A Theoretical Analysis of the Capacitance of Muscle Fibers Using a Distributed Model of the Tubular System

A model is developed to predict the changes in total capacitance (i.e. total charge stored divided by surface membrane potential) of the tubular system of muscle fibers. The tubular system is represented as a punctated disc and the area of membrane across which current flows is represented as a punctated annulus, the capacitance of the muscle fiber being proportional to this area. The area can be determined from a distributed model of the tubular system, in which the only resistance to radial current flow is presumed to be in the lumen of the tubules. Calculations are made of the variation of capacitance expected as the conductivity of the bathing solution is varied. These calculations include the effects of fixed charge in the tubular lumen and the effects of changes in the shape and volume of the tubular system in solutions of low conductivity. The calculated results fail to fit comparable experimental data, although they do qualitatively account for the known variation of the radial spread of contraction with conductivity of the bathing medium. It is pointed out that the existence of a significant "access resistance" at the mouth of the tubules might explain the discrepancy between theory and experiment.     

Impedance of Frog Skeletal Muscle Fibers in Various Solutions

The linear circuit parameters of 140 muscle fibers in nine solutions are determined from phase measurements fitted with three circuit models: the disk model, in which the resistance to radial current flow is in the lumen of the tubules; the lumped model, in which the resistance is at the mouth of the tubules; and the hybrid model, in which it is in both places. The lumped model fails to fit the data. The disk and hybrid model fit the data, but the optimal circuit values of the hybrid model seem more reasonable. The circuit values depend on sarcomere length. The conductivity of the lumen of the tubules is less than, and varies in a nonlinear manner with, the conductivity of the bathing solution, suggesting that the tubules are partially occluded by some material like basement membrane which restricts the mobility of ions and has fixed charge. The x2.5 hypertonic sucrose solution used in many voltage clamp experiments produces a large increase in the radial resistance, suggesting that control of the potential across the tubular membranes would be difficult to achieve. Glycerol-treated fibers have 90% of their tubular system insulated from the extracellular solution and 10% connected to the extracellular solution through a high resistance. We discuss the implications of our results for calculations of the nonlinear properties of muscle fibers, including the action potential and the radial spread of contraction.     

Sodium Flux in Necturus Proximal Tubule under Voltage Clamp

Na transport and electrical properties of Necturus renal proximal tubules were analyzed, in vivo, by a voltage clamp method which utilizes an axial electrode in the tubule lumen for passage of current and simultaneous determination of net fluid (or Na) flux by the split droplet method. When the average spontaneous transepithelial potential difference of –8 mv (lumen negative) was reduced to zero by current passage, net Na flux doubled from a mean of 107 to 227 pmoles/cm² per sec. The relationship between flux and potential over the range –25 to +10 mv was nonlinear, with flux equilibrium at –15 mv and droplet expansion at more negative values. Calculated Na permeability at flux equilibrium was 7.0 x 10^–6 cm/sec. Voltage transients, similar to those caused by intraepithelial unstirred layers, were observed at the end of clamping periods. Tubular electrical resistance measured by brief square or triangle wave pulses (<100 msec) averaged 43 ohm cm². The epithelial current-voltage relationship was linear over the range –100 to +100 mv, but displayed marked hysteresis during low frequency (<0.04 Hz) triangle wave clamps. The low transepithelial resistance and large opposing unidirectional ion fluxes suggest that passive ionic movements occur across extracellular shunt pathways, while the voltage transients and current-voltage hysteresis are consistent with the development of a local osmotic gradient within epithelium.     

Oscillations of voltage and resistance in Malpighian tubules of Aedes aegypti

The transepithelial voltage (V(t)) of isolated Malpighian tubules of the yellow fever mosquito Aedes aegypti spontaneously oscillates in more than half the tubules. Typically, V(t) decreases and then rises at a frequency of 2 oscillations/min with a duration of 16 s. In 6 isolated perfused tubules studied in detail, V(t) oscillates between 50.5 mV and 15.7 mV in parallel with (1) oscillations of the transepithelial resistance (R(t)) between 7.61 kOmegacm and 3.63 kOmegacm, (2) oscillations of the basolateral membrane voltage of principal cells between -56.7 mV and -72.2 mV, and (3) oscillations of the apical membrane voltage between 107.2 mV and 87.8 mV. The oscillations are dependent on the Cl concentration in the extracellular solutions. As R(t) decreases during the oscillations V(t) goes to the transepithelial equilibrium potential of Cl (E(cl)) indicating transient changes in transepithelial Cl conductance as the mechanism of voltage and resistance oscillations. Since the largest voltage oscillations take place across the whole epithelium and not across cell membranes, oscillating Cl conductances are localized to a single transepithelial Cl diffusion barrier such as the paracellular pathway. This conclusion is supported by the analysis of electrically equivalent circuits that identify the shunt pathway as the site of oscillating Cl conductances.     

Electric potential in cylindrical syncytia and muscle fibers

The model developed in an earlier paper using two coupled partial differential equations for calculating the intracellular and extracellular electric potentials in a syncytium is applied here to cylindrical geometry. Eigenfunction expansions are obtained for the potentials resulting from an intracellular point source of current. The required orthogonality relations for the two sets of coupled radial eigenfunctions are derived. The model is applied to the structure composed of the interior and the transverse tubules of a muscle fiber. Asymtotic expansions for ζ and β→0 are obtained, where ζ is the product of the effective intracellular resistivity, the fiber radius and the outer surface membrane admittance per unit area, and β is the ratio of the effective intracellular resistivity to that of the tubular lumen. Earlier results from the distributed circuit model of a muscle fiber are recovered when ζ and β are small, and for a nerve axon when β=0.     

Kinetics of Na(+) transport in necturus proximal tubule

The dependence of proximal tubular sodium and fluid readsorption on the Na(+) concentration of the luminal and peritubular fluid was studied in the perfused necturus kidney. Fluid droplets, separated by oil from the tubular contents and identical in composition to the vascular perfusate, were introduced into proximal tubules, reaspirated, and analyzed for Na(+) and [(14)C]mannitol. In addition, fluid transport was measured in short-circuited fluid samples by observing the rate of change in length of the split droplets in the tubular lumen. Both reabsorptive fluid and calculated Na fluxes were simple, storable functions of the perfusate Na(+) concentration (K(m) = 35-39 mM/liter, V(max) = 1.37 control value). Intracellular Na(+), determined by tissue analysis, and open-circuit transepithelial electrical potential differences were also saturable functions of extracellular Na(+). In contrast, net reabsorptive fluid and Na(+) fluxes were linearly dependent on intracellular Na(+) and showed no saturation, even at sharply elevated cellular sodium concentrations. These concentrations were achieved by addition of amphotericin B to the luminal perfusate, a maneuver which increased the rate of Na(+) entry into the tubule cells and caused a proportionate rise in net Na(+) flux. It is concluded that active peritubular sodium transport in proximal tubule cells of necturus is normally unsaturated and remains so even after amphotericin-induced enhancement of luminal Na(+) entry. Transepithelial movement of NaCl may be described by a model with a saturable luminal entry step of Na(+) or NaCl into the cell and a second, unsaturated active transport step of Na(+) across the peritubular cell boundary.     

A fixed charge model of the transverse tubular system of frog sartorius

Volume changes of the transverse tubular system (T system) of frog sartorius in different solutions can be explained by a model which assumes fixed negative charges in the T system lumen, an open T system mouth, and a Donnan equilibrium between the T system and external solution. The T system volume is regulated by the osmotic pressure difference between the lumen and external solution, as well as by constraining forces whose nature is as yet unclear. The decreased swelling tendency produced by hypotonic solutions and increased tendency produced by some hypertonic solutions are ascribed to changes in the pressure constraint from the sarcoplasm. Fixed charge concentration was estimated tentatively from swelling and resistivity data to be between 0.1 and 0.4 M.     

Voltage clamp simulations for multifiber bundles in a double sucrose gap: cable complications

A theoretical model is presented for voltage clamp of a bundle of cylindrical excitable cells in a double sucrose gap. The preparation in the test node is represented by a single one-dimensional cable (length/diameter ratio approximately) with standard Hodgkin-Huxley kinetics for transmembrane Na current. Imperfections of voltage control due to internal (longitudinal) resistivity and external (radial) resistance in series to the membrane are analysed. The electrical behavior of a fiber is described by the cable equation with appropriate boundary conditions and subsidiary equations reflecting the membrane characteristics. Membrane voltage and current distribution in response to a step command was obtained by numerical integration. The results are described in two papers. The present paper deals with the effect of internal resistivity with the external resistance being neglected. The closed loop response of a fiber displays a strong tendency to oscillate. To stabilize the system a phase lead was inserted and the gain of the control amplifier was reduced. Conditions for stability were examined by Nyquist analysis. When the Na system was activated by a command pulse below ENa, a voltage gradient developed between a depolarization (relative to the command signal) at the end where voltage was monitored and a hyperpolarization at the site of current injection. In spite of a poor voltage control the total measured current appeared to have a smooth transient. With large voltage gradients a small, second inward current was seen. At a low (high) Na conductance maximum peak inward current was larger (smaller) that the current expected from ideal space clamping.     

A reconstruction of charge movement during the action potential in frog skeletal muscle.

The transfer of intramembrane charge during an action potential at 4 degrees C was reconstructed for a model representing the electrical properties of frog skeletal muscle by a cylindrical surface membrane and 16 concentric annuli ("shells") of transverse tubular membrane of equal radial thickness. The lumina of the transverse tubules were separated from extracellular fluid by a fixed series resistance. The quantity, geometrical distribution and steady-state and kinetic properties of charge movement components were described by equations incorporating earlier experimental results. Introducing such nonlinear charge into the distributed model for muscle membrane diminished the maximum amplitude of the action potential within the transverse tubules by 2 mV but increased the maximum size of the after-depolarization by 3-5 mV and also its duration. However, these changes were small in comparison to the 135-mV deflection represented by the action potential. They therefore did not justify altering the values of the electrical parameters adopted by Adrian R.H., and L.D. Peachey (1973. J. Physiol. [Lond.]. 235:103-131.) and used in the present calculations. Cable properties significantly affected the time course and extent of charge movement in each shell during action potential propagation into the tubular system. Q beta charge moved relatively rapidly in all annuli, and did so without significant latency (approximately 0.3 ms) after the surface action potential upstroke. Its peak displacement varied between 53 and 58% (the range representing the difference fiber edge/fiber axis) of the total Q beta charge. This was attained at 5.4-7.3 ms after the stimulus, depending on depth within the tubules. In contrast, q gamma moved after a 1.7-2.9 ms latency and achieved a peak displacement of up to 22-34% of available charge. Both charge movement species could be driven by repetitive (47.7 Hz) action potentials without buildup of charge transfer. Such stimulus frequencies would normally cause tetanus. Latencies in q gamma charge movement in response to an action potential were resolved into (a) propagation of tubular depolarization required to gain the "threshold" of q gamma charge (0.8-1.5 ms) and (b) dielectric loss processes. The latter took consistently around 1.5 ms throughout the tubular system. Taken with (c) the earlier reports of a minimal latency in delta [Ca2+] signals attributed to tubulo-cisternal coupling following voltage sensing (approximately 2 ms: Zhu, P.H., I. Parker, and R. Miledi., 1986. Proc. R. Soc. Lond. B. Biol. Sci. 229:39-46.).(ABSTRACT TRUNCATED AT 400 WORDS)     

An improved vaseline gap voltage clamp for skeletal muscle fibers

A Vaseline gap potentiometric recording and voltage clamp method is developed for frog skeletal muscle fibers. The method is based on the Frankenhaeuser-Dodge voltage clamp for myelinated nerve with modifications to improve the frequency response, to compensate for external series resistance, and to compensate for the complex impedance of the current-passing pathway. Fragments of single muscle fibers are plucked from the semitendinosus muscle and mounted while depolarized by a solution like CsF. After Vaseline seals are formed between fluid pools, the fiber ends are cut once again, the central region is rinsed with Ringer solution, and the feedback amplifiers are turned on. Errors in the potential and current records are assessed by direct measurements with microelectrodes. The passive properties of the preparation are simulated by the "disk" equivalent circuit for the transverse tubular system and the derived parameters are similar to previous measurements with microelectrodes. Action potentials at 5 degrees C are long because of the absence of delayed rectification. Their shape is approximately simulated by solving the disk model with sodium permeability in the surface and tubular membranes. Voltage clamp currents consist primarily of capacity currents and sodium currents. The peak inward sodium current density at 5 degrees C is 3.7 mA/cm2. At 5 degrees C the sodium currents are smoothly graded with increasing depolarization and free of notches suggesting good control of the surface membrane. At higher temperatures a small, late extra inward current appears for small depolarizations that has the properties expected for excitation in the transverse tubular system. Comparison of recorded currents with simulations shows that while the transverse tubular system has regenerative sodium currents, they are too small to make important errors in the total current recorded at the surface under voltage clamp at low temperature. The tubules are definitely not under voltage clamp control.     

Bicarbonate transport mechanisms in the Ambystoma kidney proximal tubule: transepithelial potential measurements

Modes of bicarbonate entry from tubule lumen to cell were examined in isolated Ambystoma proximal tubules, using determinations of transepithelial potential differences (V3). (1) Upon removal of luminal substrate, tubules first equilibrated in bilateral (lumen and bath) 94.72 mM Cl- and 10 mM HCO3- yielded a change in V3 between the experimental and control circumstances of +1.8 mV (delta V3). (2) The identical experiment conducted under the condition of symmetrical 4.72 mM Cl- produced a delta V3 of +7.6 mV. This reduction of luminal and bath Cl- generates an amplification of delta V3 by a factor of 4.4 and reflects a substantial increase in the paracellular Cl- shunt resistance. Ensuing experiments were conducted in bilateral nominally Cl(-)-free solutions and in the absence of luminal substrate. The experimental protocols are divided into several situations where HCO3- is removed from the lumen, bath, or lumen and bath; the HCO3- removal sequences are repeated in the presence of luminal SITS and then after SITS washout. 0.5 mM SITS (4-acetoamido-4-isothiocyanostilbene-2,2'-disulfonate) was applied exclusively to the luminal perfusate. (1) Removal of luminal HCO3- in the absence of SITS produces a delta V3 of -1.9 mV, whereas, in the presence of SITS, the delta V3 measures -1.3 mV. Subsequent removal of luminal HCO3- in the presence of bath HCO3- (in the presence of luminal SITS) yields a delta V3 of -1.0 mV. All of these measurements reflect a decrease in HCO3- current across the basolateral membrane Na+ (HCO3-)n co-transporter; the role of a possible Cl-/Anion- antiport cannot be assessed. (2) Removal of bath HCO3- in the absence of SITS yields a delta V3 of +1.5 mV, whereas, in the presence of SITS, the delta V3 value measures +1.2 mV. Subsequent removal of bath HCO3- in the absence of luminal HCO3- (in the presence of SITS) yields a delta V3 of +0.8 mV. These experiments are consistent with an increase in HCO3- current across the basolateral Na+(HCO3-)n co-transporter, do not rule out the possibility of an apical HCO3- conductance pathway, and diminish the likelihood of an apical Cl-/HCO3- antiport system.     

Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system.

This paper presents the construction, derivation, and test of a mesh model for the electrical properties of the transverse tubular system (T-system) in skeletal muscle. We model the irregular system of tubules as a random network of miniature transmission lines, using differential equations to describe the potential between the nodes and difference equations to describe the potential at the nodes. The solution to the equations can be accurately represented in several approximate forms with simple physical and graphical interpretations. All the parameters of the solution are specified by impedance and morphometric measurements. The effect of wide circumferential spacing between T-system openings is analyzed and the resulting restricted mesh model is shown to be approximated by a mesh with an access resistance. The continuous limit of the mesh model is shown to have the same form as the disk model of the T-system, but with a different expression for the tortuosity factor. The physical meaning of the tortuosity factor is examined, and a short derivation of the disk model is presented that gives results identical to the continuous limit of the mesh model. Both the mesh and restricted mesh models are compared with experimental data on the impedance of muscle fibers of the frog sartorius. The derived value for the resistivity of the lumen of the tubules is not too different from that of the bathing solution, the difference probably arising from the sensitivity of this value to errors in the morphometric measurements.     

Action Potential in the Transverse Tubules and Its Role in the Activation of Skeletal Muscle

The double sucrose-gap method was applied to single muscle fibers of Xenopus. From the "artificial node" of the fiber, action potentials were recorded under current-clamping condition together with twitches of the node. The action potentials were stored on magnetic tape. The node was then made inexcitable by tetrodotoxin or by a sodium-free solution, and the wave form of the action potential stored on magnetic tape was imposed on the node under voltage-clamp condition (simulated AP). The twitch height caused by the simulated AP's was always smaller than the twitch height produced by the real action potentials, the ratio being about 0.3 at room temperature. The results strongly suggest that the transverse tubular system is excitable and is necessary for the full activation of twitch, and that the action potential of the tubules contributes to about 70 % of the total mechanical output of the normal isotonic twitch at 20°C. Similar results were obtained in the case of tetanic contraction. At a temperature near 10°C, twitches produced by the simulated AP were not very different (85 % of control amplitude) from the twitches caused by real action potentials. This indicates that the excitability of the tubules becomes less necessary for the full activation of twitch as the temperature becomes lower.     

Calcium dependence of the stimulating action of cadmium on organic acid transport in the frog kidney

The stimulatory effect of cadmium ions on the Na-dependent fluorescein transport into the frog renal proximal tubules ceased with decreasing Ca++ concentration in solution on both the sides of the cell layer down to micromolar level. The decrease in Ca++ concentration per se stimulated fluorescein uptake during short-term incubations. A further diminution of Ca++ concentration in the tubular lumen with the aid of EGTA resulted in a sharp inhibition of the organic acid transport. Amiloride, which prevented the stimulatory effect of cadmium, inhibited the fluorescein transport at both millimolar and micromolar levels of Ca++ concentration, but it failed to affect the transport process after introducing EGTA into the tubular lumen. The results are discussed within the frames of a model regarding extracellular Ca++ as an allosteric inhibitor, and intracellular Ca++ as an allosteric activator of sodium channels in the apical membrane. Cd++ is assumed to compete with Ca++ for binding to centers of the allosteric inhibition, thereby accelerating the sodium ion flux across the cells of the proximal tubules.     

Analysis of fiber types in the pigeon's metapatagialis muscle II. Effects of denervation

The pigeon's metapatagialis muscle consists of three slips, two twitch and one tonic, and these slips are distinguishable at the gross anatomical level. Comparative studies of denervation are facilitated because the two fiber types are under the same mechanical forces, can be denervated as one muscle, and can be distinguished after denervation. Both fiber types atrophied after denervation, with the twitch fibers having a more variable response. Pathological alterations observed by light microscopy suggested that the twitch fibers were more affected by denervation than the tonus fibers. Ultrastructurally, both fiber types showed the same changes, with the twitch fibers again being more consistently altered. Proliferation of the transverse tubular system and sarcoplasmic reticulum were more marked in the tonus than twitch fibers, and the sarcoplasmic reticulum proliferated prior to the transverse tubules. Filament and fibril degeneration, peripheral and central degeneration, lysosomes and their derivatives, and satellite cell proliferation were common to both fiber types. Contracture knots were common to the denervated fibers, and were suggested to be characteristic of degenerating fibers. Degenerating motor end plates were observed, and most neurons in the fibers were naked, lacking myelin sheaths. The results are discussed in relation to the function of the neuron in maintaining the muscle, and the possibility of denervation inducing a transformation of tonic to twitch fibers.     

The delayed rectifier potassium conductance in the sarcolemma and the transverse tubular system membranes of mammalian skeletal muscle fibers

A two-microelectrode voltage clamp and optical measurements of membrane potential changes at the transverse tubular system (TTS) were used to characterize delayed rectifier K currents (IK(V)) in murine muscle fibers stained with the potentiometric dye di-8-ANEPPS. In intact fibers, IK(V) displays the canonical hallmarks of K(V) channels: voltage-dependent delayed activation and decay in time. The voltage dependence of the peak conductance (gK(V)) was only accounted for by double Boltzmann fits, suggesting at least two channel contributions to IK(V). Osmotically treated fibers showed significant disconnection of the TTS and displayed smaller IK(V), but with similar voltage dependence and time decays to intact fibers. This suggests that inactivation may be responsible for most of the decay in IK(V) records. A two-channel model that faithfully simulates IK(V) records in osmotically treated fibers comprises a low threshold and steeply voltage-dependent channel (channel A), which contributes ～31% of gK(V), and a more abundant high threshold channel (channel B), with shallower voltage dependence. Significant expression of the IK(V)1.4 and IK(V)3.4 channels was demonstrated by immunoblotting. Rectangular depolarizing pulses elicited step-like di-8-ANEPPS transients in intact fibers rendered electrically passive. In contrast, activation of IK(V) resulted in time- and voltage-dependent attenuations in optical transients that coincided in time with the peaks of IK(V) records. Normalized peak attenuations showed the same voltage dependence as peak IK(V) plots. A radial cable model including channels A and B and K diffusion in the TTS was used to simulate IK(V) and average TTS voltage changes. Model predictions and experimental data were compared to determine what fraction of gK(V) in the TTS accounted simultaneously for the electrical and optical data. Best predictions suggest that K(V) channels are approximately equally distributed in the sarcolemma and TTS membranes; under these conditions, >70% of IK(V) arises from the TTS.     

Postnatal development of the Sertoli cell barrier, tubular lumen, and cytoskeleton of Sertoli and myoid cells in the rat, and their relationship to tubular fluid secretion and flow

The postnatal development of the Sertoli cell barrier, tubular lumen, fluid flow, and cytoskeletal elements in Sertoli and myoid cells was investigated in the Sprague-Dawley rat. With the aid of hypertonic fixatives, a barrier to the rapid entry of fluid was noted in the majority of tubules on the 15th and 16th postnatal (p.n.) days and was completely formed in all tubules prior to p.n. day 18. The actin forming the ectoplasmic specialization (ES), a cytoskeletal complex related to the occluding junctions composing the barrier, began its development during the period of initial barrier formation (16 p.n. day) and progressively attained its adult prominence. The ES developed its characteristic adult pattern and adult fluorescent intensity at about p.n. day 22. Some seminiferous tubules showed very small lumina as early as p.n. day 10. All tubules were not open until p.n. day 30. The size (diameter) of the lumen increased slowly from p.n. day 10 until p.n. day 30 when it started to increase rapidly until about p.n. day 50. Fluid flow in seminiferous tubules was detected as early as p.n. day 20 and increased in amount thereafter. Myoid cell actin filament bundles, running in parallel, were present at p.n. day 10. Actin formed a meshwork pattern characteristic of the adult on, or slightly prior to, p.n. day 22. These data indicate that there is a temporal relationship between the development of the actin cytoskeleton within the Sertoli cell and initial formation of the Sertoli cell barrier. Similarly, there is a temporal relationship between the development of the actin cytoskeleton of myoid cells and tubular fluid flow. The rapid increase in tubular lumen diameter, however, does not correlate with the initial development of Sertoli and myoid cytoskeletal elements.     

Core 2 GlcNAc modification and megalin ligand-binding activity

Megalin, a receptor-like transporter glycoprotein, is expressed on kidney proximal tubular cells and reabsorbs small-molecular-weight proteins from the glomerular filtrate. Here, we report that mouse megalins differently modified with core 2 beta6GlcNAc transferase had different kinetic properties to a fluorescence-labeled ligand, retinol-binding protein (RBP). BALB/c mice, a wild-type strain in terms of the expression of kidney-specific core 2 beta6GlcNAc transferase, express megalin carrying the core 2 extended Le(x) epitope, while DBA/2 mice, a mutant-strain of the core 2 beta6GlcNAc transferase, express megalin lacking the epitope. We purified these two types of megalin using lentil lectin chromatography and measured the ligand-binding activities of the megalins using Cy5-labeled RBP by applying gel permeation chromatography (GPC) and fluorescence correlation spectroscopy (FCS). The analysis by GPC indicated that the apparent V(max) of the interaction between Cy5-labeled RBP and the megalins of BALB/c and DBA/2 mice was 60 microM and 30 microM, respectively, and the apparent K(m) was 11 microM and 17 microM, respectively. Scatchard analysis demonstrated the presence of two binding sites. Linear regression analysis resulted in a two-binding-site model characterized by a high-affinity site (K(dBALB)=12.0 microM; K(dDBA)=20.9 microM) and a low-affinity site (K(dBALB)=36.2 microM; K(dDBA)=58.8 microM). FCS analysis exhibited quite different K(m) and V(max) values from those obtained by GPC, but similar K(m) values for the two types of megalin, and a lower V(max) value for DBA/2 megalin than BALB/c megalin. These results suggest that the core 2 GlcNAc extended glycan chains on megalin can change the ligand-binding affinity and capacity.     

Calculation of muscle maximal shortening velocity by extrapolation of the force-velocity relationship: afterloaded versus isotonic release contractions

The maximal shortening velocity of a muscle (V(max)) provides a link between its macroscopic properties and the underlying biochemical reactions and is altered in some diseases. Two methods that are widely used for determining V(max) are afterloaded and isotonic release contractions. To determine whether these two methods give equivalent results, we calculated V(max) in 9 intact single fibres from the lumbrical muscles of the frog Xenopus laevis (9.5-15.5 °C, stimulation frequency 35-70 Hz). The data were modelled using a 3-state cross-bridge model in which the states were inactive, detached, and attached. Afterloaded contractions gave lower predictions of Vmax than did isotonic release contractions in all 9 fibres (3.20 ± 0.84 versus 4.11 ± 1.08 lengths per second, respectively; means ± SD, p = 0.001) and underestimated unloaded shortening velocity measured with the slack test by an average of 29% (p = 0.001, n = 6). Excellent model predictions could be obtained by assuming that activation is inhibited by shortening. We conclude that under the experimental conditions used in this study, afterloaded and isotonic release contractions do not give equivalent results. When a change in the V(max) measured with afterloaded contractions is observed in diseased muscle, it is important to consider that this may reflect differences in either activation kinetics or cross-bridge cycling rates.     

An analysis of the relationship between the current and potential generated by a quantum of acetylcholine in muscle fibers without transverse tubules

Summary Miniature end plate potentials (MEPPs) were recorded in glyceroltreated muscle fibers with four microelectrodes which were used to determine the passive electrical characteristics of the same fibers. Voltage responses which were computed from miniature end plate currents (MEPCs) and the passive cable properties of a fiber, agreed very closely with experimentally recorded MEPPs confirming the hypothesis that MEPPs spread passively along a muscle fiber. The model was used to analyze the effect of variations in synaptic current and the properties of a muscle fiber on the postsynaptic response. The decrement of MEPPs was exponential for distances up to 1 to 2 mm from an origin but then deviated from the initial exponential. Variations in the growth time of the input current up to 1 msec had little effect on computed MEPPs whereas an increase in the decay time constant caused a significant increase in MEPP amplitude and effective space constant. An increase in the internal resistivity of a muscle fiber increased MEPP amplitude at the origin but decreased the effective space constant. The amplitude of MEPPs was inversely proportional to the 1.5 power of the diameter of a muscle fiber, and the MEPP space constant increased as the square root of the diameter. The amplitude of MEPPs is not necessarily determined by the input resistance of the muscle fiber. Changes in input resistance caused by changes in membrane resistance would have little effect on te amplitude or decrement of MEPPs.