A study of the motor unit action potential by means of computer simulation

In order to study the motor unit action potential a computer simulation model was developed. It is based on the superposition of single muscle fibre potentials of the fibres belonging to the motor unit. The parameters which characterize each fibre (spatial position, diameter, and a dispersion of arrival time of the potential at the electrode) are chosen from statistical distributions which can be derived from anatomical and physiological data. The electrode type, position and dimensions can be specified. Simulated motor unit action potentials are presented in the time and frequency domain. The simulation results refer to (1) the influence of the electrode position and dimensions with respect to the motor unit territory, (2) the meaning of this model for the study of pathological phenomena, (3) the variability of some parameters characterizing the motor unit, (4) the selectivity of uni- and bipolar electrodes and finally (5) the influence of the geometrical situation of the motor end-plates within the muscle, on the shape of motor unit action potentials.     

基于单个细胞动作电位计算心电:若干异常仿真心电图

根据构造的心脏电生理模型及提出的基于单细胞动作电位计算心电图的算法,介绍异常心电活动的描述方式及对若干异常心电图的仿真结果,包括心肌缺血、心肌梗死、房室传导阻滞、束支传导阻滞、以及房室旁路,并对这些心电图的 产生机制进行说明,算法及仿真结果表明,细胞间的跨缝隙连结电位差是产生场点电热进而产生各种心电图波形的原因。     

The Effect of Membrane Parameters on the Properties of the Nerve Impulse

The effect of varying membrane capacitance, conductance, and rate constants on the properties of the nerve impulse is considered in terms of the degree of regeneration in the Hodgkin-Huxley model for the squid giant axon. It is shown through computer simulation that reducing regeneration generally increases the duration of the action potential and decreases its amplitude, rate of rise, and conduction velocity. The threshold becomes much less sharp and the amplitude of the response of a patch of membrane grades with stimulus strength. A second stimulus, applied shortly after a first stimulus, considerably perturbs the membrane potential from its original time-course. Under certain conditions, the nerve signal can propagate with a small decrement.     

The Repolarization Phase of the Cardiac Ventricular Action Potential: A Time-Dependent System of Membrane Conductances

A system for the generation of the repolarization phase of the ventricular action potential is described. The system is based on time-dependent changes in membrane conductance to sodium and potassium ions. However, the changes in conductance during an action potential retain a degree of voltage dependence through the initial conditions which depend on previous depolarizations of the membrane. The equations describing the system were solved with an analog computer and various action potential forms are reproduced. The effects of hyperpolarizing and depolarizing current applied during an action potential are investigated. The changes in shape of an action potential after a change in the rate of stimulation show partial agreement with previous experimental findings. The applicability of time-dependent and voltage-dependent systems for the generation of the repolarization phase of the ventricular action potential is discussed.     

Some Relations between Action Potential and Resting Potential of the Lobster Giant Axon

Experiments were performed to determine the quantitative relation existing between action potential and resting potential of the lobster giant axon. Resting potential changes were induced by either increasing the external potassium concentration or by reducing the external calcium concentration. For either treatment the action potential amplitude is proportional to the logarithm of the resting potential minus a constant. This constant is equivalent to the minimum resting potential at which a propagated spike is possible, and is larger for depolarization in low calcium than in high potassium. Thus the change in action potential per unit change in resting potential is greater in low external calcium than in high external potassium. Analog computer solutions to the Hodgkin-Huxley equations for squid axon membrane potentials show that, if the initial conditions are properly specified, the action potential is proportional to the logarithm of the potassium potential minus a constant. The experimental results and the analog computations suggest that reducing external calcium produces changes in the invertebrate axon that cannot be accounted for solely on the basis of alterations in the potassium potential.     

Simulations of the cardiac action potential based on the Hodgkin-Huxley kinetics with the use of Microsoft Excel spreadsheets

The purpose of this study was to develop a method to simulate the cardiac action potential using a Microsoft Excel spreadsheet. The mathematical model contained voltage-gated ionic currents that were modeled using either Beeler-Reuter (B-R) or Luo-Rudy (L-R) phase 1 kinetics. The simulation protocol involves the use of in-cell formulas directly typed into a spreadsheet. The capability of spreadsheet iteration was used in these simulations. It does not require any prior knowledge of computer programming, although the use of the macro language can speed up the calculation. The normal configuration of the cardiac ventricular action potential can be well simulated in the B-R model that is defined by four individual ionic currents, each representing the diffusion of ions through channels in the membrane. The contribution of Na+ inward current to the rate of depolarization is reproduced in this model. After removal of Na+ current from the model, a constant current stimulus elicits an oscillatory change in membrane potential. In the L-R phase 1 model where six types of ionic currents were defined, the effect of extracellular K+ concentration on changes both in the time course of repolarization and in the time-independent K+ current can be demonstrated, when the solutions are implemented in Excel. Using the simulation protocols described here, the users can readily study and graphically display the underlying properties of ionic currents to see how changes in these properties determine the behavior of the heart cell. The method employed in these simulation protocols may also be extended or modified to other biological simulation programs.     

Randomness in the heparin polymer: computer simulations of alternative action patterns of heparin lyase

Heparin is a mixture of linear polysaccharides of undetermined sequence. Both biosynthetic data and computer simulation studies have established that each heparin polymer chain is comprised of oligosaccharides of defined sequence, representing ordered domains. One such ordered domian is a pentasaccharide corresponding to heparin's antithrombin III binding site. Previous computer simulation studies, performed under the assumption that heparin lyase (heparinase, EC 4.2.2.7), has a random endolytic action pattern, suggested that certain of these ordered oligosaccharide domains may themselves be nonrandomly arranged in the heparin polymer. The present work presents computer simulations of alternative action patterns for heparin lyase while assuming a random distribution of these oligosaccharide units within the heparin polymer. We consider action patterns that are determined solely by the primary structure of the substrate molecules. Results of the simulations are compared to (1) the experimental measurements of product chains formed throughout the reaction and (2) the change in weight average molecular weight Mw as a function of reaction completion as determined by absorbance at 232 nm. From the simulation of 60 action patterns for heparin lyase, we infer that one of the following statements concerning heparin and heparin lyase is true: (1) Heparin is a random arrangement of a small number of structurally defined oligosaccharide units. Heparin lyase changes its action pattern during the depolymerization of heparin (perhaps influenced by the secondary structure of substrate). (2) Heparin contain clusters of oligosaccharide sequences that are present in low concentrations (overall) in the polymer. Heparin lyase has a specificity for cleaving glycosidic linkages either exolytically at the nonreducing terminus of a chain or (endolytically) at the reducing side of these rare oligosaccharide sequence.     

Computer simulation of action potential propagation in septated nerve fibers.

The nonlinear, core-conductor model of action potential propagation down axisymmetric nerve fibers is adapted for an implicit, numerical simulation by computer solution of the differential equations. The calculation allows a septum to be inserted in the model fiber; the thin, passive septum is characterized by series resistance Rsz and shunt resistance Rss to the grounded bath. If Rsz is too large or Rss too small, the signal fails to propagate through the septum. Plots of the action potential profiles for various axial positions are obtained and show distortions due to the presence of the septum. A simple linear model, developed from these simulations, relates propagation delay through the septum and the preseptal risetime to Rsz and Rss. This model agrees with the simulations for a wide range of parameters and allows estimation of Rsz and Rss from measured propagation delays at the septum. Plots of the axial current as a function of both time and position demonstrate how the presence of the septum can cause prominent local reversals of the current. This result, not previously described, suggests that extracellular magnetic measurements of cellular action currents could be useful in the biophysical study of septated fibers.