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...

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We quantitatively analyzed the ignition and spread of collective spontaneous electrophysiological activity in networks of cultured cortical neurons growing on microelectrode arrays. Leader neurons, which form a mono-synaptically connected primary circuit, and initiate a majority of network bursts were found to be a small subset of recorded neurons. Leader/follower firing delay times formed temporally stable positively skewed distributions. Blocking inhibitory synapses usually resulted in shorter delay times with reduced variance. These distributions are characterizations of general aspects of internal network dynamics and provide estimates of pair-wise synaptic distances. The resulting analysis produced specific quantitative constraints and insights into the activation patterns of collective neuronal activity in self-organized cortical networks, which may prove useful for models emulating spontaneously active systems.

We present a general information theoretic approach for identifying functional subgraphs in complex networks. We show that the uncertainty in a variable can be written as a sum of information quantities, where each term is generated by successively conditioning mutual informations on new measured variables in a way analogous to a discrete differential calculus. The analogy to a Taylor series suggests efficient optimization algorithms for determining the state of a target variable in terms of functional groups of other nodes. We apply this methodology to electrophysiological recordings of cortical neuronal networks grown in vitro. Each cell's firing is generally explained by the activity of a few neurons. We identify these neuronal subgraphs in terms of their redundant or synergetic character and reconstruct neuronal circuits that account for the state of target cells.

Can lateral connectivity in the primary visual cortex account for the time dependence and intrinsic task difficulty of human contour detection? To answer this question, we created a synthetic image set that prevents sole reliance on either low-level visual features or high-level context for the detection of target objects. Rendered images consist of smoothly varying, globally aligned contour fragments (amoebas) distributed among groups of randomly rotated fragments (clutter). The time course and accuracy of amoeba detection by humans was measured using a two-alternative forced choice protocol with self-reported confidence and variable image presentation time (20-200 ms), followed by an image mask optimized so as to interrupt visual processing. Measured psychometric functions were well fit by sigmoidal functions with exponential time constants of 30-91 ms, depending on amoeba complexity. Key aspects of the psychophysical experiments were accounted for by a computational network model, in which simulated responses across retinotopic arrays of orientation-selective elements were modulated by cortical association fields, represented as multiplicative kernels computed from the differences in pairwise edge statistics between target and distractor images. Comparing the experimental and the computational results suggests that each iteration of the lateral interactions takes at least ms of cortical processing time. Our results provide evidence that cortical association fields between orientation selective elements in early visual areas can account for important temporal and task-dependent aspects of the psychometric curves characterizing human contour perception, with the remaining discrepancies postulated to arise from the influence of higher cortical areas.