Sparse balance: Excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights

Author summaryA class of models in computational neuroscience that have been successful at describing a variety of effects in the neocortex involve a tight balance between excitatory, inhibitory and unrealistically large external input, without which the model cannot produce robust patterns of activity. In this work, we explore what happens when these inputs are smaller in size, and we provide an alternative solution for recovering robust network activity. This solution relies on broadly distributed synaptic strengths and, interestingly, gives rise to sparse subsets of neurons firing at any given time. Unlike the conventional models, the networks exhibit nonlinear responses to uniform external input. Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.