Winnerless competition in clustered balanced networks: inhibitory assemblies do the trick

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.

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“…Recent anatomical and physiological studies point to increased local inhibitory connectivity and possible inhibitory clustering through connection strengths (Xue et al, 2014;Lee et al, 2014;Morishima et al, 2017;Khan et al, 2018;Znamenskiy et al, 2018;Shin et al, 2019;Najafi et al, 2020). We therefore combine excitatory and inhibitory clustering as we proposed previously for binary networks (Rost et al, 2017) (Fig. 1c top panel).…”

“…However, this type of model has unrealistic spiking irregularity and excessive spike rates during cluster activation and exhibits biologically plausible multistability (winnerless competition) only in a narrow parameter regime (see Fig. 2 and discussion of (Litwin-Kumar & Doiron, 2012;Deco & Hugues, 2012); also (Rost et al, 2017)).…”

“…7a). As in the binary network (Rost et al, 2017), we choose g = 1.2, where χ = 0.02 ∼ 1/ √ N and CV 2 = 0.73 (Fig. 7b).…”

“…E and E/I clustered networks We follow the same connectivity scheme that we introduced for binary networks in our previous work (see (Rost et al, 2017) for a detailed explanation). Briefly, for the E clustered networks, we first divide the excitatory population into Q equally sized clusters with uniform connection probability.…”

“…Then we require that each excitatory cluster selectively influences its corresponding inhibitory cluster and vice versa by increasing the corresponding EI, IE and II weights. We have shown in (Rost et al, 2017) that the inhibitory clustering needs to be weaker than the excitatory clustering to obtain realistic firing rates. Therefore we introduce separate excitatory and inhibitory clustering strengths, J E+ and J E− .…”