The role of gap junctions and clustered connectivity in emergent synchronisation patterns of spiking inhibitory neuronal networks

Interneurons, ubiquitous in the central nervous system, form networks connected through both inhibitory chemical synapses and gap junctions. These networks are essential for regulating neuronal activity notably by regulating temporally patterned dynamic states. We aim to understand the mechanisms that allow for synchronization to arise in networks of interneurons with both chemical synapses and electrical gap junctions (Panel 1). To this end, we use the exact mean-field reduction, often referred to as the “neural mass model” in the literature (Montbrio et al, PRX, 2015). We first analyse a single population of neurons connected through gap junctions and inhibitory synapses in order to understand how the two couplings interact with one another. We determine that the network transitions from an asynchronous to a synchronous regime either by increasing the strength of the gap junction connectivity (Panel 1a) or injecting a transient input current (Panel 1b,c). Furthermore, the strength of inhibitory synapses does not affect the bifurcation, however it does affect the population firing rate (Panel 1a). Additionally, an interesting aspect of electrical coupling is the emergence of spikelets (Hoehne et al, eLife, 2020); we therefore analysed the effect of spikelet depolarisation on the network, and found that the higher the heterogeneity in the system, the more important the role of the spikelet in increasing the network's coherence. Inspired by molecular layer interneuron classification in the cerebellum (Kim & Augustine, Neuroscience, 2021), we then analyse the behaviours that arise by connecting two neural clusters through inhibitory synapses (Panel 2). We find the emergence of distinct and complex behaviours between the two clusters. In particular, we show that breaking the electrical and chemical coupling symmetry between the two clusters induces bistability (Panel 2a,b), in which a brief transient input can allow for a switch between synchronous and asynchronous firing (Panel 2c). Finally, a numerical bifurcation analysis confirms the existence of numerous dynamical regimes in the clustered network case. Our work explores how electrical coupling, strength of inhibition and the structure of clusters play in unison to provide insights onto the mechanisms leading to complex synchronisation dynamics.