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.     

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.     

Solid state physical theory of nerve impulse conduction: Elovich kinetics of axon repolarization currents

The sodium repolarization currents of Myxicola single axons clamped at -100 mV with and without tetrodotoxin conform to the Elovich equation, which implies that in the axon, Na+ is associated with charged sites on macromolecules and water is structured, and that an activation energy barrier to conduction of Na+ exists at the axon surface.     

Volume expansion of nonmyelinated nerve fibers during impulse conduction.

Nonmyelinated nerve fibers undergo rapid volume expansion while carrying an impulse. This volume expansion is incurred as a consequence of a lateral expansion of the excited portion of the fibers, where the superficial layer is transformed into a low-density structure.     

Electrodiffusion model of a nerve impulse

Electrodiffusion equations are deduced which describe the formation of the action potential in the axone. It is suggested that the membrane dividing internal and external axone electrolytes after being stimulated with an electric impulse returns after some time to the initial "closed" state. It is shown that the overshut of the action potential takes place due to non-linear profile distortion of the shock wave of electrical field tension vector created by the movement of sodium and potassium ions through the membrane of the axone.     

Intramembrane events during the nerve impulse

In current literature the cell adhesion to solid surfaces has been treated in the context of basic physicochemical forces. However, in all these reports the concept of solid surface force has not been properly analyzed. The surface forces acting across an interface formed when two phases meet has been shown to consist of dispersion (attraction) forces and polar forces (arising from different interactions). Current theories have repeatedly neglected the role of polar forces in the cell adhesion. In order to clarify this concept, the particular case, i.e. adhesion of cells on polystyrene surfaces with varying degree of polar groups is described. In this case, the adhesion of cells was reported to increase with polarity of polystyrene, and this agrees with the present study that the solid polar force component increased in the same manner.     

The biologically relevant parameter in nerve impulse trains

Summary An experiment is described, the results of which indicate that impulse rate is the information carrying parameter of impulse trains. The demodulation of such information occurs by low-pass filtering. This conceptual model is compatible with all the features of synaptic transmission. The implications of this model for the transmission of information in integrative neurons is discussed.     

On Zeeman's equations for the nerve impulse

A model for the nerve impulse due to Zeeman (1972) and based on catastrophe theory is compared with alternative models and criticisms of Zeeman's model by Sussmann and Zahler (1977, 1978) are assessed. The criticisms of Zeeman's motivation for his model are found to carry some weight. Sussmann and Zahler (1977, 1978) list numerous features of Zeeman's model which, they state, are not in agreement with experiment. These statements as they stand are largely erroneous, and the model still remains to be tested by a critical series of experiments. However, a detailed analysis reveals defects in Zeeman's model, not among those claimed by Sussmann and Zahler, showing that the explicit equations of the model cannot be correct. The possibility of a modified approach along similar lines and its ultimate adoption remains open.     

Entropy changes associated with a nerve impulse

In this paper the problem of entropy changes in a nerve fibre when an action potential is taking place is analysed. A probability field associated with the ionic distribution in the axoplasma and the extracellular space is defined. The total variation of its entropy can be computed on the basis of Gibbs' distribution of ions in the system. The final formula deduced for the entropy variation allows computations based on experimental data for the giant axon and the myelinated fibre. It represents at the same time a derivation of Brillouin's neguentropy principle of information in the particular case of the nerve.     

Constant magnetic field and nerve impulse conduction]

It is shown that external magnetic field produces no ponderomotor effect on the nerve fibre along which the impulse propagates.     

Does nerve impulse activity modulate fast axonal transport?

The possibility that the amount of newly synthesized material made available for fast axonal transport is regulated by nerve impulse activity was examined in an in vitro preparation of bullfrog dorsal root ganglia (DRG) and sciatic nerve. Under conditions that precluded effects of impulse activity on either uptake or incorporation of precursor, patterned stimulation of the sciatic nerve (1 out of every 2 s) produced a frequency- and time-dependent decrease in the amount of radiolabeled protein accumulating at a nerve ligature. The response to patterned stimulation was significantly greater than that to continuous stimulation when the same number of stimuli were delivered. In unligated nerve preparations, patterned stimulation decreased the amplitude of the transport profile with no concomitant change in the wave front distance. Nerve stimulation produced no observable ultrastructural alterations within neuronal cell bodies of the DRG. We propose that the physiological significance of these results is not that nerve impulse activity decreases fast axonal transport, but that the amount of transport increases during periods of electrical quiescence. According to this hypothesis, activity-dependent macromolecules of the axolemma and nerve terminals are replenished during periods when the neuron is firing less frequently. These findings are discussed in light of reports that chronic in vivo stimulation increases the amount of fast-transported, radiolabeled protein (Chan et al., 1989) and that TTX-blockade of neuronal activity has no effect on protein transport (Edwards and Grafstein, 1984; Riccio and Matthews, 1985).