The threshold conditions for initiation of action potentials by excitable cells

Double Two-State Opsin Model With Autonomous Parameter Inference

Optogenetics has a lot of potential to become an effective neuromodulative therapy for clinical applications. Selecting the correct opsin is crucial to have an optimal optogenetic tool. With computational modeling, the neuronal response to the current dynamics of an opsin can be extensively and systematically tested. Unlike electrical stimulation where the effect is directly defined by the applied field, the stimulation in optogenetics is indirect, depending on the selected opsin's non-linear kinetics. With the continuous expansion of opsin possibilities, computational studies are difficult due to the need for an accurate model of the selected opsin first. To this end, we propose a double two-state opsin model as alternative to the conventional three and four state Markov models used for opsin modeling. Furthermore, we provide a fitting procedure, which allows for autonomous model fitting starting from a vast parameter space. With this procedure, we successfully fitted two distinctive opsins (ChR2(H134R) and MerMAID). Both models are able to represent the experimental data with great accuracy and were obtained within an acceptable time frame. This is due to the absence of differential equations in the fitting procedure, with an enormous reduction in computational cost as result. The performance of the proposed model with a fit to ChR2(H134R) was tested, by comparing the neural response in a regular spiking neuron to the response obtained with the non-instantaneous, four state Markov model (4SB), derived by Williams et al. (2013). Finally, a computational speed gain was observed with the proposed model in a regular spiking and sparse Pyramidal-Interneuron-Network-Gamma (sPING) network simulation with respect to the 4SB-model, due to the former having two differential equations less. Consequently, the proposed model allows for computationally efficient optogenetic neurostimulation and with the proposed fitting procedure will be valuable for further research in the field of optogenetics.

Extracellular Stimulation of Neural Tissues: Activating Function and Sub-threshold Potential Perspective

Electric stimulation of neural tissues has been an effective clinical intervention to address a variety of pathological issues such as profound deafness, retinal diseases, and Parkinson's disease. However, the knowledge about the exact mechanism of neural excitation, especially activation sites is still ambiguous. Nevertheless, in silico models utilize two approaches namely activating function and sub-threshold potential to predict the activation sites of neural tissues. This paper studies the applicability of these two approaches to model the electric stimulation of pyramidal neuron and spiral ganglion neurons using finite element models. The simulation results suggest that the activating function could be prone to geometrical irregularities of the neural tissues, yet realistically predicts the activation sites on the myelinated neurons. In contrast, the sub-threshold potential predicts the activation of unmyelinated axons by considering the electrophysiological properties of neural tissues. The present study suggests that it is necessary to choose an appropriate method to estimate the neural activation sites while modeling the extracellular stimulation of neural tissues.

Central Role of Subthreshold Currents in Myotonia

It is generally thought that muscle excitability is almost exclusively controlled by currents responsible for generation of action potentials. We propose that smaller ion channel currents that contribute to setting the resting potential and to subthreshold fluctuations in membrane potential can also modulate excitability in important ways. These channels open at voltages more negative than the action potential threshold and are thus termed subthreshold currents. As subthreshold currents are orders of magnitude smaller than the currents responsible for the action potential, they are hard to identify and easily overlooked. Discovery of their importance in regulation of excitability opens new avenues for improved therapy for muscle channelopathies and diseases of the neuromuscular junction. ANN NEUROL 2020;87:175-183.

Chloride Channels Take Center Stage in Acute Regulation of Excitability in Skeletal Muscle: Implications for Fatigue

Initiation and propagation of action potentials in muscle fibers is a key element in the transmission of activating motor input from the central nervous system to their contractile apparatus, and maintenance of excitability is therefore paramount for their endurance during work. Here, we review current knowledge about the acute regulation of ClC-1 channels in active muscles and its importance for muscle excitability, function, and fatigue.

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.

Optogenetic versus Electrical Stimulation of Human Cardiomyocytes: Modeling Insights

Optogenetics provides an alternative to electrical stimulation to manipulate membrane voltage, and trigger or modify action potentials (APs) in excitable cells. We compare biophysically and energetically the cellular responses to direct electrical current injection versus optical stimulation mediated by genetically expressed light-sensitive ion channels, e.g., Channelrhodopsin-2 (ChR2). Using a computational model of ChR2(H134R mutant), we show that both stimulation modalities produce similar-in-morphology APs in human cardiomyocytes, and that electrical and optical excitability vary with cell type in a similar fashion. However, whereas the strength-duration curves for electrical excitation in ventricular and atrial cardiomyocytes closely follow the theoretical exponential relationship for an equivalent RC circuit, the respective optical strength-duration curves significantly deviate, exhibiting higher nonlinearity. We trace the origin of this deviation to the waveform of the excitatory current-a nonrectangular self-terminating inward current produced in optical stimulation due to ChR2 kinetics and voltage-dependent rectification. Using a unifying charge measure to compare energy needed for electrical and optical stimulation, we reveal that direct electrical current injection (rectangular pulse) is more efficient at short pulses, whereas voltage-mediated negative feedback leads to self-termination of ChR2 current and renders optical stimulation more efficient for long low-intensity pulses. This applies to cardiomyocytes but not to neuronal cells (with much shorter APs). Furthermore, we demonstrate the cell-specific use of ChR2 current as a unique modulator of intrinsic activity, allowing for optical control of AP duration in atrial and, to a lesser degree, in ventricular myocytes. For self-oscillatory cells, such as Purkinje, constant light at extremely low irradiance can be used for fine control of oscillatory frequency, whereas constant electrical stimulation is not feasible due to electrochemical limitations. Our analysis offers insights for designing future new energy-efficient stimulation strategies in heart or brain.

Selective Gating of Neuronal Activity by Intrinsic Properties in Distinct Motor Rhythms

Many neural circuits show fast reconfiguration following altered sensory or modulatory inputs to generate stereotyped outputs. In the motor circuit of Xenopus tadpoles, I study how certain voltage-dependent ionic currents affect firing thresholds and contribute to circuit reconfiguration to generate two distinct motor patterns, swimming and struggling. Firing thresholds of excitatory interneurons [i.e., descending interneurons (dINs)] in the swimming central pattern generator are raised by depolarization due to the inactivation of Na(+) currents. In contrast, the thresholds of other types of neurons active in swimming or struggling are raised by hyperpolarization from the activation of fast transient K(+) currents. The firing thresholds are then compared with the excitatory synaptic drives, which are revealed by blocking action potentials intracellularly using QX314 during swimming and struggling. During swimming, transient K(+) currents lower neuronal excitability and gate out neurons with weak excitation, whereas their inactivation by strong excitation in other neurons increases excitability and enables fast synaptic potentials to drive reliable firing. During struggling, continuous sensory inputs lead to high levels of network excitation. This allows the inactivation of Na(+) currents and suppression of dIN activity while inactivating transient K(+) currents, recruiting neurons that are not active in swimming. Therefore, differential expression of these currents between neuron types can explain why synaptic strength does not predict firing reliability/intensity during swimming and struggling. These data show that intrinsic properties can override fast synaptic potentials, mediate circuit reconfiguration, and contribute to motor-pattern switching.

Biophysical mechanism of spike threshold dependence on the rate of rise of the membrane potential by sodium channel inactivation or subthreshold axonal potassium current

Spike threshold filters incoming inputs and thus gates activity flow through neuronal networks. Threshold is variable, and in many types of neurons there is a relationship between the threshold voltage and the rate of rise of the membrane potential (dVm/dt) leading to the spike. In primary sensory cortex this relationship enhances the sensitivity of neurons to a particular stimulus feature. While Na⁺ channel inactivation may contribute to this relationship, recent evidence indicates that K⁺ currents located in the spike initiation zone are crucial. Here we used a simple Hodgkin-Huxley biophysical model to systematically investigate the role of K⁺ and Na⁺ current parameters (activation voltages and kinetics) in regulating spike threshold as a function of dVm/dt. Threshold was determined empirically and not estimated from the shape of the Vm prior to a spike. This allowed us to investigate intrinsic currents and values of gating variables at the precise voltage threshold. We found that Na⁺ nactivation is sufficient to produce the relationship provided it occurs at hyperpolarized voltages combined with slow kinetics. Alternatively, hyperpolarization of the K⁺ current activation voltage, even in the absence of Na⁺ inactivation, is also sufficient to produce the relationship. This hyperpolarized shift of K⁺ activation allows an outward current prior to spike initiation to antagonize the Na⁺ inward current such that it becomes self-sustaining at a more depolarized voltage. Our simulations demonstrate parameter constraints on Na⁺ inactivation and the biophysical mechanism by which an outward current regulates spike threshold as a function of dVm/dt.

Bidirectional plasticity of intrinsic excitability controls sensory inputs efficiency in layer 5 barrel cortex neurons in vivo

Responsiveness of cortical neurons to sensory inputs can be altered by experience and learning. While synaptic plasticity is generally proposed as the underlying cellular mechanism, possible contributions of activity-dependent changes in intrinsic excitability remain poorly investigated. Here, we show that periods of rhythmic firing in rat barrel cortex layer 5 pyramidal neurons can trigger a long-lasting increase or decrease in their membrane excitability in vivo. Potentiation of cortical excitability consisted of an increased firing in response to intracellular stimulation and a reduction in threshold current for spike initiation. Conversely, depression of cortical excitability was evidenced by an augmented firing threshold leading to a reduced current-evoked spiking. The direction of plasticity depended on the baseline level of spontaneous firing rate and cell excitability. We also found that changes in intrinsic excitability were accompanied by corresponding modifications in the effectiveness of sensory inputs. Potentiation and depression of cortical neuron excitability resulted, respectively, in an increased or decreased firing probability on whisker-evoked synaptic responses, without modifications in the synaptic strength itself. These data suggest that bidirectional intrinsic plasticity could play an important role in experience-dependent refinement of sensory cortical networks.

Controlling activation site density by low-energy far-field stimulation in cardiac tissue

Tachycardia and fibrillation are potentially fatal arrhythmias associated with the formation of rotating spiral waves in the heart. Presently, the termination of these types of arrhythmia is achieved by use of antitachycardia pacing or cardioversion. However, these techniques have serious drawbacks, in that they either have limited application or produce undesirable side effects. Low-energy far-field stimulation has recently been proposed as a superior therapy. This proposed therapeutic method would exploit the phenomenon in which the application of low-energy far-field shocks induces a large number of activation sites ("virtual electrodes") in tissue. It has been found that the formation of such sites can lead to the termination of undesired states in the heart and the restoration of normal beating. In this study we investigate a particular aspect of this method. Here we seek to determine how the activation site density depends on the applied electric field through in vitro experiments carried out on neonatal rat cardiac tissue cultures. The results indicate that the activation site density increases exponentially as a function of the intracellular conductivity and the level of cell isotropy. Additionally, we report numerical results obtained from bidomain simulations of the Beeler-Reuter model that are quantitatively consistent with our experimental results. Also, we derive an intuitive analytical framework that describes the activation site density and provides useful information for determining the ratio of longitudinal to transverse conductivity in a cardiac tissue culture. The results obtained here should be useful in the development of an actual therapeutic method based on low-energy far-field pacing. In addition, they provide a deeper understanding of the intrinsic properties of cardiac cells.

Axon Physiology

Axons are generally considered as reliable transmission cables in which stable propagation occurs once an action potential is generated. Axon dysfunction occupies a central position in many inherited and acquired neurological disorders that affect both peripheral and central neurons. Recent findings suggest that the functional and computational repertoire of the axon is much richer than traditionally thought. Beyond classical axonal propagation, intrinsic voltage-gated ionic currents together with the geometrical properties of the axon determine several complex operations that not only control signal processing in brain circuits but also neuronal timing and synaptic efficacy. Recent evidence for the implication of these forms of axonal computation in the short-term dynamics of neuronal communication is discussed. Finally, we review how neuronal activity regulates both axon morphology and axonal function on a long-term time scale during development and adulthood.

A threshold equation for action potential initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.

Neurons communicate primarily with stereotypical electrical impulses, action potentials, which are fired when a threshold level of excitation is reached. This threshold varies between cells and over time as a function of previous stimulations, which has major functional implications on the integrative properties of neurons. Ionic channels are thought to play a central role in this modulation but the precise relationship between their properties and the threshold is unclear. We examined this relationship in biophysical models and derived a formula which quantifies the contribution of various mechanisms. The originality of our approach is that it provides an instantaneous time-varying value for the threshold, which applies to the highly fluctuating regimes characterizing neurons in vivo. In particular, two known ionic mechanisms were found to make the threshold adapt to the membrane potential, thus providing the cell with a form of gain control.

Response sensitivity of barrel neuron subpopulations to simulated thalamic input

Our goal is to examine the relationship between neuron- and network-level processing in the context of a well-studied cortical function, the processing of thalamic input by whisker-barrel circuits in rodent neocortex. Here we focus on neuron-level processing and investigate the responses of excitatory and inhibitory barrel neurons to simulated thalamic inputs applied using the dynamic clamp method in brain slices. Simulated inputs are modeled after real thalamic inputs recorded in vivo in response to brief whisker deflections. Our results suggest that inhibitory neurons require more input to reach firing threshold, but then fire earlier, with less variability, and respond to a broader range of inputs than do excitatory neurons. Differences in the responses of barrel neuron subtypes depend on their intrinsic membrane properties. Neurons with a low input resistance require more input to reach threshold but then fire earlier than neurons with a higher input resistance, regardless of the neuron's classification. Our results also suggest that the response properties of excitatory versus inhibitory barrel neurons are consistent with the response sensitivities of the ensemble barrel network. The short response latency of inhibitory neurons may serve to suppress ensemble barrel responses to asynchronous thalamic input. Correspondingly, whereas neurons acting as part of the barrel circuit in vivo are highly selective for temporally correlated thalamic input, excitatory barrel neurons acting alone in vitro are less so. These data suggest that network-level processing of thalamic input in barrel cortex depends on neuron-level processing of the same input by excitatory and inhibitory barrel neurons.

A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input

The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives. An action potential (spike) is generated when the membrane potential reaches a threshold, but the actual changes associated with the membrane voltage and conductances driving the action potential do not form part of the model. The synaptic inputs to the neuron are considered to be stochastic and are described as a temporally homogeneous Poisson process. Methods and results for both current synapses and conductance synapses are examined in the diffusion approximation, where the individual contributions to the postsynaptic potential are small. The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker-Planck equation. The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being sufficiently complex to capture many of the essential features of neural processing. A number of variations of the model are discussed, together with the relationship with the Hodgkin-Huxley neuron model and the comparison with electrophysiological data. A brief overview is given of two issues in neural information processing that the integrate-and-fire neuron model has contributed to - the irregular nature of spiking in cortical neurons and neural gain modulation.

Dynamical response of the Hodgkin-Huxley model in the high-input regime

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability, and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for the different features appearing in the interspike-interval distributions (like multimodality and exponential tails) are clearly identified in the various regimes.

Stimulus-dependent changes in spike threshold enhance feature selectivity in rat barrel cortex neurons

Feature selectivity is a fundamental property of sensory cortex neurons, yet the mechanisms underlying its genesis are not fully understood. Using intracellular recordings in vivo from layers 2-6 of rat barrel cortex, we studied the selectivity of neurons to the angular direction of whisker deflection. The spike output and the underlying synaptic response decreased exponentially in magnitude as the direction of deflection diverged from the preferred. However, the spike output was more sharply tuned for direction than the underlying synaptic response amplitude. This difference in selectivity was attributable to the rectification imposed by the spike threshold on the input-output function of cells. As in the visual system, spike threshold was not constant and showed trial-to-trial variability. However, here we show that the mean spike threshold was direction dependent and increased as the direction diverged from the preferred. Spike threshold was also related to the rate of rise of the synaptic response, which was direction dependent and steepest for the preferred direction. To assess the impact of the direction-dependent changes in spike threshold on direction selectivity, we applied a fixed threshold to the synaptic responses and calculated a predicted spike output. The predicted output was more broadly tuned than the obtained spike response, demonstrating for the first time that the regulation of the spike threshold by the properties of the synaptic response effectively enhances the selectivity of the spike output.

Categorization of neural excitability using threshold models

A classification of spiking neurons according to the transition from quiescence to periodic firing of action potentials is commonly used. Nonbursting neurons are classified into two types, type I and type II excitability. We use simple phenomenological spiking neuron models to derive a criterion for the determination of the neural excitability based on the afterpotential following a spike. The crucial characteristic is the existence for type II model of a positive overshoot, that is, a delayed after depolarization, during the recovery process of the membrane potential. Our prediction is numerically tested using well-known type I and type II models including the Connor, Walter, & McKown (1977) model and the Hodgkin-Huxley (1952) model.

Paradoxical loss of excitation with high intensity pulses during electric field stimulation of single cardiac cells

Transmembrane potential responses of single cardiac cells stimulated at rest were studied with uniform rectangular field pulses having durations of 0.5-10 ms. Cells were enzymatically isolated from guinea pig ventricles, stained with voltage sensitive dye di-8-ANEPPS, and stimulated along their long axes. Fluorescence signals were recorded with spatial resolution of 17 microm for up to 11 sites along the cell. With 5 and 10 ms pulses, all cells (n = 10) fired an action potential over a broad range of field amplitudes (approximately 3-65 V/cm). With 0.5 and 1 ms pulses, all cells (n = 7) fired an action potential for field amplitudes ranging from the threshold value (approximately 4-8 V/cm) to 50-60 V/cm. However, when the field amplitude was further increased, five of seven cells failed to fire an action potential. We postulated that this paradoxical loss of excitation for higher amplitude field pulses is the result of nonuniform polarization of the cell membrane under conditions of electric field stimulation, and a counterbalancing interplay between sodium current and inwardly rectifying potassium current with increasing field strength. This hypothesis was verified using computer simulations of a field-stimulated guinea pig ventricular cell. In conclusion, we show that for stimulation with short-duration pulses, cells can be excited for fields ranging between a low amplitude excitation threshold and a high amplitude threshold above which the excitation is suppressed. These results can have implications for the mechanistic understanding of defibrillation outcome, especially in the setting of diseased myocardium.

The research career of Richard B. Stein (1940–)

This report reviews the research and mentoring career of Richard B. Stein (1940–). In 1962, he completed a B.S. degree in physics at the Massachusetts Institute of Technology, USA, and thereafter an M.A. (1964), Ph.D. (1966), and postdoctoral training (1966–68) at the University of Oxford, UK. He subsequently assumed a faculty position at the University of Alberta (Canada), where he is currently an active researcher and mentor. To this point in 2004, Stein has trained and collaborated closely with over 160 scientists, largely neuroscientists and biomedical engineers, from 27 countries. He and his former trainees and collaborators have made important contributions on topics that span the cellular-to-behavioral spectrum of movement and rehabilitation–prosthetics neuroscience. His mentors, trainees, and collaborators include scientists whose countries of origin are: Australia, 2; Austria, 1; Belgium, 1; Bulgaria, 1; Canada, 64; China, 6; Denmark, 1; Germany, 1; Great Britain, 16; Hong Kong, 4; India, 5; Iraq, 2; Italy, 2; Japan, 10; Kenya, 1; New Zealand, 4; Pakistan, 1; Palestine, 1; Poland, 1; Romania, 1; South Africa, 1; Sri Lanka, 1; The Netherlands, 1; Turkey, 1; Uruguay, 1; USA, 21; and Yugoslavia, 6. In all instances, Stein's research collaborations and mentoring have advanced the careers of his trainees and junior collaborators, a well-deserved and important compliment to a stellar movement neuroscientist.Key words: movement neuroscience, rehabilitation neuroscience, prosthetics.

Noise and stochastic resonance in voltage-gated ion channels

Using Monte Carlo techniques, I calculate the effects of internally generated noise on information transfer through the passage of action potential spikes along unmyelinated axons in a simple nervous system. I take the Hodgkin-Huxley (HH) description of Na and K channels in squid giant axons as the basis of the calculations and find that most signal transmission noise is generated by fluctuations in the channel open and closed populations. To bring the model closer to conventional descriptions in terms of thermal noise energy, kT, and to determine gating currents, I express the HH equations in the form of simple relations from statistical mechanics where the states are separated by a Gibbs energy that is modified by the action of the transmembrane potential on dipole moments held by the domains. Using the HH equations, I find that the output response (in the probability of action potential spikes) from small input potential pulses across the cell membrane is increased by added noise but falls off when the input noise becomes large, as in stochastic resonance models. That output noise response is sharply reduced by a small increase in the membrane polarization potential or a moderate increase in the channel densities. Because any reduction of noise incurs metabolic and developmental costs to an animal, the natural noise level is probably optimal and any increase in noise is likely to be harmful. Although these results are specific to signal transmission in unmyelinated axons, I suggest that the conclusions are likely to be general.

Spike-dependent intrinsic plasticity increases firing probability in rat striatal neurons in vivo

The collision of pre- and postsynaptic activity is known to provide a trigger for controlling the gain of synaptic transmission between neurons. Here, using in vivo intracellular recordings of rat striatal output neurons, we analyse the effect of a single action potential, generated by ongoing synaptic activity, on subsequent excitatory postsynaptic potentials (EPSPs) evoked by electrical stimulation of the cerebral cortex. This pairing induced a short-term increase in the probability that cortically evoked EPSPs caused striatal cells to fire. This enhanced EPSP-spike coupling was associated with a decrease in the voltage firing threshold with no apparent change in the synaptic strength itself. Antidromic action potentials in striatal cells were also able to induce the facilitation while subthreshold EPSPs were ineffective, indicating that the postsynaptic spike was necessary and sufficient for the induction of the plasticity. A prior spontaneous action potential also enhanced the probability with which directly applied current pulses elicited firing, suggesting that the facilitation originated from changes in the intrinsic electrical properties of the postsynaptic cell. Using whole-cell recordings in cortico-striatal slices, we found that the increase in membrane excitability as well as in EPSP-spike coupling was abolished by low concentration of 4-aminopyridine. This suggests that the intrinsic plasticity results from a time-dependent modulation of a striatal voltage-dependent potassium current available close to the firing threshold. Action potentials thus provide a postsynaptic signal, not only for associative synaptic plasticity but also for activity-dependent intrinsic plasticity, which directly controls the efficacy of coupling between pre- and postsynaptic neurons.

Spontaneous field potentials influence the activity of neocortical neurons during paroxysmal activities in vivo

Field-potential recordings with macroelectrodes, and extra- and intracellular potentials with micropipettes were used to determine the influence of spontaneous field potentials on the activity of neocortical neurons during seizures. In vivo experiments were carried out in cats under anesthesia. Strong negative field fluctuations of up to 20 mV were associated with electroencephalogram "spikes" during spontaneously occurring paroxysmal activities. During paroxysmal events, action potentials displayed an unexpected behavior: a more hyperpolarized firing threshold and smaller amplitude than during normal activity, as determined with intracellular recordings referenced to a distant ground. Considering the transmembrane potential (the difference between extra- and intracellular potential) qualified this observation: firing threshold determined from the transmembrane potential did not decrease, and smaller action-potential amplitude was associated with depolarized firing threshold. The hyperpolarization of intracellular firing threshold was thus related to the field potentials. Similar field-potential effects on neuronal activities were observed when the paroxysmal events included very fast oscillations or ripples (80-200 Hz) that represent rapid fluctuations of field potentials (up to 5 mV in <5 ms). Neuronal firing was phase-locked to those oscillations. These results demonstrate that: (a) strong spontaneous field potentials influence neuronal behavior, and thus play an active role during paroxysmal activities; and (b) transmembrane potentials have to be used to accurately describe the behavior of neurons in conditions in which field potentials fluctuate strongly. Since neuronal activity is presumably the main generator of field potentials, and in return these potentials may increase neuronal excitability, we propose that this constitutes a positive feedback loop that is involved in the development and spread of paroxysmal activities, and that a similar feedback loop is involved in the generation of neocortical ripples. We propose a mechanism for seizure initiation involving these phenomena.

Conduction velocity is inversely related to action potential threshold in rat motoneuron axons

Intra-axonal recordings were performed in ventral roots of rats in vitro to study the conduction velocity and firing threshold properties of motoneuron axons. Mean values +/- SD were 30.5+/-5.6 m/s for conduction velocity and 11.6+/-4.5 mV for the depolarization from the resting potential required to reach firing threshold (threshold depolarization). Conduction velocity varied inversely and significantly with threshold depolarization ( P=0.0002 by linear regression). This relationship was evident even after accounting for variation in conduction velocity associated with action potential amplitude, injected current amplitude, or body weight. Conduction velocity also varied inversely with the time to action potential onset during just-threshold current pulse injection. These data suggest that the time course of depolarization leading to action potential initiation contributes to the speed of conduction in motoneuron axons.

Crucial role of sodium channel fast inactivation in muscle fibre inexcitability in a rat model of critical illness myopathy

Critical illness myopathy is an acquired disorder in which skeletal muscle becomes electrically inexcitable. We previously demonstrated that inactivation of Na+ channels contributes to inexcitability of affected fibres in an animal model of critical illness myopathy in which denervated rat skeletal muscle is treated with corticosteroids (steroid denervated; SD). Our previous work, however, did not address the relative importance of membrane depolarization versus a shift in the voltage dependence of fast inactivation in causing inexcitability. It also remained unknown whether changes in the voltage dependence of activation or slow inactivation play a role in inexcitability. In the current study we found that a hyperpolarizing shift in the voltage dependence of fast inactivation of Na+ channels is the principal factor underlying inexcitability in SD fibres. Although depolarization tends to decrease excitability, it is insufficient to account for inexcitability in SD fibres since many normal and denervated fibres retain normal excitability when depolarized to the same resting potentials as affected SD fibres. Changes in the voltage dependence of activation and slow inactivation of Na+ channels were also observed in SD fibres; however, the changes appear to increase rather than decrease excitability. These results highlight the importance of the change in fast inactivation in causing inexcitability of SD fibres.

Effect of perinatal food deficiencies on the compound action potential evoked in sensory nerves of developing rats

The aim of this study was to analyze the possible alterations produced by inadequate perinatal food intake, in quantity (undernutrition) or quality (malnutrition), on the generation and propagation of the compound action potential (CAP) evoked in sensory sural nerves, during the postnatal development of the rat. Low intensity stimulation (2-3 times the threshold of the most excitable nerve fibers; xT) of the sural nerve evoked an early potential (CAP-A component) which is due to activation of low-threshold, fast-conducting myelinated group A afferent fibers. Meanwhile, at higher stimulus intensity (20-30T) it produced a second, long-lasting potential (CAP-C component) probably due to activation of high-threshold, slow-conducting group Adelta or C afferent fibers. Compared to control nerves, the CAP-A component, but not the CAP-C component of undernourished and malnourished nerves showed significant changes in amplitude, area, electrical threshold and conduction velocity (except absolute refractory period) at several postnatal ages. Our results may suggest that a relative large number of myelinated group A afferent fibers in the sural nerve of undernourished and malnourished animals suffer severe alterations on their electrophysiological properties of generation and propagation of the action potential during the postnatal development of the rat.

Action potential threshold of hippocampal pyramidal cells in vivo is increased by recent spiking activity

Understanding the mechanisms that influence the initiation of action potentials in single neurons is an important step in determining the way information is processed by neural networks. Therefore, we have investigated the properties of action potential thresholds for hippocampal neurons using in vivo intracellular recording methods in Sprague-Dawley rats. The use of in vivo recording has the advantage of the presence of naturally occurring spatio-temporal patterns of synaptic activity which lead to action potential initiation. We have found there is a large variability in the threshold voltage (5.7+/-1.7 mV; n=22) of individual action potentials. We have identified two separate factors that contribute to this variation in threshold: (1) fast rates of membrane potential change prior to the action potential are associated with more hyperpolarized thresholds (increased excitability) and (2) the occurrence of other action potentials in the 1 s prior to any given action potential is associated with more depolarized thresholds (decreased excitability). We suggest that prior action potentials cause sodium channel inactivation that recovers with approximately a 1-s time constant and thus depresses action potential threshold during this period.

Excitability properties of motor axons in patients with spontaneous motor unit activity

OBJECTIVES

Measures of nerve excitability provide information about biophysical properties of peripheral axons in disease states. One measure, the strength duration time constant (tau(SD)), was previously reported to be prolonged in motor axons of patients with acquired neuromyotonia. The present study used a new protocol that applies a more comprehensive and sensitive panel of measures of axonal excitability, to determine firstly whether changes in tau(SD) were present in a group of patients with evidence of spontaneous motor unit activity; and secondly, if such changes in tau(SD) were present, whether other parameters of axonal excitability were affected, to clarify the mechanism of the change in tau(SD).

METHODS

Eleven patients with both symptoms and EMG evidence of spontaneous motor unit activity were studied. Eight patients had autoimmune associated acquired neuromyotonia (aNMT) and three had the cramp fasciculation syndrome. The protocol first measured stimulus-response behaviour using two stimulus durations (from which the distribution of strength-duration time constants was estimated), and then threshold tracking was used to determine threshold electrotonus to 100 ms polarising currents, a current-threshold relation (indicating inward and outward rectification), and the recovery of excitability after supramaximal activation.

RESULTS

The results were compared with previously published normal data. The value for tau(SD) of motor axons in the patient group was 0.43 (0. 02) ms (mean (SEM)), identical with the control value. Most other indices of axonal excitability, including those dependent on fast potassium channels, were also found to be normal. When compared with age matched controls however, the patients with acquired neuromyotonia had significantly greater late subexcitability after an impulse, greater excitability overshoots after depolarisation or hyperpolarisation, and more accommodation.

CONCLUSIONS

No clear evidence for the mechanism of ectopic discharge in these patients was obtained, probably because the activity was generated focally, and most often at the motor nerve terminals. The unexpected finding of increased excitability overshoots and accommodation compared with age matched controls, suggests a relative up regulation of slow potassium conductance, possibly as a consequence of the continuous motor unit activity.

Determinants of excitability in cardiac myocytes: mechanistic investigation of memory effect

The excitability of a cardiac cell depends upon many factors, including the rate and duration of pacing. Furthermore, cell excitability and its variability underlie many electrophysiological phenomena in the heart. In this study, we used a detailed mathematical model of the ventricular myocyte to investigate the determinants of excitability and gain insight into the mechanism by which excitability depends on the rate and duration of pacing (the memory effect).

RESULTS

i) The primary determinant of excitability depends upon the duration (T) of the stimulus. ii) For a short T, excitability is determined by the difference between the threshold membrane potential and the resting membrane potential. iii) For a long T, excitability is determined by the resting membrane resistance, R(m). iv) In the case of long T, pacing induced changes in [Na(+)](i) and [Ca(2+)](i) over time affect R(m) and excitability by shifting the current-voltage (IV) curve in the vertical direction and are responsible for the memory effect.

CONCLUSIONS

The results have important implications during an arrhythmia, where a cardiac cell may be subjected to rapid repetitive excitation for an extended period of time. Effective anti-arrhythmic strategies may be developed to exploit the R(m) dependence of excitability for a long T.

Bistability in the Ca(2+)/calmodulin-dependent protein kinase-phosphatase system

A mathematical model is presented of autophosphorylation of Ca(2+)/calmodulin-dependent protein kinase (CaMKII) and its dephosphorylation by a phosphatase. If the total concentration of CaMKII subunits is significantly higher than the phosphatase Michaelis constant, two stable steady states of the CaMKII autophosphorylation can exist in a Ca(2+) concentration range from below the resting value of the intracellular [Ca(2+)] to the threshold concentration for induction of long-term potentiation (LTP). Bistability is a robust phenomenon, it occurs over a wide range of parameters of the model. Ca(2+) transients that switch CaMKII from the low-phosphorylated state to the high-phosphorylated one are in the same range of amplitudes and frequencies as the Ca(2+) transients that induce LTP. These results show that the CaMKII-phosphatase bistability may play an important role in long-term synaptic modifications. They also suggest a plausible explanation for the very high concentrations of CaMKII found in postsynaptic densities of cerebral neurons.

Selectivity of chemoreceptor neuron

Discriminating ability (selectivity) of chemoreceptor neuron is compared with that of its receptor proteins. The process of neuronal triggering is expected to be cooperative and threshold-type in a sense that the neuron can fire if and only if the number of its receptor proteins, which are bound with odor molecules, is above a definite threshold. Both deterministic and stochastic pictures are considered. The stochastic case is treated based on birth and death stochastic process and first passage technique. In both pictures, it is shown that a chemoreceptor neuron can have much a higher selectivity than its individual receptor proteins, provided the chemical stimuli are presented at low concentrations, and the threshold is high enough. This is in agreement with a preliminary estimate based on simplified probabilistic reasoning (Vidybida, A.K., 1999. Cooperative mechanism for improving the discriminating ability in the chemoreceptive neuron. Binomial case. Biol. Cybern. 81, 469-473). The mechanism of selectivity improvement is similar to that described before in cooperative chemical systems. A possibility for this mechanism to be valid at higher stages of processing of chemical signals, as well as in other sensory systems is discussed.

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.

Convergent mechanosensory input structures the firing phase of a steering motor neuron in the blowfly, Calliphora

The first basalar muscle (B1) is 1 of 17 small steering muscles in flies that control changes in wing stroke kinematics during flight. The B1 is often tonically active, firing a single phase-locked action potential in each and every wingbeat cycle. Changes in activation phase alter the biomechanical properties of B1, which in turn cause aerodynamically relevant changes in wing motion. The phase-locked firing of the B1 motor neuron (MNB1), is thought to arise from an interaction of wingbeat-synchronous inputs from the wings and from specialized equilibrium organs called halteres that beat antiphase to the wings and function to detect angular rotation of the body during flight. We investigated how the wing and haltere inputs interact to determine the firing phase of MNB1. Our results indicate that both wing and haltere afferents make strong monosynaptic connections with MNB1, consisting of fast electrical and slow Ca(2+)-sensitive components. Although both the wing and haltere-evoked excitatory postsynaptic potentials (EPSPs) display the two components, their relative contribution is different for the two inputs. Whereas the haltere-evoked EPSP is dominated by the fast electrical component, the wing-evoked EPSP is dominated by a large chemically mediated component and displays an additional prolonged Ca(2+)-dependent component that is absent in the haltere-evoked EPSP. Both inputs display an activity-dependent fatigue affecting both electrical and Ca(2+)-sensitive components, from which the haltere synapse recovers more rapidly. The net result of these synaptic differences is that the two pathways differ significantly in their relative ability to evoke action potentials in MNB1. Although the haltere pathway displays greater temporal precision, the wing pathway is stronger, judged by its ability to entrain MNB1 within a background of haltere stimulation. We propose a model by which these physiological differences play a functional role in tuning the firing phase of MNB1 during flight. The wing input may serve primarily to set the background firing phase of MNB1, whereas the haltere input serves to transiently advance the firing phase during equilibrium reflexes.

Cell-attached measurements of the firing threshold of rat hippocampal neurones

1. The cell-attached configuration of the patch-clamp technique was used to assess resting membrane potential and firing threshold of CA1 pyramidal cells and interneurones of rat hippocampal slices. 2. Resting potential was inferred from the reversal potential of voltage-gated K+ currents with symmetrical intracellular and pipette K+ concentrations. Its mean value was -74 +/- 9 mV for silent interneurones (mean +/- s.d.; n = 17) and -84 +/- 7 mV for silent pyramidal cells (n = 8). Spontaneous action currents occurred in thirteen out of thirty-two interneurones and two out of ten pyramidal cells. In active cells, membrane potential values fluctuated by up to 20 mV, due in part to the large hyperpolarizations that followed an action current. 3. Membrane potential values determined from K+ current reversal were 13 +/- 6 mV more hyperpolarized than those measured in whole-cell recordings from the same neurones (n = 8), probably due to a Donnan equilibrium potential between pipette and cytoplasm. 4. Firing threshold of silent cells was determined by elevating external K+ until action currents were generated, while membrane potential was monitored from the cell-attached K+ current reversal. Spike threshold was attained at -49 +/- 8 mV for interneurones (n = 17) and at -60 +/- 8 mV for pyramidal cells (n = 8). Increasing external Ca2+ from 2 to 4 mM shifted the neuronal voltage threshold by +5 mV, without affecting resting potential. 5. For comparison with these values, we examined how the rate of membrane polarization influenced firing threshold in whole-cell records. Ramp current injections, of duration 15-1500 ms, revealed that current threshold followed a classical strength-duration relationship. In contrast voltage threshold, determined from current injection or by elevating extracellular K+, varied little with the rate of membrane polarization. 6. The state of activation and inactivation of Na+ and K+ currents might contribute to the stability of the voltage threshold. Cell-attached records showed that 79 +/- 10 % of Na+ channels and 64 +/- 10 % of K+ channels were available for activation at resting potential in silent cells (n = 8). As cells were depolarized to threshold, Na+ current availability was reduced to 23 +/- 10 %, and K+ current availability to 31 +/- 12 %. 7. The speed of transition into the inactivated states also appears to contribute to the invariance of threshold for all but the fastest depolarizations. At potentials close to threshold, the rate of inactivation of Na+ and K+ followed a double exponential time course, such that Na+ currents were 62 % inactivated and K+ currents were 63 % inactivated within 15 ms.

Depression of excitability by sphingosine 1-phosphate in rat ventricular myocytes

Sphingosine 1-phosphate (S-1-P) is a bioactive sphingolipid that is released from activated platelets. Extracellular S-1-P augments an inwardly rectifying potassium conductance in cultured atrial preparations, but the electrophysiological effects of this compound in the ventricle are unknown. The electrophysiological effects of S-1-P were examined in single myocytes from rat ventricular muscle. Action potential waveforms and underlying ionic currents in the presence and absence of 3 microM S-1-P (1-6 min) were recorded. S-1-P increased the minimum stimulus current needed to elicit an action potential by approximately 100 pA. Pertussis toxin or preexposure to S-1-P did not alter this effect. The action potential waveform was unchanged by S-1-P. The inward sodium current (INa) was examined in a range of membrane potentials just negative to the potential for firing an action potential. S-1-P reversibly inhibited peak INa by approximately 50 pA, whereas the inward rectifier potassium current was not significantly changed. The results of this study suggest that S-1-P inhibits rat ventricular excitability by reducing INa.

Inhibition as binding controller at the single neuron level

Natural stimulus for a neuron is a sum of large number of unitary excitatory postsynaptic potentials (EPSP) slightly dispersed in time. We analyze, based on numerical solution of the Hodgkin and Huxley equations, how does the triggering ability of the compound stimulus depend on the relative timing of the EPSPs it comprises. The dependences found suggest that a neuron stimulated from many synaptic inputs can be treated as performing elementary binding function and that inhibition serves as a controller of that kind of binding. The transient process characterized by EPSP operates in this context as a short-term memory mechanism inherent to a single neuron.

Regulation of action-potential firing in spiny neurons of the rat neostriatum in vivo

Both silent and spontaneously firing spiny projection neurons have been described in the neostriatum, but the reason for their differences in firing activity are unknown. We compared properties of spontaneously firing and silent spiny neurons in urethan-anesthetized rats. Neurons were identified as spiny projection neurons after labeling by intracellular injection of biocytin. The threshold for action-potential firing was measured under three different conditions: 1) electrical stimulation of the contralateral cerebral cortex, 2) brief directly applied current pulses, and 3) spontaneous action-potentials occurring during spontaneous episodes of depolarization ( state). The average membrane potential and the amplitude of noiselike fluctuations of membrane potential in the state were determined by fitting a Gaussian curve to the membrane-potential distribution. All neurons in the sample exhibited spontaneous membrane potential shifts between a hyperpolarized state and a depolarized state, but not all fired action potentials while in the state. The difference between the spontaneously firing and the silent spiny neurons was in the average membrane potential in the state, which was significantly more depolarized in the spontaneously firing than in the silent spiny neurons. There were no significant differences in the threshold, the amplitude of the noiselike fluctuations of membrane potential in the state, or in the proportion of time that the membrane potential was in the state. In both spontaneously firing and silent neurons, the threshold for action potentials evoked by current pulses was significantly higher than for those evoked by cortical stimulation. Application of more intense current pulses that reproduced the excitatory postsynaptic potential rate of rise produced firing at correspondingly lower thresholds. Because the membrane potential in the state is mainly determined by the balance between the synaptic drive and the outward potassium conductances activated in the subthreshold range of membrane potentials, either or both of these factors may determine whether firing occurs in response to spontaneous afferent activity.

Threshold tracking techniques in the study of human peripheral nerve

Conventional electrophysiological tests of nerve function focus on the number of conducting fibers and their conduction velocity. These tests are sensitive to the integrity of the myelin sheath, but provide little information about the axonal membrane. Threshold tracking techniques, in contrast, test nerve excitability, which depends on the membrane properties of the axons at the site of stimulation. These methods are sensitive to membrane potential, and to changes in membrane potential caused by activation of ion channels and electrogenic ion pumps, including those under the myelin sheath. This review describes the range of threshold tracking techniques that have been developed for the study of human nerves in vivo: resting threshold is compared with the threshold altered by a change in environment (e.g., ischemia), by a preceding single impulse (e.g., refractoriness, superexcitability) or impulse train, or by a subthreshold current (e.g., threshold electrotonus). Few clinical studies have been reported so far, mainly in diabetic neuropathy and motor neuron disease. Threshold measurements seem well suited for studies of metabolic and toxic neuropathies but insensitive to demyelination. Until suitable equipment becomes more widely available, their full potential is unlikely to be realized.

Magnetic stimulation excites skeletal muscle via motor nerve axons in the cat

Surface magnetic stimulation has been applied directly over skeletal muscle (triceps surae) in decerebrated cats. Recordings were made of the twitch contraction and electromyographic responses in triceps surae, and of the centripetal nerve volley in the sciatic nerve or spinal roots. Stimulus/response curves were established up to the maximum output of the magnetic stimulator. Neuromuscular blockade abolished the twitch contraction and muscle action potential leaving the nerve volley unaffected. Raising the stimulator output to its maximum increased the size of the nerve volley but failed to produce any muscle response. We conclude that magnetic stimulation applied directly to skeletal muscle excites via stimulation of motor nerve axons. The maximum output of the stimulator was incapable of exciting muscle fibers by direct depolarization. Use of magnetic stimulation in the clinical appraisal of muscle function should be interpreted in the knowledge that the stimulator elicits contraction only indirectly through nerve stimulation.

Neuron as time coherence discriminator

Neuronal excitability under stimuli with a complex time course is investigated on the basis of the numerical solution of the Hodgkin-Huxley equations. Each stimulus is composed of 100-1000 unitary excitatory postsynaptic potentials (uEPSP) that start randomly within a definite time window. Probability of initiating a spike [firing probability, FP(W)] as a function of the window width W is calculated by the Monte Carlo method. FP(W) has a step-like shape: it becomes equal to 1 for small W and almost vanishes as W exceeds some value Ws. The role of long-lasting somatic inhibition is analysed. Ws depends on the inhibition potential, but the step-like shape of FP is preserved. It is concluded that the capability of multisynaptic stimulation to cause a spike can be expressed in terms of temporal coherence between the synaptic inputs. Namely, the spike is initiated if the temporal coherence between active inputs is above a definite threshold. The threshold value can be effectively regulated by varying the inhibition potential.

Threshold variability in fibers with field stimulation of excitable membranes

The central focus of this report is the evolution of transmembrane potentials following initiation of a point-source field stimulus, particularly when the stimulus is short and the stimulating electrode is close to the fiber. The transmembrane voltage threshold in response to a point-source field stimulus was determined in a numerical model of a single unmyelinated fiber. Both nerve (Hodgkin-Huxley) and cardiac (Ebihara-Johnson [1]) models of the fiber membrane were evaluated. A central question is whether it is possible to know in advance whether a stimulus of specific magnitude, duration, and location will result in a subsequent action potential. Such determination can be based on the membrane's "voltage threshold." In contrast to the commonly held view, the voltage threshold was found to vary markedly depending on the duration and location of the field stimulus. Voltage thresholds ranged from about 8 mV above baseline to more than 100 mV above baseline, the higher thresholds occurring with shorter stimuli and electrode locations closer to the membrane. A related question is whether the passive membrane response can be used as a tool in determining whether a subsequent action potential is elicited. If the answer is affirmative, this finding can be very useful, since passive properties are linear and thereby much simpler to evaluate than active ones. The results show that the passive response tracks active responses long enough to be a good estimator of subsequent action potential development. Examples show that the evaluation of Vm at 0.2-0.5 msec after stimulus initiation, times chosen on the basis of membrane characteristics, was a better predictor of subsequent excitation than was either initial transmembrane current or Vm at the time when the stimulus ends. Most of the circumstances analyzed here with electric field stimulation also appear likely to be valid with magnetic field stimulation.

Do neurons have a voltage or a current threshold for action potential initiation?

The majority of neural network models consider the output of single neurons to be a continuous, positive, and saturating firing rate f (t), while a minority treat neuronal output as a series of delta pulses sigma delta (t-ti). We here argue that the issue of the proper output representation relates to the biophysics of the cells in question and, in particular, to whether initiation of somatic action potentials occurs when a certain threshold voltage or a threshold current is exceeded. We approach this issue using numerical simulations of the electrical behavior of a layer 5 pyramidal cell from cat visual cortex. The dendritic tree is passive while the cell body includes eight voltage- and calcium-dependent membrane conductances. We compute both the steady-state (Istatic(infinity)(Vm)) and the instantaneous (I0(Vm)) I-V relationships and argue that the amplitude of the local maximum in Istatic(infinity)(Vm) corresponds to the current threshold Ith for sustained inputs, while the location of the middle zero-crossing of I0 corresponds to a fixed voltage threshold Vth for rapid inputs. We confirm this using numerical simulations: for "rapid" synaptic inputs, spikes are initiated if the somatic potential exceeds Vth, while for slowly varying input Ith must be exceeded. Due to the presence of the large dendritic tree, no charge threshold Qth exists for physiological input. Introducing the temporal average of the somatic membrane potential <Vm> while the cell is spiking repetitively, allows us to define a dynamic I-V relationship Idynamic(infinity)(<Vm>). We find an exponential relationship between <Vm> and the net current sunk by the somatic membrane during spiking (diode-like behavior). The slope of Idynamic(infinity)(<Vm>) allows us to define a dynamic input conductance and a time constant that characterizes how rapidly the cell changes its output firing frequency in response to a change in its input.

The time constants of motor and sensory peripheral nerve fibers measured with the method of latent addition

The time constants of motor and sensory fibers in the human ulnar, median and tibial nerves were determined using the method of latent addition. Two square-wave stimuli were applied: the first one was subthreshold and the second, at various delays relative to the first, was adjusted to achieve threshold activation. Strength-delay curves were obtained, from which the time constant was determined using a mathematical model. Sensory fibers had time constants that were about 3 times the time constant for motor fibers. The strength-delay curves gave similar time constants as those obtained from strength-duration curves.