Peripheral nerve at extreme low temperatures 1: Effects of temperature on the action potential

Hypothermia is an important means of neuroprotection. Understanding the effects of temperature on a physiologic measurement such as the nerve action potential (NAP) is important in monitoring its effects. The effects of hypothermia on the NAP amplitude, conduction velocity, and response to paired pulse stimulation were quantified in a rat sciatic nerve preparation from 37 to 10 °C. The time course of temperature related changes and the effect of repeated cycles of cooling and rewarming are explored using the following measures of the NAP: peak-to-peak amplitude, conduction velocity, duration, area under the curve and response to paired pulse stimuli. The NAP amplitude initially increases as temperature is reduced to 27 °C and then drops to roughly 50% of its baseline value by 16 °C while the area under the curve increases gradually until it begins to decline at 16 °C. Permanent loss of the NAP appears only after cooling below 10 °C for extended periods. Although the dependence of amplitude on temperature is approximately sigmoidal, the conduction velocity declines linearly at a rate of 2.8 m/s/°C. The response to paired pulse stimulation is strongly dependent on both temperature and the interstimulus interval with the responses at shorter interstimulus intervals being more temperature sensitive. With repetitive cycles of cooling and rewarming, the NAP amplitude declines by roughly 4% with every cycle without changes in the temperature at which the NAP amplitude reaches 50% of baseline. Only minor differences in conduction velocity are seen during cooling and rewarming.     

Conduction along myelinated and demyelinated nerve fibres with a reorganized axonal membrane during the recovery cycle: model investigations

The changes in the excitability of the reorganized axonal membrane in myelinated and demyelinated nerve fibres as well as the causes conditioning such changes have been investigated by paired stimulation during the first 30 ms of the recovery cycle. The variations of the action potential parameters (amplitude and velocity) are traced also. The simulation of the conduction along the normal fiber is based on the Frankenhaeuser and Huxley (1964) and Goldman and Albus (1968) equations, while the demyelination is considered to be an elongation of the nodes of Ranvier. The axonal membrane reorganization is achieved by means of potassium channel blocking and increase of the sodium-channel permeability. It is shown that potassium channels block decreases membrane excitability for the myelinated and demyelinated fibres in the cases of initial and paired stimulation. With increasing sodium-channel permeability on the background of the blocked potassium channels, the membrane excitability is increased. For the fibres with a reorganized membrane, a supernormality of the membrane excitability is obtained, the latter remaining unrecovered during the 30 ms cycle under investigation. The supernormality of the excitability grows from the demyelinated fibre without reorganized membrane to the demyelinated fibre with reorganized one. For short interstimulus intervals, the second action potential propagates along the fibres with a reduced velocity and a decreased amplitude. No supernormality of the potential parameters (amplitude, velocity) is observed during the cycle up to 30 ms. The membrane properties of the myelinated and demyelinated fibres with blocked potassium channels recover in the interval from 15 to 20 ms depending on whether the sodium channels' increase of the permeability is added on the background of the blocked potassium channel or not. In the recovery cycle, the axonal membrane reorganization leads to an improvement of the conduction along most severely demyelinated fibres.     

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.     

Regulatory Evolution and Voltage-Gated Ion Channel Expression in Squid Axon: Selection-Mutation Balance and Fitness Cliffs

It has been suggested that optimization of either axonal conduction velocity or the energy efficiency of action potential conduction predominates in the selection of voltage-gated sodium conductance levels in the squid axon. A population genetics model of channel gene regulatory function was used to examine the role of these and other evolutionary forces on the selection of both sodium and potassium channel expression levels. In this model, the accumulating effects of mutations result in degradation of gene regulatory function, causing channel gene expression to fall to near-zero in the absence of positive selection. In the presence of positive selection, channel expression levels fall to the lowest values consistent with the selection criteria, thereby establishing a selection-mutation balance. Within the parameter space of sodium and potassium conductance values, the physiological performance of the squid axon model showed marked discontinuities associated with conduction failure and excitability. These discontinuities in physiological function may produce fitness cliffs. A fitness cliff associated with conduction failure, combined with the effects of phenotypic noise, can account for the selection of sodium conductance levels, without considering either conduction velocity or metabolic cost. A fitness cliff associated with a transition in axonal excitability, combined with phenotypic noise, can explain the selection of potassium channel expression levels. The results suggest that voltage-gated ion channel expression will fall to low levels, consistent with key functional constraints, even in the absence of positive selection for energy efficiency. Channel expression levels and individual variation in channel expression within the population can be explained by regulatory evolution in combination with genetic variation in regulatory function and phenotypic noise, without resorting to more complex mechanisms, such as activity-dependent homeostasis. Only a relatively small region of the large, nominally isofunctional parameter space for channel expression will normally be occupied, because of the effects of mutation.     

Rate of excitation propagation in a reduced Hodgkins-Huxley model. II. Slow relaxation of the sodium current]

The influence of sodium current activation on the value of nerve excitation conduction velocity is investigated on the basis of Hodgkin-Huxley model. The potassium activation and sodium inactivation are considered as slow processes which do not develop to an appreciable extent in the region of conduction velocity formation. The system of equations was derived and solved analytically after neglecting the dependency of sodium relaxation time on potential; the approximation of steady-state sodium activation was also used with the help of Hevyside function. The algebraic equation for conduction velocity was obtained; its solution has a simple analytical form in two limits of rapid and slow sodium current relaxation. The comparison with the experimental data has shown that at not very high temperatures the slow (compared to the potential dynamics) sodium current relaxation approximation is more appropriate. The dependency of impulse velocity on capacitance and conductance of the fiber was analyzed.     

Contactin orchestrates assembly of the septate-like junctions at the paranode in myelinated peripheral nerve

Rapid nerve impulse conduction depends on specialized membrane domains in myelinated nerve, the node of Ranvier, the paranode, and the myelinated internodal region. We report that GPI-linked contactin enables the formation of the paranodal septate-like axo-glial junctions in myelinated peripheral nerve. Contactin clusters at the paranodal axolemma during Schwann cell myelination. Ablation of contactin in mutant mice disrupts junctional attachment at the paranode and reduces nerve conduction velocity 3-fold. The mutation impedes intracellular transport and surface expression of Caspr and leaves NF155 on apposing paranodal myelin disengaged. The contactin mutation does not affect sodium channel clustering at the nodes of Ranvier but alters the location of the Shaker-type Kv1.1 and Kv1.2 potassium channels. Thus, contactin is a crucial part in the machinery that controls junctional attachment at the paranode and ultimately the physiology of myelinated nerve.     

Model of adaptation of the nerve fiber ranvier node membrane to the action of a steady current as the result of sodium channel inactivation

The effect of the second-order kinetics of the sodium channel inactivation system on spike activity was studied on a modified Hodgkin-Huxley model of the amphibian Ranvier node (Dodge model). The results of calculations based on the experimental data of Chiu, Kniffki, et al. suggest that the cause of adaptation of the amphibian nerve fiber membrane may be the second-order kinetics of the sodium channel inactivation system. Unlike the potassium mechanism of adaptation, the sodium mechanism is associated with constancy or a progressive decline of response amplitudes.     

Bistable nerve conduction

It has been demonstrated experimentally that slow and fast conduction waves with distinct conduction velocities can occur in the same nerve system depending on the strength or the form of the stimulus, which give rise to two modes of nerve functions. However, the mechanisms remain to be elucidated. In this study, we use computer simulations of the cable equation with modified Hodgkin-Huxley kinetics and analytical solutions of a simplified model to show that stimulus-dependent slow and fast waves recapitulating the experimental observations can occur in the cable, which are the two stable conduction states of a bistable conduction behavior. The bistable conduction is caused by a positive feedback loop of the wavefront upstroke speed, mediated by the sodium channel inactivation properties. Although the occurrence of bistable conduction only requires the presence of the sodium current, adding a calcium current to the model further promotes bistable conduction by potentiating the slow wave. We also show that the bistable conduction is robust, occurring for sodium and calcium activation thresholds well within the experimentally determined ones of the known sodium and calcium channel families. Since bistable conduction can occur in the cable equation of Hodgkin-Huxley kinetics with a single inward current, i.e., the sodium current, it can be a generic mechanism applicable to stimulus-dependent fast and slow conduction not only in the nerve systems but also in other electrically excitable systems, such as cardiac muscles.     

Voltage-dependent membrane capacitance in rat pituitary nerve terminals due to gating currents

We investigated the voltage dependence of membrane capacitance of pituitary nerve terminals in the whole-terminal patch-clamp configuration using a lock-in amplifier. Under conditions where secretion was abolished and voltage-gated channels were blocked or completely inactivated, changes in membrane potential still produced capacitance changes. In terminals with significant sodium currents, the membrane capacitance showed a bell-shaped dependence on membrane potential with a peak at approximately -40 mV as expected for sodium channel gating currents. The voltage-dependent part of the capacitance showed a strong correlation with the amplitude of voltage-gated Na+ currents and was markedly reduced by dibucaine, which blocks sodium channel current and gating charge movement. The frequency dependence of the voltage-dependent capacitance was consistent with sodium channel kinetics. This is the first demonstration of sodium channel gating currents in single pituitary nerve terminals. The gating currents lead to a voltage- and frequency-dependent capacitance, which can be well resolved by measurements with a lock-in amplifier. The properties of the gating currents are in excellent agreement with the properties of ionic Na+ currents of pituitary nerve terminals.     

Pulsed magnetic fields enhance the rate of recovery of damaged nerve excitability

Pulsed magnetic fields (PMFs) have well‐known beneficial effects on nerve regeneration. However, little research has examined the nerve conduction characteristics of regenerating peripheral nerves under PMF. The main goal of this study was to examine the conduction characteristics of regenerating peripheral nerves under PMFs. The sucrose‐gap recording technique was used to examine the conduction properties of injured sciatic nerves of rats exposed to PMF. Following the injury, peripheral nerves were very sensitive to repetitive stimulation. When the stimulation frequency was increased, the amplitude of the compound action potential (CAP) decreased more at 15 days post‐crush injury (dpc) than at 38 dpc. PMF treatment for 38 days after injury caused significant differences in the conduction of CAPs. Moreover, application of PMF ameliorated the abnormal electrophysiological activities of nerves such as hyperpolarizing afterpotentials and delayed depolarizations that were revealed by 4‐aminopyridine (4‐AP). Consequently, characteristic findings in impulse conduction of recovered nerves under PMF indicate that the observed abnormalities in signaling or aberrant ion channel functions following injury may be restored by PMF application. Bioelectromagnetics 32:200–208, 2011. © 2010 Wiley‐Liss, Inc.     

Immobilizing the moving parts of voltage-gated ion channels

Voltage-gated ion channels have at least two classes of moving parts, voltage sensors that respond to changes in the transmembrane potential and gates that create or deny permeant ions access to the conduction pathway. To explore the coupling between voltage sensors and gates, we have systematically immobilized each using a bifunctional photoactivatable cross-linker, benzophenone-4-carboxamidocysteine methanethiosulfonate, that can be tethered to cysteines introduced into the channel protein by mutagenesis. To validate the method, we first tested it on the inactivation gate of the sodium channel. The benzophenone-labeled inactivation gate of the sodium channel can be trapped selectively either in an open or closed state by ultraviolet irradiation at either a hyperpolarized or depolarized voltage, respectively. To verify that ultraviolet light can immobilize S4 segments, we examined its relative effects on ionic and gating currents in Shaker potassium channels, labeled at residue 359 at the extracellular end of the S4 segment. As predicted by the tetrameric stoichiometry of these potassium channels, ultraviolet irradiation reduces ionic current by approximately the fourth power of the gating current reduction, suggesting little cooperativity between the movements of individual S4 segments. Photocross-linking occurs preferably at hyperpolarized voltages after labeling residue 359, suggesting that depolarization moves the benzophenone adduct out of a restricted environment. Immobilization of the S4 segment of the second domain of sodium channels prevents channels from opening. By contrast, photocross-linking the S4 segment of the fourth domain of the sodium channel has effects on both activation and inactivation. Our results indicate that specific voltage sensors of the sodium channel play unique roles in gating, and suggest that movement of one voltage sensor, the S4 segment of domain 4, is at least a two-step process, each step coupled to a different gate.     

An analytical study of the physiology and pathology of the propagation of cardiac action potentials

Many cardiac diseases are caused by the abnormal propagation of electrical waves. Previous experimental and modelling work is reviewed, then a detailed study of the mathematics of cardiac propagation is presented. Pathologies are examined in the context of the models by varying parameters in the models to mimic different pathological states. Ionic models of cells are simplified to form analytically tractable models of the propagation of electrical cardiac waves. The roles that sodium channel activation and inactivation play in determining the conduction velocity are studied in detail, and the roles of resting potential currents in conduction block are calculated. The effect of curvature on the conduction velocity is examined, and the conditions in which curvature leads to conduction block and fibrillation are discussed. Hyperkalaemia (important during ischaemia) is modelled, and the model correctly describes the bi-phasic relation between propagation velocity and extracellular potassium.     

G-protein activation modulates pseudo-periodic oscillation of Na channel

We have shown before that the duration and amplitude of both prolonged (1-160 s) and short (100-1000 ms) depolarizing prepulse altered all the steady-state and kinetic parameters of rNav1.2a voltage-gated sodium channel in a pseudo-oscillatory fashion with variable time period and amplitude, often superimposed on a linear trend. In this study, we have examined the effect of G-protein activation on pseudo-oscillatory properties of the rNav1.2a sodium channel alpha subunit, heterologously expressed in Chinese hamster ovary cells. G-protein modification caused insignificant changes in the slow pseudo-periodic oscillation of the activation properties of sodium channel; only the time period of the oscillation was altered from approximately 30 to 21s. In contrast, G-protein activation abolished the faster component of pseudo-periodic oscillation in steady-state inactivation properties of sodium channel; the conditioning duration dependence of steady-state inactivation becomes monotonic in nature.     

Can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels?

Ion channels are protein molecules, which can assume distinct open and closed conformational states, a phenomenon termed ion channel kinetics. The transitions from one state to another depend on the potential energy barrier that separates those two states. Therefore, it is rational to suppose that electromagnetic waves could interact with this barrier and induce changes in the rate transitions of this kinetic process. Our aim is to answer the question: can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels? We simulated the effects of the low and high frequency electromagnetic waves on the sodium and potassium channels of the giant axon of Loligo. The key parameter measured was the fractional open time (fv), because it reflects the voltage dependence of the kinetics of channels. The electromagnetic radiations induced the following changes in the kinetics of the potassium and sodium channels: i/ low frequency waves kept the potassium channel 50% of the time open independent on the mean voltage applied through the membrane; ii/ a gradual inhibition of the inactivation on the sodium channel, when the amplitudes of the low frequency waves were increased; iii/ high frequency waves on the potassium channel, decreased both Vo (voltage in which the channel stays 50% open) and the steepness of fv (d fv/dV) as the amplitudes of the waves increased, and iv/ high frequency and low amplitude radiations on the sodium channel decreased the maximum value of fv (in relation to control), while high amplitudes increased this value. In conclusion, high and low frequency electromagnetic radiations were able to change the kinetics of the potassium and sodium channels in a squid giant axon model.     

A model for axonal propagation incorporating both radial and axial ionic transport.

We present an axonal model that explicitly includes ionic diffusion in the intracellular, periaxonal, and extracellular spaces and that incorporates a Hodgkin-Huxley membrane, extended with potassium channel inactivation and active ion transport. Although ionic concentration changes may not be significant in the time course of one action potential, they are important when considering the long-term behavior (seconds to minutes) of an axon. We demonstrate this point with simulations of transected axons where ions are moving between the intra- and extracellular spaces through an opening that is sealing with time. The model predicts that sealing must occur within a critical time interval after the initial injury to prevent the entire axon from becoming permanently depolarized. This critical time interval becomes considerably shorter when active ion transport is disabled. Furthermore, the model can be used to study the effects of sodium and potassium channel inactivation; e.g., sodium inactivation must be almost complete (within 0.02%) to obtain simulation results that are realistic.     

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.     

Mechanisms of conduction slowing during myocardial stretch by ventricular volume loading in the rabbit

Acute ventricular loading by volume inflation reversibly slows epicardial electrical conduction, but the underlying mechanism remains unclear. This study investigated the potential contributions of stretch-activated currents, alterations in resting membrane potential, or changes in intercellular resistance and membrane capacitance. Conduction velocity was assessed using optical mapping of isolated rabbit hearts at end-diastolic pressures of 0 and 30 mmHg. The addition of 50 microM Gd3+ (a stretch-activated channel blocker) to the perfusate had no effect on slowing. The effect of volume loading on conduction velocity was independent of changes in resting membrane potential created by altering the perfusate potassium concentration between 1.5 and 8 mM. Bidomain model analysis of optically recorded membrane potential responses to a unipolar stimulus suggested that the cross-fiber space constant and membrane capacitance both increased with loading (21%, P = 0.006, and 56%, P = 0.004, respectively), and these changes, when implemented in a resistively coupled one-dimensional network model, were consistent with the observed slowing (14%, P = 0.005). In conclusion, conduction slowing during ventricular volume loading is not attributable to stretch-activated currents or altered resting membrane potential, but a reduction of intercellular resistance with a concurrent increase of effective membrane capacitance results in a net slowing of conduction.     

Bioelectric properties of frog sciatic nerves during exposure to stationary magnetic fields

The bioelectric properties of frog sciatic nerves have been measured during exposure to homogeneous, stationary magnetic fields. The action potential amplitude, conduction velocity, absolute refractory period and relative refractory period were found to be unaffected by a continuous 4-h exposure to perpendicular or parallel 2.0 T (1 T equal 10(4) G) magnetic fields. These parameters also remained unchanged during a 1-h post-exposure period. The conduction velocity was similarly found to be unchanged when the field was applied continuously for 17 h. Exposure of sciatic nerves to a 1.0-T field led to no alteration in the threshold for neural excitation. The absence of magnetic field effects on nerve electrical activity observed in the present experiments contrasts with the positive findings reported previously by other investigators. These discrepancies may be attributable to an inadequate control of ambient temperature in the earlier studies.     

Optical recording of action potential propagation in demyelinated frog nerve.

Conduction in focally demyelinated frog nerves has been measured optically using potential-sensitive dyes. Absorption changes were recorded with an array of photodiodes positioned in the image plane of a microscope. Both the amplitude and conduction velocity of the optical signals decreased in the demyelinated region. Conduction was improved after exposure to the potassium channel blocking agent 4-aminopyridine.