Functional structure of cortical neuronal networks grownin vitro

Abstract

We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light into the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their ex vivo development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient, network diameter and assortative mixing. Specifically we show that these networks are weakly disassortative small world graphs, which differ significantly in their structure from randomized graphs with the same degree. We expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks, derived from time series data. I. INTRODUCTIONUnderstanding and quantifying the dynamical mechanisms used by the nervous system to store and process information remains one of the greatest challenges to contemporary science. At present, broad outlines of the physical mechanisms that underpin the basic functioning of single neurons and synapses in the brain are understood [1]. However, this detailed knowledge of individual units sheds little light into the origin of the unmatched computational power of mammalian nervous systems, achieved despite characteristic operating times that are six orders of magnitude slower than those of modern digital computers.The computational nature of the brain lies therefore principally in the ensemble properties of neurons, synapses and their emergent complex, dynamical networks. Over the last few years the interaction structure of many complex systems has been mapped in terms of graphs, which can in turn be characterized using tools of statistical physics [2]. This approach has revealed broad classes of networks such as small world graphs [3] and scale free networks [4], which occur across fields of study, from technological networks, such as the internet, to various biological and social systems. The structural properties of these graphs, such as their degree distribution or their local transitivity, moreover, have been suggested to result from optimization constraints [5,6] or network growth dynamics [6], thus connecting graph structure to operational definitions of function, independent of a system's details. These lines of research provide new quantitative insights, connecting the interaction structure of a complex systems to nove...

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