Chloride action potentials and currents in embryonic skeletal muscle of the chick

Chloride-dependent action potentials were elicited from embryonic skeletal muscle fibers of the chick during the last week of in ovo development. The duration of the action potentials was extremely long (greater than 8 sec). The action potentials were reversibly blocked by the stilbene derivative, SITS, a specific blocker of chloride permeability. Using patch clamp pipettes, in which the intracellular chloride concentration was controlled and with other types of ion channels blocked, the membrane potential at the peak of the action potential closely coincided with the chloride equilibrium potential calculated from the Nernst equation. These data indicate that activation of a chloride-selective conductance underlies the long duration action potential. The occurrence of the chloride-dependent action potential was found to increase during embryonic development. The percentage of fibers that displayed the action potential increased from approximately 20% at embryonic day 13 to approximately 70% at hatching. Chloride-dependent action potentials were not found in adult fibers. The voltage and time-dependent currents underlying the action potential were recorded under voltage clamp using the whole-cell version of the patch pipette technique. The reversal potential of the currents was found to shift with the chloride concentration gradient in a manner predicted by the Nernst equation, and the currents were blocked by SITS. These data indicate that chloride ions were the charge carriers. The conductance was activated by depolarization and exhibited very slow activation and deactivation kinetics.     

The propagation of the nerve impulse.

A partial differential equation for the propagated action potential is derived using symmetry, charge conservation, and Ohm's law. Charge conservation analysis explicitly includes the gating charge when applied in the laboratory frame. When applied in the system of reference in which capacitive currents are zero, it yields a relation between orthogonal components of the ionic current allowing us to express the nonlinear ionic current in terms of the voltage-dependent membrane capacitance C(V) and the axial current that satisfies Ohm's law. The ionic current is shown to behave as C(V)V[C(V)V2]' at the foot of the action potential while the gating current behaves as C(V)V[Cg(V)V]' where Cg(V) is the capacitance associated with gating. Improved knowledge of the nonlinear current makes it possible to describe the propagated action potential in an approximated way with quasilinear partial differential equations. These equations have analytical solutions that travel with constant velocity, retain their shape, and account for other properties of the action potential. Furthermore, the quasilinear approximation is shown to be equivalent to the FitzHugh-Nagumo equation without recovery making apparent its physical content.     

A Quantitative Description of the Relationship between the Area of Rabbit Ventricular Action Potentials and the Pattern of Stimulation

Intracellular microelectrodes were used to record action potentials from fibres of the isolated rabbit right ventricle and the areas of the action potentials were measured. The action potential area was found to depend in a reproducible way on the preceding pattern of stimulation. A mathematical model reproducing all the observed changes in the action potential area was developed. In the model the action potential area is taken as a linear function of the product of two time and stimulation dependent variables, M and N. The behaviour of each variable between action potentials is described by the solution of a second order differential equation. During each action potential the variables are assumed to change discontinuously, the magnitudes of the discontinuous changes being given by a set of subsidiary equations. It was found that the behaviour of all the fibres tested was described by the same set of equations, each single fibre being characterized by a set of ten independent constants.     

Ionic processes in excitable membranes

The dynamical theory of ionized media is applied to the semi-electrolyte component of an excitable cell membrane, and the adjacent electrolytes. The equations of conservation of charge and momentum for the ions, and Poisson's equation for the electrostatic potential, are applied first to investigate the steady states of the membrane, and then transient effects in the membrane. A dispersion equation is derived, and the characteristic modes of relaxation within the membrane are determined. Among these are oscillating modes whose frequencies and amplitudes are of the correct order of magnitude to explain the observed excitation phenomena.A pair of coupled non-linear equations in the ionic potentials, with action potential solutions, is derived from the time-dependent electrodiffusion equations, and calculations are presented which model the behaviour of the excitable membrane during the voltage clamp. It is not necessary to postulate large changes in the ionic permeabilities in the course of the action potential and the voltage clamp to account for the large transient membrane conductances. It is suggested that the sodium hypothesis be replaced by one which attributes the action potential to non-linear plasma oscillations.     

关于耦合神经元活动时的能量原理

最近美国耶鲁大学的神经科学家们用实验数据表明,哺乳动物大脑皮层中神经信号的传递是一个代价昂贵的能量支出过程,而神经信号的编码是与能量代谢紧密地耦合在一起的,但是到目前为止还无法定量给出神经元活动时的能量函数。在这篇文章中,能量原理被用于神经活动和神经信息处理机制的研究,在电生理实验数据的基础上,建立神经元活动的用能量函数表示的运动方程。结果表明用能量函数表达耦合神经元的阈下电活动和动作电位,数值计算结果与用Hodgkin-Huxley方程所描述的动作电位一致。从而有可能依据能量原理从脑信息处理的角度揭示和理解大脑神经网络系统的信息表现规律。     

Sodium and potassium currents recorded during an action potential

A simple method was used to measure directly sodium and potassium currents underlying the action potential in single nerve fibres of Xenopus laevis. A short rectangular stimulus under current-clamp conditions elicited an action potential which was digitally stored and later used as command when voltageclamping the same fibre. The currents thus obtained nearly reproduced the original rectangular stimulus. Adding first 100 nM TTX and subsequently 100 nM TTX plus 10 mM TEA to the extracellular Ringer solution revealed the sodium and the potassium currents during an action potential. They were converted to permeabilities by use of the constant-field equation and are in good agreement with the curves which had been calculated from conventional voltage-clamp data. Thus experimentally determined currents and permeabilities are shown as they are changing during an action potential.     

激光育种机理非线性研究

本文对激光与ＤＮＡ分子相互作用,考虑了随机力作用,建立了ＤＮＡ分子在激光作用下的Ｆｏｋｋｅｒ－ｐｌａｎｃｋ方程（ＦＰＥ）。分析了ＤＮＡ分子系统的ＦＰＥ势函数,对激光育种中的ＤＮＡ遗传变异的随机不确定性现象进行了解释。     

Theoretical analysis on relationship between the neural activity and the EEG

Firstly, a collective oscillation mode of the neural activity is derived from the neural network system by using the multicompartment equation and the projection operator technique. This technique takes into account higher order interactions among neurons. The solution of the equation gives a chain structure with an infinite number of circuit loops in which each of them is only composed of four neurons. The obtained eigenvalues are quite similar to the spectrum of frequencies of the EEG. Secondly, the time-dependent behavior of the observed EEG is simulated by starting from the elementary process of action potential trains of neurons, which includes the effect of the collective oscillation mode mentioned above. This gives a comprehensive derivation of the EEG from the neural activity of action potentials. The simulation assumes that information of the action potential trains can be transmitted to the EEG through the intermediate states of the postsynaptic potential trains and the slow waves. The paper reports that a slightly modulated activity of a relatively small amount of neurons can cause a strong influence on the shape of the global EEG and that the calculated results reproduce the characteristic features of the EEG in a rat such as the theta rhythm, the spindle wave and the arousal wave.     

Some properties of motor unit action potential trains recorded during constant force isometric contractions in man

A specially designed needle electrode was used to record motor unit action potentials for the complete time duration of constant force isometric contractions varying in discrete steps from minimum to maximum force levels. A total of 70 motor unit action potential trains were recorded and analyzed.Several properties of the motor unit action potentials were observed. The inter-pulse intervals between adjacent motor unit action potentials of a particular motor unit action potential train were measured and subsequently analyzed as a real continuous random variable. The distribution of the values of the inter-pulse intervals was described by the Weibull probability distribution function with time and force dependent parameters. Furthermore the Survivor function and the Hazard function of the Weibull probability distribution function described certain characteristics of the motor unit firing intervals. Most important of all, it became possible to derive an equation that would generate a real continuous random variable whose properties would be identical to those of the inter-pulse intervals.     

An eikonal-curvature equation for action potential propagation in myocardium

We derive an eikonal-curvature equation to describe the propagation of action potential wavefronts in myocardium. This equation is used to study the effects of fiber orientation on propagation in the myocardial wall. There are significant computational advantages to the use of an eikonal-curvature equation over a full ionic model of action potential spread. With this model, it is shown that the experimentally observed misalignment of spreading action potential ellipses from fiber orientation in level myocardial surfaces is adequately explained by the rotation of fiber orientation through the myocardial wall. Additionally, it is shown that apparently high propagation velocities on the epicardial and endocardial surfaces are the result of propagation into the midwall region and acceleration along midwall fibers before reemergence at an outer surface at a time preceding what could be accomplished with propagation along the surface alone.Research was supported in part by NSF Grant DMS-8801446     

A mathematical analysis of the action potential plateau duration of a human ventricular myocyte

The plateau phase of a human ventricular myocyte is analysed. The plateau duration is a function of the time required for a myocyte's transmembrane voltage to decrease by a certain voltage, DeltaV. The timing of the plateau is shown to be controlled by two slowly changing gate variables, the inactivation gate that controls the inward/depolarizing L-type calcium current and the inactivation gate that controls the outward/repolarizing slow rectifier potassium current. The amount of current controlled by these variables is a function of the net conductivity of the corresponding sodium and potassium channels. An equation is derived that relates action potential duration to these net conductivities and the time dependence of the slowly moving variables. This equation is used to estimate plateau duration for a given value of DeltaV. The initial conditions of the slowly moving inactivation variables are shown to affect plateau duration. These initial conditions depend on the amount of time that has elapsed between a previous repolarization and a current depolarization (diastolic interval). The analysis thus helps to quantify the characteristics of action potential duration restitution.     

Computation of Impulse Initiation and Saltatory Conduction in a Myelinated Nerve Fiber

A mathematical model of the electrical properties of a myelinated nerve fiber is given, consisting of the Hodgkin-Huxley ordinary differential equations to represent the membrane at the nodes of Ranvier, and a partial differential cable equation to represent the internodes. Digital computer solutions of these equations show an impulse arising at a stimulating electrode and being propagated away, approaching a constant velocity. Action potential curves plotted against distance show discontinuities in slope, proportional to the nodal action currents, at the nodes. Action potential curves plotted against time, at the nodes and in the internodes, show a marked difference in steepness of the rising phase, but little difference in peak height. These results and computed action current curves agree fairly accurately with published experimental data from frog and toad fibers.     

On the nerve impulse equation: The dynamic responses of nerve impulse

With the assumption of dipole interaction with the membrane matrix, the dipole barrier under an applied field shows a minimum in its time transient. Kinetic equations governing the migration of ions are presented. Na⁺ activation, Na⁺ inactivation and K⁺ delay are all part of the same mechanism in this model with no other separate assumptions needed. Voltage Clamp equation and action potential equation are presented. Supported in part by Physics Research Center, National Science Council, The Republic of China.     

Effects of external ions on membrane potentials of a lobster giant axon

The effects of varying external concentrations of normally occurring cations on membrane potentials in the lobster giant axon have been studied and compared with data presently available from the squid giant axon. A decrease in the external concentration of sodium ions causes a reversible reduction in the amplitude of the action potential and its rate of rise. No effect on the resting potential was detected. The changes are of the same order of magnitude, but greater than would be predicted for an ideal sodium electrode. Increase in external potassium causes a decrease in resting potential, and a decrease in potassium causes an increase in potential. The data so obtained are similar to those which have been reported for the squid giant axon, and cannot be exactly fitted to the Goldman constant field equation. Lowering external calcium below 25 mM causes a reduction in resting and action potentials, and the occasional occurrence of repetitive activity. The decrease in action potential is not solely attributable to a decrease in resting potential. Increase of external calcium from 25 to 50 mM causes no change in transmembrane potentials. Variations of external magnesium concentration between zero and 50 mM had no measurable effect on membrane potentials. These studies on membrane potentials do not indicate a clear choice between the use of sea water and Cole's perfusion solution as the better external medium for studies on lobster nerve.     

Parameter estimation in Hodgkin-Huxley-Type equations for membrane action potentials in nerve and heart muscle

A method is presented which renders parameter estimation possible in systems of non-linear differential equations where normally no solution exists in terms of analytic functions and which have to be solved numerically. The method uses the concept of sensitivity equations. Two examples are given, taking mathematical models for membrane action potentials in nerve and heart muscle by Hodgkin and Huxley and by Beeler and Reuter. The model equations together with the corresponding system of sensitivity equations are given, which are necessary to estimate maximum conductivity coefficients defining the interactions of different ionic current components. A computer program is described and results of action potential numerical analysis are presented using simulated data. It can be seen, that even with superimposed simulated noise the real parameter values are estimated in an excellent manner. The method can be used to interpret observed changes in action potential time courses under physiological and pharmacological conditions.     

Experimental study of the conducted action potential in cardiac Purkinje strands

Conduction velocity is a complex physiological process that integrates the active and passive properties of the excitable cell. The relations between these properties in determining the conduction velocity are not intuitively obvious, and models have been used frequently to illustrate important relationships. To study the relationships of important parameters and to evaluate commonly used models, we changed conduction velocity experimentally in sheep cardiac Purkinje strands by reducing extracellular Na systematically. Cable analyses were also performed to obtain passive membrane and cable properties. Resting membrane resistance and capacitance did not change, nor did core resistance. Active properties measured in addition to conduction velocity included maximal upstroke velocity, action potential height, time constant of the foot, peak inward current, and upstroke power. With reduction in extracellular Na, all of these parameters of the action potential changed nonlinearly and not in direct proportion to the change in conduction velocity. The only simple relation found was a linear relationship between maximal upstroke velocity and peak inward current, normalized by the capacity of the foot. Models based on the cable equation and the wave equation offer a basis for quantitative analysis of conduction, and these data can be used to test the models.     

The electrostatic contribution to interactions of some enzymes with polyelectrolytes

To explain the inhibitory action of polyelectrolytes on enzymes and, in particular, to define potentially reactive zones for the binding of polyelectrolyte, the electric potential of enzymes lactate dehydrogenase and glutamate dehydrogenase was calculated using the solution of the Poisson-Boltzmann equation by a numerical method with the use of the Gauss-Seidel relaxation method at three pH values: 6.5, 7.0, and 8.0 and three values of ionic strength: 50, 100, and 150 mm. On the basis of these calculations and their visualization, representative sites for favorable binding of polyanions were determined as extended areas on the surface of proteins with the positive potential in the neutral pH region. It was shown that there is a correlation between the area of positive potential and the efficiency of enzyme inactivation for a number of pH values and concentrations of salt for two enzymes. The calculations performed allowed one to explain the inhibitory action of polyelectrolytes on the specified enzymes to understand the difference between the values of polyelectrolyte inactivation constants for the two enzymes and estimate the minimal areas of the positive potential on the protein surface that provide their effective inhibition.     

Inward current generated by Na-Ca exchange during the action potential in single atrial cells of the rabbit.

To investigate the underlying ionic mechanism of the late plateau phase of the action potential in rabbit atrium the whole-cell patch-clamp technique with intracellular perfusion was used. We recorded the inward current during repolarizations following a brief 2 ms depolarizing pulse to +40 mV from a holding potential of between -70 and -80 mV. The development of this current coincides with the onset of the late plateau phase of the action potential. Peak activation of the current occurs about 10 ms from the beginning of the depolarizing pulse, and it decays spontaneously with a slow timecourse. Its voltage dependency from -40 mV to +40 mV shows very steep activation (-40 to -20 mV) and shows almost the same maximum magnitude between -10 mV and +40 mV. This behaviour is quite different from that of the calcium current. The inward current and the late plateau phase of the action potential were both abolished by the application of 5 mM EGTA, 1 microM ryanodine and by reducing the Na+ gradient. The fully activated current-voltage relation of the inward current was plotted as the difference current before and after treatment with Ryanodine, Diltiazem, 20 mM Na+ inside or 30% Na+ outside and shows an exponential voltage dependence with the largest magnitude of the current occurring at negative potentials. The current-voltage (I-V) curve was well fitted by the Na-Ca exchange equation, i = A exp (-(1 - r)EF/RT). The results suggest that the inward current contributes to the generation of the late plateau phase of the rabbit atrial action potential, and is activated by intracellular calcium released from the sarcoplasmic reticulum. Sarcoplasmic reticulum calcium release appears to be triggered both by the membrane voltage and by the calcium current. It is concluded that the inward current is generated by Na-Ca exchange.     

Kinetics of nerve impulse blocking by protein cross-linking aldehydes Apparent critical thermal points

The effect of formaldehyde, crotonaldehyde, butyraldehyde, glutaraldehyde and cinnamaldehyde on the compound action potential of frog sciatic nerve was studied in the temperature domain 20–35°C at various aldehyde concentrations. All these reagents gradually decrease the amplitude of nerve action potential, up to the complete block, the order of effectiveness being: crotonaldehyde > cinnamaldehyde > butyraldehyde > formaldehyde > glutaraldehyde. The effect of cinnamaldehyde is almost completely reversible, while all others have irreversible action. The dependence of the blocking time on temperature and concentration is well expressed in all cases by the same empirical equation. This dependence points to the existence of critical temperatures, specific for each aldehyde, at which impulse blocking would be instantaneous, regardless of concentration. These temperatures (obtained by extrapolation) lie between 43°C (for crotonaldehyde) and 57.5°C (for butyraldehyde). The existence of free amino groups within ionic channels, as main sites of aldehyde attack, is inferred.