Mathematical analysis of the possibility of detecting correlation between spike trains of weakly interacting neurons

The number of spikes which must be recorded in order to detect significant correlation between spike trains of two synaptically connected neurons was estimated by a mathematical model. Dependence of this number of spikes on importance of interneuronal connection (measured as the amplitude of the EPSP evoked by a single spike of the input neuron in the output cell) and on the intensity of total spontaneous excitatory influences on the output neuron and on its own parameters was studied. For cells which corresponded in the weight of connections between them, their intrinsic parameters, and characteristics of spontaneous activity to real spinal neurons, the necessary number of spikes was 10⁷–10⁸. An increase in amplitude of the single EPSP and also a decrease in the intensity of the input spontaneous spike train and parameters of after-hyperpolarization of the postsynaptic neuron led to a decrease in the number of spikes necessary for the detection of significant correlation. On the basis of the results of this and previous investigations the possible principles for construction of a spinal locomotor generator are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 3, pp. 290–296, May–June, 1980.