Weak noise in neurons may powerfully inhibit the generation of repetitive spiking but not its propagation.

Henry C Tuckwell,Jürgen Jost

doi:10.1371/journal.pcbi.1000794

Abstract

Many neurons have epochs in which they fire action potentials in an approximately periodic fashion. To see what effects noise of relatively small amplitude has on such repetitive activity we recently examined the response of the Hodgkin-Huxley (HH) space-clamped system to such noise as the mean and variance of the applied current vary, near the bifurcation to periodic firing. This article is concerned with a more realistic neuron model which includes spatial extent. Employing the Hodgkin-Huxley partial differential equation system, the deterministic component of the input current is restricted to a small segment whereas the stochastic component extends over a region which may or may not overlap the deterministic component. For mean values below, near and above the critical values for repetitive spiking, the effects of weak noise of increasing strength is ascertained by simulation. As in the point model, small amplitude noise near the critical value dampens the spiking activity and leads to a minimum as noise level increases. This was the case for both additive noise and conductance-based noise. Uniform noise along the whole neuron is only marginally more effective in silencing the cell than noise which occurs near the region of excitation. In fact it is found that if signal and noise overlap in spatial extent, then weak noise may inhibit spiking. If, however, signal and noise are applied on disjoint intervals, then the noise has no effect on the spiking activity, no matter how large its region of application, though the trajectories are naturally altered slightly by noise. Such effects could not be discerned in a point model and are important for real neuron behavior. Interference with the spike train does nevertheless occur when the noise amplitude is larger, even when noise and signal do not overlap, being due to the instigation of secondary noise-induced wave phenomena rather than switching the system from one attractor (firing regularly) to another (a stable point).

Highlights

Rhythmic or almost regular periodic neuronal spiking is found in many parts of the central nervous system, including, for example, thalamic relay cells [1,2,3], dopaminergic neurons [4], respiratory neurons [5,6], locus coeruleus neurons [7] and dorsal raphe serotonergic neurons [7,8]
Especially those found in subcortical nuclei, often exhibit repetitive approximately periodic firing of action potentials
We have previously demonstrated how weak noise may inhibit repetitive activity in the HodgkinHuxley point model and in pairs of coupled type 1 model neurons

Summary

Introduction

Rhythmic or almost regular periodic neuronal spiking is found in many parts of the central nervous system, including, for example, thalamic relay cells [1,2,3], dopaminergic neurons [4], respiratory neurons [5,6], locus coeruleus neurons [7] and dorsal raphe serotonergic neurons [7,8]. Periodic behavior is found in the activity of neuronal populations [9,10]. Since stochasticity is a prominent component of neuronal activity at all levels [11,12], it is of interest to see what effects noise may have on the repetitive activity of neurons. There are many kinds of neuronal model which could be used, an immediate dichotomy being provided by Hodgkin’s defining classes of type 1 and type 2 neurons [13,14]. We have chosen to first examine the behavior of the classic type 2 neural model in its full spatial version [15] which has been employed in recent studies of reliability [16]. The methods we use can be extended to more complicated models such as in [1,2,3,5,17]

Methods

Results

Discussion

Conclusion