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The synaptic connectivity of cortical networks features an overrepresentationof certain wiring motifs compared to simple random-network models. Thisstructure is shaped, in part, by synaptic plasticity that promotes orsuppresses connections between neurons depending on their spiking activity.Frequently, theoretical studies focus on how feedforward inputs driveplasticity to create this network structure. We study the complementaryscenario of self-organized structure in a recurrent network, with spiketiming-dependent plasticity driven by spontaneous dynamics. We develop aself-consistent theory that describes the evolution of network structure bycombining fast spiking covariance with a fast-slow theory for synaptic weightdynamics. Through a finite-size expansion of network dynamics, we obtain alow-dimensional set of nonlinear differential equations for the evolution oftwo-synapse connectivity motifs. With this theory in hand, we explore how theform of the plasticity rule drives the evolution of microcircuits in corticalnetworks. When potentiation and depression are in approximate balance, synapticdynamics depend on the frequency of weighted divergent, convergent, and chainmotifs. For additive, Hebbian STDP, these motif interactions createinstabilities in synaptic dynamics that either promote or suppress the initialnetwork structure. Our work provides a consistent theoretical framework forstudying how spiking activity in recurrent networks interacts with synapticplasticity to determine network structure.

Self-organization of microcircuits in networks of neurons with plastic synapses