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. Instead of taking into account three sites and beyond, we propose a novel excitable-wave mean-field approximation . Such approach is also a single-site approximation, but it manages to keep track of the excitable-wave direction of propagation. It shows good agreement with simulations  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.
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.
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Instead of taking into account three sites and beyond, we propose a novel
We propose an
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. Such approach is also a single-site approximation, but it manages to keep track of the excitable-wave direction of propagation. It
which
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simulations
previously published simulation results
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Gollo et al., PLoS Comput. Biol. 5(6) e1000402 (2009)