Abstract
Balanced networks are a frequently employed basic model for neuronal networks in the mammalian neocortex. Large numbers of excitatory and inhibitory neurons are recurrently connected so that the numerous positive and negative inputs that each neuron receives cancel out on average. Neuronal firing is therefore driven by fluctuations in the input and resembles the irregular and asynchronous activity observed in cortical in vivo data. Recently, the balanced network model has been extended to accommodate clusters of strongly interconnected excitatory neurons in order to explain persistent activity in working memory-related tasks. This clustered topology introduces multistability and winnerless competition between attractors and can capture the high trial-to-trial variability and its reduction during stimulation that has been found experimentally. In this prospect article, we review the mean field description of balanced networks of binary neurons and apply the theory to clustered networks. We show that the stable fixed points of networks with clustered excitatory connectivity tend quickly towards firing rate saturation, which is generally inconsistent with experimental data. To remedy this shortcoming, we then present a novel perspective on networks with locally balanced clusters of both excitatory and inhibitory neuron populations. This approach allows for true multistability and moderate firing rates in activated clusters over a wide range of parameters. Our findings are supported by mean field theory and numerical network simulations. Finally, we discuss possible applications of the concept of joint excitatory and inhibitory clustering in future cortical network modelling studies.
Highlights
Neural responses in the mammalian neocortex are notoriously variable
In the more interesting intermediate range of intra-cluster weights, the variance in the population firing rates causes the networks to switch between different states, each defined by a specific set of active clusters with higher firing rates
We have shown that multistability with moderate firing rates can be achieved in balanced networks with joint excitatory and inhibitory clusters
Summary
Neural responses in the mammalian neocortex are notoriously variable. Even when identical sensory stimuli are provided and animal behaviour is consistent across repetitions of experimental tasks, the neuronal responses look very different each time. In the more interesting intermediate range of intra-cluster weights, the variance in the population firing rates causes the networks to switch between different states, each defined by a specific set of active clusters with higher firing rates (winnerless competition) This results in a scenario where individual units exhibit multistability in their firing rates and as a result introduce variance in firing rates that increases the trial-to-trial variability to levels that match those observed in vivo. Selective stimulation of subsets of clusters causes certain attractors to become more stable, which in turn quenches the switching-dynamics, a mechanism that has been proposed as a potential model for working memory and perceptual bistability (Amit and Brunel 1997; Renart et al 2007) One problem with this family of models is that the active clusters tend to have firing rates close to saturation, where spike trains become very regular (clock-like). We use the mean field approach to analyse the attractors of clustered networks and show that the introduction of inhibitory clustering can moderate the firing rates of the active clusters and facilitate winnerless competition among clusters
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