Slow volume transients in amphibian skeletal muscle fibres studied in hypotonic solutions

Passive skeletal muscle can function as an osmotic engine

Muscles are composite structures. The protein filaments responsible for force production are bundled within fluid-filled cells, and these cells are wrapped in ordered sleeves of fibrous collagen. Recent models suggest that the mechanical interaction between the intracellular fluid and extracellular collagen is essential to force production in passive skeletal muscle, allowing the material stiffness of extracellular collagen to contribute to passive muscle force at physiologically relevant muscle lengths. Such models lead to the prediction, tested here, that expansion of the fluid compartment within muscles should drive forceful muscle shortening, resulting in the production of mechanical work unassociated with contractile activity. We tested this prediction by experimentally increasing the fluid volumes of isolated bullfrog semimembranosus muscles via osmotically hypotonic bathing solutions. Over time, passive muscles bathed in hypotonic solution widened by 16.44 ± 3.66% (mean ± s.d.) as they took on fluid. Concurrently, muscles shortened by 2.13 ± 0.75% along their line of action, displacing a force-regulated servomotor and doing measurable mechanical work. This behaviour contradicts the expectation for an isotropic biological tissue that would lengthen when internally pressurized, suggesting a functional mechanism analogous to that of engineered pneumatic actuators and highlighting the significance of three-dimensional force transmission in skeletal muscle.

Functional consequences of NKCC2 splice isoforms: insights from a Xenopus oocyte model

The Na(+)-K(+)-2Cl(-) cotransporter NKCC2 is exclusively expressed in the renal thick ascending limb (TAL), where it exists as three main splice isoforms, NKCC2B, NKCC2A, and NKCC2F, with the latter two predominating. NKCC2A is expressed in both medullary and cortical TAL, but NKCC2F localizes to the medullary TAL. The biochemical characteristics of the isoforms have been extensively studied by ion uptake studies in Xenopus oocytes, but the functional consequences of alternative splicing remain unclear. We developed a charge-difference model of an NKCC2-transfected oocyte. The model closely recapitulated existing data from ion-uptake experiments. This allowed the reconciliation of different apparent Km values reported by various groups, which have hitherto either been attributed to species differences or remained unexplained. Instead, simulations showed that apparent Na(+) and Cl(-) dependencies are influenced by the ambient K(+) or Rb(+) bath concentrations, which differed between experimental protocols. At steady state, under bath conditions similar to the outer medulla, NKCC2F mediated greater Na(+) reabsorption than NKCC2A. Furthermore, Na(+) reabsorption by the NKCC2F-transfected oocyte was more energy efficient, as quantified by J NKCC/J Pump. Both the increased Na(+) reabsorption and the increased efficiency were eroded as osmolarity decreased toward levels observed in the cortical TAL. This supports the hypothesis that the NKCC2F is a medullary specialization of NKCC2 and demonstrates the utility of modeling in analyzing the functional implications of ion uptake data at physiologically relevant steady states.

Relationships between resting conductances, excitability, and t-system ionic homeostasis in skeletal muscle

Activation of skeletal muscle fibers requires rapid sarcolemmal action potential (AP) conduction to ensure uniform excitation along the fiber length, as well as successful tubular excitation to initiate excitation–contraction coupling. In our companion paper in this issue, Pedersen et al. (2011. J. Gen. Physiol. doi:10.1085/jgp.201010510) quantify, for subthreshold stimuli, the influence upon both surface conduction velocity and tubular (t)-system excitation of the large changes in resting membrane conductance (G_M) that occur during repetitive AP firing. The present work extends the analysis by developing a multi-compartment modification of the charge–difference model of Fraser and Huang to provide a quantitative description of the conduction velocity of actively propagated APs; the influence of voltage-gated ion channels within the t-system; the influence of t-system APs on ionic homeostasis within the t-system; the influence of t-system ion concentration changes on membrane potentials; and the influence of Phase I and Phase II G_M changes on these relationships. Passive conduction properties of the novel model agreed with established linear circuit analysis and previous experimental results, while key simulations of AP firing were tested against focused experimental microelectrode measurements of membrane potential. This study thereby first quantified the effects of the t-system luminal resistance and voltage-gated Na⁺ channel density on surface AP propagation and the resultant electrical response of the t-system. Second, it demonstrated the influence of G_M changes during repetitive AP firing upon surface and t-system excitability. Third, it showed that significant K⁺ accumulation occurs within the t-system during repetitive AP firing and produces a baseline depolarization of the surface membrane potential. Finally, it indicated that G_M changes during repetitive AP firing significantly influence both t-system K⁺ accumulation and its influence on the resting membrane potential. Thus, the present study emerges with a quantitative description of the changes in membrane potential, excitability, and t-system ionic homeostasis that occur during repetitive AP firing in skeletal muscle.

Regional differences in osmotic behavior in brain during acute hyponatremia: an in vivo MRI-study of brain and skeletal muscle in pigs

Brain edema is suggested to be the principal mechanism underlying the symptoms in acute hyponatremia. Identification of the mechanisms responsible for global and regional cerebral water homeostasis during hyponatremia is, therefore, of utmost importance. To examine the osmotic behavior of different brain regions and muscles, in vivo-determined water content (WC) was related to plasma sodium concentration ([Na(+)]) and brain/muscle electrolyte content. Acute hyponatremia was induced with desmopressin acetate and infusion of a 2.5% glucose solution in anesthetized pigs. WC in different brain regions and skeletal muscle was estimated in vivo from T(1) maps determined by magnetic resonance imaging (MRI). WC, expressed in gram water per 100 g dry weight, increased significantly in slices of the whole brain [342(SD = 14) to 363(SD = 21)] (6%), thalamus [277(SD = 13) to 311(SD = 24)] (12%) and white matter [219(SD = 7) to 225(SD = 5)] (3%). However, the WC increase in the whole brain and white mater WC was less than expected from perfect osmotic behavior, whereas in the thalamus, the water increase was as expected. Brain sodium content was significantly reduced. Muscle WC changed passively with plasma [Na(+)]. WC determined with deuterium dilution and tissue lyophilzation correlated well with MRI-determined WC. In conclusion, acute hyponatremia induces brain and muscle edema. In the brain as a whole and in the thalamus, regulatory volume decrease (RVD) is unlikely to occur. However, RVD may, in part, explain the observed lower WC in white matter. This may play a potential role in osmotic demyelination.

Malformed mdx myofibers have normal cytoskeletal architecture yet altered EC coupling and stress-induced Ca2+ signaling

Skeletal muscle function is dependent on its highly regular structure. In studies of dystrophic (dy/dy) mice, the proportion of malformed myofibers decreases after prolonged whole muscle stimulation, suggesting that the malformed myofibers are more prone to injury. The aim of this study was to assess morphology and to measure excitation-contraction (EC) coupling (Ca(2+) transients) and susceptibility to osmotic stress (Ca(2+) sparks) of enzymatically isolated muscle fibers of the extensor digitorum longus (EDL) and flexor digitorum brevis (FDB) muscles from young (2-3 mo) and old (8-9 mo) mdx and age-matched control mice (C57BL10). In young mdx EDL, 6% of the myofibers had visible malformations (i.e., interfiber splitting, branched ends, midfiber appendages). In contrast, 65% of myofibers in old mdx EDL contained visible malformations. In the mdx FDB, malformation occurred in only 5% of young myofibers and 11% of old myofibers. Age-matched control mice did not display the altered morphology of mdx muscles. The membrane-associated and cytoplasmic cytoskeletal structures appeared normal in the malformed mdx myofibers. In mdx FDBs with significantly branched ends, an assessment of global, electrically evoked Ca(2+) signals (indo-1PE-AM) revealed an EC coupling deficit in myofibers with significant branching. Interestingly, peak amplitude of electrically evoked Ca(2+) release in the branch of the bifurcated mdx myofiber was significantly decreased compared with the trunk of the same myofiber. No alteration in the basal myoplasmic Ca(2+) concentration (i.e., indo ratio) was seen in malformed vs. normal mdx myofibers. Finally, osmotic stress induced the occurrence of Ca(2+) sparks to a greater extent in the malformed portions of myofibers, which is consistent with deficits in EC coupling control. In summary, our data show that aging mdx myofibers develop morphological malformations. These malformations are not associated with gross disruptions in cytoskeletal or t-tubule structure; however, alterations in myofiber Ca(2+) signaling are evident.

Control of cell volume in skeletal muscle

Regulation of cell volume is a fundamental property of all animal cells and is of particular importance in skeletal muscle where exercise is associated with a wide range of cellular changes that would be expected to influence cell volume. These complex electrical, metabolic and osmotic changes, however, make rigorous study of the consequences of individual factors on muscle volume difficult despite their likely importance during exercise. Recent charge-difference modelling of cell volume distinguishes three major aspects to processes underlying cell volume control: (i) determination by intracellular impermeant solute; (ii) maintenance by metabolically dependent processes directly balancing passive solute and water fluxes that would otherwise cause cell swelling under the influence of intracellular membrane-impermeant solutes; and (iii) volume regulation often involving reversible short-term transmembrane solute transport processes correcting cell volumes towards their normal baselines in response to imposed discrete perturbations. This review covers, in turn, the main predictions from such quantitative analysis and the experimental consequences of comparable alterations in extracellular pH, lactate concentration, membrane potential and extracellular tonicity. The effects of such alterations in the extracellular environment in resting amphibian muscles are then used to reproduce the intracellular changes that occur in each case in exercising muscle. The relative contributions of these various factors to the control of cell volume in resting and exercising skeletal muscle are thus described.

Extracellular charge adsorption influences intracellular electrochemical homeostasis in amphibian skeletal muscle

The membrane potential measured by intracellular electrodes, E_m, is the sum of the transmembrane potential difference (E₁) between inner and outer cell membrane surfaces and a smaller potential difference (E₂) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space. This study investigates the influence of E₂ upon transmembrane ion fluxes, and hence cellular electrochemical homeostasis, using an integrative approach that combines computational and experimental methods. First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations. Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume. Second, the novel analytic glycocalyx formulation was incorporated into the charge-difference cellular model of Fraser and Huang to simulate the influence of extracellular fixed charges upon intracellular ionic homeostasis. Experimental measurements of E_m supported the resulting predictions that an increased magnitude of extracellular fixed charge increases net transmembrane ionic leak currents, resulting in either a compensatory increase in Na⁺/K⁺-ATPase activity, or, in cells with reduced Na⁺/K⁺-ATPase activity, a partial dissipation of transmembrane ionic gradients and depolarization of E_m.

Membrane potentials in Rana temporaria muscle fibres in strongly hypertonic solutions

Conventional microelectrode methods were used to measure variations in resting membrane potentials, E(m), of intact amphibian skeletal muscle fibres over a wide range of increased extracellular tonicities produced by inclusion of varying extracellular concentrations of sucrose. Moderate increases in extracellular tonicity to up to 2.6x normal (2.6tau) under Cl(-) free conditions produced negative shifts in E(m) that followed expectations for the K(+) Nernst equation (E(K)) applied to a perfect osmometer containing a conserved intracellular K(+) content despite any accompanying cell volume change. In contrast, E(m) remained stable in fibres studied in otherwise similar Cl(-) containing solutions, consistent with E(m) stabilization despite negative shifts in E(K) through inward cation-Cl(-) co-transport activity. Short exposures to higher tonicities (>3tau) similarly produced negative shifts in E(m) in Cl(-) free but not Cl(-) containing solutions. However, prolonged exposures to solutions of >3tau caused gradual net positive changes in E (m) in both Cl(-) containing and Cl(-) free solutions suggesting that these changes were independent of cation-Cl(-) transport. Indeed, there was no evidence of cation-Cl(-) co-transport activity in strongly hypertonic solutions despite its predicted energetic favourability, suggesting its possible regulation by E (m) in muscle. Additional findings implicated a failure to maintain greatly increased transmembrane [K(+)] gradients in these E(m) changes. Thus: (1) halving or doubling [K(+)](e) produced negative or positive shifts in E(m), respectively in isotonic or moderately hypertonic (<2.7tau), but not strongly hypertonic (>3tau) solutions; (2) subsequent restoration of isotonic extracellular conditions produced further positive changes in E(m) consistent with a dilution of the depleted [K(+)](i) by fibres regaining their original resting volumes; (3) quantitative modelling similarly predicted a gradual net efflux of K(+) as the balance between active and passive [K(+)] fluxes altered due to increased transmembrane [K(+)] gradients in hypertonic and low [K(+)](e) solutions. However, the observed positive changes in E(m) in the most strongly hypertonic solutions eventually exceeded these predictions suggesting additional limitations on Na(+)/K(+)-ATPase activity in strongly hypertonic solutions.

Quantitative techniques for steady-state calculation and dynamic integrated modelling of membrane potential and intracellular ion concentrations

The membrane potential (E(m)) is a fundamental cellular parameter that is primarily determined by the transmembrane permeabilities and concentration gradients of various ions. However, ion gradients are themselves profoundly influenced by E(m) due to its influence upon transmembrane ion fluxes and cell volume (V(c)). These interrelationships between E(m), V(c) and intracellular ion concentrations make computational modelling useful or necessary in order to guide experimentation and to achieve an integrated understanding of experimental data, particularly in complex, dynamic, multi-compartment systems such as skeletal and cardiac myocytes. A variety of quantitative techniques exist that may assist such understanding, from classical approaches such as the Goldman-Hodgkin-Katz equation and the Gibbs-Donnan equilibrium, to more recent "current-summing" models as exemplified by cardiac myocyte models including those of DiFrancesco & Noble, Luo & Rudy and Puglisi & Bers, or the "charge-difference" modelling technique of Fraser & Huang so far applied to skeletal muscle. In general, the classical approaches provide useful and important insights into the relationships between E(m), V(c) and intracellular ion concentrations at steady state, providing their core assumptions are fully understood, while the more recent techniques permit the modelling of changing values of E(m), V(c) and intracellular ion concentrations. The present work therefore reviews the various approaches that may be used to calculate E(m), V(c) and intracellular ion concentrations with the aim of establishing the requirements for an integrated model that can both simulate dynamic systems and recapitulate the key findings of classical techniques regarding the cellular steady state. At a time when the number of cellular models is increasing at an unprecedented rate, it is hoped that this article will provide a useful and critical analysis of the mathematical techniques fundamental to each of them.

The contribution of refractoriness to arrhythmic substrate in hypokalemic Langendorff-perfused murine hearts

The clinical effects of hypokalemia including action potential prolongation and arrhythmogenicity suppressible by lidocaine were reproduced in hypokalemic (3.0 mM K⁺) Langendorff-perfused murine hearts before and after exposure to lidocaine (10 μM). Novel limiting criteria for local and transmural, epicardial, and endocardial re-excitation involving action potential duration (at 90% repolarization, APD₉₀), ventricular effective refractory period (VERP), and transmural conduction time (Δlatency), where appropriate, were applied to normokalemic (5.2 mM K⁺) and hypokalemic hearts. Hypokalemia increased epicardial APD₉₀ from 46.6 ± 1.2 to 53.1 ± 0.7 ms yet decreased epicardial VERP from 41 ± 4 to 29 ± 1 ms, left endocardial APD₉₀ unchanged (58.2 ± 3.7 to 56.9 ± 4.0 ms) yet decreased endocardial VERP from 48 ± 4 to 29 ± 2 ms, and left Δlatency unchanged (1.6 ± 1.4 to 1.1 ± 1.1 ms; eight normokalemic and five hypokalemic hearts). These findings precisely matched computational predictions based on previous reports of altered ion channel gating and membrane hyperpolarization. Hypokalemia thus shifted all re-excitation criteria in the positive direction. In contrast, hypokalemia spared epicardial APD₉₀ (54.8 ± 2.7 to 60.6 ± 2.7 ms), epicardial VERP (84 ± 5 to 81 ± 7 ms), endocardial APD₉₀ (56.6 ± 4.2 to 63.7 ± 6.4 ms), endocardial VERP (80 ± 2 to 84 ± 4 ms), and Δlatency (12.5 ± 6.2 to 7.6 ± 3.4 ms; five hearts in each case) in lidocaine-treated hearts. Exposure to lidocaine thus consistently shifted all re-excitation criteria in the negative direction, again precisely agreeing with the arrhythmogenic findings. In contrast, established analyses invoking transmural dispersion of repolarization failed to account for any of these findings. We thus establish novel, more general, criteria predictive of arrhythmogenicity that may be particularly useful where APD₉₀ might diverge sharply from VERP.

The influence of intracellular lactate and H+ on cell volume in amphibian skeletal muscle

The combined effects of intracellular lactate and proton accumulation on cell volume, Vc, were investigated in resting Rana temporaria striated muscle fibres. Intracellular lactate and H+ concentrations were simultaneously increased by exposing resting muscle fibres to extracellular solutions that contained 20-80 mm sodium lactate. Cellular H+ and lactate entry was confirmed using pH-sensitive electrodes and 1H-NMR, respectively, and effects on Vc were measured using confocal microscope xz-scanning. Exposure to extracellular lactate up to 80 mm produced significant changes in pH and intracellular lactate (from a pH of 7.24 +/- 0.03, n = 8, and 4.65 +/- 1.07 mm, n = 6, respectively, in control fibres, to 6.59 +/- 0.03, n = 4, and 26.41 +/- 0.92 mm, n = 3, respectively) that were comparable to those observed following fatiguing stimulation (6.30-6.70 and 18.04 +/- 1.78 mm, n = 6, respectively). Yet, the increase in intracellular osmolarity expected from such an increase in intracellular lactate did not significantly alter Vc. Simulation of these experimental results, modified from the charge difference model of Fraser & Huang, demonstrated that such experimental manoeuvres produced changes in intracellular [H+] and [lactate] comparable to those observed during muscle fatigue, and accounted for this paradoxical conservation of Vc through balancing negative osmotic effects resulting from the net cation efflux that would follow a titration of intracellular membrane-impermeant anions by the intracellular accumulation of protons. It demonstrated that with established physiological values for intracellular buffering capacity and the permeability ratio of lactic acid and anionic lactate, P(LacH): P(Lac-), this would provide a mechanism that precisely balanced any effect on cell volume resulting from lactate accumulation during exercise.

Effect of repetitive stimulation on cell volume and its relationship to membrane potential in amphibian skeletal muscle

The effect of electrical stimulation on cell volume, V (c), and its relationship to membrane potential, E (m), was investigated in Rana temporaria striated muscle. Confocal microscope xz-plane scanning and histology of plastic sections independently demonstrated significant and reversible increases in V (c) of 19.8+/-0.62% (n=3) and 27.1+/-8.62% (n=3), respectively, after a standard stimulation protocol. Microelectrode measurements demonstrated an accompanying membrane potential change, DeltaE (m), of +23.6+/-0.98 mV (n=3). The extent to which this DeltaE (m) might contribute to the observed changes in V (c) was explored in quiescent muscle exposed to variations in extracellular potassium concentration, [K(+)](e). E (m) and V (c) varied linearly with log [K(+)](e) and [K(+)](e), respectively, in the range 2.5-15 mM (R (2)=0.99 and 0.96), and these results were used to reconstruct an approximately linear relationship between V (c) and E (m) (DeltaV (c)=0.85E (m)+68.53; R (2)=0.99) and hence derive the DeltaV (c) expected from the DeltaE (m) during stimulation. This demonstrated that both the time course and magnitude of the increase and recovery of V (c) observed in active muscles could be reproduced by the corresponding [K(+)](e)-induced depolarisation in quiescent muscles, suggesting that the depolarisation associated with membrane activity makes a substantial contribution to the cell swelling during exercise. Furthermore, conditions of Cl(-) deprivation abolished the relationship between E (m) and V (c), supporting a mechanism in which the depolarisation of E (m) drives a passive redistribution of Cl(-) and hence cellular entry of Cl(-) and K(+) and an accompanying, osmotically driven, increase in V (c).