Ultrastructure of dynamic and static skeletofusimotor endings in a cat muscle spindle

Summary Endings of four skeletofusimotor axons in a spindle of the cat tenuissimus muscle were examined in semithin (1-m thick) and ultrathin transverse serial sections. Two (dynamic) axons terminated on the nuclear bag₁ intrafusal muscle fiber and on extrafusal fibers of the dark type. Two (static) axons terminated on the nuclear chain intrafusal fibers and extrafusal fibers of the intermediate type. The degree of indentation of axon terminals into the muscle surface, thickness of the sole plate and extent of folding of subjunctional membranes differed among intrafusal and extrafusal terminations of the same axon. Endings of axons on the bag₁ and chain fibers were also morphologically dissimilar. Motor axons may not determine ending morphology. Rather the form and structure of a bag₁ or chain ending may be determined by the type of intrafusal fiber on which the ending lies and the ending's distance from the primary sensory axon.     

Role of biomechanics and muscle activation strategy in the production of endpoint force patterns in the cat hindlimb

We used a musculoskeletal model of the cat hindlimb to compare the patterns of endpoint forces generated by all possible combination of 12 hindlimb muscles under three different muscle activation rules: homogeneous activation of muscles based on uniform activation levels, homogeneous activation of muscles based on uniform (normalized) force production, and activation based on the topography of spinal motoneuron pools. Force patterns were compared with the patterns obtained experimentally by microstimulation of the lumbar spinal cord in spinal intact cats. Magnitude and orientation of the force patterns were compared, as well as the proportion of the types found, and the proportions of patterns exhibiting points of zero force (equilibrium points). The force patterns obtained with the homogenous activation and motoneuron topography models were quite similar to those measured experimentally, with the differences being larger for the patterns from the normalized endpoint forces model. Differences in the proportions of types of force patterns between the three models and the experimental results were significant for each model. Both homogeneous activation and normalized endpoint force models produced similar proportions of equilibrium points as found experimentally. The results suggest that muscle biomechanics play an important role in limiting the number of endpoint force pattern types, and that muscle combinations activated at similar levels reproduced best the experimental results obtained with intraspinal microstimulation.     

Observations on the primary sensory ending of tenuissimus muscle spindles in the cat

Summary The arrangement of preterminal and terminal axon branches in the primary sensory endings of cat tenuissimus muscle spindles was studied using whole-mount and serial-section techniques. Although in every case one firstorder preterminal branch was supplied exclusively to the bag₁ type of intrafusal muscle fibre, the preterminal branching patterns differed considerably in detail.Terminals varied widely in size and location. Their precise form varied according to their position on the intrafusal muscle fibres rather than their relationship to preterminal branches. Terminals derived from separate preterminal branches remained separate and did not fuse with themselves or each other. Individually bag₁ fibres had most terminals, chain fibres least. The surface of the muscle fibres were differentially indented by the terminals, least in bag₁ fibres and most in chain fibres.The results are discussed in relation to mechanosensory transduction and to the factors involved in determining the form of the primary ending.     

A parametric model of muscle moment arm as a function of joint angle: Application to the dorsiflexor muscle group in mice

A parametric model was developed to describe the relationship between muscle moment arm and joint angle. The model was applied to the dorsiflexor muscle group in mice, for which the moment arm was determined as a function of ankle angle. The moment arm was calculated from the torque measured about the ankle upon application of a known force along the line of action of the dorsiflexor muscle group. The dependence of the dorsiflexor moment arm on ankle angle was modeled as r=R sin(a+Δ), where r is the moment arm calculated from the measured torque and a is the joint angle. A least-squares curve fit yielded values for R, the maximum moment arm, and Δ, the angle at which the maximum moment arm occurs as offset from 90°. Parametric models were developed for two strains of mice, and no differences were found between the moment arms determined for each strain. Values for the maximum moment arm, R, for the two different strains were 0.99 and 1.14 mm, in agreement with the limited data available from the literature. While in some cases moment arm data may be better fitted by a polynomial, use of the parametric model provides a moment arm relationship with meaningful anatomical constants, allowing for the direct comparison of moment arm characteristics between different strains and species.     

A biomechanical model for analysis of muscle force,power output and lower jaw motion in fishes

Fish skulls are complex kinetic systems with movable components that are powered by muscles. Cranial muscles for jaw closing pull the mandible around a point of rotation at the jaw joint using a third-order lever mechanism. The present study develops a lever model for the jaw of fishes that uses muscle design and the Hill equation for nonlinear length-tension properties of muscle to calculate dynamic power output. The model uses morphometric data on skeletal dimensions and muscle proportions in order to predict behavior and force transmission mediated by lever action. The computer model calculates a range of dynamic parameters of jaw function including muscle force, torque, effective mechanical advantage, jaw velocity, bite duration, bite force, work and power. A complete list of required morphometrics is presented and a software program (MandibLever 2.0) is available for implementing lever analysis. Results show that simulations yield kinematics and timing profiles similar to actual fish feeding events. Simulation of muscle properties shows that mandibles reach their peak velocity near the start of jaw closing, peak force at the end of jaw closing, and peak power output at about 25% of the closing cycle time. Adductor jaw muscles with different mechanical designs must have different contractile properties and/or different muscle activity patterns to coordinate jaw closing. The effective mechanical advantage calculated by the model is considerably lower than the mechanical advantage estimated from morphological lever ratios, suggesting that previous studies of morphological lever ratios have overestimated force and underestimated velocity transmission to the mandible. A biomechanical model of jaw closing can be used to interpret the mechanics of a wide range of jaw mechanisms and will enable studies of the functional results of developmental and evolutionary changes in skull morphology and physiology.     

A comparison of optimisation methods and knee joint degrees of freedom on muscle force predictions during single-leg hop landings

The aim of this paper was to compare the effect of different optimisation methods and different knee joint degrees of freedom (DOF) on muscle force predictions during a single legged hop. Nineteen subjects performed single-legged hopping manoeuvres and subject-specific musculoskeletal models were developed to predict muscle forces during the movement. Muscle forces were predicted using static optimisation (SO) and computed muscle control (CMC) methods using either 1 or 3 DOF knee joint models. All sagittal and transverse plane joint angles calculated using inverse kinematics or CMC in a 1 DOF or 3 DOF knee were well-matched (RMS error<3°). Biarticular muscles (hamstrings, rectus femoris and gastrocnemius) showed more differences in muscle force profiles when comparing between the different muscle prediction approaches where these muscles showed larger time delays for many of the comparisons. The muscle force magnitudes of vasti, gluteus maximus and gluteus medius were not greatly influenced by the choice of muscle force prediction method with low normalised root mean squared errors (<48%) observed in most comparisons. We conclude that SO and CMC can be used to predict lower-limb muscle co-contraction during hopping movements. However, care must be taken in interpreting the magnitude of force predicted in the biarticular muscles and the soleus, especially when using a 1 DOF knee. Despite this limitation, given that SO is a more robust and computationally efficient method for predicting muscle forces than CMC, we suggest that SO can be used in conjunction with musculoskeletal models that have a 1 or 3 DOF knee joint to study the relative differences and the role of muscles during hopping activities in future studies.     

Effect of electrical stimulation-induced muscle force and streptomycin treatment on muscle and trabecular bone mass in early-stage disuse musculoskeletal atrophy

Objectives:

The aim was to determine whether daily muscle electrical stimulation (ES) and streptomycin treatment would have positive or negative effects on trabecular bone mass in disuse rats.

Methods:

Seven-week-old male F344 rats were randomly divided into five groups of eight animals each: an age-matched control group (CON); a sciatic denervation group (DN); a DN + direct electrical stimulation group (DN+ES); a DN + streptomycin treatment group (DN+SM); and a DN+ES+SM group. The tibialis anterior (TA) muscles in all ES groups were stimulated with 16mA at 10Hz for 30 min/day, six days/week, for one week. Bone volume and structure were evaluated using micro-CT, and histological examinations of the tibiae were performed.

Results:

Direct ES significantly reduced the disuse-induced trabecular bone loss. Osteoid thickness were also significantly greater in the ES groups than in the DN group. Micro CT and histomorphological parameters were significantly lower in the DN+ES+SM group than in the DN+ES group, while there were no significant differences between the DN and DN+SM groups.

Conclusions:

These results suggest that ES-induced muscle force reduced trabecular bone loss, and streptomycin treatment did not induce bone loss, but attenuated the effects of ES-induced muscle force on reducing the loss of disused bone.     

A predictive model of moment-angle characteristics in human skeletal muscle: application and validation in muscles across the ankle joint

In the present work, a generic model for the prediction of moment-angle characteristics in individual human skeletal muscles is presented. The model's prediction is based on the equation M = V x Lo(-1)sigma c cos phi x d, where M, V, and Lo are the moment-generating potential of the muscle, the muscle volume and the optimal muscle fibre length, respectively, and sigma, phi and d are the stress-generating potential of the muscle fibres, their pennation angle and the tendon moment arm length, respectively, at any given joint angle. The input parameters V, Lo, sigma, phi and d can be measured or derived mechanistically. This eliminates the common problem of the necessity to estimate one or more of the input parameters in the model by fitting its outcome to experimental results often inappropriate for the function modelled. The model's output was validated by comparisons with the moment-angle characteristics of the gastrocnemius (GS) and tibialis anterior (TA) muscles in six men, determined experimentally using voluntary contractions at several combinations of ankle and knee joint angles for the GS muscle and electrical stimulation for the TA muscle. Although the model predicted realistically the pattern of moment-angle relationship in both muscles, it consistently overestimated the GS muscle M and consistently underestimated the TA muscle M, with the difference gradually increasing from dorsiflexion to plantarflexion in both cases. The average difference between predicted and measured M was 14% for the GS muscle and 10% for the TA muscle. Approximating the muscle fibres as a single sarcomere in both muscles and failing to achieve complete TA muscle activation by electrical stimulation may largely explain the differences between theory and experiment.     

Heterogeneity of muscle activation in relation to force direction: A multi-channel surface electromyography study on the triceps surae muscle

Several skeletal muscles can be divided into sub-modules, called neuromuscular compartments (NMCs), which are thought to be controlled independently and to have distinct biomechanical functions. We looked for distinct muscle activation patterns in the triceps surae muscle (TS) using surface electromyography (EMG) during voluntary contraction. Nine subjects performed isometric and isotonic plantar flexions combined with forces along pre-defined directions. Besides the forces under the ball of the foot, multi-channel surface EMG was measured with electrodes homogeneously distributed over the entire TS. Using principal component analysis, common (global) components were omitted from the EMG signals, thereby estimating muscle activity sufficiently accurate to track fine fluctuations of force during an isotonic contraction (r = 0.80 ± 0.09). A subsequent cluster analysis showed a topographical organization of co-activated parts of the muscle that was different between subjects. Low and negative correlations between the EMG activity within clusters were found, indicating a substantial heterogeneity of TS activation. The correlations between cluster time series and forces at the foot in specific directions differed substantially between clusters, showing that the differentially activated parts of the TS had specific biomechanical functions.     

An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine

Muscle force partitioning methods and musculoskeletal system simplifications are key modeling issues that can alter outcomes, and thus change conclusions and recommendations addressed to health and safety professionals. A critical modeling concern is the use of single-joint equilibrium to estimate muscle forces and joint loads in a multi-joint system, an unjustified simplification made by most lumbar spine biomechanical models. In the context of common occupational tasks, an EMG-assisted optimization method (EMGAO) is modified in this study to simultaneously account for the equilibrium at all lumbar joints (M-EMGAO). The results of this improved approach were compared to those of its conventional single-joint equivalent (S-EMGAO) counterpart, the latter method being applied to the same lumbar joints but one at a time. Despite identical geometrical configurations and passive contributions used in both models, computed outcomes clearly differed between single- and multi-joint methods, especially at larger trunk flexed postures and during asymmetric lifting. Moreover, muscle forces predicted by L5-S1 single-joint analyses do not maintain mechanical equilibrium at other spine joints crossed by the same muscles. Assuming that the central nervous system does not attempt to balance the external moments one joint at a time and that a given muscle cannot exert different forces at different joints, the proposed multi-joint method represents a substantial improvement over its single-joint counterpart. This improved approach, hence, resolves trunk muscle forces with biological integrity but without compromising mechanical equilibrium at the lumbar joints.     

Inhibitory effects of HgCl2 on excitation-secretion coupling at the motor nerve terminal and excitation-contraction coupling in the muscle cell

Summary 1. Indirect and direct twitch (0.1-Hz) stimulation of the rat phrenic nerve-diaphragm disclosed that the inhibitory effect of HgCl₂, 3.7 × 10^–5M, on the neuromuscular transmission and in the muscle cell, was accelerated by 10-sec periods of 50-Hz tetanic stimulation every 10 min. This activity-dependent enhancement suggested an inhibitory mechanism of HgCl₂ related to the development of fatigue, like membrane depolarization or decreased excitability, decreased availability of transmitter, or interference with the factors controlling excitation-secretion coupling of the nerve terminal, i.e. (Ca²⁺)₀ or (Ca²⁺)_i, and excitation-contraction coupling in the muscle cell, i.e., (Ca²⁺)_i.2. During both indirect and direct stimulation, HgCl₂-induced inhibition was enhanced markedly by pretreatment with caffeine, which releases Ca²⁺ from endoplasmic and sarcoplasmic reticulum in the nerve terminal and muscle cell, respectively. This caffeine-induced enhancement was completely antagonized by dantrolene, which inhibits the caffeine-induced release. However, dantrolene alone did not antagonize the HgCl₂-induced inhibition.3. Since caffeine depletes the intracellular Ca²⁺ stores of the smooth endoplasmic reticulum, HgCl₂ probably inhibits by binding to SH groups of transport proteins conveying the messenger function of (Ca²⁺)_i. In the muscle cell this leads to inhibition of contraction. In the nerve terminal, an additional enhancement of the HgCl₂-induced inhibition, by inhibiting reuptake of choline by TEA and tetanic stimulation, suggested that HgCl₂ inhibited a (Ca²⁺)_i signal necessary for this limiting factor in resynthesis of acetylcholine.4. The (Ca²⁺)₀ signal necessary for stimulus-induced release of acetylcholine was not affected by HgCl₂. Hyperpolarization in K⁺-free solution antagonized the inhibitory effect of HgCl₂ at indirect stimulation, and Ca²⁺-free solution enhanced the inhibitory effect at direct stimulation. K⁺ depolarization, membrane electric field increase with high Ca²⁺, membrane stabilization with lidocaine, and half-threshold stimulation, did not change the inhibitory effect of HgCl CH₃HgCl, 1.85 × 10^–5M, disclosed a synergistic interaction with caffeine during direct, but not during indirect, stimulation.     

Post-exercise ketosis and the glycogen content of liver and muscle in rats on a high carbohydrate diet

Post-exercise ketosis is known to be suppressed by physical training and by a high carbohydrate diet. As a result it has often been presumed, but not proven, that the development of post-exercise ketosis is closely related to the glycogen content of the liver. We therefore studied the effect of 1 h of treadmill running on the blood 3-hydroxybutyrate and liver and muscle glycogen concentrations of carbohydrate-loaded trained (n = 72) and untrained rats (n = 72). Resting liver and muscle glycogen levels were 25%-30% higher in the trained than in the untrained animals. The resting 3-hydroxybutyrate concentrations of both groups of rats were very low: less than 0.08 mmol.l-1. Exercise did not significantly influence the blood 3-hydroxybutyrate concentrations of trained rats, but caused a marked post-exercise ketosis (1.40 +/- 0.40 mmol.l-1 h after exercise) in the untrained animals, the time-course of which was the approximate inverse of the changes in liver glycogen concentration. Interpreting the results in the light of similar data obtained after a normal and low carbohydrate diet it has been concluded that trained animals probably owe their relative resistance to post-exercise ketosis to their higher liver glycogen concentrations as well as to greater peripheral stores of mobilizable carbohydrate.     

TWIG: a model to simulate the gravitropic response of a tree axis in the frame of elasticity and viscoelasticity, at intra-annual time scale

Trees are able to maintain or modify the orientation of their axes (trunks or branches) by tropic movements. For axes in which elongation is achieved but cambial growth active, the tropic movements are due to the production of a particular wood, called reaction wood which is prestressed within the growing tree. Several models have been developed to simulate the gravitropic response of axes in trees due to the formation of reaction wood, all within the frame of linear elasticity and considering the wood maturation as instantaneous. The effect viscoelasticity of wood has, to our knowledge, never been considered. The TWIG model presented in this paper aims at simulating the gravitropic movement of a tree axis at the intra-annual scale. In this work we studied both the effect of a non-instantaneous maturation process and of viscoelasticity. For this purpose, we considered the elastic case with maturation considered as an instantaneous process as the reference. The introduction of viscoelasticity in TWIG has been done by coupling TWIG to a model developed for bridges. Indeed from a purely mechanical point of view, bridges and trees are very similar: they are structures which are built in stages, they are made of several materials (composite structures), their materials are prestressed (wood is prestressed during the maturation process as a result of polymerisation of lignin and cellulose to form the secondary cell wall and concrete is prestressed during drying). Simulations gave evidence that the reorientation process of axes can be significantly influenced by the kinetics of maturation. Moreover the model has now to be tested with more experimental data of wood viscoelasticity but it appears that in the range of a relaxation time from 0 to 50 days, viscoelasticity has an important effect on the evolution of tree shape as well as on the values of prestresses.     

The effects of isoproterenol, UDCG 115, and caffeine on the heart related to excitation-contraction coupling in heart muscle

A myothermal technique was used to measure initial heat and tension independent heat from isometrically contracting papillary muscles taken from the right ventricle of rabbits. Tension independent heat produced by the muscle at Lo was isolated with a 2,3-butanedione monoxime (diacetyl monoxime)--hyperosmotic Krebs solution. The effects of the inotropic drugs isoproterenol (1 X 10(-7) M), UDCG 115 (2 X 10(-4) M), and caffeine (2 X 10(-3) M) on heat and mechanical output were measured. We tested the hypothesis that these drugs alter peak twitch tension by increasing the total amount of Ca2+ cycled during the twitch, assuming that net tension independent heat is proportional to total Ca2+ cycled. The hypothesis was rejected for each drug as the positive inotropic effects of isoproterenol and UDCG 115 on twitch tension were not accompanied by increases in net tension independent heat. Net tension independent heat was actually depressed by UDCG 115. The negative inotropic effect of caffeine on twitch tension was accompanied by an increase in tension independent heat at times between the end of mechanical relaxation and the next stimulus. Possible mechanisms to account for these results are discussed.     

The recombinant limb as a model for the study of limb patterning, and its application to muscle development

The recombinant limb is a model system that has proved fruitful for analyzing epithelial-mesenchymal interactions and understanding the functional properties of the components of the limb bud. Here we present an overview of some of the insights obtained through the use of this technique. Among these are the understanding that fore or hind limb identity is inherent to the limb bud mesoderm, that the apical ectodermal ridge (AER) is a permissive signaling center and that the limb bud ectoderm plays a central role in the control of dorsoventral polarity. Recombinant limb studies have also allowed the identification of the affected tissue component in several limb mutants. More recently this model has been applied to the study of regulation of gene expressions related to patterning. In this report we use recombinant limbs to analyze pattering of the Pax3 expressing limb muscle cell lineage in the early stages of limb development. In recombinant limbs made without the zone of polarizing activity (ZPA), myoblasts appear intermingled with other mesodermal cells at the beginning of the recombinant limb development. Rapidly thereafter, the muscle precursors segregate and organize around the central forming chondrogenic core of the recombinant. Although this segregation is reminiscent of that occurring during normal development, the myoblasts in the recombinant fail to proliferate appropriately and also fail to migrate distally. Consequently, the muscle pattern in the recombinant limb is defective indicating that normal patterning cues are absent. However, recombinant limbs polarized with a ZPA exhibited a larger mass of muscle cells and a more normal morphogenesis, supporting a role for this signaling center in limb muscle development. Finally, we have ruled out host somite contributions to recombinant limbs by grafting chick recombinant limbs to quail hosts. This initial report demonstrates the value of the recombinant limb model system for dissecting the environmental cues required for normal muscle limb patterning. Received: 31 August 1998 / Accepted: 29 September 1998     

The effects of the metal ions Mn2+ and Co2+ on muscle contraction in the Norway lobster Nephrops norvegicus (L.)

The effects of the metal ions manganese and cobalt on force production by the abdominal superficial flexor muscle of the Norway lobster, Nephrops norvegicus, have been studied in response to both neuronal stimulation and electrical field stimulation applied to an isolated neuromuscular preparation, and by selectively blocking synaptic transmission with ivermectin. In response to both forms of stimulation, low concentrations of manganese added to the standard N. norvegicus saline increased the contractile force produced by the muscle, whereas higher concentrations of manganese inhibited both responses in a dose-dependent manner, until force was completely abolished at concentrations above 2.9 mM manganese. Cobalt ions produced similar effects, and no significant difference was found between the concentration of the two ions at 50% force inhibition (K_m) or between the two stimulation methods (manganese: 1.22 mM; cobalt: 1.29 mM, P = 0.86). This suggests that they have a similar mode of action, and a postsynaptic site of inhibition. These K_m values are considerably higher than the concentrations of these ions known to accumulate in the haemolymph of N. norvegicus under eutrophic conditions, and it therefore seems unlikely that accumulations of manganese or cobalt ions under such conditions would cause any significant inhibition of muscle contraction force. Accepted: 28 April 1999     

Effect of fasting and refeeding on gluconeogenesis and glyconeogenesis in the muscle of the crab Chasmagnathus granulatus previously fed a protein- or carbohydrate-rich diet

The present study investigated the participation of the muscle gluconeogenic and glyconeogenic pathways in lactate metabolism after 15 fasting and during different periods of refeeding in Chasmagnathus granulatus previously maintained on a carbohydrate-rich (HC) or high-protein (HP) diet. In C. granulatus the metabolic adjustments during the fasting use different pathways according to the composition of the diet previously offered to the crab. During fasting, the gluconeogenic capacity is reduced in crabs maintained on the HC diet. In animals maintained on the HP diet, an increase in activity of the glyconeogenic pathway occurs after 15 days of fasting. In the animals fed HC diet, the glyconeogenesis is one of the pathways responsible for maintenance of the lactate levels in the fed and refeeding states. In crabs fed on the HP diet, the gluconeogenesis and glyconeogenesis pathways are involved in the reduction of lactate levels during the refeeding period. This study shows that protein or carbohydrates levels in the diet previously administrated to the crabs modulate the gluconeogenesis, glyconeogenesis in muscle and lactate concentration in the hemolymph in fed, fasting and refeeding states.     

Long-term effects of selection based on the animal model BLUP in a finite population

Monte Carlo simulation was used to assess the long-term effects of truncation selection within small populations using indices (I=f+m) combining mid-parent [f=(a _i+a _d)/2] and Mendelian-sampling (m=a-f) evaluations provided by an animal model BLUP (a=f+m). Phenotypic values of panmictic populations were generated for 30 discrete generations. Assuming a purely additive polygenic model, heritability (h ₂) values were 0.10, 0.25 or 0.50. Two population sizes were considered: five males and 25 females selected out of 50 candidates of each sex (small populations, S) and 50 males and 250 females selected out of 500 candidates in each sex (large populations, L). Selection was carried out on the index defined above with = 1 (animal model BLUP), =1/2, or =0 (selection on within-family deviations). Mass selection was also considered. Selection based on the animal model BLUP (=1) maximized the cumulative genetic gain in L populations. In S populations, selection using = 1/2 and mass selection were more efficient than selection under an animal model (+ 3 to + 7% and + 1 to + 4% respectively, depending on h ²). Selection on within-family deviations always led to the lowest gains. In most cases, the variance of response to selection between replicates did not depend on the selection method. The within-replicate genetic variance and the average coefficient of inbreeding (F) were highly affected by selection with =1 or 1/2, especially in populations of size S. As expected, selection based on within-family deviations was less detrimental in that respect. The number of copies of founder neutral genes at a separate locus, and the probability vector of origin of the genes in reference to the founder animals, were also observed in addition to F values. The conclusion was that selection procedures placing less emphasis on family information might be interesting alternatives to selection based on animal model BLUP, especially for small populations with long-term selection objectives.     

End-plate potentials in a model muscle fiber. Corrections for the effects of membrane potential on currents and on channel lifetimes.

At the neuromuscular junction, the end-plate potential is generated by a conductance increase in the end-plate membrane. The end-plate depolarization brings the membrane potential toward the reversal potential, which diminishes the driving force for inward current flow. A. R. Martin (1955, J. Physiol. [Lond.]. 130:114-122) devised a simple formula to correct end-plate potential amplitudes for a diminished driving force based on a purely resistive model of the end-plate membrane. The model ignores the membrane capacity, the complexity of the equivalent circuit for a muscle fiber, the variation in channel lifetimes with changes in membrane potential, and the extension of the end plate along a length of the cable. We have developed a model that incorporates all of these features. The calculations show that Martin's correction is, in theory, quite satisfactory for a cable that has the characteristics of a muscle fiber unless the recording is made at a distance from the site of inward current flow. However, there is a discrepancy between models of the frog neuromuscular junction and the available experimental data, which suggests that the end-plate depolarization produced by a given current is greater than expected from their model.