Cortical circuits exhibit strong spatiotemporal variability. Balanced network models offer an appealing theoretical framework for studying this neural variability since they produce intrinsically noisy dynamics with statistical features similar to those observed in cortical recordings [1]. The majority of balanced network studies assume a homogeneous network structure in which connection probability depends only on cell type (excitatory or inhibitory), but anatomical and electrophysiological studies reveal that connection probability depends on distance in physical space and, in sensory systems, tuning space. We extend theory of balanced and asynchronous networks to account for the spatial dependence of connection probability and feedforward input statistics. We propose that this extension to space captures several salient features of cortical circuits that are not captured by spatially homogeneous network models.

First, we show that surround suppression is a natural consequence of balance in a model of primary visual cortex with a retinotopic map, even when excitatory synaptic projections are broader than inhibitory. Next we show that spatially extended, densely connected balanced networks can produce correlated spiking activity in addition to the asynchronous activity produced by homogeneous balanced networks [2]. This finding could potentially resolve the ongoing debate over the magnitude of correlations in cortical networks [3,4]. 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 [5]. Taken together our results show that spatially extended balanced networks offer a parsimonious model of cortical circuits.

[1] C. Van Vreeswijk and H. Sompolinsky. Science. 274:1724-6 (1996).
[2] A. Renart, J. de la Rocha, et al. Science. 327:587-90 (2010).
[3] A.S. Ecker, P. Berens, et al. Science. 327:584-7 (2010).
[4] M.R. Cohen and A. Kohn. Nat Neurosci. 14:811-9 (2011).
[5] D. Sussillo and L.F. Abbott. Neuron. 63:544-57 (2009).