Correlations and dynamics in spatially extended balanced networks

Balanced networks offer an appealing theoretical framework for studying neural variability since they produce intrinsically noisy dynamics with some statistical features similar to those observed in cortical recordings. However, previous balanced network models face two critical shortcomings. First, they produce extremely weak spike train correlations, whereas cortical circuits exhibit both moderate and weak correlations depending on cortical area, layer and state. Second, balanced networks exhibit simple mean-field dynamics in which firing rates linearly track feedforward input. Cortical networks implement non-linear functions and produce non-trivial dynamics, for example, to produce motor responses. We propose that these shortcoming of balanced networks are overcome by accounting for the distance dependence of connection probabilities observed in cortex. We generalize the mean-field theory of firing rates, correlations and dynamics in balanced networks to account for distance-dependent connection probabilities. We show that, under this extension, balanced networks can exhibit either weak or moderate spike train correlations, depending on the spatial profile of connections. Networks that produce moderate correlation magnitudes also produce a signature spatial correlation structure. A careful analysis of in vivo primate data reveals this same correlation structure. Finally, we show that spatiotemporal firing rate dynamics can emerge spontaneously in spatially extended balanced networks. Principal component analysis reveals that these dynamics are fundamentally high-dimensional and reliable, suggesting a realistic spiking model for the rich dynamics underlying non-trivial neural computations. Taken together our results show that spatially extended balanced networks offer a parsimonious model of cortical circuits.Non UBCUnreviewedAuthor affiliation: University of Notre DameFacult