The computational properties of a simplified cortical column model
ABSTRACT :
The cortical column is a modular neuronal circuit that broadly tiles the six-layered neocortex of mammalian brains. It is of considerable interest to determine if there is a single canonical computation performed by such cortical columns in the transformation of sensory input to higher cognitive processes such as perception and memory. Dynamical models have been successfully used to simulate the functioning of different components of the brain in order to study the neural basis of behavior. In order to understand the dynamics of neurons and neuronal networks, several classes of single neuron models with differing degrees of complexity have been developed. The leaky integrate-and-fire neuron model is a simplified abstraction that captures essential characteristics of single neuron dynamics. Potjans and Diesmann (Cereb. Cortex, 2014) parameterized a four-layer, two cell type (i.e. excitatory and inhibitory) model of a cortical column with homogeneous populations of leaky integrate-and-fire neurons and cell type dependent connection probabilities. To explore computations subserved by this model, we used a displacement integro-partial differential equation (DiPDE) population density model to characterize each neuronal population in the column. In the limit of large homogeneous populations, this reduces to a mean field model and provides a fast numerical method to solve equations describing the full probability density distribution of neuronal membrane potentials. It lends itself to quickly analyzing the mean response properties of population-scale firing rate dynamics. I will outline the development of the DiPDE population density model starting with the master equation for leaky integrate-and-fire neurons with shot noise input and compare it with analyses of neuronal population dynamics using the Fokker-Planck equation. I will describe how it can be used to explore the influence of different input weight distributions on the dynamics of neuronal populations. I will then show how we used this strategy to examine the input-output relationship of the Potjans and Diesmann cortical column model to understand its computational properties. When inputs are constrained to jointly and equally target excitatory and inhibitory neurons, we found a large linear regime where the effect of a multi-layer input signal can be reduced to a linear combination of component signals. One of these, a simple subtractive operation, can act as an error signal passed between hierarchical processing stages.