THEORY RELATING PROPERTIES OF NEURONAL FIRING TO STATISTICS OF SYNAPTIC INPUT

G. Svirskis,

Center for Neural Science, New York University, New York, USA, and

Laboratory of Neurophysiology, Biomedical Research Institute, KaunasUniversity of Medicine, Kaunas, Lithuania

Information between neurons is carried by stochastic spike trains. In recent research, temporal correlations inside and between spike trains emerge as potential information carrier. In order to understand how information is processed in neuronal networks, it is necessary to be able to describe an impact of general statistical properties of synaptic input on membrane fluctuations and firing of postsynaptic neuron. The theory of general random point processes (Stratonovich, 1963) uses correlation functions to describe statistical relations between events and can relate properties of random point processes with properties of resulting continues stochastic processes. Such an approach (Svirskis and Rinzel, 2000) shows that temporal correlations in the synaptic input enhance membrane fluctuations and firing rate of the postsynaptic neuron and influence the variance of the output spike trains. The same correlation functions can be used to describe synchronization of spikes between neurons sharing part of the synaptic input. Mathematical analysis and modeling suggest that membrane time constant and temporal correlation functions of synaptic input define temporal dependence of spike synchronization for low firing rate. Also, a sustained inward current, which supports spiking in the postsynaptic neuron, can decrease spike synchronization between neurons. The mathematical theory is not restricted to stationary stochastic processes, and similar correlation functions were used in experimental studies previously. Since experimental studies indicate the involvement of spike synchrony in information coding and processing, the mathematical methods and usage of correlation functions of synaptic trains can be a useful tool for understanding mechanisms of neuronal function.

1. Stratonovich,R.L. 1963. Topics in the theory of random noise, Volume I. Gordon and Breach, New York-London.

2. Svirskis,G. and J.Rinzel. 2000. Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons. Biophys J, 79: 629-637.