The effects of ADP and phosphate on the contraction of muscle fibers.

The products of MgATP hydrolysis bind to the nucleotide site of myosin and thus may be expected to inhibit the contraction of muscle fibers. We measured the effects of phosphate and MgADP on the isometric tensions and isotonic contraction velocities of glycerinated rabbit psoas muscle at 10 degrees C. Addition of phosphate decreased isometric force but did not affect the maximum velocity of shortening. To characterize the effects of ADP on fiber contractions, force-velocity curves were measured for fibers bathed in media containing various concentrations of MgATP (1.5-4 mM) and various concentrations of MgADP (1-4 mM). As the [MgADP]/[MgATP] ratio in the fiber increases, the maximum velocity achieved by the fiber decreases while the isometric tension increases. The inhibition of fiber velocities and the potentiation of fiber tension by MgADP is not altered by the presence of 12 mM phosphate. The concentration of both MgADP and MgATP within the fiber was calculated from the diffusion coefficient for nucleotides within the fiber, and the rate of MgADP production within the fiber. Using the calculated values for the nucleotide concentration inside the fiber, observed values of the maximum contraction velocity could be described, within experimental accuracy, by a model in which MgADP competed with MgATP and inhibited fiber velocity with an effective Ki of 0.2-0.3 mM. The average MgADP level generated by the fiber ATPase activity within the fiber was approximately 0.9 mM. In fatigued fibers MgADP and phosphate levels are known to be elevated, and tension and the maximum velocity of contraction are depressed. The results obtained here suggest that levels of MgADP in fatigued fibers play no role in these decreases in function, but the elevation of both phosphate and H+ is sufficient to account for much of the decrease in tension.     

Action currents, internodal potentials, and extracellular records of myelinated mammalian nerve fibers derived from node potentials.

The potential distribution within the internodal axon of mammalian nerve fibers is derived by applying known node potential waveforms to the ends of an equivalent circuit model of the internode. The complete spatial/temporal profile of action potentials synthesized from the internodal profiles is used to compute the node current waveforn, and the extracellular action potential around fibers captured within a tubular electrode. For amphibia, the results agreed with empirical values. For mammals, the amplitude of the node currents plotted against conduction velocity was fitted by a straight line. The extracellular potential waveform depended on the location of the nodes within the tube. For tubes of length from 2 to 8 internodes, extracellular wave amplitude (mammals) was about one-third of the product of peak node current and tube resistance (center to ends). The extracellular potentials developed by longitudinal and radial currents in an anisotropic medium (fiber bundle) are compared.     

Electrophysiological correlates of rapid escape reflexes in intact earthworms,Eisenia foetida. II. Effects of food deprivation on the functional development of giant nerve fibers

Noninvasive electrophysiological recording methods were used to study the effects of prolonged food deprivation on the postembryonic patterns of giant fiber growth, as indicated by age-dependent changes in giant fiber conduction velocity and diameter, in the earthworm, Eisenia foetida. In addition, giant fiber growth was compared to patterns of somatic growth, as indicated by increases in body weight. Within a wide range of food deprivation levels, normal age-dependent increases in conduction velocity and diameter occurred in spite of marked stunting of somatic growth. Stunting of giant fiber velocity and diameter occurred only during severe food deprivation, but giant fiber spikes and associated rapid escape responses were still readily evoked. The stunting effects of prolonged and severe food deprivation upon giant fiber conduction velocity and diameter were readily reversed by replenishing food. The results demonstrate the persistence of rapid escape reflex functioning, as well as the priority of giant fiber growth relative to somatic growth, during severe and prolonged food deprivation. As a consequence of the priority of giant fiber growth during limited food availability, giant fiber conduction velocity appears to be a more reliable predictor of animal age than body size.     

Simulation analysis of conduction of excitation in the atrioventricular node

The excitation conduction in the atrioventricular node was simulated based on the spatially discrete model of the heart proposed in an earlier paper (Kawato et al., 1986). We constructed a model system composed of the atrium, the atrioventricular node and the Purkinje fiber. Coupling coefficients between these tissues were quantitatively estimated from experimental data on size and membrane capacitance of the three kinds of cardiac cells. We found the following three important features in the simulated excitation conduction along the atrioventricular node. First, shape of action potential was found to be different at different locations of the atrioventricular node although the membrane properties were assumed uniform through the atrioventricular node. Our analysis suggests that the difference in the action potential waveforms observed by Paes de Carvalho & De Almedia (1960) can be ascribed to the electrical influences of the atrium and the His bundle on the atrioventricular node. Second, when the excitation wavefront invaded the atrioventricular node from the atrium, a step was observed in the depolarization phase of the action potential at the atrioventricular node neighboring with the atrium. Janse found a similar step in the real experiment (1969). It is revealed that this step is caused by termination of the junctional current which flows from the atrium to the atrioventricular node. Finally, we found that the conduction velocity measured near the boundary between the atrium and the atrioventricular node was lower than that in the middle part of the atrioventricular node, which is in accordance with the experimental observation by Scher et al. (1959).     

Electrical Wave Propagation in an Anisotropic Model of the Left Ventricle Based on Analytical Description of Cardiac Architecture

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher–Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation.     

Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model

This work presents a discrete multidomain model that describes ionic diffusion pathways between connected cells and within the interstitium. Unlike classical models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic/static boundary conditions that electrically couple neighboring spaces. The model is used to investigate the impact of nonuniform geometrical and electrical properties of the interstitial space surrounding a fiber on conduction velocity and action potential waveshape. Comparison of the multidomain and bidomain models shows that although the conduction velocity is relatively insensitive to cases that confine 50% of the membrane surface by narrow extracellular depths (≥2 nm), the action potential morphology varies greatly around the fiber perimeter, resulting in changes in the magnitude of extracellular potential in the tight spaces. Results also show that when the conductivity of the tight spaces is sufficiently reduced, the membrane adjacent to the tight space is eliminated from participating in propagation, and the conduction velocity increases. Owing to its ability to describe the spatial discontinuity of cardiac microstructure, the discrete multidomain can be used to determine appropriate tissue properties for use in classical macroscopic models such as the bidomain during normal and pathophysiological conditions.     

Computation of Impulse Conduction in Myelinated Fibers; Theoretical Basis of the Velocity-Diameter Relation

For myelinated fibers, it is experimentally well established that spike conduction velocity is proportional to fiber diameter. However no really satisfactory theoretical treatment has been proposed. To treat this problem a theoretical axon was described consisting of lengths of passive leaky cable (internode) regularly interrupted by short isopotential patches of excitable membrane (node). The nodal membrane was assumed to obey the Frankenhaeuser-Huxley equations. The explicit diameter dependencies of the various parameters were incorporated into the equations. The fiber diameter to axon diameter ratio was taken to be constant, and the internode length was taken to be proportional to the fiber diameter. Both these conditions reflect the situation that exists in real, experimental fibers. Dimensional analysis shows that these anatomical conditions are equivalent to Rushton's (1951) assumption of corresponding states. Hence, conduction velocity will be proportional to fiber diameter, in complete agreement with the experimental findings. Digital computer solutions of these equations were made in order to compute a set of actual velocities. Computations made with constant internode length or constant myelin thickness (i.e., nonconstant fiber diameter to axon diameter ratio) did not show linearity of the velocity-diameter relation.     

The influence of an unmyelinated terminal on repetitive firing of a mammalian receptor afferent fiber

The distal end of a myelinated receptor afferent fiber consists of an unmyelinated terminal membrane which is assumed to be the site of sensory transduction, whereas the action potential encoding appears at a distal node of Ranvier. In the present paper a model of a mammalian myelinated nerve fiber was augmented by an unmyelinated terminal segment into which stimulating current was injected thus modelling the situation at a myelinated receptor afferent fiber. It was found that the introduction of the unmyelinated terminal reduces the repetitive firing rate shown by the model. However, also the amplitude of the spikes at the site of action potential generation diminishes through the large electrical load which the unmyelinated terminal imposes onto the active parts of the nerve fiber model. This "loss" of spike amplitude can abolish the ability of the model to show repetitive activity, if the unmyelinated terminal increases in size. On the other hand, the incorporation of sodium channels into the terminal membrane compensates the spike amplitude reduction introduced by the electrical load of that membrane. This allows repetitive firing at a lower frequency than would be possible for a model with an equivalent sodium-channel-free terminal. The results show that the unmyelinated terminal present at the distal end of myelinated receptor afferent fibers has not only the ability to provide sensory transduction but evokes also a reduction in the discharge rate of the encoding membrane.     

Physiology of a microgravity environment invited review: microgravity and skeletal muscle.

Spaceflight (SF) has been shown to cause skeletal muscle atrophy; a loss in force and power; and, in the first few weeks, a preferential atrophy of extensors over flexors. The atrophy primarily results from a reduced protein synthesis that is likely triggered by the removal of the antigravity load. Contractile proteins are lost out of proportion to other cellular proteins, and the actin thin filament is lost disproportionately to the myosin thick filament. The decline in contractile protein explains the decrease in force per cross-sectional area, whereas the thin-filament loss may explain the observed postflight increase in the maximal velocity of shortening in the type I and IIa fiber types. Importantly, the microgravity-induced decline in peak power is partially offset by the increased fiber velocity. Muscle velocity is further increased by the microgravity-induced expression of fast-type myosin isozymes in slow fibers (hybrid I/II fibers) and by the increased expression of fast type II fiber types. SF increases the susceptibility of skeletal muscle to damage, with the actual damage elicited during postflight reloading. Evidence in rats indicates that SF increases fatigability and reduces the capacity for fat oxidation in skeletal muscles. Future studies will be required to establish the cellular and molecular mechanisms of the SF-induced muscle atrophy and functional loss and to develop effective exercise countermeasures.     

Modeling analysis of an intercalated-spiral alternate-dead-ended hollow fiber bioreactor for mammalian cell cultures

The model analysis of a bioreactor with two intercalated-spiral sets of hollow fibers with alternated dead ends is presented. Design equations are derived based on a model with two jumped fibers and an approximation of the fluid mechanics with a small fiber radius-to-length ratio. The performance of the bioreactor is simulated with and without cell growth utilizing a segregated radial flow model in the extracapillary space. The pressure modulus, the wall Peclet number, the Thiele modulus, and the Monod constant are used as model parameters. The results can be used to assess the proper choice of fiber permeability, fiber length, fiber spacing, and flow velocity.     

On the velocity of conduction in nerve fibers with saltatory transmission

Using an electrical model to represent certain features of a nerve fiber together with a one-factor theory of excitation, an expression is obtained for the velocity of propagation of a nerve impulse along a nerve fiber exhibiting saltatory transmission. The velocity shows a maximum with respect to internodal length. A critical internodal length, a critical radius, and a critical value for the resistance of the external medium are required in order to make transmission of the impulse possible.     

A three-dimensional muscle model: a quantified relation between form and function of skeletal muscles

A three-dimensional muscle model with complex geometry is described and tested against experimental data. Using this model, several muscles were constructed. These muscles have equal optimum length but differ in architecture. The force exerted by the constructed muscles, in relation to their actual length and velocity of shortening, is discussed. Generally speaking, the constructed muscles with considerable pennation have great fiber angles, a great physiological cross section, a narrow active and steep passive length-force relation, and a low maximal velocity of shortening. The maximal power (force times velocity) delivered by the constructed muscles is shown to be almost independent of the architecture of the muscles. The steepness of the passive length-force relation is determined mainly by the shortest fibers within the group of constructed muscles, whereas maximal velocity of shortening and the width of the active length-force relation are determined mainly by the longest fibers. The validity of the three-dimensional muscle model with respect to some morphological and functional characteristics is tested. Length-force relations of constructed muscles are compared with the actual length-force relations of mm. gastrocnemii mediales and mm. semimembranosi of male Wistar rats. Moreover, actual fiber angle, fiber length, and muscle thickness of three mm. gastrocnemii mediales are compared with values found for constructed muscles. It is concluded that the three-dimensional muscle model closely approximates the actual muscle form and function.     

Subtle Paranodal Injury Slows Impulse Conduction in a Mathematical Model of Myelinated Axons

This study explores in detail the functional consequences of subtle retraction and detachment of myelin around the nodes of Ranvier following mild-to-moderate crush or stretch mediated injury. An equivalent electrical circuit model for a series of equally spaced nodes of Ranvier was created incorporating extracellular and axonal resistances, paranodal resistances, nodal capacitances, time varying sodium and potassium currents, and realistic resting and threshold membrane potentials in a myelinated axon segment of 21 successive nodes. Differential equations describing membrane potentials at each nodal region were solved numerically. Subtle injury was simulated by increasing the width of exposed nodal membrane in nodes 8 through 20 of the model. Such injury diminishes action potential amplitude and slows conduction velocity from 19.1 m/sec in the normal region to 7.8 m/sec in the crushed region. Detachment of paranodal myelin, exposing juxtaparanodal potassium channels, decreases conduction velocity further to 6.6 m/sec, an effect that is partially reversible with potassium ion channel blockade. Conduction velocity decreases as node width increases or as paranodal resistance falls. The calculated changes in conduction velocity with subtle paranodal injury agree with experimental observations. Nodes of Ranvier are highly effective but somewhat fragile devices for increasing nerve conduction velocity and decreasing reaction time in vertebrate animals. Their fundamental design limitation is that even small mechanical retractions of myelin from very narrow nodes or slight loosening of paranodal myelin, which are difficult to notice at the light microscopic level of observation, can cause large changes in myelinated nerve conduction velocity.     

Functional implications of cold-stable microtubules in kinetochore fibers of insect spermatocytes during anaphase

In normal anaphase of crane fly spermatocytes, the autosomes traverse most of the distance to the poles at a constant, temperature-dependent velocity. Concurrently, the birefringent kinetochore fibers shorten while retaining a constant birefringent retardation (BR) and width over most of the fiber length as the autosomes approach the centrosome region. To test the dynamic equilibrium model of chromosome poleward movement, we abruptly cooled or heated primary spermatocytes of the crane fly Nephrotoma ferruginea (and the grasshopper Trimerotropis maritima) during early anaphase. According to this model, abrupt cooling should induce transient depolymerization of the kinetochore fiber microtubules, thus producing a transient acceleration in the poleward movement of the autosomal chromosomes, provided the poles remain separated. Abrupt changes in temperature from 22 degrees C to as low as 4 degrees C or as high as 31 degrees C in fact produced immediate changes in chromosome velocity to new constant velocities. No transient changes in velocity were observed. At 4 degrees C (10 degrees C for grasshopper cells), chromosome movement ceased. Although no nonkinetochore fiber BR remained at these low temperatures, kinetochore fiber BR had changed very little. The cold stability of the kinetochore fiber microtubules, the constant velocity character of chromosome movement, and the observed Arrhenius relationship between temperature and chromosome velocity indicate that a rate-limiting catalyzed process is involved in the normal anaphase depolymerization of the spindle fiber microtubules. On the basis of our birefringence observations, the kinetochore fiber microtubules appear to exist in a steady-state balance between comparatively irreversible, and probably different, physiological pathways of polymerization and depolymerization.     

Electrophysiological correlates of rapid escape reflexes in intact earthworms,Eisenia foetida. I. Functional development of giant nerve fibers during embryonic and postembryonic periods

Grids of recording electrodes etched onto printed circuit boards were used for noninvasive recording of medial (MGF) and lateral (LGF) giant nerve fiber spikes in developing earthworms, Eisenia foetida. Stereotyped patterns of throughconducted giant fiber spikes, evoked by light tactile stimulation, were first detectable in the normal crawling embryonic stage and continuned to be detectable throughout postembryonic development. Giant fiber spiking activity in normal crawling embryos was accompanied by stereotyped muscle activity and rapid escape withdrawal, suggesting that giant fiber reflex pathways are functionally intact before the worm hatches. For both the MGF and LFG, several age-de-pendent changes were noted, including the following: increases in spike conduction velocity, increases in giant fiber diameter, and decreases in spike duration. The MGF conduction velocity in normal crawling embryos was 1.1–1.6 m s^?1 (6–7 μm diameter) and increased to 7.0–8.5 m s^?1 (20–25 μm diameter) by 60 days after hatching. The LGF conduction velocity in normal crawling embryos was 0.7–1.1 m s^?1 (2.5–4.0 μm diameter) and increased to 4.0–5.5 m s^?1 (8–14 μm diameter) by 60 days after hatching. During postembryonic development MGF and LGF conduction velocities were linearly related to fiber diameter.     

Ionic currents of the nodal membrane underlying the fastest saltatory conduction in myelinated giant nerve fibers of the shrimp Penaeus japonicus.

The myelinated giant nerve fiber of the shrimp, Penaeus japonicus, is known to have the fastest velocity of saltatory impulse conduction among all nerve fibers so far studied, owing to its long distances between nodal regions and large diameter. For a better understanding of the basis of this fast conduction, a medial giant fiber of the ventral nerve cord of the shrimp was isolated, and ionic currents of its presynaptic membrane (a functional node) were examined using the sucrose-gap voltage-clamp method. Inward currents induced by depolarizing voltage pulses had a maximum value of 0.5 microA and a reversal potential of 120 mV. These currents were completely suppressed by tetrodotoxin and greatly prolonged by scorpion toxin, suggesting that they are the Na current. Both activation and inactivation kinetics of the Na current were unusually rapid in comparison with those of vertebrate nodes. According to a rough estimation of the excitable area, the density of Na current reached 500 mA/cm2. In many cases, the late outward currents were induced only by depolarizing pulses larger than 50 mV in amplitude. The slope conductance measured from late currents were mostly smaller than that measured from the Na current, suggesting a low density of K channels in the synaptic membrane. These characteristics are in good harmony with the fact that the presynaptic membrane plays a role as functional node in the fastest impulse conduction of this nerve fiber.     

The effect of temperature on a simulated systematically paranodally demyelinated nerve fiber

The temperature dependence (from 10° to 50°C) of the intracellular action potentials' parameters as well as of the ionic currents' kinetics in normal and demyelinated nerve fiber is studied. The simulation of the conduction in the normal fiber is based on the Frankenhaeuser and Huxley (1964) and Goldman and Albus (1968) equations, while in the case of a demyelinated fiber according to the same equations modified by Stephanova (1988). The temperature coefficients (Q ₁₀) for the rate constants as well as for the sodium and potassium permeabilities are introduced. It is shown that increased temperature blocks conduction in the simulated demyelinated fiber at temperatures much lower than the blocking temperature for the normal fiber. When temperature is increased, the amplitude as well as the wavelength and the asymmetry of the potential decrease. The relationship between conduction velocity and temperature is non-linear. The velocity increases when the temperature approaches the blocking temperature, after which abruptly drops. At a given degree of demyelination with increasing temperatures, the ionic currents' flow and the membrane conduction respectively increase, but, at lower temperatures, when the degree of the demyelination is increased, the conduction is blocked.     

Stretch-induced enhancement of mechanical work production in frog single fibers and human muscle

Takarada, Yudai, Hiroyuki Iwamoto, Haruo Sugi, YuichiHirano, and Naokata Ishii. Stretch-induced enhancement ofmechanical work production in frog single fibers and human muscle.J. Appl. Physiol. 83(5):1741-1748, 1997.The relations between the velocity of prestretchand the mechanical energy liberated during the subsequent isovelocityrelease were studied in contractions of frog single fibers and humanmuscles. During isometric contractions of frog single fibers, a rampstretch of varied velocity (amplitude, 0.02 fiber length; velocity,0.08-1.0 fiber length/s) followed by a release (amplitude, 0.02 fiber length; velocity, 1.0 fiber length/s) was given, and the amountof work liberated during the release was measured. For human muscles,elbow flexions were performed with a prestretch of variedvelocity (range, 40°; velocity, 30-180°/s) followed by anisokinetic shortening (velocity, 90°/s). In both frog single fibersand human muscles, the work production increased with both the velocityof stretch and the peak of force attained before the release up to acertain level; thereafter it declined with the further increases ofthese variables. In human muscles, the enhancement of work productionwas not associated with a significant increase in integratedelectromyogram. This suggests that changes in intrinsic mechanicalproperties of muscle fibers play an important role in thestretch-induced enhancement of work production.

     

Detection of motor unit action potentials with surface electrodes: influence of electrode size and spacing

A model of the motor unit action potential was developed to investigate the amplitude and frequency spectrum contributions of motor units, located at various depths within muscle, to the surface detected electromyographic (EMG) signal. A dipole representation of the transmembrane current in a three-dimensional muscle volume was used to estimate detected individual muscle fiber action potentials. The effects of anisotropic muscle conductance, innervation zone location, propagation velocity, fiber length, electrode area, and electrode configuration were included in the fiber action potential model. A motor unit action potential was assumed to be the sum of the individual muscle fiber action potentials. A computational procedure, based on the notion of isopotential layers, was developed which substantially reduced the calculation time required to estimate motor unit action potentials. The simulations indicated that: 1) only those motor units with muscle fibers located within 10–12 mm of the electrodes would contribute significant signal energy to the surface EMG, 2) variation in surface area of electrodes has little effect on the detection depth of motor unit action potentials, 3) increased interelectrode spacing moderately increases detection depth, and 4) the frequency content of action potentials decreases steeply with increased electrode-motor unit territory distance.     

Ionic currents of the nodal membrane underlying the fastest saltory conduction in myelinated giant nerve fibers of the shrimp Penaeus japonicus

The myelinated giant nerve fiber of the shrimp, Penaeus japonicus, is known to have the fastest velocity of saltatory impulse conduction among all nerve fibers so far studied, owing to its long distances between nodal regions and large diameter. For a better understanding of the basis of this fast conduction, a medial giant fiber of the ventral nerve cord of the shrimp was isolated, and ionic currents of its presynaptic membrane (a functional node) were examined using the sucrose-gap voltage-clamp method. Inward currents induced by depolarizing voltage pulses had a maximum value of 0.5 μA and a reversal potential of 120 mV. These currents were completely suppressed by tetrodotoxin and greatly prolonged by scorpion toxin, suggesting that they are the Na current. Both activation and inactivation kinetics of the Na current were unusually rapid in comparison with those of vertebrate nodes. According to a rough estimation of the excitable area, the density of Na current reached 500 mA/cm². In many cases, the late outward currents were induced only by depolarizing pulses larger than 50 mV in amplitude. The slope conductance measured from late currents were mostly smaller than that measured from the Na current, suggesting a low density of K channels in the synaptic membrane. These characteristics are in good harmony with the fact that the presynaptic membrane plays a role as functional node in the fastest impulse conduction of this nerve fiber.