Biophysical basis for three distinct dynamical mechanisms of action potential initiation

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.     

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⁺ inactivation 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.     

Pre & postsynaptic tuning of action potential timing by spontaneous GABAergic activity

Frequency and timing of action potential discharge are key elements for coding and transfer of information between neurons. The nature and location of the synaptic contacts, the biophysical parameters of the receptor-operated channels and their kinetics of activation are major determinants of the firing behaviour of each individual neuron. Ultimately the intrinsic excitability of each neuron determines the input-output function. Here we evaluate the influence of spontaneous GABAergic synaptic activity on the timing of action potentials in Layer 2/3 pyramidal neurones in acute brain slices from the somatosensory cortex of young rats. Somatic dynamic current injection to mimic synaptic input events was employed, together with a simple computational model that reproduce subthreshold membrane properties. Besides the well-documented control of neuronal excitability, spontaneous background GABAergic activity has a major detrimental effect on spike timing. In fact, GABA(A) receptors tune the relationship between the excitability and fidelity of pyramidal neurons via a postsynaptic (the reversal potential for GABA(A) activity) and a presynaptic (the frequency of spontaneous activity) mechanism. GABAergic activity can decrease or increase the excitability of pyramidal neurones, depending on the difference between the reversal potential for GABA(A) receptors and the threshold for action potential. In contrast, spike time jitter can only be increased proportionally to the difference between these two membrane potentials. Changes in excitability by background GABAergic activity can therefore only be associated with deterioration of the reliability of spike timing.     

Impact of fast sodium channel inactivation on spike threshold dynamics and synaptic integration

Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration.     

Ionic Mechanism Underlying Optimal Stimuli for Neuronal Excitation: Role of Na + Channel Inactivation

The ionic mechanism underlying optimal stimulus shapes that induce a neuron to fire an action potential, or spike, is relevant to understanding optimal information transmission and therapeutic stimulation in the nervous system. Here we analyze for the first time the ionic basis for stimulus optimality in the Hodgkin and Huxley model and for eliciting a spike in squid giant axons, the preparation for which the model was devised. The experimentally determined stimulus is a smoothly varying biphasic current waveform having a relatively long and shallow hyperpolarizing phase followed by a depolarizing phase of briefer duration. The hyperpolarizing phase removes a small degree of the resting level of Na ⁺ channel inactivation. This result together with the subsequent depolarizing phase provides a signal that is energetically more efficient for eliciting spikes than rectangular current pulses. Sodium channel inactivation is the only variable that is changed during the stimulus waveform, other than the membrane potential, V. The activation variables for Na ⁺ and K ⁺ channels are unchanged throughout the stimulus. This result demonstrates how an optimal stimulus waveform relates to ionic dynamics and may have implications for energy efficiency of neural excitation in many systems including the mammalian brain.     

Effects of H₂O₂ on electrical membrane properties of skeletal myotubes

Reactive oxygen species (ROS), normally generated in skeletal muscles, could control excitability of muscle fibers through redox modulation of membrane ion channels. However, the mechanisms of ROS action remain largely unknown. To investigate the action of ROS on electrical properties of muscle cells, patch-clamp recordings were performed after application of hydrogen peroxide (H₂O₂) to skeletal myotubes. H₂O₂ facilitated sodium spikes after a hyperpolarizing current pulse, by decreasing the latency for spike initiation. Importantly, the antioxidant N-acetylcysteine induced the opposite effect, suggesting the redox control of muscle excitability. The effect of H₂O₂ was abolished in the presence of catalase. The kinetics of sodium channels were not affected by H₂O₂. However, the fast inward rectifier K⁺ (K_IR) currents, activated by hyperpolarization, were reduced by H₂O₂, similar to the action of the potassium channel blockers Ba²⁺ and Cs⁺. The block of the outward tail current contributing to K_IR deactivation can explain the shorter latency for spike initiation. We propose that the K_IR current is an important target for ROS action in myotubes. Our data would thus suggest that ROS are involved in the control of the excitability of myotubes and, possibly, in the oscillatory behavior critical for the plasticity of developing muscle cells.     

Computational study of enhanced excitability in Hermissenda: membrane conductances modulated by 5-HT

Serotonin (5-HT) applied to the exposed but otherwise intact nervous system results in enhanced excitability of Hermissenda type-B photoreceptors. Several ion currents in the type-B photoreceptors are modulated by 5-HT, including the A-type K⁺ current (I_K,A), sustained Ca²⁺ current (I_Ca,S), Ca-dependent K⁺ current (I_K,Ca), and a hyperpolarization-activated inward rectifier current (I_h). In this study, we developed a computational model that reproduces physiological characteristics of type B photoreceptors, e.g. resting membrane potential, dark-adapted spike activity, spike width, and the amplitude difference between somatic and axonal spikes. We then used the model to investigate the contribution of different ion currents modulated by 5-HT to the magnitudes of enhanced excitability produced by 5-HT. Ion currents were systematically varied within limits observed experimentally, both individually and in combinations. A reduction of I_K,A or I_K,Ca, or an increase in I_h enhanced excitability by 20–50%. Decreasing I_Ca,S produced a dramatic decrease in excitability. Reductions of I_K,V produced only minimal increases in excitability, suggesting that I_K,V probably plays a minor role in 5-HT induced enhanced excitability. Combinations of changes in I_K,A, I_K,Ca, I_h and I_Ca,S produced increases in excitability comparable to experimental observations. After 5-HT application, the cell's depolarization force is shifted from the I_h–I_Ca,S combination to predominantly I_h.     

Dynamics of action potential initiation in the GABAergic thalamic reticular nucleus in vivo

Understanding the neural mechanisms of action potential generation is critical to establish the way neural circuits generate and coordinate activity. Accordingly, we investigated the dynamics of action potential initiation in the GABAergic thalamic reticular nucleus (TRN) using in vivo intracellular recordings in cats in order to preserve anatomically-intact axo-dendritic distributions and naturally-occurring spatiotemporal patterns of synaptic activity in this structure that regulates the thalamic relay to neocortex. We found a wide operational range of voltage thresholds for action potentials, mostly due to intrinsic voltage-gated conductances and not synaptic activity driven by network oscillations. Varying levels of synchronous synaptic inputs produced fast rates of membrane potential depolarization preceding the action potential onset that were associated with lower thresholds and increased excitability, consistent with TRN neurons performing as coincidence detectors. On the other hand the presence of action potentials preceding any given spike was associated with more depolarized thresholds. The phase-plane trajectory of the action potential showed somato-dendritic propagation, but no obvious axon initial segment component, prominent in other neuronal classes and allegedly responsible for the high onset speed. Overall, our results suggest that TRN neurons could flexibly integrate synaptic inputs to discharge action potentials over wide voltage ranges, and perform as coincidence detectors and temporal integrators, supported by a dynamic action potential threshold.     

Analysis of bursting in a thalamic neuron model

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a–c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes. Received: 18 July 1993/Accepted in revised form: 22 January 1994     

Relation between Membrane Potential Changes and Tension in Barnacle Muscle Fibers

Constant current pulses have been applied to single muscle fibers of the barnacle, Balanus nubilus Darwin, with an axial metal electrode. The membrane potential change, which took place over a large part of the muscle fiber, was measured with a similar electrode. Depolarizing pulses, if the voltage was greater than threshold, produced tension. The size of the tension was a function of the magnitude and the duration of the depolarizing pulses. The latency between the onset of depolarization and tension can be only in part attributable to mechanical factors. AC stimulation produced tension, but 5 to 10 seconds were required for the steady-state level of the tension to be reached. Muscles were depolarized in elevated K and studied after the contracture had terminated. If not too depolarized, further depolarization produced tension. Termination of hyperpolarizing pulses also produced tension, which decayed quite slowly. Hyperpolarizing pulses reduced, or abolished, any preexisting tension. Thus, it appears that at certain values of the membrane potential tension is set up, but there is also a slow process of accommodation present.     

The Temporal Profiles of Changes in Nerve Excitability Indices in Familial Amyloid Polyneuropathy

Familial amyloid polyneuropathy (FAP) caused by a mutation in transthyretin (TTR) gene is an autosomal dominant inherited disorder. The aim of this study is to explore the pathophysiological mechanism of FAP. We prospectively recruited 12 pauci-symptomatic carriers, 18 patients who harbor a TTR mutation, p.A97S, and two-age matched control groups. Data of nerve excitability test (NET) from ulnar motor and sensory axons were collected.NET study of ulnar motor axons of patients shows increased threshold and rheobase, reduced threshold elevation during hyperpolarizing threshold electrotonus (TE), and increased refractoriness. In sensory nerve studies, there are increased threshold reduction in depolarizing TE, lower slope of recovery and delayed time to overshoot after hyperpolarizing TE, increased refractoriness and superexcitability in recovery cycle. NET profiles obtained from the ulnar nerve of carriers show the increase of threshold and rheobase, whereas no significant threshold changes in hyperpolarizing TE and superexcitability. The regression models demonstrate that the increase of refractoriness and prolonged relative refractory period are correlated to the disease progression from carriers to patients. The marked increase of refractoriness at short-width stimulus suggests a defect in sodium current which may represent an early, pre-symptomatic pathophysiological change in TTR-FAP. Focal disruption of basal lamina and myelin may further increase the internodal capacity, manifested by the lower slope of recovery and delayed time to overshoot after hyperpolarization TE as well as the increase of superexcitability. NET could therefore make a pragmatic tool for monitoring disease progress from the very early stage of TTR-FAP.     

Impact of slow K<Superscript>+</Superscript> currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K⁺ currents, such as the M-type K⁺ current (I _M ) or the Ca²⁺-activated K⁺ current (I _AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K⁺ currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K⁺ current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K⁺ currents have a differential effect on the noise tolerance in neural coding.     

Extension of the neuronal membrane model to account for suppression of the action potential by a constant magnetic field

A biophysical explanation of the reduced excitability in neurons exposed to a constant magnetic field is based on an extended neuronal membrane model. In the presence of a constant magnetic field, reduced excitability is manifested as an increase in the excitation threshold and a decrease in the frequency of action potentials. The proposed explanation for the reduced excitability rests on the well-known Hall effect. The separation of charges resulting from the Lorentz force exerted on moving intracellular ions leads to the formation of a Hall electric field in a direction perpendicular to that of action-potential transmission. Consequently, the ion current for discharging the membrane capacitance is reduced in the presence of a magnetic field, thereby limiting initiation of the action potential. The validity of the proposed biophysical explanation is justified analytically and verified by simulations based on the Hodgkin and Huxley model for the electrical excitability of a neuron. Based on derivation of the current segregation ratio α characterizing the reduction in the stimulating current from first principles, the equivalent circuit model of the neuronal membrane is extended to account for the reduced excitability of neurons exposed to a constant magnetic field.     

Kinetics of anaerobic degradation of glycol-based Type I aircraft deicing fluids

The kinetics of anaerobic degradation of glycol-based Type I aircraft deicing fluids (ADFs) were characterized using suspended-growth fill-and-draw reactors. Both Type I ADFs tested showed near-complete anaerobic degradability. First-order degradation rate constants of 3.5 d^-1 for the propylene glycol-based Type I ADF and 5.2 d^-1 for the ethylene glycol-based Type I ADF were obtained through continuous-culture means under mesophilic conditions (35 °C). Fill-and-draw operation at lower temperatures affected anaerobic degradability only minimally down to 25 °C but substantially below 25 °C. High Type I ADF feed concentrations substantially affected degradability. Batch testing of fill-and-draw reactors resulted in first-order degradation rate constants of 1.9 d^-1 for propylene glycol-based Type I ADF and 3.5 d^-1 for ethylene glycol-based Type I ADF.     

Magnesium induces neuronal apoptosis by suppressing excitability

In clinical obstetrics, magnesium sulfate (MgSO₄) use is widespread, but effects on brain development are unknown. Many agents that depress neuronal excitability increase developmental neuroapoptosis. In this study, we used dissociated cultures of rodent hippocampus to examine the effects of Mg⁺⁺ on excitability and survival. Mg⁺⁺-induced caspase-3-associated cell loss at clinically relevant concentrations. Whole-cell patch-clamp techniques measured Mg⁺⁺ effects on action potential threshold, action potential peak amplitude, spike number and changes in resting membrane potential. Mg⁺⁺ depolarized action potential threshold, presumably from surface charge screening effects on voltage-gated sodium channels. Mg⁺⁺ also decreased the number of action potentials in response to fixed current injection without affecting action potential peak amplitude. Surprisingly, Mg⁺⁺ also depolarized neuronal resting potential in a concentration-dependent manner with a +5.2 mV shift at 10 mM. Voltage ramps suggested that Mg⁺⁺ blocked a potassium conductance contributing to the resting potential. In spite of this depolarizing effect of Mg⁺⁺, the net inhibitory effect of Mg⁺⁺ nearly completely silenced neuronal network activity measured with multielectrode array recordings. We conclude that although Mg⁺⁺ has complex effects on cellular excitability, the overall inhibitory influence of Mg⁺⁺ decreases neuronal survival. Taken together with recent in vivo evidence, our results suggest that caution may be warranted in the use of Mg⁺⁺ in clinical obstetrics and neonatology.     

Redox Mechanism of S-Nitrosothiol Modulation of Neuronal CaV3.2 T-Type Calcium Channels

T-type calcium channels in the dorsal root ganglia (DRG) have a central function in tuning neuronal excitability and are implicated in sensory processing including pain. Previous studies have implicated redox agents in control of T-channel activity; however, the mechanisms involved are not completely understood. Here, we recorded T-type calcium currents from acutely dissociated DRG neurons from young rats and investigated the mechanisms of Ca_V3.2 T-type channel modulation by S-nitrosothiols (SNOs). We found that extracellular application of S-nitrosoglutathione (GSNO) and S-nitroso-N-acetyl-penicillamine rapidly reduced T-type current amplitudes. GSNO did not affect voltage dependence of steady-state inactivation and macroscopic current kinetics of T-type channels. The effects of GSNO were abolished by pretreatment of the cells with N-ethylmaleimide, an irreversible alkylating agent, but not by pretreatment with 1H-(1,2,4) oxadiazolo (4,3-a) quinoxalin-1-one, a specific soluble guanylyl cyclase inhibitor, suggesting a potential effect of GSNO on putative extracellular thiol residues on T-type channels. Expression of wild-type Ca_V3.2 channels or a quadruple Cys-Ala mutant in human embryonic kidney cells revealed that Cys residues in repeats I and II on the extracellular face of the channel were required for channel inhibition by GSNO. We propose that SNO-related molecules in vivo may lead to alterations of T-type channel-dependent neuronal excitability in sensory neurons and in the central nervous system in both physiological and pathological conditions such as neuronal ischemia/hypoxia.     

Hexamethonium increases the excitability of sympathetic neurons by the blockade of the Ca2+-activated K+ channels

Effects of hexamethonium (C6) on the excitability of sympathetic ganglion cells were examined by means of intracellular recording. When DC currents were injected, high concentrations of C6 significantly augmented the repetitive firing of the cells without any change in threshold voltage for initiation of the spike. The Ca2+-sensitive component of the after-hyperpolarization following a spike was reduced by C6 in a dose-dependent fashion (0.3 to 10 mM). C6 slightly affected parameters for the spike but neither the resting membrane potential nor the input membrane resistance. The amplitude of the Ca2+ spike (in the presence of 1 microM tetrodotoxin and 10 mM tetraethylammonium) was not affected even by 30 mM C6. Bee venom (0.3 micrograms/ml) which contains apamin showed similar effects. These results suggest that C6 blocks the Ca2+-activated K+ channels, resulting in an increase in excitability of the cells.     

Diffusion models for firing of a neuron with varying threshold

A stochastic model for the firing of a neuron with refractory properties is treated analytically. Refractory behavior is modeled by a threshold function θ(t) which is infinite immediately after the neuron fires, as well as during the absolute refractory period, and then decreases monotonically to the quiescent threshold level, θ_∞, during the relative refractory period. Using Wald's identity, input-output relations are derived analytically for the exponential threshold which has a time constant equal to the membrane time constant. A method for computing these relations for a general threshold is presented and is explicitly used for the general exponential threshold and the Hagiwara threshold, θ(t) = θ_∞e^α/t, where a is a constant.