Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

TL;DR

This paper derives mesoscopic population equations from microscopic neuron models, linking single-neuron properties to large-scale brain activity, and demonstrates their effectiveness in simulating cortical microcircuits.

Contribution

It introduces a novel derivation of stochastic population equations from integrate-and-fire neuron models, connecting single-neuron dynamics with population-level phenomena.

Findings

Reproduces population activity statistics from microscopic simulations

Describes nonlinear dynamics like stochastic transitions and synchronization

Provides an efficient framework for modeling cortical circuits

Abstract

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics like finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly simulate a model of a local cortical microcircuit consisting of eight neuron types. 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.