Analysis of synchronization in the response of neurons to noisy periodic synaptic input

A first-order nonhomogeneous Markov model for the response of spiking neurons stimulated by small phase-continuous signals

We present a first-order nonhomogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics and the other of which describes only the signal characteristics. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.

Information transfer in entrained cortical neurons

Cortical interneurons connected by gap junctions can provide a synchronized inhibitory drive that can entrain pyramidal cells. This was studied in a single-compartment Hodgkin-Huxley-type model neuron that was entrained by periodic inhibitory inputs with low jitter in the input spike times (i.e. high precision), and a variable but large number of presynaptic spikes on each cycle. During entrainment the Shannon entropy of the output spike times was reduced sharply compared with its value outside entrainment. Surprisingly, however, the information transfer as measured by the mutual information between the number of inhibitory inputs in a cycle and the phase lag of the subsequent output spike was significantly increased during entrainment. This increase was due to the reduced contribution of the internal correlations to the output variability. These theoretical predictions were supported by experimental recordings from the rat neocortex and hippocampus in vitro.