ACCOMMODATION IN MYELINATED NERVE FIBRES OF XENOPUS LAEVIS AS COMPUTED ON THE BASIS OF VOLTAGE CLAMP DATA

Rethinking the Role of Normalization and Residual Blocks for Spiking Neural Networks

Biologically inspired spiking neural networks (SNNs) are widely used to realize ultralow-power energy consumption. However, deep SNNs are not easy to train due to the excessive firing of spiking neurons in the hidden layers. To tackle this problem, we propose a novel but simple normalization technique called postsynaptic potential normalization. This normalization removes the subtraction term from the standard normalization and uses the second raw moment instead of the variance as the division term. The spike firing can be controlled, enabling the training to proceed appropriately, by conducting this simple normalization to the postsynaptic potential. The experimental results show that SNNs with our normalization outperformed other models using other normalizations. Furthermore, through the pre-activation residual blocks, the proposed model can train with more than 100 layers without other special techniques dedicated to SNNs.

Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.

Ionic concentrations in the brain are not constant. We show that during intense neuronal activity, they can change on the order of seconds and even switch neuronal spiking patterns under identical stimulation from a regular firing mode to an intermittently interrupted one. Triggered by an accumulation of extracellular potassium, such a transition is caused by a specific, qualitative change in of the neuronal voltage dynamics—a so-called bifurcation—which affects crucial features of action-potential generation and bears consequences for how information is encoded and how neurons behave together in the network. Also, changes in intracellular sodium can induce measurable effects, like a reduction of spike amplitude that occurs independently of the fast amplitude effects attributed to sodium channel inactivation. Taken together, our results demonstrate that a neuron can respond very differently to the same stimulus, depending on its previous activity or the current brain state. This finding may be particularly relevant when other regulatory mechanisms of ionic homeostasis are challenged, for example, during pathological states of glial impairment or oxygen deprivation. Finally, categorization of cortical neurons as intrinsically bursting or regular spiking may be biased by the ionic concentrations at the time of the observation, highlighting the non-static nature of neuronal dynamics.

Small and large cutaneous fibers display different excitability properties to slowly increasing ramp pulses

The excitability of large nerve fibers is reduced when their membrane potential is slowly depolarizing, i.e., the fibers display accommodation. The aim of this study was to assess accommodation in small (mainly Aδ) and large (Aβ) cutaneous sensory nerve fibers using the perception threshold tracking (PTT) technique. Linearly increasing ramp currents (1 ms-200 ms) were used to assess the excitability of the nerve fibers by cutaneous electrical stimulation. To investigate the PPT technique's ability to preferentially activate different fiber types, topical application of lidocaine/prilocaine (EMLA) or a placebo cream was applied. By means of computational modeling, the underlying mechanisms governing the perception threshold in the two fiber types was studied. The axon models included the voltage-gated ion channels: transient TTX-sensitive sodium current, transient TTX-resistant sodium current (Na_TTXr), persistent sodium current, delayed rectifier potassium channel (K_Dr), slow potassium channel, and hyperpolarization-activated current. Large fibers displayed accommodation, whereas small fibers did not display accommodation (P < 0.05). For the pin electrode, a significant interaction was observed between cream (EMLA or placebo) and pulse duration (P < 0.05); for the patch electrode, there was no significant interaction between cream and duration, which supports the pin electrode's preferential activation of small fibers. The results from the computational model suggested that differences in accommodation between the two fiber types may originate from selective expression of voltage-gated ion channels, particularly the transient Na_TTXr and/or K_Dr. The PTT technique could assess the excitability changes during accommodation in different nerve fibers. Therefore, the PTT technique may be a useful tool for studying excitability in nerve fibers in both healthy and pathological conditions.NEW & NOTEWORTHY When large nerve fibers are stimulated by long, slowly increasing electrical pulses, interactive mechanisms counteract the stimulation, which is called accommodation. The perception threshold tracking technique was able to assess accommodation in both small and large fibers. The novelty of this study is that large fibers displayed accommodation, whereas small fibers did not. Additionally, the difference in accommodation between the fiber could be linked to expression of voltage-gated ion channels by means of computational modeling.

A computational study to model the effect of electrode-to-auditory nerve fiber distance on spectral resolution in cochlear implant

Spectral ripple discrimination (SRD) has been widely used to evaluate the spectral resolution in cochlear implant (CI) recipients based on its strong correlation with speech perception performance. However, despite its usefulness for predicting speech perception outcomes, SRD performance exhibits large across-subject variabilities even among subjects implanted with the same CIs and sound processors. The potential factors of this observation include current spread, nerve survival, and CI mapping. Previous studies have found that the spectral resolution reduces with increasing distance of the stimulation electrode from the auditory nerve fibers (ANFs), attributable to increasing current spread. However, it remains unclear whether the spread of excitation is the only cause of the observation, or whether other factors such as temporal interaction also contribute to it. In this study, we used a computational model to investigate channel interaction upon non-simultaneous stimulation with respect to the electrode–ANF distance, and evaluated the SRD performance for five electrode–ANF distances. The SRD performance was determined based on the similarity between two neurograms in response to standard and inverted stimuli and used to evaluate the spectral resolution in the computational model. The spread of excitation was observed to increase with increasing electrode–ANF distance, consistent with previous findings. Additionally, the preceding pulses delivered from neighboring channels induced a channel interaction that either inhibited or facilitated the neural responses to subsequent pulses depending on the electrode–ANF distance. The SRD performance was also found to decrease with increasing electrode–ANF distance. The findings of this study suggest that variation of the neural responses (inhibition or facilitation) with the electrode–ANF distance in CI users may cause spectral smearing, and hence poor spectral resolution. A computational model such as that used in this study is a useful tool for understanding the neural factors related to CI outcomes, such as cannot be accomplished by behavioral studies alone.

Temporal Considerations for Stimulating Spiral Ganglion Neurons with Cochlear Implants

A wealth of knowledge about different types of neural responses to electrical stimulation has been developed over the past 100 years. However, the exact forms of neural response properties can vary across different types of neurons. In this review, we survey four stimulus-response phenomena that in recent years are thought to be relevant for cochlear implant stimulation of spiral ganglion neurons (SGNs): refractoriness, facilitation, accommodation, and spike rate adaptation. Of these four, refractoriness is the most widely known, and many perceptual and physiological studies interpret their data in terms of refractoriness without incorporating facilitation, accommodation, or spike rate adaptation. In reality, several or all of these behaviors are likely involved in shaping neural responses, particularly at higher stimulation rates. A better understanding of the individual and combined effects of these phenomena could assist in developing improved cochlear implant stimulation strategies. We review the published physiological data for electrical stimulation of SGNs that explores these four different phenomena, as well as some of the recent studies that might reveal the biophysical bases of these stimulus-response phenomena.

Electrostatic tuning of cellular excitability

Voltage-gated ion channels regulate the electric activity of excitable tissues, such as the heart and brain. Therefore, treatment for conditions of disturbed excitability is often based on drugs that target ion channels. In this study of a voltage-gated K channel, we propose what we believe to be a novel pharmacological mechanism for how to regulate channel activity. Charged lipophilic substances can tune channel opening, and consequently excitability, by an electrostatic interaction with the channel's voltage sensors. The direction of the effect depends on the charge of the substance. This was shown by three compounds sharing an arachidonyl backbone but bearing different charge: arachidonic acid, methyl arachidonate, and arachidonyl amine. Computer simulations of membrane excitability showed that small changes in the voltage dependence of Na and K channels have prominent impact on excitability and the tendency for repetitive firing. For instance, a shift in the voltage dependence of a K channel with -5 or +5 mV corresponds to a threefold increase or decrease in K channel density, respectively. We suggest that electrostatic tuning of ion channel activity constitutes a novel and powerful pharmacological approach with which to affect cellular excitability.

Deciphering the contribution of intrinsic and synaptic currents to the effects of transient synaptic inputs on human motor unit discharge

The amplitude and time course of synaptic potentials in human motoneurons can be estimated in tonically discharging motor units by measuring stimulus-evoked changes in the rate and probability of motor unit action potentials. However, in spite of the fact that some of these techniques have been used for over 30 years, there is still no consensus on the best way to estimate the characteristics of synaptic potentials or on the accuracy of these estimates. In this review, we compare different techniques for estimating synaptic potentials from human motor unit discharge and also discuss relevant animal models in which estimated synaptic potentials can be compared to those directly measured from intracellular recordings. We also review the experimental evidence on how synaptic noise and intrinsic motoneuron properties influence their responses to synaptic inputs. Finally, we consider to what extent recordings of single motor unit discharge in humans can be used to distinguish the contribution of changes in synaptic inputs versus changes in intrinsic motoneuron properties to altered motoneuron responses following CNS injury.

Biomimetics — a review

Biology can inform technology at all levels (materials, structures, mechanisms, machines, and control) but there is still a gap between biology and technology. This review itemizes examples of biomimetic products and concludes that the Russian system for inventive problem solving (teoriya resheniya izobreatatelskikh zadatch (TRIZ)) is the best system to underpin the technology transfer. Biomimetics also challenges the current paradigm of technology and suggests more sustainable ways to manipulate the world.

The sciatic nerve of the toad Xenopus laevis as a physiological model of the human cochlear nerve

The response of single fibres of the human cochlear nerve to electrical stimulation by a cochlear implant has previously been inferred from the response of the cochlear nerve in other mammals. These experiments are hindered by stimulus artefact and the range of stimulus currents used is therefore much less than the perceptual dynamic range (from threshold to discomfort) of human subjects. We have investigated use of the sciatic nerve of the toad Xenopus laevis as a convenient physiological model of the human cochlear nerve. Use of this completely dissected nerve reduces the problems of stimulus artefact whilst maintaining the advantages of a physiological preparation. The validity of the model was assessed by measuring the refractory periods, excitation time-constant, and relative spread of single fibres using microelectrode recording. We have also investigated the response of nerve fibres to sinusoidal stimulation. Based on these measurements, we propose that the sciatic nerve may be a suitable model of the human cochlear nerve if the timescales of stimuli are decreased by a factor of about five to compensate for the slower dynamics of the sciatic nerve and if noise is added to the stimuli to compensate for the lower internal noise of sciatic nerve fibres.

Effects of androstenedione on long term potentiation in the rat dentate gyrus. Relevance for affective and degenerative diseases

We studied the effects of the androgenic hormone androstenedione, a 17-ketosteroid, on long term potentiation (LTP) in the dentate gyrus (DG) of intact, urethane anesthetized rats. Intravenous injection of 10mg of the hormone dissolved in Nutralipid produced a significant increase of the population spike (PS), but not of the excitatory post-synaptic potentials (EPSPs). The results are discussed in terms of the potential enhancement that androstenedione may have on some aspects of memory processes as reported for other androgenic steroids. Also noted are the plausible beneficial effects of the hormone on depression as well as in recovery following both central and peripheral neural injury.

Input-output functions of mammalian motoneurons

Our intent in this review was to consider the relationship between the biophysical properties of motoneurons and the mechanisms by which they transduce the synaptic inputs they receive into changes in their firing rates. Our emphasis has been on experimental results obtained over the past twenty years, which have shown that motoneurons are just as complex and interesting as other central neurons. This work has shown that motoneurons are endowed with a rich complement of active dendritic conductances, and flexible control of both somatic and dendritic channels by endogenous neuromodulators. Although this new information requires some revision of the simple view of motoneuron input-output properties that was prevalent in the early 1980's (see sections 2.3 and 2.10), the basic aspects of synaptic transduction by motoneurons can still be captured by a relatively simple input-output model (see section 2.3, equations 1-3). It remains valid to describe motoneuron recruitment as a product of the total synaptic current delivered to the soma, the effective input resistance of the motoneuron and the somatic voltage threshold for spike initiation (equations 1 and 2). However, because of the presence of active channels activated in the subthreshold range, both the delivery of synaptic current and the effective input resistance depend upon membrane potential. In addition, activation of metabotropic receptors by achetylcholine, glutamate, noradrenaline, serotonin, substance P and thyrotropin releasing factor (TRH) can alter the properties of various voltage- and calcium-sensitive channels and thereby affect synaptic current delivery and input resistance. Once motoneurons are activated, their steady-state rate of repetitive discharge is linearly related to the amount of injected or synaptic current reaching the soma (equation 3). However, the slope of this relation, the minimum discharge rate and the threshold current for repetitive discharge are all subject to neuromodulatory control. There are still a number of unresolved issues concerning the control of motoneuron discharge by synaptic inputs. Under dynamic conditions, when synaptic input is rapidly changing, time- and activity-dependent changes in the state of ionic channels will alter both synaptic current delivery to the spike-generating conductances and the relation between synaptic current and discharge rate. There is at present no general quantitative expression for motoneuron input-output properties under dynamic conditions. Even under steady-state conditions, the biophysical mechanisms underlying the transfer of synaptic current from the dendrites to the soma are not well understood, due to the paucity of direct recordings from motoneuron dendrites. It seems likely that resolving these important issues will keep motoneuron afficiandoes well occupied during the next twenty years.

Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo

Cortical neurons are sensitive to the timing of their synaptic inputs. They can synchronize their firing on a millisecond time scale and follow rapid stimulus fluctuations with high temporal precision. These findings suggest that cortical neurons have an enhanced sensitivity to synchronous synaptic inputs that lead to rapid rates of depolarization. The voltage-gated currents underlying action potential generation may provide one mechanism to amplify rapid depolarizations. We have tested this hypothesis by analyzing the relations between membrane potential fluctuations and spike threshold in cat visual cortical neurons recorded intracellularly in vivo. We find that visual stimuli evoke broad variations in spike threshold that are caused in large part by an inverse relation between spike threshold and the rate of membrane depolarization preceding a spike. We also find that spike threshold is inversely related to the rate of rise of the action potential upstroke, suggesting that increases in spike threshold result from a decrease in the availability of Na(+) channels. By using a simple neuronal model, we show that voltage-gated Na(+) and K(+) conductances endow cortical neurons with an enhanced sensitivity to rapid depolarizations that arise from synchronous excitatory synaptic inputs. Thus, the basic mechanism responsible for action potential generation also enhances the sensitivity of cortical neurons to coincident synaptic inputs.

Time-frequency analysis of infant cry: measures that identify individuals

As part of a larger study designed to test the predictive power of recordings of infant cry for neurological development at a year of age, we have developed a summary measure of a cry which shows a very high consistency within an individual. This measure may be useful in making assessments of anatomical structure in the infant vocal tract.

Computed potential responses of small cultured rat hippocampal neurons

1. The potential responses of small hippocampal neurons were computed on the basis of a previous mathematical description of the currents recorded under voltage-clamp conditions. 2. The computed action potentials were graded with respect to stimulus strength, in accordance with previous experimental findings. 3. The time course of the membrane currents and of the permeabilities and permeability variables during the impulse was computed for different stimulus intensities. 4. The effect of the membrane time constant on the impulse amplitude was investigated. It was concluded that the value of the time constant used was not per se sufficient to explain the amplitude variation of the impulse. 5. The effect of the magnitudes of the different potential-dependent permeabilities on the impulse amplitude was investigated. A Na+ permeability within a certain range caused impulses of variable amplitude, and this variability was affected by the K+ permeability.

Postoperative ileus

Postoperative ileus follows any operation. Although worsened if the peritoneum is entered, the length and duration of surgery does not influence the severity of postoperative ileus. Inhibitory alpha 2-adrenergic reflexes with peptidergic afferents contribute to postoperative ileus. Clinically, treatment of ileus centers around symptomatic relief with nasogastric suction. Trials of adrenergic blockade combined with cholinergic stimulation have met with limited success. Prokinetic drugs have not been proved effective in the treatment of this disorder. Two types of ileus exist: postoperative and paralytic. Postoperative ileus resolves spontaneously after two to three days, and probably reflects inhibition of colonic motility. Paralytic ileus is more severe, last more than three days, and seems to represent inhibition of small bowel activity. No discrete structural changes cause postoperative ileus and the role of peptidergic neuronal systems of the enteric nervous system has not been elucidated. Possible central or humoral mechanisms have not been studied extensively. The possible direct inhibition of enteric or spinal nerves by anesthetic agents not cleared from these tissues remains to be studied. Also in need of study is the potential alteration of neurotransmitter receptor activity within the enteric nervous plexus after manipulation of the bowel.

The inactivation of sodium channels in the node of Ranvier and its chemical modification

The many experimental studies reported demonstrate the complexity of what is termed inactivation, the decrease of current flow through sodium channels at maintained depolarization. Even at the normal resting potential of, say, -70 mV for a frog node of Ranvier, ca. 20% of the channels are closed and inactivated, i.e., incapable of passing current on a sudden depolarization, in contrast to the remaining 80% of closed but resting channels. The term inactivation has thus evolved from bulk current ("macroscopic") phenomena and is applied to channels although its single-channel ("microscopic") basis is not entirely clear and may even vary among preparations. It is conceivable that the macroscopic phenomenon may have more than a single microscopic cause; this point will probably not be settled until a physical description of the conformational states of the channel macromolecule becomes available. At any rate, channel transition into an inactivated closed state can be easily affected by numerous reagents of highly diverse chemical nature and, most likely, different primary sites of action as already suggested by the sidedness of effective application, e.g., iodate and endopeptidases to the inside, polypeptide toxins to the outside. But also the search for a common denominator, a secondary target of all these treatments, has not been very successful as demonstrated by the experiments with group-specific reagents. Since modification of inactivation is often accompanied by shifts in the voltage dependence of gating parameters, a target could be the "voltage sensor" of the channel, charged and/or dipolar components of the channel macromolecule that, by being moved in the electric field, somehow induce gating and whose movement is measured as gating current (e.g, Hille, 1984). The fraction of open channels as a function of membrane potential, F(E), may serve as an indicator. It may be simply shifted (to more negative potentials) as by veratridine (Leibowitz et al., 1987) or flattened (reduction of gating charge?) and shifted (in the positive direction) as by Anemonia sulcata toxin II (Ulbricht and Schmidtmayer, 1981) or chloramine-T (Drews, 1987). On the other hand, the steady-state inactivation curve is shifted to more negative potentials by the toxin (Ulbricht and Schmidtmayer, 1981), but to more positive potentials by chloramine-T (Wang, 1984a; Schmidtmayer, 1985). Obviously, modifiers may affect activation and inactivation quite differently, a result that touches on the question as to what extent inactivation derives its potential dependence from activation.(ABSTRACT TRUNCATED AT 400 WORDS)

Depolarization changes the mechanism of accommodation in rat and human motor axons

1. We have previously studied accommodation in rat and human motor axons by testing excitability with combinations of long and short current pulses. We found that normally polarized axons accommodate slowly and partially (over about 50 ms) to subthreshold depolarizing currents, and that the principal mechanism is the activation of slow potassium channels (Bostock & Baker, 1988). To understand the response of human nerves to ischaemia, we have now extended these observations to axons already depolarized before the testing currents were applied. 2. Rat ventral root axons were depolarized by passing continuous currents or by raising the extracellular potassium concentration. Human forearm nerves were depolarized by ischaemia, induced by inflating a sphygmomanometer cuff on the upper arm. Depolarized rat and human motor axons accommodated much more rapidly and completely than normally polarized axons (e.g. accommodation in rat axons was 50% complete within 2 ms at about 15 mV depolarized to rest). 3. The fast component of accommodation in depolarized rat fibres was not blocked by tetraethylammonium ions or 4-aminopyridine, was not accompanied by a conductance or potential change, and had a time constant of 1.7 ms at 30 degrees C. It was attributed to inactivation of closed sodium channels. 4. In depolarized rat fibres exhibiting fast accommodation, a brief rise in excitability was seen at the break of an anodal current. Our prediction that human motor axons would show anode-break excitation during ischaemia was readily confirmed. 5. The results are discussed in relation to Hill's (1936) mathematical description of accommodation in nerve, and it is concluded that his description is only applicable to depolarized axons.

An early outward conductance modulates the firing latency and frequency of neostriatal neurons of the rat brain

An in vitro slice preparation was used to obtain intracellular recordings of neostriatal neurons. Indirect evidence for the presence of an early outward conductance in neostriatal neurons is presented. With near threshold stimulation neostriatal neurons fired very late during the pulse. The long firing latency was associated with a slow (ramp-like) depolarization. In the presence of TTX the slow depolarization was lost and outward-going rectification dominated the subthreshold response. This finding demonstrated that both, outward- and inward-going conductances play a role during the ramp-like depolarization. Outward-going rectification during depolarizing responses could be further augmented if the depolarizing stimulus was preceded by a conditioning hyperpolarization. A conditioning hyperpolarization prolonged the firing latency and slowed the firing frequency. A conditioning depolarization had opposite effects. After TTX treatment, the response showed a hyperpolarizing "sag" when depolarizing stimulation was preceded by conditioning hyperpolarization. 4-AP (0.5-2.5 mM) blocked the effects of the conditioning hyperpolarization on the firing latency and on the voltage trajectory. 4-AP also disclosed a slow depolarization which could produce neuronal firing very early during the pulse. This depolarization was TTX-sensitive and Co++-insensitive. In contrast to 4-AP, TEA (20 mM) did not produce a reduction in the firing latency but disclosed a membrane oscillatory behavior most probably produced by the interplay of these opposing conductances: the slow inward (probably Na+) and the transient outward (probably K+). Repetitive firing during 4-AP treatment was of the "phasic-tonic" type with an initial burst riding on the initial Co++-insensitive slow depolarization and a somehow irregular train of spikes during the remainder of the stimulation. Action potentials during 4-AP treatment were followed by an afterdepolarization which dominated the initial part of the interspike interval.

The frequency response function and sinusoidal threshold properties of the Hodgkin-Huxley model of action potential encoding

The behavior of the space-clamped Hodgkin-Huxley model has been studied using band-limited white noise (0-50 Hz) as the input membrane current and taking the output as a point process in time given by the peaks of the action potentials. The frequency response and coherence functions were measured by use of the Fourier transform and digital filtering of the spike train. The results obtained are in good agreement with those already published for the simple integrator and leaky integrator models of neuronal encoding, as well as the earlier studies on the response of the Hodgkin-Huxley model to steady currents. In addition, the threshold of the model to sinusoidal membrane currents has been measured as a function of frequency over the range of 0.1-100 Hz. This shows a relatively constant level up to 2 Hz and then a clear minimum at 60 Hz, in agreement with measured thresholds of squid axons. These results are discussed in terms of the possible contributions of action potential encoding mechanisms to the frequency responses and sinusoidal thresholds which have been measured for rapidly adapting receptors.

Impulse firing in the slowly adapting stretch receptor neurone of lobster and its numerical simulation

A mathematical model of the electrical activity of the slowly adapting lobster stretch receptor neurone is presented. The model is based on constant field and state transition theory and employs measurements of the kinetics of membrane currents in sub- and near-threshold voltage regions (Gestrelius, Grammp & Sjölin 1981, Gestrelius & Grampp 1983, Gestrelius, Grampp & Sjölin 1983, Edman, Gestrelius & Grampp 1983). In addition to the classical action potential generating mechanisms (Hodgkin & Huxley 1952) the model also includes the processes of slow Na and K inactivation, ion flux dependent changes of the intracellular Na+ and K+ concentrations, and the activity of an electrogenic Na-K pump sensitive to intracellular Na+ accumulation. The model is able to correctly simulate recorded action potentials as well as repetitive firing both with respect to stimulus dependence (sensitivity) and time dependence (adaptation) during prolonged electrical stimulation. In the living cell firing adaptation is found to consist of an initial phase with a relatively high, and a later phase with a lower rate of adaptation. From the model properties it can be concluded that the initial phase is mainly caused by the slow Na inactivation, while the later phase is due to a slow Na+ influx dependent pump current activation.

The Cole-Moore effect in nodal membrane of the frog Rana ridibunda: evidence for fast and slow potassium channels

The K conductance (gK) kinetics were studied in voltage-clamped frog nodes (Rana ridibunda) in double-pulse experiments. The Cole-Moore translation for gK--t curves associated with different initial potentials (E) was only observed with a small percentage of fibers. The absence of the translation was found to be caused by the involvement of an additional, slow, gK component. This component cannot be attributed to a multiple-state performance of the k channel. It can only be accounted for by a separate, slow K channel, the fast channel being the same as the n4 K channel in R. pipiens. The slow K channel is characterized by weaker sensitivity to TEA, smaller density, weaker potential (E) dependence, and somewhat more negative E range of activation than the fast K channel. According to characteristics of the slow K system, three types of fibers were found. In Type I fibers (most numerous) the slow K channel behaves as and n4 HH channel. In Type II fibers (the second largest group found) the slow K channel obeys the HH kinetics within a certain E range only; beyond this range the exponential decline of the slow gK component is preceded by an E-dependent delay, its kinetics after the delay being the same as those in Type I fibers. In Type III fibers (rare) the slow K channel is lacking, and it is only in these fibers that the Cole-Moore translation of the measured gK--t curves can be observed directly. The physiological role of the fast and slow K channel in amphibian nerves is briefly discussed.

Differences between K channels in motor and sensory nerve fibres of the frog as revealed by fluctuation analysis

Differences between K channels in the nodal membrane of sensory and motor myelinated nerve fibres of the frog were investigated by fluctuation analysis. Spectral densities, S(f), between 3 Hz and 5 kHz were determined from K-current fluctuations measured between 145 and 460 ms after the onset of depolarizations V between 16 and 80 mV. Fits by the sum of a 1/f component and Lorentzian spectra corresponding to Hodgkin-Huxley n4-kinetics gave significant deviations from the measured spectra. The best fit was obtained by: S(f) = S1/[1+(f/fc)1.5]+S2. The first term can be interpreted as a diffusion spectrum which would originate from gating of K channels governed by an electrodiffusion process. To describe the spectral density at frequencies above 1 kHz it was necessary to add the plateau S2. Time constants taun* = 1/(2pifc) are roughly equal to the conventional Hodgkin-Huxley time constant taun only for pulses V < 40mV. At higher depolarizations taun increases with increasing depolarization in contrast to taun. The variance, var, of conductance fluctuations was determined by integration of the first component of S(f). From var, the probability of the open channel state, and the steady-state K current the single-channel conductance gamma and the number N of K channels per node were calculated; all parameters were corrected for K accumulation during depolarizing pulses. gamma and N were found to be only weakly voltage-dependent. The mean values over all voltages are for motor fibres: gamma=2.7 pS, N = 5.7 x 10(4), and for sensory fibres: gamma = 4.6 pS, N = 5.2 x 10(4). The results suggest two different kinds of K channels in motor and sensory nerve fibres.

The standard Hodgkin-Huxley model and squid axons in reduced external Ca++ fail to accommodate to slowly rising currents

Accommodation may be defined as an increase in the threshold of an excitable membrane when the membrane is subjected to a sustained subthreshold depolarizing stimulus. Some excitable membranes show accommodation in response to currents which rise linearly at a very slow rate. In this report we point out a theoretical and an experimental counterexample, i.e., a nerve model and an axon which do not accommodate. The nerve model is the standard Hodgkin-Huxley axon, which Hodgkin and Huxley expected not to be excited by a very slowly rising current. This expectation is often quoted as fact, in spite of contrary calculations which we confirm. We have found that squid axons in seawater with reduced divalent cation concentration also do not accommodate to slowly rising currents.

A fully coupled transient excited state model for the sodium channel. II. Implications for action potential generation, threshold, repetitive firing, and accommodation

The axon membrane is simulated by standard Hodgkin-Huxley leakage and potassium channels plus a coupled transient excited state kinetic scheme for the sodium channel. This scheme for the sodium channel is as proposed previously by the author. Simulations are presented showing the form of the action potential, threshold behavior, accommodation, and repetitive firing. It is seen that the form of the individual action potential, its all-or-none nature, and its refractory period are well simulated by this model, as they are by the standard Hodgkin-Huxley model. However, the model differs markedly from the Hodgkin-Huxley model with respect to repetitive firing and accommodation to stimulating currents of slowly rising intensity, in ways that are shown to be related to those features of the sodium inactivation which are anomalous to the H-H model. The tendency for repetitive firing is highly dependent on that parameter which primarily determines the existence of the inactivation shift in voltage clamp experiments, in such a way that the more pronounced the inactivation shift, the less the tendency for repetitive firing. The tendency for accommodation is highly dependent on that parameter which primarily determines the 'tauc-tauh' separation, in such a way that the greater the separation the greater the tendency for the membrane to accommodate without firing action potentials to a slowly rising current.

Slow mechanism for sodium permeability inactivation in myelinated nerve fibre of Xenopus laevis

1. Single myelinated nerve fibres were isolated and the nodal currents were recorded under potential clamp conditions. The effect of membrane potential on the Na permeability (PNa) mechanism was analysed. 2. The available PNa increased slowly during negative polarization of the membrane. The time course of this change was about 10(3) times slower than the time course of the mechanism for the usual PNa inactivation (h-system). The slow PNa changes could be distinguished from changes in h because of the difference in rate. 3. The slow PNa variation was independent of the state of the h-system and was largely due to a slow inactivation system, which empirically could be described as separate from the other permeability variables. 4. In the steady state the slow inactivation appeared almost absent at a holding potential of -120 mV, whereas it was 30% complete at the resting potential (-70 mV) and 80% complete at a holding potential of -20 mV. 5. Changes in the slow inactivation system showed an approximately exponential time course. At 10-12 degrees C the time constant was about 3 sec with U = -70 mV, 7 sec with U = -100 mV and 1-5 sec with U = -127 mV. 6. High Ca shifted the steady state slow inactivation curve in the positive direction along the potential axis.

Effect of urea on some electrophysiological properties of the frog muscle cell membrane

The effect of urea on the electrophysiological properties of the frog muscle cell membrane was studied with intracellular microelectrodes, together with an analysis of the electrolyte composition of the muscle. The different parameters were measured and evaluated after soaking the muscle for 60 min at urea concentrations up to 2.25 M. The resting membrane potential was markedly decreased above 1.50 M and fell to about -50mV at 2.25 M. The specific membrane resistance (Rm) was almost unaffected at concentrations of 0.75 M and 1.50 M but was reduced after 60 min in 2.25 M to very low values indicating a leaky membrane. The maximum rate of rise of the action potential (VA) was unaffected up to 0.50 M but was reduced to about 50% of control value at 0.75 M. Between 0.75 M and 1.25 M it was constant and at higher concentrations reduced to almost zero. The reduction of VA at the lower concentrations was not accompanied by changes in neither the resting membrane potential nor Rm. It is proposed that urea perturbs protein systems concerned with the generation of the muscle action potential without affecting the passive electrical properties of the muscle membrane. The electrolyte analysis revealed an increase in intracellular Na+ and K+ concentrations, mainly due to loss of intracellular water.

Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons

The Hodgkin-Huxley equations for space-clamped squid axon (18 degrees C) have been modified to approximate voltage clamp data from repetitive-firing crustacean walking leg axons and activity in response to constant current stimulation has been computed. The m infinity and h infinity parameters of the sodium conductance system were shifted along the voltage axis in opposite directions so that their relative overlap was increased approximately 7 mV. Time constants tau m and tau h, were moved in a similar manner. Voltage-dependent parameters of delayed potassium conductance, n infinity and tau n, were shifted 4.3 mV in the positive direction and tau n was uniformly increased by a factor of 2. Leakage conductance and capacitance were unchanged. Repetitive activity of this modified circuit was qualitatively similar to that of the standard model. A fifth branch was added to the circuit representing a transient potassium conductance system present in the repetitive walking leg axons and in other repetitive neurons. This model, with various parameter choices, fired repetitively down to approximately 2 spikes/s and up to 350/s. The frequency vs. stimulus current plot could be fit well by a straight line over a decade of the low frequency range and the general appearance of the spike trains was similar to that of other repetitive neurons. Stimulus intensities were of the same order as those which produce repetitive activity in the standard Hodgkin-Huxley axon. The repetitive firing rate and first spike latency (utilization time) were found to be most strongly influenced by the inactivation time constant of the transient potassium conductance (tau b), the delayed potassium conductance (tau n), and the value of leakage conductance (gL). The model presents a mechanism by which stable low frequency discharge can be generated by millisecond-order membrane conductance changes.

Spike frequency of the nodal membrane generated by high-frequency alternating current

Changes in membrane potential of single frog motor nerve fibres due to alternating current (ac) between 4 kHz and 20 kHz were recorded in the air gap equipment under constant current conditions at 20 degrees C. The experimental findings were compared with the results of computations on the basis of potential clamp data. Ac shifted mean membrane potential (averaged for every ac period) in the direction of depolarization. The mean depolarization Vm depended on current strength I; it disappeared when the sodium permeability was blocked, in the experiments by tetrodotoxin. In a current range between about 1 and 3 fold threshold strength the ac initiated repetitive activity with response frequencies v between averaged 120 Hz and 820 Hz or in the computations even higher; v depended logarithimically on current strength, but was independent of ac frequency. Elimination of current amplitude I from the nonlinear realtions v(I) and Vm(I) led to a linear function between v and Vm. Both v and Vm depended markedly on prepolarization of the node. The results were attributed to the preferred activation of the sodium permeability under maintained high frequency ac stimulation. Differences between computations and constant current experiments occurred for very long stimulus duration when rhythmical discharges died out in the experiment.

Differences in action potentials and accommodation of sensory and motor myelinated nerve fibres as computed on the basis of voltage clamp data

1. Voltage clamp experiments were performed on sensory and motor nerve fibres of the frog using a digital computer for automatic experiment control and data recording. 2. Rates of rise and maximum amplitudes of potassium currents were determined in both sensory and motor fibres, so that comparative values of n infinity and tau-n could be obtained. 3. The results indicate that the n infinity-V curve for sensory fibres is displaced from the curve for motor fibres in a depolarising direction. The potassium kinetics are similar in both for voltage steps up to about - 20 m V, beyond which tau-n becomes progressively smaller for sensory than for motor fibres. 4. These comparative values of n affinity and tau-n have been used to calculate alpha-n and beta-n values for a model "motor" action potential by considering the Frankenhaeuser-Huxley computed action potential to be "sensory". This modification of the potassium system, together with some alteration to the sodium inactivation system produces a satisfactory model "motor" action potential. 5. The model sensory and motor action potentials behave quite similarly to their experimentally recorded counterparts with respect to action potential shape and relative duration, repetitive firing, accomodation and the simulated action of T.E.A.

Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons

All analysis of the sodium and potassium conductances of Myxicola giant axons was made in terms of the Hodgkin-Huxley m, n, and h variables. The potassium conductance is proportional to n(2). In the presence of conditioning hyperpolarization, the delayed current translates to the right along the time axis. When this effect was about saturated, the potassium conductance was proportional to n(3). The sodium conductance was described by assuming it proportional to m(3)h. There is a range of potentials for which tau(h) and h(infinity) values fitted to the decay of the sodium conductance may be compared to those determined from the effects of conditioning pulses. tau(h) values determined by the two methods do not agree. A comparison of h(infinity) values determined by the two methods indicated that the inactivation of the sodium current is not governed by the Hodgkin-Huxley h variable. Computer simulations show that action potentials, threshold, and subthreshold behavior could be accounted for without reference to data on the effects of initial conditions. However, recovery phenomena (refractoriness, repetitive discharges) could be accounted for only by reference to such data. It was concluded that the sodium conductance is not governed by the product of two independent first order variables.