Recent experimental studies showed that electrically coupled neural networks like in mammalian inferior olive nucleus generate synchronized rhythmic activity by the subthreshold sinusoidal-like oscillations of the membrane voltage. Understanding the basic mechanism and its implication of such phenomena in the nervous system bears fundamental importance and requires preemptively the connectome information of a given nervous system. Inspired by these necessities of developing a theoretical and computational model to this end and, however, in the absence of connectome information for the inferior olive nucleus, here we investigated interference phenomena of the subthreshold oscillations in the reference system Caenorhabditis elegans for which the structural anatomical connectome was completely known recently. We evaluated how strongly the sinusoidal wave was transmitted between arbitrary two cells in the model network. The region of cell-pairs that are good at transmitting waves changed according to the wavenumber of the wave, for which we named a wavenumber-dependent transmission map. Also, we unraveled that (1) the transmission of all cell-pairs disappeared beyond a threshold wavenumber, (2) long distance and regular patterned transmission existed in the body-wall muscles part of the model network, and (3) major hub cell-pairs of the transmission were identified for many wavenumber conditions. A theoretical and computational model presented in this study provided fundamental insight for understanding how the multi-path constructive/destructive interference of the subthreshold oscillations propagating on electrically coupled neural networks could generate wavenumber-dependent synchronized rhythmic activity.

Developmental and epileptic encephalopathies (DEEs), a class of devastating neurological disorders characterized by recurrent seizures and exacerbated by disruptions to excitatory/inhibitory balance in the brain, are commonly caused by mutations in ion channels. Disruption of, or variants in, FGF13 were implicated as causal for a set of DEEs, but the underlying mechanisms were clouded because FGF13 is expressed in both excitatory and inhibitory neurons, FGF13 undergoes extensive alternative splicing producing multiple isoforms with distinct functions, and the overall roles of FGF13 in neurons are incompletely cataloged. To overcome these challenges, we generated a set of novel cell-type-specific conditional knockout mice. Interneuron-targeted deletion of Fgf13 led to perinatal mortality associated with extensive seizures and impaired the hippocampal inhibitory/excitatory balance while excitatory neuron-targeted deletion of Fgf13 caused no detectable seizures and no survival deficits. While best studied as a voltage-gated sodium channel (Na_v) regulator, we observed no effect of Fgf13 ablation in interneurons on Na_vs but rather a marked reduction in K⁺ channel currents. Re-expressing different Fgf13 splice isoforms could partially rescue deficits in interneuron excitability and restore K⁺ channel current amplitude. These results enhance our understanding of the molecular mechanisms that drive the pathogenesis of Fgf13-related seizures and expand our understanding of FGF13 functions in different neuron subsets.