I. INTRODUCTION

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Thanks to the pioneering work by W. O. Fenn during the 1930s, it was convincingly demonstrated that K⁺ was lost from skeletal muscles during repeated contractions (194). Frog, rat, and cat muscles were studied during direct and indirect stimulation as well as during voluntary contractions. All showed the same general pattern of K⁺ loss (192, 193). Simultaneous changes of intracellular Na⁺ were also described, and both K⁺ and Na⁺ changes were monitored during recovery (195).

However, a number questions were unresolved, such as which mechanisms on the sarcolemmal level cause these ion shifts, i.e., change in distribution between compartments? What is the magnitude of the changes in terms of content or concentration in the various spaces (intracellular, interstitial, and vascular spaces)? How are the K⁺ fluxes regulated during muscle activity as well as during recovery? Muscle activity refers to the generation of action potentials in the muscle that may lead to development of force and/or shortening. Special attention must in this context be paid to the 1997 Danish Nobel prize winner in Chemistry J. C. Skou, who in 1957 presented convincing evidence for the existence of an enzyme system involved in the active extrusion of Na⁺ from nerve fibers (603). Through a series of systematic studies (604-606) he was able to ascertain the molecular basis for active membrane transport systems and later reviewed the enzymatic basis for active transport of Na⁺ and K⁺ across the cell membrane in Physiological Reviews (607). Today this enzyme system is commonly referred to as the Na⁺-K⁺ pump and has been the focus of attention of several more recent reviews (99, 103, 112).

Another more recent finding that sparked new interest in the role of K⁺ for skeletal muscle function was the very large fluctuations of plasma [K⁺] witnessed during and immediately after exercise (189, 206, 207, 262, 467, 658). In Figure 1, we have reproduced data from two different experiments, one with dynamic bicycle exercise, and the other with static hand-grip contraction. In both cases very rapid and large increases were observed in venous plasma [K⁺] during exercise. When contractile activity ceased, venous [K⁺] rapidly fell to below normal resting value.

View larger version (15K): [in this window] [in a new window]   Fig. 1. Effluent venous plasma K+ concentration ([K+]v) monitored in the femoral vein in one representative experiment by a K+-selective electrode during bicycling at 140% of maximum O2 consumption (O2 max) (solid line without symbols) and in blood samples from the antebrachial vein during static handgrip contraction at 30% of maximal voluntary contraction (open circles; means ± SE). Muscle activity started at time 0 and ceased at times indicated by arrows. The transient, postexercise reduction of [K+]v to below normal resting values lasted for 10-15 min. [Data from Vøllestad et al. (658) and Fallentin et al. (189).]

The ultimate function of muscle tissue is its ability to develop mechanical tension. A prerequisite for tension development, however, is the membrane excitability, i.e., its ability to generate and propagate action potentials (AP). This unique feature, which muscle cells have in common with nerve fibers, depends on [K⁺] gradients across the membranes. From the large changes shown in Figure 1, it has been suggested that the K⁺ shifts might affect excitability and contractile force.

One of the most crucial questions that is examined in detail in this review is the significance of K⁺ translocations for muscle performance and fatigue. Scrutinizing the variability of responses in different species or muscle fiber types may reveal common mechanisms. It was not until the 1960s that the different fiber types became a focus of research regarding ionic composition at rest and with exercise (616, 617, 619). At rest, important differences were revealed between slow-twitch and fast-twitch muscles regarding electrolytes and membrane potential (E_m) (84, 95, 96, 619). It is important to conduct a detailed analysis of such differences if one is to properly understand and predict the responses in humans during voluntary contractions connected with training and fatigue.

K⁺ shifts may also be important for cardiac function (385). First of all, variations in beating frequency will cause K⁺ shifts within the heart as will exposure of the heart to catecholamines. It is of special interest to compare the heart with skeletal muscle, because the normal heart is capable of minimizing K⁺ perturbations much more effectively than skeletal muscle (564). However, in this review it would be unrealistic to cover the vast literature regarding the role of K⁺ in cardiac excitability, especially since ischemia causes rapid and large perturbations of cardiac K⁺ homeostasis, which has been the focus of intensive research (11, 121, 230, 289, 357, 358, 365, 533, 581, 680, 683, 697, 712). We therefore restrict references to the cardiac literature to those occasions when we want to make comparisons with skeletal muscle that may help in clarifying important control mechanisms. The second point to make is that the rise in plasma K⁺ that occurs with exercise will of course affect other excitable tissues, especially the heart.

The development of new analytical tools provided for more insight into the subtle electrolyte fluxes. One line of development was the introduction of ion-selective electrodes that allowed continuous measurements both on the microscopic level inside living cells and in the extracellular spaces (204, 248, 254, 290, 296, 396, 424, 425). Methods for analysis of ion concentrations are dealt with in section II. Another line of development was the biochemical analysis and quantification of membrane proteins, e.g., the Na⁺-K⁺ pump (99). The perturbations to which various preparations have been exposed are often nonphysiological, and often only a single variable is manipulated at a time. We certainly learn from these manipulations, but to fully understand the complex ion shifts and their effects on muscle and heart function, all this information must be integrated and tested in in vivo.

A large amount of literature is available which deals with the translocation of K⁺ in muscle tissue that is active, and a variety of approaches have been used. This is also the reason why many different terminologies are being used. When studying a single muscle cell in bathing solution, it is necessary to distinguish between intracellular [K⁺] and [K⁺] outside the cell, that is, the bathing solution or the extracellular concentration on the surface of the cell membrane. The nomenclatures outside and extracellular are used interchangeably in the literature and suffixes such as "o" (81, 588, 613), "out" (120, 585), or "e" (294, 296) are also used. When dealing with the in vivo situation, the extracellular space is composed of two distinctly separated spaces: the interstitial space and the intravascular space, and one might also add the intralymphatic space. This has led to confusion because the suffix "i" may denote any of the different spaces inside the various compartments: interstitial (125), intravascular (i.e., including capillary and lymph) or just inside-the-capillary (214), but most often intracellular (122, 496, 585, 595, 616). Sometimes "i" simply stands for intramuscular (123). Interstitial may also be abbreviated "is" (122) or "isf" (270) in contrast to "icf" for intracellular versus "ecf" for extracellular (84), the latter of which corresponds to "isf." Therefore, in this review we have totally omitted the suffix "i" and instead we introduce "c" to denote cellular or cytosolic concentration or content. As far as the spaces outside the cell are concerned, we use "s" to specify surface concentrations, which then correspond to the interstitial concentration, and "e" for the gross extracellular space, including interstitial as well as vascular compartments. Further details of terminology and definitions are dealt with in the model description in section II.

	II. DISTRIBUTION SPACES FOR POTASSIUM

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Sampling site, sampling technique, and analytical technique must all be considered when judging a measured value of K⁺ content or concentration. As an example of the importance of the sampling site and technique, Farber et al. (191) noted more than 40 years ago that the standard technique of opening and closing the fist to fill the veins so as to facilitate puncturing consistently caused an artifactual increase of [K⁺] in the sampled plasma. K⁺ can be measured in the whole body, in tissue samples, in body fluids including the intracellular compartment and even in subcellular domains. Obtaining a proper sample of extracellular fluid with a sufficient time resolution during exercise has proven to be especially difficult. The various approaches that have been used comprise sampling of lymph draining the muscle (636) or inserting a wick (G. L. Nilsen and O. M. Sejersted, unpublished data) or semipermeable capsules into the tissue (404). Recently, microdialysis has been used to measure extracellular [K⁺] ([K⁺]_s) (240, 334, 438a, 450). Furthermore, some investigators have inserted K⁺-selective minielectrodes directly into the muscle tissue as discussed in section VIIIA (296, 297). It should be noted that even a minor mechanical injury of the muscle cells will lead to vast overestimation of [K⁺]_s when the intracellular K⁺ leaks out. Such injury is especially likely to occur with electrodes or catheters inserted into the exercising muscle. Table 1 summarizes the various analytical techniques that have been used. Of special interest for this review are the techniques for measuring or estimating the [K⁺] in plasma ([K⁺]_p), intracellular [K⁺] ([K⁺]_c ), and [K⁺]_s and possibly [K⁺] in the t tubules and in the subsarcolemmal space.

Ion-selective electrodes have now largely replaced flame photometry in the laboratory. Such electrodes can also be manufactured for intracellular and intravasal use (254, 396). These electrodes measure ion activities which by definition are lower than concentration measured by flame photometry (707). Original observations also indicated that intracellular ion activities were lower than expected compared with [K⁺] in simple solution (97, 396). This led the authors to point out that some K⁺ may be bound or compartmentalized in the cytoplasm. The ³⁹K-NMR technique substantiated that compartmentalization was likely, and it was shown that under certain conditions up to 15% of K⁺ may be sequestered within an intracellular compartment (3). However, because similar differences are reported even in blood, binding of K⁺ cannot be excluded in plasma and serum samples (204, 707). In recent years, ion-selective fluorescent dyes in combination with ordinary or confocal microscopy have largely replaced ion-selective electrodes in cellular work. A fluorescent probe for K⁺ was recently proven to be suited for intracellular application (471). With regard to the role of K⁺ in muscle fatigue, the concentration in the t-tubular system is probably important as discussed in section IVD. As yet, few studies have addressed this directly. One attempt to quantify electrolyte concentration was made by electron probe X-ray microanalysis in fatigued muscles with vacuolated t tubules (236, 610). Other studies have based estimates on changes in intra-t-tubular electrolyte concentration on indirect evidence or mathematical modeling that takes into account the narrow and tortuous diffusion path for K⁺ in the lumen of the t tubules (14, 222, 386, 387), as will be further discussed in section IVD.

Radioactive isotopes of K⁺ or its congener Rb⁺ have been extensively used to measure unidirectional fluxes between compartments and were instrumental in the early studies (299). The use of isotopes is still the preferred method of choice for this purpose. This has not been illustrated in Table 1 but is discussed in section VIIIA. It should also be pointed out that some methods are not ethically applicable to humans (e.g., the use of some isotopes), although combining such methods in animal studies with those acceptable in humans does provide reliable estimates.

The total body K⁺ content in normal human adults ranges from ~2,000 to >4,000 mmol (58, 448). The total quantity depends on body weight and body fat content, and values in the order of 60 mmol/kg fat free body mass, ranging from 50 to 70 mmol/kg, have been reported (283, 432). The distribution of K⁺ within the various body tissues is highly variable, which is true in terms of concentration as well as content. Around 2% of total K⁺ is located in the extracellular space with normal plasma concentrations at rest ranging from 3.5 to 5.3 mM (707), while 98% is located intracellularly with concentrations in muscle tissues around 160 mM . The largest fraction of K⁺ (corresponding to 75%) is located in the skeletal muscles, which constitute ~40% of body weight or ~30 kg wet wt, while heart muscle weighing around 0.3 kg accounts for only ~1% of total body K⁺. The erythrocytes carry ~7% of total body K⁺ and 8% is located in the bones, while the rest is located in other tissues. The muscle K⁺ content is 75-105 mmol/kg wet wt, depending on the fat content of the muscles. In obese people, if correction is not made for fat content, muscle K⁺ content may be considerably reduced, as the K⁺ content per kilogram body weight (383). In the following muscle K⁺ content refers to fat-free tissue and comprises the sum of K⁺ content in all muscle compartments (K_m⁺). Also, in a number of species, different muscle fiber populations show differences in K_m⁺ as well as in intracellular [K⁺], with the slow-twitch muscles having lower values than the fast-twitch muscle (84, 95, 619). However, species differences do exist, and in humans, the two main muscle fiber types did not differ in this respect (589). The loss of K⁺ from the body mainly occurs in feces and urine and is in general <25 mmol/day (503). The K⁺ loss in sweat is usually small but can approach a few percent of body content per day during very heavy sweating. The resting concentrations in the different body compartments are maintained within narrow limits by regulatory mechanisms of the cell surface membranes.

The complexity of the processes involved in K⁺ shifts in the body with exercise along with the relatively large number of compartments involved prompted us to create a simple model to make it easier to understand and analyze the kinetics and magnitude of the shifts. When there is a change in K⁺ flux across the endothelium or sarcolemma, or a volume change of the muscle tissue, K⁺ concentrations in several compartments will be affected. Figure 2 shows that in muscle there are three main compartments among which K⁺ moves: the intracellular muscle cell volume, the interstitial space, and the plasma volume of the microcirculation, which have been designated with the letters c, s, and p, respectively. We consider the volume of lymphatics (l) as part of the interstitial space. In addition circulating red blood cells (r) in the capillaries represent a possible exchange volume. The exchange of K⁺ between plasma and the red blood cells is treated separately in section VIIID. At rest, the intracellular compartment contains 85-91% of the total skeletal muscle water content, whereas 9-15% is located extracellularly (5, 592, 600). The corresponding values for the rat heart were reported as 73% and as high as 27%, respectively. The capillary volume in skeletal muscle is only ~1% of the tissue wet weight and thus takes up ~10% of the extracellular water volume (147). Again, in the rat heart, the capillary volume seems to be fairly large, amounting to almost 6% of the tissue wet weight or ~30% of the extracellular water volume. In many circumstances, [K⁺] in the interstitial space and in the plasma are similar and may be regarded as the common extracellular concentration, denoted "e." However, the interstitial space is large enough to have a considerable capacity for accumulating K⁺ in which case a change of K⁺ flux across the sarcolemma will only be evident in the venous effluent with an attenuation as described below. Therefore, K⁺ events at the sarcolemma must be considered separate from the exchange of K⁺ between the muscle tissue and the general circulation. Correspondingly, quantification of K⁺ release from the cells (Fig. 2) based on measurements of [K⁺]_p together with muscle blood flow call for careful assumptions, the validity of which may not always be justified.

View larger version (20K): [in this window] [in a new window]   Fig. 2. Simplified model of the various compartments inside the whole muscle. There is a K+ release from and uptake into the cell. There is a K+ efflux out of or influx into the interstitium. Finally, there is a K+ input by way of arterial plasma into the muscle and an output via the vein and lymph. We use accumulation as opposite to dissipation to describe net changes of K+ content in the cell, interstitial space, or capillary plasma. For the exchange of K+ between the whole muscle and the general circulation, we use the term gain as opposed to loss.

There is no standard nomenclature for the fluxes between the different compartments in the muscle tissue, and Tables 2 and 3 have been constructed as an attempt to establish an unequivocal terminology. The following model is to a large extent based on the models published by Hallén and Sejersted (254) and Sjøgaard (594), but has now been extended and presented more systematically. Figure 3 shows in more detail the various flux expressions (J) and abbreviations used for volume, K⁺ content, and concentration in the various compartments. In addition, [K⁺]_{v_mix} and [K⁺]_{p_mix} are used for the concentration of K⁺ in mixed venous blood and at unspecified sampling sites, respectively.

View larger version (41K): [in this window] [in a new window]   Fig. 3. A cartoon of the various compartments within the muscle depicting the flux paths for K+ and fluid. J is flux; subscripts sc, ps, and pr indicate that a positive flux is from interstitial space (s) to the cell (c), from the capillary plasma (p) to the interstitial space (s) or red blood cell (r). For subscripts Kl, Kv, Ka, Fl, and Fv, Fa is K+ (K) or fluid (F) in the lymph (l), venous plasma (v), or arterial plasma (a). V is volume. See Table 2 for further identification of the symbols.

For any compartment, the terms K⁺ accumulation rate or K⁺ dissipation rate are used for net changes in K⁺ content (Table 2). At the cell membrane level, the term K⁺ release rate means the normal net K⁺ flux through various channels. In the model, the release rate (J_Ksc) will be negative for an outward repolarizing K⁺ current (Table 3). This nomenclature contrasts with the convention of electrophysiology today where inward currents are negative. However, we wanted to maintain K⁺ gain by the whole muscle as a positive value, and for the sake of consistency, inward currents are therefore positive.

Normally, the driving force for K⁺ is directed out of the cell, resulting in an outward electrodiffusion of K⁺. This is normally opposed by K⁺ uptake mediated by the ATP-requiring Na⁺-K⁺ pump. Under certain circumstances discussed below, the net electrochemical driving force for K⁺ may be directed into the cell, which means that there may be an inward K⁺ flux through channels, i.e., a K⁺ uptake in addition to that carried by the Na⁺-K⁺ pump (Table 2). Figure 3 and Table 3 also refer to K⁺ transport through separate transporters, which may be important but which have been studied very little in muscle tissue. They may comprise the Na⁺-K⁺-2Cl transporter and possibly a K⁺/H⁺ exchanger (see sect. IIID).

Two terms, gain and loss, that are used in this review will need some clarification. When the net diffusion of K⁺ across the capillary endothelium is directed from the interstitium into the capillary plasma, it is referred to as net K⁺ efflux (which is a rate), whereas a net influx means that K⁺ moves from the capillaries into the interstitium. The whole muscle will gain K⁺ at a certain gain rate when a net amount of K⁺ is transferred from the general circulation into the muscle, whereas the muscle tissue loses K⁺ when the net movement of K⁺ is in the opposite direction. It is important to take into consideration that the muscle tissue is supplied with K⁺ from the arterial plasma (K⁺ input rate) and that K⁺ comes out of the muscle through both lymph and venous plasma. The sum of these two output rates is then the total K⁺ output, with K⁺ loss rate or K⁺ gain rate being the absolute difference between the input and total output of K⁺.

The amount of K⁺ lost from one muscle or from the heart will distribute first in the plasma, then in the extracellular space of various organs, and finally K⁺ will be taken up into cells of other muscles and other tissues. We have chosen to name this movement of K⁺ redistribution. The rate of redistribution will depend on many factors that are included in standard pharmacokinetic models. For the sake of simplicity, it is assumed that there are two accessible distribution volumes outside the working muscle, namely, the extra- and intracellular fluid volumes of other tissues. Some authors only take the plasma volume into account, for instance when the effect of hemoconcentration on arterial [K⁺] ([K⁺]_a) is considered (239). This is clearly wrong since with the exception of the capillaries of the central nervous system K⁺ is rapidly equilibrated with the interstitial fluid volume of remote tissues that are adequately perfused. It is important that the rate of mixing within the extracellular fluid space is dependent on the flow rate through these tissues. For instance, with high-intensity exercise, flow through the splanchnic area may be reduced, and mixing in this area will then be slowed (251). It is of note that this mixing may still be considered fast relative to redistribution into other cells. The rate of intracellular accumulation is governed by the balance between K⁺ release and uptake rates across the cell membranes and, as will be discussed in section IVA2, membrane conductance to K⁺ varies with the [K⁺]_s. Hence, four factors, tissue blood flow, the [K⁺] gradient, membrane conductance, and activity of the Na⁺-K⁺ pump, will together be major determinants of the rate of gain of K⁺ by cells in the remote tissues. Control mechanisms of the Na⁺-K⁺ pump and K⁺ uptake mechanisms are treated in more detail in section IIIB.

One of the aims of this review is to assess the magnitude of the fluxes illustrated in Figures 2 and 3 and described in Table 4, to which end various approaches have been taken. Radioisotopes have been widely used in all kinds of models, ranging from single cells, isolated muscles, muscle strips, perfused muscles, Langendorff heart preparations, and also intact organs in situ. Basically, because J_{Na-K pump} + J_Ksc = dK_c⁺· dt¹, one of these three parameters can be calculated on the basis of measurements of the two others. Significantly, when using ⁴²K⁺, not only the net shift of K⁺ from one compartment to the other will be measured but also the exchange of K⁺ in addition to J_{Na,K pump} or J_Ksc. Therefore, radioisotopes are often used in conjunction with specific blockers, for instance, digitalis which blocks the Na⁺-K⁺ pump, various channel blockers, or blockers of other transport proteins (e.g., bumetanide, amiloride).

Another approach was taken by Sjøgaard et al. (598) and more recently by Lindinger and Hawke (410). They perfused the isolated rat hindlimb with blood containing ⁴²K⁺ at rest and during continuous stimulation at 4 Hz. ⁴²K⁺ was equilibrated for 30 min with the extracellular space. The specific activity of ⁴²K⁺ in the intracellular space was expected to remain negligible throughout the experiments, and therefore, no ⁴²K⁺ release from the intracellular space would bias the data (646). With the assumption of a constant extracellular ⁴²K⁺ content, J_{Na-K pump} was calculated as the product [⁴²K⁺]_(v-a) · [K⁺]_a · [⁴²K⁺]_a¹ · J_{Fa_in}, where [K⁺]_a · [⁴²K⁺]_a¹ is the inverse of the specific activity of ⁴²K⁺. The intracellular K⁺ dissipation rate was calculated as [K⁺]_(v-a) · J_{Fa_in}, assuming that little or no accumulation of [K⁺]_s occurred, which implies that d[K⁺]_c · dt¹ equals K⁺ loss rate. The assumption that a possible variation in interstitial K⁺ and ⁴²K⁺ does not influence the results significantly was justified by the almost unrestricted diffusion across the capillary wall, which does not allow for large gradients between [K⁺]_s and [K⁺]_p in the well-perfused muscle, and the small size of the interstitial space, i.e., ~10% of total muscle water content as mentioned above. From these two estimates, J_Ksc was calculated.

An alternative is to monitor continuously [K⁺]_v after a sudden change in J_Ksc or J_{Na-K pump}. A sudden stepwise change in J_Ksc occurs at the onset and cessation of exercise and sudden changes in cardiac beating frequency. The onset of exercise is accompanied by a sudden appearance of AP in the recruited muscle cells. The frequency of AP (firing rate) reaches a level depending on the exercise intensity; in the human, it is normally reported to be in the range of 8-30 Hz (56, 630). Heart rate can increase suddenly from a resting level of ~1 Hz to at most slightly above 3 Hz in humans. In this way in both tissues repolarizing K⁺ currents will suddenly arise, thus increasing K⁺ release rate (J_Ksc < 0) by J_Ksc. Hallén and Sejersted (254) analyzed this situation and concluded that the magnitude of J_Ksc could be estimated from the rate of rise of [K⁺]_v, since J_Ksc = d[K⁺]_v · dt¹. Their argument was based on three assumptions. First, the analysis requires that the diffusion of K⁺ over the capillary endothelium is rapid so that for practical purposes [K⁺]_s is equal to [K⁺]_v and the extracellular volume can be regarded as one compartment (294, 295). Interestingly, it was recently reported that the permeability of capillaries to K⁺ increases with flow and that this increase of permeability is due to the shear-stress-induced stimulation of vascular nitric oxide production (338-340). Also, increments in flow to perfused resting rat hindlimb muscles caused a more rapid exchange of ⁴²K between the perfusate and the intracellular compartment (410). This means that it may not be correct to extrapolate permeability data for capillaries from a low-flow situation to situations with increased flow. The second assumption implies that the extracellular volume V_e (= V_s + V_p) remains constant for a few seconds. Third, it is required that activation of uptake, J_{Na-K pump}, is not instantaneous but has a lag (Na⁺ pump lag). The large heterogeneities in local blood flow or large K⁺ gradients within the interstitial space may restrict the conclusions that can be drawn from this analysis.

By a similar method, beat-related J_Ksc was estimated in pig hearts on the basis of recordings of [K⁺]_v in the coronary sinus during sudden increments and decrements of beating frequency (177). Also, Na⁺-K⁺ pump rate has been estimated in the pig heart after abrupt injection of ouabain into the coronary artery to suddenly block the Na⁺-K⁺ pump (176). As is the case with all these methods, estimates of J_Ksc cannot always be related to the actual size of the repolarizing K⁺ currents associated with an AP. In skeletal muscle, this estimate will in addition require knowledge of the fiber recruitment and firing frequency.

With maintained stimulation of the muscle, J_{Na-K pump} will increase, and in the heart and in some circumstances in skeletal muscle, eventually J_Ksc = J_{Na-K pump} (disregarding a possible transport component by other transporters). If the firing frequency is then suddenly reduced (exercise is stopped or heart rate reduced), a similar line of reasoning will lead to the conclusion that J_{Na-K pump} = d[K⁺]_v · dt¹. In other words, therefore, initial changes in [K⁺]_v may under certain circumstances be used to estimate both the increase in K⁺ release associated with increased firing frequency and the accompanying rise in K⁺ uptake rate provided by the Na⁺-K⁺ pump.

The rate of K⁺ loss or gain for the whole muscle can be calculated if fluid volumes in the muscle remain fairly constant for a short period (J_{Fa_in} = J_{Fl_out} + J_{Fv_out}). Also in many circumstances [K⁺]_s ~ [K⁺]_p = [K⁺]_v. Normally, lymph flow is very low compared with plasma flow and may often be ignored. In this case, and assuming constant muscle water content, i.e., J_{Fa_in}  J_{Fv_out} = 0, total K⁺ output will equal J_{Fa_in} · [K⁺]_v, and rate of K⁺ loss will be equal to J_{Fa_in} · ([K⁺]_v  [K⁺]_a) or J_{Fa_in} · [K⁺]_v-a (arterial plasma flow times the venoarterial concentration difference for K⁺). If, in addition dK_s⁺ · dt¹ = dK_p⁺ · dt¹ = 0, (no accumulation of K⁺ in the interstitial space or in the vascular volume) so that J_Kps + J_{Na-K pump} + J_Ksc + J_{Kl_out} = J_{Ka_in}  J_{Kv_out}  J_Kps, loss rate will reflect the balance between uptake and release rates across the sarcolemma since the equation transforms to J_Ksc + J_{Na-K pump} = J_{Ka_in}  J_{Kv_out}  J_{Kl_out} ~ J_{Fa_in} · [K⁺]_a-v. Because J_{Na-K pump} + J_Ksc = dK_c⁺ · dt¹ intracellular K⁺ dissipation rate equals arterial plasma flow times [K⁺]_v-a provided muscle volumes and extracellular K⁺ content inside the muscle remain unchanged. Naturally with vascular occlusion or occluded microcirculation during contraction, there is no flow and whole muscle K⁺ gain or loss rates will be zero.

The existence of an interstitial space has important implications for the study of K⁺ fluxes in muscle in that this space serves as a reservoir for K⁺ storage, in electrical terms a capacitance. There are two important consequences of this that we would like to highlight. First, loss or gain of K⁺ for the whole muscle will not reflect intracellular dissipation or accumulation of K⁺ if interstitial K⁺ is changing. Second, [K⁺]_v will only to a small extent vary with flow through the muscle.

Previous authors have indirectly inferred that cellular uptake and release of K⁺ can be deduced from measurements of [K⁺]_v-a and flow (332, 462). As pointed out by Hallén and Sejersted (254), this can only be done if [K⁺]_v is constant and in equilibrium with [K⁺]_s. If [K⁺]_v is not stable, it means that K_s⁺ is constantly changing. Thus, at the onset of exercise, all the K⁺ leaving the muscle cells will initially accumulate in the interstitial space, but soon K⁺ will also leave the muscle by the perfusing blood. Thus initial [K⁺]_v-a will grossly underestimate the real release of K⁺ from the muscle cells. The same holds true at cessation of exercise when [K⁺]_v-a will grossly underestimate K⁺ uptake since [K⁺]_v is falling rapidly. At these points the release/uptake rate for K⁺ will therefore actually be J_Ksc = dK_s⁺ · dt¹ + dK_p⁺ · dt¹. Because V_p is small relative to V_s and [K⁺]_s ~ [K⁺]_v as argued above, the relationship can be written as J_Ksc · V_e¹ = d[K⁺]_v · dt¹. What is more, small variations in [K⁺]_v when exercise is continued for several minutes can contribute considerably to the calculated loss (252).

Interestingly, because the intracapillary volume is roughly 10 times smaller than the interstitial volume both in skeletal muscle and heart muscle, the magnitude of the flow, J_{FA_in}, will not greatly affect the initial rate of rise or fall of [K⁺]_v at onset and cessation of exercise (254). This is due to the fact that the rate at which K⁺ is removed by the flow is small compared with the rate at which K_s⁺ rises or falls initially. To avoid the confounding effect of flow on the rate of rise or fall of [K⁺]_v, initial rates were estimated in several studies by means of K⁺-selective electrodes in the femoral vein of exercising human subjects (246, 252-254, 658). Also, in these experiments [K⁺]_v rose or fell linearly over 5-10 s (see Fig. 1), indicating that even a rapid rise of muscle blood flow as seen at the onset of exercise or a maintained high muscle blood flow at the end of exercise do not seem to affect the rate of change of [K⁺]_v to any great extent even over a time period of just a few seconds (254). At the other hypothetical extreme, the rate of rise of [K⁺]_v would vary in proportion to flow if the interstitial volume was very small, which is clearly not the case.

The various ways of estimating K⁺ translocations as outlined above, and the corresponding prescribed assumptions, make it clear that there is no simple relationship between rate of K⁺ loss from the whole muscle and rates of K⁺ release and uptake at the sarcolemma. Furthermore, estimates of [K⁺]_v-a and blood flow, J_{Fa_in}, can only be used to deduct reliable data on uptake and release at the cellular level when K_s⁺, as reflected in [K⁺]_v, is constant. More reliable estimates of J_Ksc and J_{Na-K pump} are provided by the use of isotopes or by estimates of initial rates of concentration changes following sudden changes in electrical activity. However, there is certainly a need for better ways of measuring [K⁺]_s directly.

The resting plasma [K⁺] in the general circulation ([K⁺]_{v_mix} or [K⁺]_{p_mix} or [K⁺]_a) is kept within narrow limits (3.5-5.5 mM) (191, 622). Interestingly, some investigators claim that [K⁺]_s in resting skeletal muscle is slightly higher than [K⁺]_v (404, 636) (G. L. Nilsen and O. M. Sejersted, personal communication). The reason for this is unclear, since the interstitial Cl concentration is not correspondingly low as one would expect for a Donnan effect of negatively charged macromolecules in the interstitium. The kidneys are responsible for the long-term clearance from plasma of ingested or injected K⁺, and they also respond with increased fractional reabsorption of K⁺ when intake is low. Extrarenal tissues like muscle which contains the largest exchangeable pool of K⁺ probably play the most important role in the acute buffering of a K⁺ load and control of [K⁺]_a. Clearly, exchange kinetics for K⁺ between the extracellular and intracellular spaces differ greatly depending on whether, for example, the muscle is active, stimulated by hormones, or well perfused. These and other examples are discussed in subsequent sections of this review. Here we briefly go through the data relating to the resting condition.

Several hormones cause a decrease of [K⁺]_{v_mix}. This effect is well established for epinephrine, -agonists, and insulin (137, 139, 284, 639, 656), although D'Silva (158a) originally reported an increase of [K⁺] with epinephrine. These effects have already been reviewed on a number of occasions (see for instance Refs. 48, 135).

At rest, K⁺ is taken up quite slowly by the extrarenal tissues. After about 1-h infusion of KCl to normal subjects, only 15% had been excreted by the kidneys whereas 25% was still located in the extracellular space (540), which contrasts the normal extracellular fraction of just 2%. Lindinger et al. (409) showed that 3.5 h after ingestion of KHCO₃ only 37% had been taken up by peripheral tissues. The mechanism for slow cellular uptake remains, however, unclear. Adrenalectomy reduces the extrarenal disposition rate (138, 586), and part of the disposition rate is recovered by administration of aldosterone (49). In addition, -adrenoceptor blockade reduces the rate of extrarenal uptake of infused K⁺, and simultaneous infusion of -agonists may completely ameliorate the rise of plasma [K⁺] (136). Kubota and Ingbar (375) showed that ₂-adrenoceptor stimulation increased extrarenal disposal rate of K⁺, and disposition rate was higher in hyperthyroid animals, but there was no interaction between the two hormones. Stimulation of -adrenoceptors has the same effect as -adrenoceptor blockade (703). Finally, absence of insulin leads to decreased tolerance to infused K⁺ (138, 139). Possibly, both insulin and catecholamines are instrumental in facilitating the extrarenal tissues to temporarily store ingested K⁺ until it is excreted by the kidneys.

Increased uptake of K⁺ in resting muscle may be achieved by increased Na⁺-K⁺ pump rate or decreased K⁺ release from the cells. As discussed below, Na⁺-K⁺ pump rate can be increased slightly by a rise above normal of [K⁺]_s. Also, conductance of the inwardly rectifying K⁺ channel is increased by higher extracellular [K⁺]. These two effects can possibly explain muscle uptake of K⁺ when extracellular [K⁺] rises. However, in isolated cardiac Purkinje fibers, [K⁺]_c did not change when the concentration in the bath was varied, thus indicating that stimulation of the Na⁺-K⁺ pump did not occur under these in vitro conditions. (475). What these findings indicate is that a basal level of several hormones, including epinephrine, insulin, and aldosterone, is in fact required for the muscle cells to respond with a K⁺ uptake when the [K⁺]_s is raised.

	III. TRANSPORT ACROSS THE SARCOLEMMA

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In relation to exercise, the short-term regulation of K⁺ is essential. This section looks at processes that are vital for rapid K⁺ shifts across the cell membrane. Membrane is here used as a general expression for the cell membrane, as in E_m, membrane transport proteins, etc. The cell membrane of muscle cells, by definition, comprises the sarcolemma as well as the much larger t-tubular membrane. The specific properties of the t-tubular structure are dealt with in section IVD. Many of the same membrane proteins are present in the t tubules and the sarcolemma.

A.  K⁺ Channels in Muscle

1.  K⁺ channel superfamilies

There is an extremely large diversity of K⁺ channels in striated muscle, especially in the heart, and several reviews have recently appeared (36, 65, 87, 131, 133, 319, 487a, 489-491, 625, 627, 641, 698). There seem to be two dominating superfamilies of channel-forming proteins that have been named Kv (v for voltage sensitive) and Kir (ir for inward rectifier). In addition, a third type of protein, the so-called minimal or minK, has been identified as an integral part of some K⁺ channels. Finally, Kv channels have associated -subunits that speed up inactivation (531). To add to the complexity, a novel cardiac two-pore background K⁺ channel was recently cloned (347).

In the voltage-sensitive Kv superfamily, each peptide chain has the classical structure of six membrane-spanning segments which is also typical for Na⁺ and Ca²⁺ channels (92, 133). Four peptide chains associate to form voltage-sensitive channels (homo- or heterotetramers) (444). Four subfamilies have been identified within this superfamily (Shaker, Shab, Shaw, and Shal), and there are several varieties within each subfamily. Only peptide chains from the same subfamily can form functional channels, with the possible exception of association with minK (see below).

In the Kir superfamily, each subunit is much smaller, having only two membrane-spanning regions and lacking the positively charged segment that provides voltage sensitivity (157). These proteins can also form homo- or heterotetramers with a central channel that typically exhibits inward rectification (36, 374). There are at least six subfamilies (490).

The minK (or I_sK) was recently cloned and has only one transmembrane segment (36). The minK protein alone cannot associate to form channels (487a). They can associate with Kv proteins to form a delayed rectifier belonging to the voltage-sensitive channels (32, 456, 556). Interestingly, the minK gene seems to be expressed preferentially in the conducting system of the mouse heart (379).

The variety of K⁺ channels is further extended by alternative splicing, something that seems to be quite important in at least some species (319, 444, 710). Finally, the variability arises from the fact mentioned above that various subunits with different properties can associate to form a functional channel (133, 444). In this way, for instance, ligand-controlled gating can be introduced in voltage-sensitive channels (374). This is in contrast to Na⁺ and Ca²⁺ channels where the corresponding four peptide chains are actually linked so that the channel-forming protein is one large as opposed to four different smaller proteins. A brief account of the two most important classes of channels will be given below, since it is the properties of these channels that determine the K⁺ release from the heart and from active skeletal muscle.

These channels show voltage- and time-dependent activation but only some show voltage-dependent inactivation. The great diversity of voltage-sensitive K⁺ channels is reflected in the different voltage sensitivities and kinetics. In both heart and skeletal muscle, the delayed rectifier plays a role for the repolarizing K⁺ current (I_K) during action potentials, and this in turn contributes to K⁺ release during muscle activity. This channel is quite abundant in skeletal muscle and, moreover, it displays significantly more rapid kinetics than in the heart, which in one way accounts for the much shorter AP (298, 579, 625). At E_m values positive to 70 mV, the delayed rectifier in mouse extensor digitorum longus muscles (EDL) showed inactivation that was half-maximal at 50 mV (298). In the heart, one finds both a rapid current that inactivates (I_K,r) and a slow current that does not show inactivation (I_K,s) (557). There is also a rapidly activating, noninactivating K⁺ current (I_Kur; Ref. 487a). However, there are species and/or regions of the heart where the expression of these channels is very low (36, 558). In skeletal muscle, there seems to be variable expression of some channel genes depending on fiber type and pattern of excitation (662). To some extent, these channels show the classic behavior described by Hodgkin and Huxley (301). They slowly activate when the cells become depolarized and exhibit some outward rectification, which means that they easily pass an outward current. It has been shown that these channels are subject to hormonal control in the heart, but it is presently unclear whether this is the case in skeletal muscle. The channel proteins can be phosphorylated probably both by protein kinase A and protein kinase C, which both increase the current (313, 640, 665).

The Ca²⁺-activated K⁺ channels [I_K(Ca)] are further examples of channels common to both heart and skeletal muscle. They are activated by both intracellular Ca²⁺ ([Ca²⁺]_c) and depolarization, but closed by low intracellular pH (40, 83, 392, 464, 465, 516). Barrett et al. (35) found a strong interaction between Ca²⁺ and voltage so that at 50 mV openings were recorded at 1 µM Ca²⁺, whereas at +50 mV only 0.01 µM Ca²⁺ was required. There are two types of Ca²⁺-activated K⁺ channels, one of which has very large conductance (670). A detailed analysis of the gating kinetics of the large-conductance Ca²⁺-activated K⁺ (BK) channels from rat skeletal muscle was recently published (541). These channels may be quite important for the repolarization since [Ca²⁺]_c is raised during contraction, although their voltage dependence is much less than that of the delayed rectifiers. These channels can open at lower [Ca²⁺]_c concentrations than previously expected, although only during long-lasting depolarizations, and hence they can be of importance either during sustained muscle activity or in exhausted fibers (317). It was recently proposed that in the heart, the L-type Ca²⁺ current could activate these K⁺ channels either directly or indirectly via the triggering of Ca²⁺ release from the sarcoplasmic reticulum (666). In line with the properties of these channels, Fink and Lüttgau (198) described a large increase in membrane K⁺ conductance in metabolically exhausted frog skeletal muscle fibers and later ascribed this to a rise of [Ca²⁺]_c (197, 435). However, it is possible that part of the conductance increase these authors observed also could be ascribed to opening of ATP-dependent K⁺ channels (see sect. IIIA3).

In heart muscle, a Na⁺- and voltage-sensitive K⁺ current has also been identified [I_K(Na)] (342, 433). This channel has yet to be cloned. Its role in normal situations is unclear, since [Na⁺]_c in the range of 20 mM is required for opening (653), and it was recently identified in guinea pig, but not in rat ventricular myocytes (393).

Finally, an important class of channels present in the heart gives rise to the transient outward current (I_to) (119, 711). They rapidly activate and inactivate on depolarization and contribute to the early "notch" in the cardiac AP. In actual fact, in the regions of the heart where they are present (that is especially in the epicardium, Ref. 36), these channels seem to be quite important for the level of the plateau phase in heart cells, thereby determining in part both the size of the Ca²⁺ current and the length of the AP (625).

The inward rectifiers (belonging to the Kir family) comprise three channel types or currents. The classic inward rectifier (IRK) gives rise to the I_K1 current. The ATP-sensitive K⁺ channel opens [I_K(ATP) current] when intracellular ATP concentration ([ATP]_c) is lowered (501), while the acetylcholine-sensitive K⁺ channel [muscarinic, I_K(ACh) current] opens through a direct interaction with G proteins (380, 431). The latter is found only in the heart, whereas the two others are highly expressed in tissue both in heart and skeletal muscle (315, 316, 446, 501, 615). The inward rectifiers do not possess the positively charged S4 transmembrane segment as do the voltage-sensitive channels. Instead, block of the channel is achieved by intracellular Mg²⁺ or polyamines, such as spermine, spermidine, or putrescine (490). The rectification is rapid, and there is no inactivation, which means that the channels remain open or closed as long as voltage, ion concentrations, and ligand control remain the same. Apparently, in the heart, control of this channel can also be achieved through its anchoring to the cytoskeleton and through a slight -adrenergic inhibitory effect (370, 371, 449).

The most important effect of these channels is to stabilize the E_m, which means that when they are open more current will be needed to alter E_m since membrane resistance is low. As described in section IVA, opening of these channels will force the E_m to become very close to E_K, since they are highly selective for K⁺. The strong rectification of I_K1 means that it passes little current throughout the AP. However, some outward current can be passed as repolarization approaches the resting E_m and in this way this channel also contributes to the exercise-induced K⁺ release (see sect. IVC). It is first of all responsible for most of the basal K⁺ conductance (272, 579). The two other channels exhibit much weaker rectification, which means that ligand-gated control predominates and that outward current is also passed (502). The effect of opening these ligand-gated channels in resting cells may therefore only be a very small transient K⁺ release until the E_m is stabilized at a more negative level. However, because more current will have to be passed to depolarize cells sufficiently to trigger an AP, cell excitability is reduced, and cells may become unexcitable (196, 559). Furthermore, because they conduct outward currents, the inward Na⁺ current (and Ca²⁺ current in the heart) will be short circuited during the AP, and more inward current will have to be passed to elicit an AP. Hence, opening of these channels may well cause enhanced K⁺ release during muscle activity, something which was clearly shown during -adrenergic stimulation of the heart (16, 177).

In recent years there has been much focus on the ATP-sensitive K⁺ channels. They open at [ATP]_c well below the millimolar range (395, 501), although openings are seen at 2 mM (615). Such low [ATP]_c are not seen under physiological conditions nor in the ischemic myocardium (12). Several additional factors are important. First, the K_ATP channels are pH sensitive (although less so in heart compared with skeletal muscle) so that when intracellular pH is lowered open probability is increased (130, 132, 395). Second, it has been pointed out that the channels are so numerous that even a small increase in the probability of opening that occurs with quite small reductions of the [ATP]_c may be sufficient to cause a large current (488, 685). It has also been argued that the [ATP] in the subsarcolemmal space may be different from that of the cytosol (304, 682). However, recently, in an ingenious experiment on heart cells where the Na⁺-K⁺ pump was manipulated to run in both normal and reverse mode to vary the subsarcolemmal [ATP], Priebe et al. (521) compared results of cell-attached and isolated patch-clamp experiments. They concluded that variable consumption of ATP (and in the reverse mode production of ATP by the pump) will transiently affect I_K(ATP), but the effect was passing and they therefore concluded that the submembrane [ATP] is readily controlled by the cytosolic ATP pool. In a recent study, Kabakov (336) also noted a tight relationship between Na⁺-K⁺ pump rate and I_K(ATP) and that a stable submembrane depletion of ATP seemed to occur that could explain the activation of the ATP-sensitive K⁺ channels. Interestingly, this author also points out that the interaction of these two membrane proteins via the submembrane [ATP] will affect the way the Na⁺-K⁺ pump contributes to E_m. In accordance with these results, it was recently confirmed that inhibition of the Na⁺-K⁺ pump with digitalis in metabolically stressed cardiomyocytes will also close the ATP-sensitive K⁺ channels (644). Third, it has recently been shown that these channels may also open during mechanical stress (648), possibly through their anchorage to the cytoskeleton (216). Fourth, at least in heart, although not necessarily in skeletal muscle, MgADP is an important regulator of channel activity, since ADP can antagonize channel closure by ATP (131). MgADP binds to the sulfonylurea receptor that is associated with the channel protein. Thus the K_ATP channel is highly sensitive to the [ATP]/[ADP], which has caused some investigators to call it "metabolic sensor" (641). All these mechanisms may help explain why K_ATP channels are responsible for the great increase of membrane K⁺ conductance seen during ischemia and in metabolically exhausted skeletal muscle fibers (212, 228, 366, 435, 685).

The issue of tissue content of Na⁺-K⁺ pumps has been extensively reviewed (99, 103, 560), so let it here suffice to mention that the number of [³H]ouabain binding sites that reflect the Na⁺-K⁺ pump density in skeletal muscle is in the range of 300 pmol/g wet tissue wt and slightly higher in fast-twitch muscles compared with slow-twitch muscles (see sect. V). In the heart, the tissue content is much higher, approaching 2,000 pmol/g in rats (389), whereas about one-third of that is found in human and pig cardiac tissues (174, 560, 561, 566). With the assumption of an in vivo maximum pumping rate of 450 Na⁺ or 300 K⁺ per second per pump protein, these levels translate into maximum pump capacities for K⁺ of ~100 and 200-600 nmol · g¹ · s¹ (6 and 12-36 mmol · kg¹ · min¹) in skeletal muscle and heart, respectively. Several studies have confirmed that these pump rates calculated from [³H]ouabain binding measurements can actually be measured in the intact tissue after Na⁺ loading of the cells to [Na⁺]_c levels that saturate the internal site of the pump protein (105, 574). From these data it is clear that skeletal muscle has a much lower reserve capacity of the Na⁺-K⁺ pump as compared with the heart, since stimulation frequencies are often in the range of 10-30 Hz, although they can even exceed 100 Hz in fast muscles, at least for short periods (41, 242, 341, 609). In contrast, stimulation frequencies in the heart are at maximum between 3 and 10 Hz depending on species. Therefore, as discussed in more detail in section VIIIB, Clausen (100) has calculated that under certain conditions of sustained high-frequency stimulation of skeletal muscle K⁺ release may actually exceed pump capacity. This may cause considerable dissipation of K_c⁺.

It has been generally held that muscle activity does not acutely change the number of active Na⁺-K⁺ pumps in the muscle. However, recently, Juel et al. (333a) reported a significant translocation of Na⁺-K⁺ pumps to the plasma membrane during exercise. Provided this is correct, it is an important way of increasing the maximum pump capacity. In the following we focus on other means of increasing Na⁺-K⁺ pump rate.

A) THE CONCEPT OF NA⁺ pump lag. An important issue is whether the Na⁺-K⁺ pump is activated quickly enough to cope with increases in K⁺ release in situations where the maximum pump capacity is not taxed. In excitable tissues this is clearly not the case. In nervous tissue as well as in heart and skeletal muscle, the sudden increase of outward repolarizing K⁺ currents associated with higher firing frequency clearly exceeds pump-mediated K⁺ uptake rate for a period (195, 385, 626). Eventually, pump-mediated uptake may or may not match release. During the transition from one steady state to another with a higher firing frequency, there is a transient dissipation of intracellular K⁺ (177, 252, 314, 332). To explain this slow activation of the pump, the concept of the Na⁺ pump lag was put forward (384, 706). It was based on the assumption that activation of the pump was merely due to the rise in [Na⁺]_c that followed electrical activity (706). Also, the rapid extracellular accumulation of K⁺ has been implied to activate the pump, and also other means of activating the pump, such as electrical and mechanical activity, have been proposed, (184, 186, 496).

B) NA⁺-k⁺ pump stimulation by k⁺ and na⁺. Clearly, very important control of Na⁺-K⁺ pump rate is achieved by its sensitivity to [K⁺]_s and [Na⁺]_c. This issue was recently reviewed by Semb and Sejersted (576). The stimulation of the pump by [K⁺]_s seems to have a k_0.5 (i.e., the [K⁺]_s that stimulates the Na⁺-K⁺ pump to 50% of its maximum pump rate) of 0.8-1.5 mM. This value is obtained in isolated cells where the problem of extracellular clefts and diffusion through restricted space in multicellular preparations have been eliminated (117, 486, 527). Hence, at a normal [K⁺]_s of 4 mM, the extracellular K⁺ site of the enzyme will be ~80% saturated. In this way, pump activation due to extracellular K⁺ accumulation cannot amount to more than 20%. On the other hand, a reduction in [K⁺]_s can cause a significant reduction in Na⁺-K⁺ pump rate. This may be relevant during recovery after exercise, when [K⁺]_v below normal resting value is observed. In fact, the sensitivity of the Na⁺-K⁺ pump to [K⁺]_s may in this situation prevent the pump from lowering [K⁺]_s too much. In a clinical setting, during hypokalemia due to renal or gastrointestinal losses, reduced pump activity can explain several of the symptoms.

Pump sensitivity to [Na⁺]_c is somewhat less clear. There are at least three reasons why data based on experiments with the isolated enzyme may not be extrapolated to the intact tissue. First, vectorial transport with different concentrations on each side of the membrane cannot be replicated in the vial. Second, there might be important limitations to diffusion in the subsarcolemmal space of intact cells (fuzzy space) (576), which is likely to disappear when the membrane is ruptured. Third, the Na⁺-K⁺ pump is probably anchored to the cytoskeleton by ankyrin (144, 487). This connection may be important for function (382) and will probably be ruptured in isolated membrane fractions as well as in excised giant patches. As reviewed by Semb and Sejersted (576), investigations on intact heart cells from several species indicate that when expressed in terms of the Hill equation constants, k_0.5 seems to be ~15 mM in terms of concentration, and the Hill coefficient is ~2. However, in the rat heart, k_0.5 is probably higher, which tallies with the higher resting [Na⁺]_c in heart cells from this species (575). At the time of publishing, we are only aware of one preliminary study in which [Na⁺]_c was measured directly in the rat soleus muscle, and k_0.5 was found to be slightly higher than 15 mM (57).

One important consideration arises from this estimate, namely, how in resting skeletal muscle is it possible that Na⁺-K⁺ pump rate is as small as 4-5% of its maximum capacity (94, 99, 105, 188). With ion-selective microelectrodes, [Na⁺]_c in resting mouse soleus muscle has been reported at 11.1 and 12.7 mM (329, 331), and at about the same level in frog muscle (26). Doing repeated impalements (n = 60) on isolated rat soleus muscles at 37°C with a conventional and an Na⁺-selective electrode, Bjørklund and Sejersted found E_m to be 67.2 mV and [Na⁺]_c 18.5 mM (unpublished data). With more indirect techniques the estimates of [Na⁺]_c are between 20 and 30 mM in rat muscles (183, 496) and in human muscle between 6 and 13 mM (595) and ~21 mM (589). Therefore, it would be safe to say that [Na⁺]_c is probably in the range of 15 mM in resting slow-twitch skeletal muscle. In fast-twitch muscle, [Na⁺]_c is significantly lower (183). With a k_0.5 of 15 mM, Na⁺-K⁺ pump rates should be ~50% and not 4-5% in the soleus muscle. Unless a large fraction of the pumps are silent, it follows that the k_0.5 for pump stimulation by [Na⁺]_c must be considerably higher than 15 mM in resting skeletal muscle. So far, this is in seeming contrast to existing estimates. In contrast, in quiescent heart tissue, [Na⁺]_c is well below 10 mM (143, 396, 574, 580), which fits with a k_0.5 of 15 mM and a basal Na⁺-K⁺ pump rate in the order of 10% of maximum (575). In skeletal muscle, there are several observations that fit with a k_0.5 of ~15 mM when the muscle is active. For instance, maximum pump rates seem to be achieved with [Na⁺]_c not much higher than 30 mM (496, 574). Following this simple line of reasoning, it would make sense to assume that the sensitivity of the Na⁺-K⁺ pump for Na⁺ is probably regulated in skeletal muscle. Further evidence for this is presented below.

C) FACTORS THAT CAN AFFECT LOCAL CONCENTRATIONS OF K⁺ and na⁺ in the cell. Let us first examine the basic concept of the Na⁺ pump lag with a constant k_0.5. The rate of activation that can be achieved by an increase of [Na⁺]_c is dependent on the ratio between the increase in K⁺ release (release per AP multiplied by the increase in firing frequency) and the amount of Na⁺-K⁺ pumps available in addition to the Na⁺ sensitivity of the pump. In Figure 4 we present some simulation data (571). In Figure 4, A and C, Na⁺-K⁺ pump activation has been plotted as a function of time after an increase in heart rate of 3 Hz and an increase in muscle firing frequency of 30 Hz, provided increased [Na⁺]_c was the only pump stimulus. In both tissues the starting [Na⁺]_c was set at a level equal to 8 mM. This value is probably slightly higher than in resting heart cells in most species, while at the same time somewhat lower than the value discussed above for skeletal muscle. These deviations do not affect the results of the simulation with regard to the main conclusions. Clearly, in heart tissue, complete adjustment of pump rate can in theory be achieved in the course of a few minutes with an increase of [Na⁺]_c of ~1 mM (Fig. 4, full drawn line in A and C). In contrast to heart tissue, the number of pumps available in skeletal muscle is fewer while the firing frequency is higher. Therefore, more Na⁺ must accumulate intracellularly to achieve adequate pump activation. However, even if the simulation allows [Na⁺]_c to rise to well above 20 mM (dotted line in C), pump activation would be slow and incomplete if this were the only stimulus for pump activation (dotted line in A). Hence, these simple simulations that utilize existing data for Na⁺-K⁺ pump density and K⁺ release (incorporating firing frequency and the size of the repolarizing current) show that the original Na⁺ pump lag concept may account for the complete compensation that occurs in heart tissue but do not provide a full explanation for Na⁺-K⁺ pump activation in skeletal muscle. The question therefore is whether other mechanisms contribute to pump activation during exercise.