Maurizio Mattia, Collective Dynamics of Interacting Spiking Neurons: From Theory to Experiments

The computational capabilities of the nervous system are the result of nonlinear dynamics emerging from the exchange among neurons of stereotyped messages, the action potentials. This web of cells sparsely linked through synaptic contacts is a heterogeneous excitable medium whose collective dynamics can be effectively described by mean-field theories. I will introduce a widely used approach relying on a multi-dimensional Fokker-Planck equation for the time-dependent densities of neuronal membrane potentials. Additional dimensions take into account of other activity-dependent variables and non-instantaneous synaptic transmission. I will show how from this equation an effective dynamics for the rate of spikes emitted by the whole network can be worked out, allowing to predict a rich repertoire of collective dynamical regimes. Finally, I will use such theoretical framework to characterize the neuronal substrate of the so called “slow rhythms” (< 1 Hz) occurring during slow-wave sleep and under deep anesthesia of intact brains, and in cortical slices of mammals maintained in vitro. In this spontaneous activity regime of the nervous tissue, Up states at relatively high firing rate alternate with almost quiescent periods (Down states). The constructive role of endogenous noise and of heterogeneities in these nonlinear neuronal networks will be also discussed.