Tilo Schwalger, Laboratory of Computational Neuroscience, EPFL

Mesoscopic dynamics of spiking neural networks

How dynamics and fluctuations of brain activity emerge from the interactions of thousands of spiking neurons is crucial for understanding neural variability and cognitive states. Heurisic models of neural populations such as Wilson-Cowan equations or field models are widely used to model cortical activity on the mesoscopic or macroscopic scale, but the link to the microscopic level of spiking neurons remains largely unclear. Here we derive stochastic population equations at the mesoscopic level starting from a microscopic network model of spiking neurons. The derived coarse-grained population model accounts for temporal correlations of single neuron spike trains caused by refractoriness and adaptation. Furthermore, the stochastic population equations accurately reproduce stationary and non-stationary mesoscopic activity obtained from a direct simulations of the microscopic model. Going beyond classical mean-field theories for an infinite number of neurons, our finite-size theory describes emerging phenomena such as stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. We also use the mesoscopic equations to efficiently simulate a model of a cortical microcircuit. Our theory opens the door for analytically tractable models of spiking neuron populations that can be used to understand dynamics and computations on the mesoscopic level.