Effective neurons and attractor neural networks in cortical environment

Abstract

Single-neuron spike dynamics is reconsidered in a situation in which the neural afferent spike input, originating from non-specific spontaneous activity, is very large compared with the input produced by specific (task related) operation of a cortical module. This the authors argue is the situation prevailing in associative cortex. It is shown that the Frolov-Cowan 'point approximation' can be derived systematically in this case, even in the presence of shunting inhibition.

The same type of logic is then applied to the cable theory equation for the neuron. Also, here under low ratio of signal to spontaneous activity in the input, the dynamics linearizes, leading to an integrate-and-fire behaviour for the effective neuron. This element sums its synaptic inputs linearly. Its parameters are the resting parameters of the bare neuron, renormalized by the heavy barrage of impinging spontaneous activity. The only remnant of the geometric structure of the dendritic tree is an effective weakening of the postsynaptic potential due to the spatial decay of the spike influence, travelling from the synapse to the spike-emitting part of the membrane, and a time delay for the arrival of the peak of the spike influence.

This description can then be re-expressed in terms of rates. The role of the low rates of the selectively spiking neurons is found to be essential at many stages in the argument.