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Communication Dans Un Congrès Année : 2016

Phase transition approach to bursting in neuronal cultures: quorum percolation models

Résumé

The Quorum Percolation model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of statistical physics rather than from a dynamical synchronization approach. It is based upon information propagation on a directed graph with a threshold activation rule; this leads to a phase diagram which exhibits a giant percolation cluster below some critical value mC of the excitability. We describe the main characteristics of the original model and derive extensions according to additional relevant biological features. Firstly, we investigate the effects of an excitability variability on the phase diagram and show that the percolation transition can be destroyed by a sufficient amount of such a disorder; we stress the weakly averaging character of the order parameter and show that connectivity and excitability can be seen as two overlapping aspects of the same reality. Secondly, we elaborate a discrete time stochastic model taking into account the decay originating from ionic leakage through the membrane of neurons and synaptic depression; we give evidence that the decay softens and shifts the transition, and conjecture than decay destroys the transition in the thermodynamical limit. We were able to develop mean-field theories associated with each of the two effects; we discuss the framework of their agreement with Monte Carlo simulations. It turns out that the the critical point mC from which information on the connectivity of the network can be inferred is affected by each of these additional effects. Lastly, we show how dynamical simulations of bursts with an adaptive exponential integrate-and-fire model can be interpreted in terms of Quorum Percolation. Moreover, the usefulness of the percolation model including the set of sophistication we investigated can be extended to many scientific fields involving information propagation, such as the spread of rumors in sociology, ethology, ecology.
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hal-01483960 , version 1 (06-03-2017)

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  • HAL Id : hal-01483960 , version 1

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Pascal Monceau, Stéphane Métens, Samuel Bottani, Tanguy Fardet. Phase transition approach to bursting in neuronal cultures: quorum percolation models. CCP2016 28th IUPAP Conference on Computational Physics, Jul 2016, PRETORIA, South Africa. ⟨hal-01483960⟩
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