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Abstract

In the study of the cerebral cortex, the roughly uniform six-layer structure and the prominence of functional columns have raised the question of the relationship between structure and function of cortical microcircuits. Nevertheless, experimental work has only slowly begun to systematically unveil the connectivity of local recurrent cortical circuits, and most theoretical work has until now dealt only with simple random connectivity. Even recent realistic numerical studies have used only cell-type connection probabilities accumulated from different experimental techniques, animals, species, and brain regions. The rodent barrel cortex has become an attractive site for experimental work on the structure-function relationship because of its anatomically observable somatotopy and readily isolatable sensory input channels. In this collaborative project, we combine recent anatomical work on the rat barrel cortex which has yielded a coherent, realistic, anatomically constrained cell-to-cell connectivity matrix, with both theoretical and numerical analysis in order to shed new light on the relationship between structure and function in cortical microcircuits. We explore the dynamics of a full-scale spiking neuron network model under realistic cell-to-cell connectivity and identify constraints imposed by the connectivity beginning with one complete Layer 4 Barrel. In particular, we use numerical and theoretical tools to explore the implications of the heterogeneity in the number of connections on the dynamical state. We simulate the network model alongside others with simplified connectivity schemes, and also apply dynamical mean-field theory to a connectivity model that reflects realistic heterogeneity in order to derive analytical results. We address the trade-off between sparsity and irregularity in the balanced state. Furthermore, we probe the signal propagation yielded by the realistic connectivity matrix, exploring the spatial distribution of spontaneous, primary whisker evoked, and secondary whisker evoked firing. We compare the results of our network model to physiological findings and make further predictions. Our work is an important step toward bridging between theory and experiment, connecting the abstract study of the dynamics of cortical circuits to the increasingly detailed experimental account of their real connectivity structure and the biophysical properties of different cell types.