Microcircuits of stochastic neurons

Abstract

Event Abstract Back to Event Microcircuits of stochastic neurons Stefano Cardanobile1* and Stefan Rotter1 1 BCCN Freiburg, Germany Multiplicatively interacting point processes and applications to neural modelling Stefano Cardanobile & Stefan Rotter BCCN Freiburg Mathematical analysis of complex neural network dynamics is both challenging and important for research in neuroscience. Most current approaches, though, rely on mean-field approximations, which have difficulties to evalutate the influence of network structure on its spiking dynamics. We exploit the stochastic nature of neuronal firing and set up a point process framework, based on the observation that the escape noise of real neurons is exponential with respect to their membrane voltage [1]. Assuming linear integration of inputs, this translates into a multiplicative interaction rule on the level of instantaneous firing rates: each incoming spike effectively multiplies the instantaneous firing rate by a fixed "synaptic weight". This approach is in contrast to Hawkes’ linear model [2], where the instantaneous firing rate is given by a convolution of the input spike rate with a linear temporal filter. This effectively prevents the implementation of inhibition in this model. We proved that the equations governing the dynamics of the expected firing rates in our multiplicative system are of Lotka-Volterra type, if one ignores covariances [3]. Based on numerical simulations, we show that this approximation works quite well under very general conditions. Asymptotically, the observed firing rates coincide with the solutions of the associated rate equations even in cases where the rates do not converge to a fixed point, but exhibit transient dynamics. Multiplicatively interacting point processes offer an interesting novel framework for the study of complex neural network dynamics. To illustrate this claim, we finally describe some structured networks that are able to process information, and discuss specifically competing neural populations to describe experiments where rivaling features are perceived. Our model qualitatively replicates the unimodal distribution of dwell times as observed in experiments, and it leads to an intuitive explanation of the switching dynamics. The project has been supported by BMBF grant 01GQ0420 to the BCCN Freiburg.