Neural Comput - Stability against fluctuations: scaling, bifurcations, and spontaneous symmetry breaking in stochastic models of synaptic plasticity.

Tópicos

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Resumo

In stochastic models of synaptic plasticity based on a random walk, the control of fluctuations is imperative. We have argued that synapses could act as low-pass filters, filtering plasticity induction steps before expressing a step change in synaptic strength. Earlier work showed, in simulation, that such a synaptic filter tames fluctuations very well, leading to patterns of synaptic connectivity that are stable for long periods of time. Here, we approach this problem analytically. We explicitly calculate the lifetime of meta-stable states of synaptic connectivity using a Fokker-Planck formalism in order to understand the dependence of this lifetime on both the plasticity step size and the filtering mechanism. We find that our analytical results agree very well with simulation results, despite having to make two approximations. Our analysis reveals, however, a deeper significance to the filtering mechanism and the plasticity step size. We show that a filter scales the step size into a smaller, effective step size. This scaling suggests that the step size may itself play the role of a temperature parameter, so that a filter cools the dynamics, thereby reducing the influence of fluctuations. Using the master equation, we explicitly demonstrate a bifurcation at a critical step size, confirming this interpretation. At this critical point, spontaneous symmetry breaking occurs in the class of stochastic models of synaptic plasticity that we consider.

Resumo Limpo

stochast model synapt plastic base random walk control fluctuat imper argu synaps act lowpass filter filter plastic induct step express step chang synapt strength earlier work show simul synapt filter tame fluctuat well lead pattern synapt connect stabl long period time approach problem analyt explicit calcul lifetim metast state synapt connect use fokkerplanck formal order understand depend lifetim plastic step size filter mechan find analyt result agre well simul result despit make two approxim analysi reveal howev deeper signific filter mechan plastic step size show filter scale step size smaller effect step size scale suggest step size may play role temperatur paramet filter cool dynam therebi reduc influenc fluctuat use master equat explicit demonstr bifurc critic step size confirm interpret critic point spontan symmetri break occur class stochast model synapt plastic consid

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