How plasticity shapes the formation of neuronal assemblies driven by oscillatory and stochastic inputs

Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Previous theoretical work has studied how such Hebbian plasticity rules shape network connectivity when firing rates are constant, or slowly varying in time. However, oscillations and fluctuations, which can arise through sensory inputs or intrinsic brain mechanisms, are ubiquitous in neuronal circuits. Here we study how oscillatory and fluctuating inputs shape recurrent network connectivity given a temporally asymmetric plasticity rule. We do this analytically using a separation of time scales approach for pairs of neurons, and then show that the analysis can be extended to understand the structure in large networks. In the case of oscillatory inputs, the resulting network structure is strongly affected by the phase relationship between drive to different neurons. In large networks, distributed phases tend to lead to hierarchical clustering. The analysis for stochastic inputs reveals a rich phase plane in which there is multistability between different possible connectivity motifs. Our results may be of relevance for understanding the effect of sensory-driven inputs, which are by nature time-varying, on synaptic plasticity, and hence on learning and memory.