  In neural systems, synaptic plasticity is usually driven by spike trains. Due
to the inherent noises of neurons, synapses and networks, spike trains
typically exhibit externally uncontrollable variability such as spatial
heterogeneity and temporal stochasticity, resulting in variability of synapses,
which we call efficacy variability. Spike patterns with the same population
rate but inducing different efficacy variability may result in neuronal
networks with sharply different structures and functions. However, how the
variability of spike trains influences the efficacy variability remains
unclear. Here, we systematically study this influence when spike patterns
possess four aspects of statistical features, i.e. synchronous firing,
auto-temporal structure, heterogeneity of rates and heterogeneity of
cross-correlations, under spike-timing dependent plasticity (STDP) after
dynamically bounding the mean strength of plastic synapses into or out of a
neuron (synaptic homeostasis). We then show the functional importance of
efficacy variability on the encoding and maintenance of connection patterns and
on the early development of primary visual systems driven by retinal waves. We
anticipate our work brings a fresh perspective to the understanding of the
interaction between synaptic plasticity and dynamical spike patterns in
functional processes of neural systems.
