Diffusion-mediated nonlinear coupling drives ephaptic synchronization and Cross-Frequency Coordination

Action-potential synchronization mediated by ephaptic interactions poses a fundamental biophysical challenge: extracellular ionic fluctuations from a single spike are generally considered too small to significantly influence neighboring neurons. However, experimental evidence demonstrates that transient changes in extracellular ion concentrations can modulate adjacent cell excitability and promote mutual synchronization. To reconcile this discrepancy, we propose that extracellular ion diffusion functions as a nonlinear coupling term between excitable cells possessing limit-cycle dynamics. We demonstrate that even minute extracellular perturbations are amplified by the intrinsic nonlinear dynamics of the membrane potential governing voltage-gated ion channels. Within this framework, ephaptic synchronization enhances the reliability of neuronal firing and supports robust signal propagation. Furthermore, these interactions facilitate cross-frequency synchronization, where neurons with distinct intrinsic firing rates achieve coordination while maintaining stable phase offsets. Beyond temporal alignment, synchronized firing increases action-potential amplitude, potentially strengthening synaptic efficacy. At the network level, global synchronization induced by ephaptic coupling operates as a functional gate for external inputs, where weak stimuli are suppressed and sufficiently strong inputs are permitted to propagate. Notably, these complex behaviors emerge from a minimal framework governed by a single diffusion-mediated coupling constant, drawing a direct parallel to the large-scale synchronization principles observed in Dictyostelium discoideum .