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

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.

Simulation code available from https://github.com/schwalger/mesopopdyn_gif

References in corpus (10)

• Macroscopic description for networks of spiking neurons
• Dynamics of multi-stable states during ongoing and evoked cortical activity
• The Role of the Hes1 Crosstalk Hub in Notch-Wnt Interactions of the Intestinal Crypt
• Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation
• Linking structure and activity in nonlinear spiking networks
• Network events on multiple space and time scales in cultured neural networks and in a stochastic rate model
• Identifying anatomical origins of coexisting oscillations in the cortical microcircuit
• Fundamental activity constraints lead to specific interpretations of the connectome
• Stochastic Wilson-Cowan models of neuronal network dynamics with memory and delay
• Population Density Equations for Stochastic Processes with Memory Kernels

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• How random connectivity shapes the fluctuating dynamics of finite-size neural populations
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