Synaptic plasticity in a stochastic model of neural networks

Abstract

In Galves and Loecherbach (2013), a new stochastic model for neural networks was introduced. It consists of a system comprising a countable set of interacting stochastic chains with memory of variable length. While simple enough to allow for a mathematical treatment, this model is rich enough to describe realistically neurobiological phenomena. However, at this point it presents the clear limitation of not accounting for synaptic plasticity. In mathematical terms, this means that the synaptic weights remain fixed instead of evolving as a result of neural activity, as is been observed experimentally. Extending the model in order to include these phenomena, and studying the resulting behaviour of the system, are the main aims of the present project.The neurobiological framework that embeds and at the same time motivates the project comes from one of the main open questions in neuroscience, i.e. how do neurons transmit information to each other. Synaptic plasticity, the capacity of synapses (the links between neurons) to change as a result of neural activity, seems to have a prominent role for this. This is why this plasticity will be considered, in particular in terms of spike-timing-dependent-plasticity (STDP), where the synaptic changes are determined by the precise times of neural spikes.Our project aims at tackling the aforementioned biological problem by adding the proposed extensions to the model introduced in Galves and Loecherbach (2013). This purpose will be carried out in close connection to available experimental results and the mathematical conceptual framework employed by the NeuroMat team.