Synchronization of electrically coupled resonate-and-fire neurons

TL;DR

This paper investigates how electrical coupling and intrinsic resonant properties of neurons influence synchronization, revealing that both spike-mediated and subthreshold interactions can promote or oppose synchrony depending on network conditions.

Contribution

It extends the theory of weakly coupled oscillators to include resonant subthreshold effects and introduces a novel analysis of reset-induced shear impacting synchrony.

Findings

Both spikes and subthreshold fluctuations promote synchronization.

Resonant subthreshold activity is most influential with post-spike voltage elevation.

Reset-induced shear can oppose synchrony in asymmetric networks.

Abstract

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.