Large neuronal networks: from structure to function, and back

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The long-term goal of our research program is to develop novel theoretical and computational methods that will help neuroscientists to decipher the intricate relationship between the structure and the function of nervous systems at different levels: cell, population, and system. To do so, we will target three specific projects and then apply the methods developed in each project to real neuronal systems. First, we propose to identify neurons and communities of neurons that are critical to specific functions of the whole network. Briefly, a neuron or a community is critical if its alteration produces dramatic changes in the global activity of the network and results in a loss of function. This first project is thus related to the impact of the structure on its function. Second, we aim to develop new methods that accurately detect causal interactions from activity data. For neuronal networks, causality is closely related to network structure since a neuron may influence another neuron only if the former is connected to the latter. We thus want to use the function of a neuronal network to predict its structure. Third, we will combine structure and function. Our goal is to develop new methods that predict the resilience of neuronal networks in which both the structure and the function constantly influence each other via synaptic plasticity. We will identify the critical characteristics of both structure (e.g., low reciprocity) and adaptation (e.g., fast synaptic potentiation) that make the whole network less vulnerable to perturbations (e.g., loss of connectivity, synaptic potentiation). To reach our goals, we will need to improve the current methods used for reducing the dimension of complex dynamical systems, which work well only for over-simplistic network structure (e.g., random connectivity) and neuronal dynamics with low biological foundation (e.g., leaky integrate-and-fire model). This is why several tools will be borrowed from statistical physics, nonlinear dynamics, and spectral analysis. Only neuron models with a clear biophysical interpretation, such as the HodgkinHuxley model, will be considered. At the end of the 5-year period, we will have a unique theoretical and computational framework that will allow to analyze the structure-function relation and to design targeted interventions aimed at restoring the good function of neuronal networks submitted to perturbations.