Stochastic population dynamics of finite networks of spiking neurons

Neural population equations such as Wilson-Cowan equations, neural mass or field models are widely used to model brain activity on the mesoscopic or macroscopic scale. It is not known, however, how such large-scale models relate to underlying biophysical properties at the microscopic scale. By principled coarse-graining, we here derive stochastic population equations at the mesoscopic level starting from a microscopic network model of biologically-verified spiking neurons. We solved the critical problem of treating both fluctuations of the population activity due to the finite number of neurons and pronounced spike-history effects of single-neurons such as refractoriness and adaptation. The derived mesoscopic dynamics accurately reproduces the mesoscopic activity obtained from a direct simulations of the microscopic spiking neural network model. Going beyond classical mean-field theories for infinite N, our finite-N theory describes new emerging phenomena such as stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. We use the mesoscopic equations to efficiently simulate a model of a cortical microcircuit consisting of eight neuron types. Our theory opens a general framework for modeling and analyzing finite-size neural population dynamics based on realistic single cell and synapse parameters.

Reference: T. Schwalger, M. Deger, and W. Gerstner. PLoS Comput. Biol., 13(4):e1005507, 2017. dx.doi.org/10.1371/journal.pcbi.1005507