Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.
Department of Neuroscience, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America; Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America.
Gabriel Koch
GK
Ocker
Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America; Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America; Center for Theoretical Neuroscience, Columbia University, New York, New York, United States of America.
Ashok
A
Litwin-Kumar
Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America; Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America.
Brent
B
Doiron
D000200:Action Potentials; D019295:Computational Biology; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009473:Neuronal Plasticity / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology*