首页|STOCHASTIC MODELS OF NEURAL SYNAPTIC PLASTICITY: A SCALING APPROACH
STOCHASTIC MODELS OF NEURAL SYNAPTIC PLASTICITY: A SCALING APPROACH
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NSTL
Siam Publications
In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dy-namics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A spike-timing-dependent plasticity (STDP) rule is a biologically based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. A general mathematical framework has been introduced in [P. Robert and G. Vignoud, SIAM. J. Appl. Math., 81 (2021), pp. 1821-1846]. In this paper, we develop and investigate a scaling approach of these models based on several biological assumptions. Experiments show that long-term synaptic plasticity evolves on a much slower timescale than the cellular mechanisms driving the activity of neuronal cells, like their spiking activity or the concentration of various chemical compo-nents created/suppressed by this spiking activity. For this reason, a scaled version of the stochastic model of Robert and Vignoud [SIAM. J. Appl. Math., 81 (2021), pp. 1821--1846] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [P. Robert and G. Vignoud, J. Stat. Phys. 183 (2021), 47] is entirely devoted to the tightness properties used to prove these convergence results. These averaging principles are used to study two important STDP models: pair-based rules and calcium-based rules. Our results are compared with the approximations of neuroscience STDP models. A class of discrete models of STDP rules is also investigated for the analytical tractability of its limiting dynamical system.
NSTL
Siam Publications
