, can be limited by the sarcolemma and that if chemically skinned fibers are treated with trypsin to break down the extracellular matrix, further swelling ensues.

Because the extent of sarcolemmal removal varies considerably with different skinning techniques, one would expect a wide range of contributions from these structures. This probably accounts for much of the variability in equilibrium lattice spacings observed in skinned muscles or fibers, particularly when there is no external osmotic pressure compressing the lattice.

Cross bridges linking thick and thin filaments will normally be at an angle to the filament axis, and this angle may vary considerably with the individual cross bridge and the physiological state of the muscle. Schoenberg, in a detailed theoretical treatment of this problem (252, 253), pointed out that at any cross-bridge angle (other than 0 or 90°), longitudinal stress on the cross bridge will give rise to a force in the radial direction (i.e., perpendicular to the filament axis). In his calculations, Schoenberg (252, 253) showed that the relationship between axial and radial force will depend on the geometry and orientation of the cross bridge. In the simplest models, axial force would be independent of filament separation and depend only on the amount of filament overlap and the fraction of cross bridges attached (252), but, in general, there will be a radial component to the force vector that will vary as the interfilament separation changes (253). On the basis of the structural evidence available at that time, Schoenberg (253) suggested that the radial force could be about one-tenth of the axial force.

At the same time that Schoenberg was analyzing the effects of cross-bridge geometry, several groups started using large inert polymers to exert osmotic force on the filament lattice (see sect. IVB). The results of these osmotic stress experiments have demonstrated the presence of radial forces in skinned and intact muscle and have enabled calculations of the direction and magnitude of such radial forces. The first published results from osmotic stress experiments were by Maughan and Godt (197-199), who used mechanically skinned frog fibers to measure changes in fiber width in response to different concentrations of PVP in relaxed and rigor fibers. They defined a "radial force" as that force, perpendicular to the fiber axis, required to restore the rigor fiber (or lattice) to the width (or spacing) found in the relaxed fiber (i.e., in an unstressed skinned fiber). They assumed that the forces they observed were entirely due to cross bridges and determined radial forces per thick filament that were of the same order of magnitude as the axial forces (199) (Table 6). Maughan and Godt (199) also compared the radial stiffness (K), which they defined as equal to d·D²/dD², where D is fiber width and  is applied osmotic pressure, and found that during rigor, the radial stiffness was about two orders of magnitude smaller than the Young's modulus in the axial direction.

Using a slightly different measure of radial stiffness (K = d·D/dD), Umazume and Kasuga (275) showed that stiffness in frog fibers is about four times greater in rigor than in relaxation and that with pyrophosphate (PP_i) the stiffness is intermediate. Both rigor and PP_i stiffness were increased almost twofold in the presence of free Ca²⁺ (8 × 10⁷ M). They also showed that the radial stiffness in rigor decreased at longer sarcomere lengths, reaching the resting value when there was no filament overlap (i.e., sarcomere lengths >3.6 µm), demonstrating that the stiffness was due to cross bridges. Later, with the use of similar techniques to measure radial stiffness as a function of lattice spacing, a sharp change in stiffness was found at d₁₀ of 35 nm with full filament overlap and at d₁₀ of 29 nm at saromere lengths where there was no filament overlap (274). This was interpreted as indicating contact between thick filament projections (myosin heads) and adjacent thin or thick filaments, respectively, at these lattice spacings. These results are similar to those obtained by Millman and Irving (215), although the interpretation differs somewhat.

Matsubara and colleagues (82, 186), in a detailed study of the effects of osmotic stress directly on the filament lattice, used mechanically skinned frog skeletal muscle fibers over a full range of sarcomere lengths. They found that lattice spacing was linearly related to sarcomere length under both relaxed and rigor conditions and that the difference between relaxed and rigor spacings was proportional to filament overlap in both the presence and absence of osmotic agents (PVP). They considered the radial forces that could be present in the lattice, concluded that electrostatic and van der Waals forces were small, and analyzed their data as a balance among a radial cross-bridge component, a structural component and the applied osmotic pressure (186). They determined radial and axial forces per thick filament similar to those determined by Maughan and Godt (199) (Table 6).

Using chemically skinned mouse toe muscle, Matsubara and colleagues (191) also found that the lattice spacing of the relaxed skinned fiber, when not osmotically stressed, decreased upon shifting into rigor or being calcium activated. Osmotic compression caused both relaxed and calcium-activated fibers to shrink. At a lattice spacing (d₁₀) of 38 nm, the same spacing as found in the intact muscle, there was no spacing change on moving into either the rigor or activated state. Furthermore, based on the equatorial intensity ratio I₁₀/I₁₁ (see sect. IIIE), they concluded that the number of cross bridges formed during calcium activation was almost the same (98%) as in rigor muscle. The radial and axial forces they calculated were similar to those determined earlier for frog muscle fibers (Table 6).

Osmotic compression of chemically skinned rabbit psoas fibers was studied by Brenner and Yu (32), who showed that the lattice spacing (d₁₀) decreased from its value in relaxed, unstressed fibers (44 nm) to that found in rigor fibers (38 nm) during full calcium activation. The spacing decrease was proportional to the isometric force developed during calcium activation. They interpreted this lattice shrinking as resulting from a radial component of cross-bridge force but did not determine the magnitude of the radial force at this time. Later, they used dextran to shrink the lattice and found that when osmotically compressed to d₁₀ of 34 nm there was no change in lattice spacing on calcium activation (33). With greater osmotic compression (d₁₀ <34 nm), the lattice swelled on calcium activation; with less (d₁₀ >34 nm), the lattice shrunk on activation. The equilibrium spacing or point at which no spacing change occurred on activation (d₁₀ = 34 nm) differs from that found by Matsubara et al. (191) in mouse toe muscle (d₁₀ = 38 nm) for reasons that are unclear. Brenner and Yu (32) suggest that either the fiber preparation technique (Matsubara et al. used no ATP back-up system, which may have resulted in some rigor) or the longer periods over which Matsubara's experiments were run may have caused a (partial) shift into rigor (where the lattice spacing for zero change is ~38 nm). However, apart from the different species, the temperature in the experiments differed; Brenner and Yu kept their fibers at 5-7°C, whereas the fibers of Matsubara et al. (191) were at 21°C. It is known that at room temperature and above, the cross-bridge ordering of rabbit and chicken skeletal muscle, as seen in electron micrographs, is increased as compared with at low temperature (e.g., 4°C), whereas that of frog and fish skeletal muscle is unaffected by temperature (157, 159, 160). Also, in rabbit psoas muscle at the higher temperatures, the X-ray layer-line intensities are stronger (171, 288) and the equatorial 1,0 and 1,1 intensities are more comparable to those found in frog skeletal muscle (171).

Most calculations of lattice forces have assumed that the cross-bridge force is the only component that changes during a change in physiological state. But the net surface charge on the thick filaments changes with the muscle's state (Table 3), as well as the radial position of the cross bridges, and these can change the magnitude of electrostatic forces (218, 263). These effects, along with van der Waals forces, were considered in calculations by Millman and Irving (215). They found that at lattice spacings above the equilibrium spacing, which was near the in vivo spacing, the lattice shrinks upon being activated or moving into rigor. At spacings below the equilibrium spacing, however, the lattice swells when it contracts or moves into rigor (see sects. IIID and IVE). The (osmotic) pressure change required to restore lattice dimensions in this second regime (below equilibrium spacing) is much greater, indicating much greater radial forces. Millman and Irving (215) interpreted this difference as arising from two different radial forces: a strong one associated with rigor (~80 pN/myosin head) and a much weaker one associated with relaxation (~2.6 pN/myosin head). With the use of the above values for radial forces and surface charges from Table 3, lattice spacings were modeled under osmotic stress in relaxed and rigor frog skeletal muscle at both short (2.3 µm) and nonoverlap (>3.6 µm) sarcomere lengths and found to give reasonable fits to the data (215; Fig. 7).

Xu et al. (290) applied the osmotic stress technique in skinned rabbit muscle fibers to study the radial force, particularly the equilibrium spacing or point at which contraction causes no lattice spacing change, i.e., no radial cross-bridge force, in the presence of several different nucleotides that are believed to produce different states of the cross-bridge cycle. The spacing where there is no radial force was found to depend on the particular nucleotide used but to be independent of the concentration of the nucleotide (Table 7). Furthermore, the "radial equilibrium length" for cross bridges varies in different states from 10.5 nm for force-generating cross bridges to 12.0 nm for weakly bound cross bridges and 13.0 nm for rigor cross bridges (31). Thus radial stiffness depends on cross-bridge state and not only on the number of cross bridges or the axial stiffness. As information becomes available on cross-bridge configurations in different (nucleotide) states, this information may help to elucidate the relation between cross-bridge structure and function.

Calculations of radial force in several skinned muscle preparations give ~500 pN/thick filament in either rigor or Ca²⁺-activated states (Table 6). If there are six cross bridges per 14.3 nm along the thick filament in rigor, there will be an average radial force per cross bridge of ~2 pN.

The radial force can be coupled with the the longitudinal force measured from physiological experiments (Table 6) to estimate the effective angle between the "neck" of the cross bridge (S2) and the filament axis. Under zero compression (swollen fibers), radial and longitudinal forces per cross bridge are approximately equal (Table 6). In the simplest scenario (252), this implies an effective angle in the vicinity of 45°. At the somewhat smaller lattice spacing of the normal intact fiber, the angle would be smaller. At moderate to high compression, where the radial force is >10 times the longitudinal force, the cross-bridge angle would be much smaller. This variation in cross-bridge angle is consistent with the observation that radial stiffness does not always change in parallel with longitudinal stiffness as measured by stretches or releases (290). The actual angles of individual cross bridges will, however, depend on a number a factors (252): the number of cross bridges acting at any time, the relation between force and stiffness in both radial and longitudinal directions, and whether or not myosin heads that are not forming cross bridges can contribute to radial stiffness.

Changes of lattice spacing in intact muscle fibers would be expected to be much smaller than in skinned fibers because of constraints exerted by the cell membrane (16, 252). Such changes have recently been determined during isometric tetani, stretches, and releases in intact single fibers of frog skeletal muscle that show an increase in d₁₀ as tension is developed (41, 91). These measurements are complicated by the relatively large spacing increase that accompanies sarcomere shortening because of series elasticity. Correction for such shortening in normal Ringer solutions results in a small decrease in lattice volume, effectively reversing the direction of lattice spacing change; this result was confirmed in length-clamp experiments where a lattice volume decrease was observed directly (41) and during tension recovery after ramp releases or stretches during isometric tetani (40). Experiments where the osmolarity of the Ringer solutions was varied showed that in solutions of normal tonicity there was an early lattice expansion, all or most of which could be explained by sarcomere shortening, followed by a small lattice compression (16). In hypertonic solutions (1.4 times isotonic), there was virtually no change in lattice spacing, whereas in hypotonic solutions (0.8 times isotonic), much larger spacing changes were observed (16, 91). Very similar lattice changes during isometric tetani have been observed in whole frog sartorius muscles over a range of external osmolarities (Fig. 8). During isotonic shortening in frog single fibers, there is a lattice expansion that cannot be accounted for by changes in sarcomere length (16).

The above results show that during contraction of intact muscle, constant lattice volume is not always maintained, particularly when the lattice is osmotically compressed. In such cases, there can be substantial lattice expansion. This effect was missed in earlier experiments (60, 107), probably because of the smallness of the change in isotonic Ringer solution and the long times over which the early experiments were continued, which enabled long-term effects to mask any small volume changes. The newer results indicate the presence of a radial force associated with contraction, similar to that observed in skinned preparations, which is expansive in compressed lattices, may be compressive in swollen lattice, and is quite small in the lattice of fibers near in vivo conditions. There have been some recent attempts to model the effects of osmotic compression on lattice structure and forces (39, 89, 90, 222), but at this time, these efforts remain speculative, largely because of data limitations. Calculation of the radial force in intact muscle is much more difficult than in skinned fibers because of the effects of the cell membrane that controls ionic movement and volume in the intact case. Recently, an attempt has been made to tackle this problem (212), and it is summarized in section VIII.

Both P_ES and P_OM are functions of ionic strength and osmolarity. Ionic strength and osmolarity inside the intact fiber were calculated assuming that "osmotically active" water occupies 70% of the lattice volume in normal Ringer solution (219). The ionic strength and osmolarity inside the intact fiber in normal Ringer solution were estimated from the data of Godt and Maughan (74) as 178 mM and 244.2 mosM, respectively. The latter assumed a transmembrane osmolarity difference of 0.8 mosM, estimated from the lattice swelling following skinning (215). Ionic strength and osmolarity in swollen and shrunken lattices were calculated by dividing the values in Ringer solution by the internal water volume relative to that in normal Ringer. Electrostatic pressure was determined as described by Millman and Irving (215) (see sect. VIIA).

The results of this calculation for tetanic contraction (using the data in Fig. 8) are shown in Figure 18. Calculation from relaxed, skinned muscle (where P_XB is absent) showed that P_PST is small between 245 and 300 mosM (Fig. 18, open circles). It was assumed to be the same in skinned and intact muscle and significant only at very large or very small spacings (Fig. 18, solid line). Over most of the spacing range, electrostatic pressure (Fig. 18, solid circles) is very small. The radial (cross bridge) pressure resisting compression (Fig. 18, triangles) was found to increase roughly linearly as the lattice was compressed. The slope of the pressure-spacing curve (Fig. 18, dashed line), which gives a measure of the average radial stiffness during contraction (calculated as ·d₁₀/d₁₀ , see sect. VIIH), is ~80 × 10⁴ N/m², considerably larger than that found for relaxed and rigor radial stiffness in skinned fibers (275). This radial stiffness corresponds to an outward radial force per thick filament during contraction of ~3 × 10⁹ N (calculated as in Table 6) or an average radial force per cross bridge of ~12 pN.

View larger version (17K): [in this window] [in a new window]   FIG. 18.   Lattice pressure as a function of lattice spacing in isometric tetanic contractions of frog sartorius muscle. Data are from Fig. 8. Positive pressures represent compressive forces. Open circles and heavy solid line, passive structural pressure (PPST); solid circles and dotted line, electrostatic pressure (PES); open triangles and dashed line, cross-bridge pressure (PXB). Dashed line is least-squares regression for PXB.

	VIII. CONCLUSIONS

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The conclusions below apply to all vertebrate and invertebrate striated muscles studied to date.

1) The filament A-band lattice can shrink by as much as 30% of its volume when compressed osmotically by hypertonic solutions in the intact muscle, or bathing solutions containing high concentrations of impenetrant osmotic agents in the case of skinned muscle fibers. Swelling to a lesser extent (~15%) can be induced in living muscle by hyposmotic solutions or by the removal of the cell membrane during the skinning process. Over most of this range, the lattice behaves as a simple osmometer.

2) Lattice shrinkage from the in vivo spacing in either intact or skinned muscle is usually accompanied by a reduction of physiological performance. Isometric force and shortening speed fall, stiffness increases, and calcium sensitivity decreases as the lattice shrinks. Isometric tension falls by ~80% when the volume decreases by ~50%. Shortening speed falls similarly but drops more rapidly than force at larger lattice spacings. Stiffness increases as the lattice spacing decreases, probably because of frictional effects. There is less change in physiological performance as the lattice swells above the in vivo spacing; isometric force and calcium sensitivity drop, but shortening speed increases.

3) Lattice spacing decreases with sarcomere length in both intact and skinned fibers. In intact muscle, except for highly swollen or shrunken conditions, the lattice spacing changes with sarcomere length so as to give a constant lattice volume.

In skinned muscle, the lattice spacing is governed by a balance between repulsive electrostatic forces and various structural forces (M band, Z line, cytoskeletal, cross bridge). Because small differences in skinning conditions and in the composition and pH of the bathing solution can have significant effects on both electrostatic and structural forces, the actual position of force balance, and thus the equilibrium spacing, can be quite variable.

4) A-band lattice stability results from a balance of forces within and around the fiber. Except under conditions of extreme compression, where steric interference of the filaments and cross bridges limits further shrinking, the chief swelling force in relaxed muscle is probably electrostatic repulsion between the negatively charged thick and thin filaments. Over the physiological range, this force is limited by osmotic forces across the membrane in intact muscle and by other structural forces in skinned muscle.

5) When skinned muscles contract or move into rigor, radial forces from the cross bridges are added to electrostatic and structural forces. The cross-bridge forces expand a compressed lattice and compress a swollen one, thus tending to bring the spacing of shrunken or swollen lattice closer to an equilibrium spacing, which is usually close to that found in the in vivo state. During contractions in vivo, there are similar but smaller changes in lattice spacing. Large spacings, produced by low ionic strength or hypotonic solutions, appear to be limited by external structural forces that control lattice swelling.

6) By osmotically stressing muscle fibers under different physiological conditions, estimates can be made of the radial contributions from different types of forces as a function of lattice spacing. From these radial force components, the contribution of cross bridges to radial force can be calculated. From these, estimates can be made of the average effective angle between a cross bridge and the filament axis.

	ACKNOWLEDGEMENTS

  I am grateful to the Natural Sciences and Engineering Research Council of Canada for grant support while writing this review and to many collegues, particularly Drs. Gerald Elliott, Bob Godt, Tom Irving, Don Stevens, and Roy Worthington, for discussions and comments on the text.

	FOOTNOTES

¹   In some cases, a muscle can be studied in vivo; for example, Worthington (286) taped a blowfly to the slits of his X-ray camera so that the X-ray beam passed through the flight muscles in the insect's thorax. After a 5-h exposure, during which a diffraction pattern was recorded, the fly was released and flew off  the ultimate in experimental control.

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