M. di Volo, UNIC, CNRS, Gif sur Yvette, France
A. Romagnoni, C. Capone & A. Destexhe.

A general framework for conductance-based mean field models of adaptive cortical networks

Mean-field models were applied for many type of neural networks,
both for rate-based models and spiking neurons. However, the
integration of conductance-based synaptic interactions has always
been difficult, and similarly for complex cellular properties
such as adaptation or bursting. We discuss here a mean field approach to the activity of excitatory-inhibitory networks with voltage dependent conductance interactions. According to its generality we apply this formalism to different neurons models (Hodkin-Huxley and two-dimensional integrate-and-fire), showing
its capability to predict the average activity of excitatory and inhibitory populations in asynchronous irregular regimes. We then investigate the time course of the response to a relatively fast external stimuli, where adaptation in excitatory cells affects network firing rate temporal dynamics. Finally, a transition to bistable network states in function of cells excitability is discussed, permitting the alternation of low (DOWN) and high (UP) activity states driven by noise and adaptation. We investigate this transition and its dynamics in the
context of the mean field model, able to predict both qualitatively and quantitatively the network dynamics.
We speculate that realistic mean-field models based on real-neuron
properties are reachable in a near future.