Synchronicity transitions determine coupling fluctuations in a model of coupled oscillators with plasticity

Sleep and rest are crucial to knowledge abstraction and creativity. During these periods, synapses undergo plastic modification, while neuronal activities are collectively synchronized, accompanied by large shifts in the excitation-inhibition (EI) balance. These phenomena differ from the learning processes that occur during task engagement. However, the detailed mechanism by which synchronized neuronal activity reshapes neural circuits through plasticity remains unclear. The Kuramoto model is used to study the collective synchronization of oscillators, including neurons. We previously proposed the EI-Kuramoto model, in which an EI balance was implemented in the Kuramoto model. The model alters its synchronicity based on the EI balance of the interaction strength. In this study, we further developed the EI-Kuramoto model by implementing Hebbian and homeostatic plasticity, leading to a plastic EI-Kuramoto model. Models with robust inhibition consistently showed desynchronization and stable coupling. Contrastingly, weaker inhibition produced a bistable synchronization state, in which couplings with intermediate strengths fluctuated, while strong couplings remained stable. Our findings suggest that the dynamic interplay between network activity and plasticity explains why stronger synapses in the brain exhibit greater stability than their weaker counterparts. Moreover, this mechanism facilitated network reorganization during sleep and rest. Significance StatementThe reorganization of neuronal circuits during sleep and rest is essential for knowledge abstraction and creativity. These states involve synaptic plasticity and collective neuronal synchronization, accompanied by significant shifts in the excitation-inhibition (EI) balance. However, the precise mechanism through which synchronized activity reshapes neural circuits via plasticity remains unclear. We developed a novel computational model, the plastic EI-Kuramoto model, which incorporates both coupling plasticity and EI balance. Our model demonstrates that robust inhibition leads to desynchronization and stable coupling. In contrast, weaker inhibition induces bistable synchronization, in which the intermediate-strength couplings fluctuate, whereas strong couplings remain stable. These findings provide a fundamental mechanism for network reorganization during sleep and rest.