Multilayer Network Regulation of Critical Neuronal Dynamics

Abstract.  The cortex operates in a regime where the overall strength of excitatory and inhibitory synapses is precisely balanced, and it has been hypothesized that this regime corresponds to the critical point of a phase transition. At the same time, neuronal networks are highly adaptive, with the strength of synapses changing over time to allow the network to learn. This poses the question of how can these neuronal networks deal with the opposing needs of maintaining the balance between excitatory and inhibitory synapses, and constantly adjusting these strengths in response to learning. In this talk I will describe a model in which the activity of the neuronal network is regulated by transport of resources across a secondary network of glial neurons. For a large range of parameter models, the interaction between the two networks results in self-organization of the neural network to the critical point. The operation of the neural network at this critical point continues even after completing a learning task. While operating at the critical point, the neural networks produces power-law distributed avalanches of activity as observed in experiments. Furthermore, the secondary glial network protects the system against the destabilizing effect of heterogeneities in parameters. A simplified model can be analyzed in terms of a 3-dimensional map which gives insight into the robustness of these results to the choice of model parameters.