Dynamics of Cell Assemblies in Binary Neuronal Networks

Connectivity in local cortical networks is far from random: Reciprocal connections are over-represented, and there are subgroups of neurons which are stronger connected among each other than to the remainder of the network [1,2]. These observations provide a growing evidence for the existence of neuronal assemblies, that is groups of neurons with stronger and/or more numerous connections between members compared to non-members. To study quantitatively the dynamics of these building blocks, we consider a single assembly of binary neurons embedded in a larger randomly connected EI-network and explore its properties by analytical methods and simulation. In dynamical mean field theory [3], we obtain expressions for mean activities, auto- and cross-correlations, and response to input fluctuations using a Gaussian closure. For sufficiently strong assembly self-feedback, a bifurcation from a mono-stable to a bistable regime exists. The critical regime around the bifurcation is of interest, as input variations can drive the assembly to high or low activity states and large spontaneous fluctuations are present. These could be a source of neuronal avalanches observed in cortex, and the robust response to input could constitute attractor states supporting classification in sensory perception. In this regime however, the gaussian approximation is not accurate due to large fluctuation corrections. We therefore work on a path-integral formulation of such systems built on developments in the application of statistical field theory to neuronal networks [4]. This formulation allows the derivation of an effective potential, a systematic treatment of approximations and the quantification of the response to inputs.References1. Ko H, Hofer SB, Pichler B, Buchanan KA , Sjöström PJ, Mrsic-Flogel TD, (2011) Functional specificity of local synaptic connections in neocortical networks. Nature 473: 87-912. Perin R, Berger TK, Markram H, (2011) A synaptic organizing principle for cortical neuronal groups. PNAS 108: 5419-54243. Helias M, ...