Exploring Neuronal Bistability at the Depolarization Block

Abstract

Many neurons display bistability–coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels. We consider the spike-producing currents in two neurons, models of which differ by the parameter values. Our dopaminergic neuron model displays bistability in a wide range of applied currents at the depolarization block. The Hodgkin-Huxley model of the squid giant axon shows no bistability. We varied parameter values for the model to analyze transitions between the two parameter sets. We show that bistability primarily characterizes the inactivation of the Na+ current. Our study suggests a connection between the amount of the Na+ window current and the length of the bistability range. For the dopaminergic neuron we hypothesize that bistability can be linked to a prolonged action of antipsychotic drugs.

Mathematical analysis of depolarization block mediated by slow inactivation of fast sodium channels in midbrain dopamine neurons

“…4C1 could be obtained. In a current-clamp mode, both models predict hysteresis in that less current is required to maintain depolarization block than is required to induce it (Dovzhenok and Kuznetsov 2012). Our simple model has focused on the mechanism of depolarization block and ignores the subthreshold calcium oscillations that can be observed in substantia nigra pars compacta cells (Wilson and Callaway 2000).…”

“…Spiking is initiated in the 2D model by a saddle node bifurcation and in the 3D model by a supercritical Hopf with a very steep dependence of the amplitude of the oscillation on applied current. In both cases, spiking terminates at a saddle node of periodics (SNP), and there is a region of bistability (Dovzhenok and Kuznetsov 2012) between depolarization block (rightmost red branch of stable fixed points) and pacemaking (green branches indicate maxima and minima during spiking). The bifurcation diagrams can be presented in a form more familiar to electrophysiologists, the I-V curve.…”

The domain of neuronal firing on a plane of input current and conductance

“…2e). Presumably, this scenario relates to the supercritical Andronov-Hopf bifurcation (Dovzhenok and Kuznetsov 2012;Izhikevich 2007), occurring with the slow change of adaptation. The silent state is stable.…”

“…1e). This scenario is supposed to correspond to the saddle-node of limit cycles bifurcation (Dovzhenok and Kuznetsov 2012). The saddle-node of limit cycles bifurcation is coupled with the subcritical Andronov-Hopf bifurcation.…”

A Regulated Double-Negative Feedback Decodes the Temporal Gradient of Input Stimulation in a Cell Signaling Network

“…For example, Hodgkin's Type III excitable neuron fires for a step input (an abrupt increase of stimulation) but not a slow ramp input though these inputs have the same final level, named as slope sensitivity [14–16]. Such slope sensitivity was also found in auditory brainstem neurons, spinal cord neurons, and dopaminergic neurons [14, 17]. Another example was displayed by Young et al who examined the environmental pathway using Bacillus subtilis [18].…”