Statistical Physics approach to dendritic computation: The excitable-wave mean-field approximation

Abstract

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a non-equilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5(6) e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

30 pages, 8 figures

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Cited by in corpus (7)

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• Single-Neuron Criticality Optimizes Analog Dendritic Computation
• Signal integration enhances the dynamic range in neuronal systems
• Diversity improves performance in excitable networks
• Scaling behaviour in probabilistic neuronal cellular automata
• Statistical physics of neural systems with non-additive dendritic coupling
• Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements