Weak Noise in Neurons May Powerfully Inhibit the Generation of Repetitive Spiking but Not Its Propagation

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).