Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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BCCN AG-Seminar

Thursday, 04.05.2017 11 s.t.

Linking scales in cortical circuits - From spiking neurons to mesoscopic population dynamics

by Dr. Tilo Schwalger
from Laboratory of Computational Neuroscience, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

Contact person: Rainer Engelken

Location

Ludwig Prandtl lecture hall

Abstract

Neural population equations such as Wilson-Cowan equations, neural mass or field models are widely used to model mesoscopic and macroscopic brain activity. How these large-scale models are linked to the properties of single neurons is however not well understood. Here we derive stochastic mean-field equations for several interacting populations at the mesoscopic scale starting from a microscopic model of generalized integrate-and-fire (GIF) neurons. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. On the mesoscopic level, the stochastic equations that we find account for both finite-size fluctuations of the population activity and pronounced spike-history effects in single-neuron activity such as refractoriness and adaptation. The mesoscopic dynamics reproduces the rich stochastic population dynamics obtained from microscopic simulations of the full spiking neural network model. Going beyond classical mean-field theories for infinite N, our finite-N theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. We use the mesoscopic equations to efficiently integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. Reference: T. Schwalger, M. Deger, and W. Gerstner. PLoS Comput. Biol., 13(4):e1005507, 2017, https://arxiv.org/abs/1611.00294

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