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Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity
Coarse-graining microscopic models of biological neural networks to obtain
mesoscopic models of neural activities is an essential step towards multi-scale
models of the brain. Here, we extend a recent theory for mesoscopic population
dynamics with static synapses to the case of dynamic synapses exhibiting
short-term plasticity (STP). Under the assumption that spike arrivals at
synapses have Poisson statistics, we derive analytically stochastic mean-field
dynamics for the effective synaptic coupling between finite-size populations
undergoing Tsodyks-Markram STP. The novel mean-field equations account for both
finite number of synapses and correlations between the neurotransmitter release
probability and the fraction of available synaptic resources. Comparisons with
Monte Carlo simulations of the microscopic model show that in both feedforward
and recurrent networks the mesoscopic mean-field model accurately reproduces
stochastic realizations of the total synaptic input into a postsynaptic neuron
and accounts for stochastic switches between Up and Down states as well as for
population spikes. The extended mesoscopic population theory of spiking neural
networks with STP may be useful for a systematic reduction of detailed
biophysical models of cortical microcircuits to efficient and mathematically
tractable mean-field models