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Towards a neural field theory for spiking neuron networks with electrical synapses

Project description

Pioneering insight into the role of electrical synapses

Electrical synapses were first identified more than six decades ago in the crayfish nervous system. They transmit neuronal signals via ionic currents that pass directly from the cytoplasm of one neuron to the next through intercellular channels. Their importance in the mammalian nervous system has only recently been recognised, and their incorporation into current mathematical models of spiking neural networks based on conventional chemical synapses has been challenging. With the support of the Marie Skłodowska-Curie Actions programme, the NeuralFieldTheoriES project is developing the mathematics required to describe these junctions. Simulations incorporating them for the first time promise to reveal their unique role in the complex spiking patterns that underlie behaviour and cognition.


A major challenge in statistical physics, nonlinear dynamics and theoretical neuroscience over the last half century has been to understand the self-organizing principles governing the dynamics of large networks of neurons. Physicists and applied mathematicians have proposed simple mean-field descriptions of spatially-extended neural networks in terms of a relevant macroscopic observable, the firing rate. This approach has been particularly successful and so-called Neural Field Models (NFM) have become an extremely popular mathematical tool in neuroscience, physics and applied mathematics. Yet, to date, mean-field theories describe networks with chemical synapses, but it remains a major theoretical challenge to incorporate electrical synaptic interactions in such mathematical descriptions. Recently, a mean-field theory for large networks of spiking neurons has been proposed, which exactly links the dynamics of single neurons with that of two mean-field variables: The firing rate and the mean membrane potential. Remarkably, this theory permits to incorporate electrical interactions, but the mathematical derivation and the analysis of the dynamics of the first NFM is lagging. This project proposes the formal mathematical derivation of such NFM, as well as the thorough analysis of its dynamics and bifurcations. Towards this goal, at the host institution UPF in Barcelona, the ER will apply mean-field methods and nonlinear dynamical systems theory to derive the novel NFM (which we conjecture is of reaction-diffusion type). During a secondment at VU Amsterdam, the ER will be trained to become an expert in numerical analysis of partial differential equations, which will further allow him to perform extensive state-of-the-art computer simulations. The expected results will provide completely novel mechanistic insights on the emergence of complex spatio-temporal patterns of neuronal activity due to the intricate interplay between chemical and electrical synapses.



Net EU contribution
€ 160 932,48
Placa de la merce, 10-12
08002 Barcelona

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Este Cataluña Barcelona
Activity type
Higher or Secondary Education Establishments
Other funding
€ 0,00