The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

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.     

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.     

Theoretical consideration of a possible mechanism in the conduction process of thin-sheathed nerve fibers

The propagation of a transverse disturbance along a tubular membrane enclosing a fluid medium and embedded in another is considered. It is shown that the velocity of propagation of such a disturbance can be identified with the velocity of the conduction process of thin-sheathed nerve fibers. The required values of the associated parameters, tension and pressure, appear not unreasonable. The results obtained indicate that experimental observations on the relation between the conduction velocity and the fiber diameter, as well as the effects of longitudinal stretching and transverse squeezing on the velocity of the conduction process in nerve, may be correlated on such a basis.     

A Note on the Local Current Associated with the Rising Phase of a Propagating Impulse in Nonmyelinated Nerve Fibers

To extend our recent paper dealing with the cable properties and the conduction velocity of nonmyelinated nerve fibers (Bull. Math. Biol. 64, 1069; 2002), the behavior of the local current associated with the rising phase of a propagating action potential is discussed. It is shown that the process of charging the membrane capacity by means of the local current plays a crucial role in determining the velocity of nerve conduction. The symmetry of the local current with respect to the boundary between the resting and active regions of the nerve fiber is emphasized. It is noted that there are several simple quantitative rules governing the intensities of the capacitive, resistive and total membrane currents observed during the rising phase of an action potential.     

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.     

Anatomical basis for an apparent paradox concerning conduction velocities of two identified axons in Aplysia.

Larger axons usually have faster conduction velocities, lower thresholds, and larger extracellular action potentials than smaller axons. However, it has been shown that the largest fiber, R2, in the right pleurovisceral connective of the marine mollusc, Aplysia, has a higher threshold and a slower conduction velocity than does the smaller axon of cell RI, even though the amplitude of R2's spike is larger than R1's spike. One explanation of this apparent parodox is that the two axons have different "intrinsic membrane and axoplasmic constants" (Goldman, L. (1961), J. Cell Comp. Physiol. 57: 185-191). However, the deep infolding of R2's axonal membrane suggested that differences in the shape of the two axons might also account for the paradox. Accordingly, we measured the conduction velocities of the two axons and then examined the same axons in the electron microscope in order to measure their volumes and surface areas. Our morphological observations indicate that the extensive infolding of surface membrane causes R2 to have a smaller volume to surface area ratio than R1. Thus, since conduction velocity is proportional to the square root of the volume to surface area ratio (Hodgkin, A.L. (1954), J. Physiol. 125: 221-224), it is predictable that the smaller axon would have a faster conduction velocity. The results suggest that the paradoxical conduction velocities can be explained largely as resulting from differences in the shapes of the two axons. However, certain discrepancies between the measured and the predicted values suggest that other factors are contributing as well.     

TOCP对鸡迷走神经不同纤维成份传导速度和兴奋性的影响

对磷酸三邻甲苯醋(TOCP)染毒母鸡进行迷走神经不同纤维成份传导速度和兴奋性测定,发现实验组动物在染毒后14天迷走神经第5波(类似于C纤维)传导速度减慢30%,染毒后21天时减慢52%,并出现迷走神经各波兴奋性显著降低.实验结果说明,TOCP所致迟发性神经病可损害与内脏活动有关的迷走神经.     

On the cable theory of nerve conduction

Conduction of an impulse in the nonmyelinated nerve fiber is treated quantitatively by considering it as a direct consequence of the coexistence of two structurally distinct regions, resting and active, in the fiber. The profile of the electrical potential change induced in the vicinity of the boundary between the two regions is analyzed by using the cable equations. Simple mathematical formulae relating the conduction velocity to the electrical parameters of the fiber are derived from the symmetry of the potential profile at the boundary. The factors that determine the conduction velocity in the myelinated nerve fiber are reexamined.     

The nerve impulse in the axon — a new theory

The Classical Theory of function in the nervous system postulates that the nerve impulse is the result of a sequential reversal of the membrane potential due to an increased permeability of the membrane, first to sodium ions, then to potassium ions. The new theory presents a bio-physical model which depicts the nerve impulse as an event involving the motions of electrons and waves, and their interactions with sodium and potassium atoms and ions. The velocity of the nerve impulse (the most important parameter of nerve function) is determined by the product of two constants: c = the speed of light, which is a constant for all nerves; k =a constant for each nerve and is believed to be a specific property of nerve matter related in some way to the atomic process. The theory proposes that the nerve impulse in the axon is dualistic in nature (particles and waves play equally significant roles). The dualistic nature accounts for the three most fundamental characteristics of conduction of the nerve impulse: periodicity (conduction of a nerve impulse over long distances with constant velocity and form); non-summing (two nerve impulses cannot be in the same place at the same time); quantum nature of each nerve impulse — i.e., the unit message of the nerve impulse is an indivisible unit.     

Anatomical basis for an apparent paradox concerning conduction velocities of two identified axons in Aplysia

Larger axons usually have faster conduction velocities, lower thresholds, and larger extracellular action potentials than smaller axons. However, it has been shown that the largest fiber, R2, in the right pleurovisceral connective of the marine mollusc, Aplysia, has a higher threshold and a slower conduction velocity than does the smaller axon of cell R1, even though the amplitude of R2's spike is larger than R1's spike. One explanation of this apparent paradox is that the two axons have different “intrinsic membrane and axoplasmic constants” (Goldman, L. (1961), J. Cell Comp. Physiol. 57: 185–191). However, the deep infolding of R2's axonal membrane suggested that differences in the shape of the two axons might also account for the paradox. Accordingly, we measured the conduction velocities of the two axons and then examined the same axons in the electron microscope in order to measure their volumes and surface areas. Our morphological observations indicate that the extensive infolding of surface membrane causes R2 to have a smaller volume to surface area ratio than R1. Thus, since conduction velocity is proportional to the square root of the volume to surface area ratio (Hodgkin, A. L. (1954), J. Physiol. 125: 221–224), it is predictable that the smaller axon would have a faster conduction velocity. The results suggest that the paradoxical conduction velocities can be explained largely as resulting from differences in the shapes of the two axons. However, certain discrepancies between the measured and the predicted values suggest that other factors are contributing as well.     

Effect of diameter on membrane capacity and conductance of sheep cardiac Purkinje fibers

Membrane electrical properties were measured in sheep cardiac Purkinje fibers, having diameters ranging from 50 to 300 mum. Both membrane capacitance and conductance per unit area of apparent fiber surface varied fourfold over this range. Membrane time constant, and capacitance per unit apparent surface area calculated from the foot of the action potential were independent of fiber diameter, having average values of 18.8 +/- 0.7 ms, and 3.4 +/- 0.25 muF/cm2, respectively (mean +/- SEM). The conduction velocity and time constant of the foot of the action potential also appeared independent of diameter, having values of 3.0 +/- 0.1 m/s and 0.10 +/- 0.007 ms. These findings are consistent with earlier suggestions that in addition to membrane on the surface of the fiber, there exists a large fraction of membrane in continuity with the extracellular space but not directly on the surface of the fiber. Combining the electrical and morphological information, it was possible to predict a passive length constant for the internal membranes of about 100 mum and a time constant for chaning these membranes in a passive 100-mum fiber of 1.7 ms.     

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.     

Morphallaxis in an aquatic oligochaete, Lumbriculus variegatus: reorganization of escape reflexes in regenerating body fragments

We describe functional and anatomical correlates of the reorganization of giant nerve fiber-mediated escape reflexes in body fragments of an aquatic oligochaete, Lumbriculus variegatus, a species that reproduces asexually by fragmentation. Since fragments from any axial position always regenerate short heads (seven or eight segments long) and much longer tail sections, segments originating from posterior fragments become transposed along the longitudinal axis and acquire, by morphallaxis, features of escape reflex organization that conform to their new anterior position. Using noninvasive electrophysiological recordings we have quantified, on a day-to-day and a segment-by-segment basis, the reorganization that occurs in sensory field arrangements of the medial (MGF) and lateral (LGF) giant nerve fibers, as well as changes in giant fiber conduction velocity and morphometry. Our results show that (1) posterior fragments, originally subserved by the LGF sensory field gradually become subserved by the MGF sensory field; (2) appropriate increases in the ratio of MGF:LGF cross-sectional area, perimeter, and conduction velocity accompany the reorganization in giant fiber sensory fields; and (3) sensory field reorganization can be repeatedly reversed by additional amputations. These results demonstrate that the functional organization of escape reflexes is highly plastic and that morphallaxis may result from the counterbalance of morphogenic influences localized within the anterior and posterior ends of regenerating body fragments.     

外周诱发电位的模型研究

本文根据容积导体中有关动作电位的电生理理论,用三点源模型模拟单根纤维动作电位(SFAP),并假设神经束的复合动作电位(CAP)是由SFAP线性叠加而成,给出了神经束CAP的模型.通过运用上述模型,计算了正常人正中神经纤维传导速度分布,分析了刺激腕部正中神经引导的传感诱发电位(SEP)的N~-_9成分;另外,还得出一些描述此外周传导通路性质的其它参数,如平均传导速度、神经纤维活动最可几传速度分布范围等.此方法可用来研究其它各种外围诱发电位.     

Some physiological characteristics of myelinated and unmyelinated fibers with very low conduction velocity

The compound action potential arising in response to supramaximal stimulation of Aδ- or C-fibers of a cat cutaneous nerve (the saphenous nerve) was investigated by methods improving the signal/noise ratio in the record of the unit evoked response. By the use of optical and computer (BÉSM-3M) methods of coherent signal accumulation followed by averaging, potentials of nerve fibers ranging in amplitude from 20 to 0.05 µV and in duration from 10 to 0.4 msec were distinguished from the apparatus noise. A continuous distribution of nerve fibers by conduction velocity was found over the range from 80 to 0.15 m/sec. The conditions of appearance of low-amplitude action potentials of nerve fibers with a low conduction velocity are discussed.     

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.