Ephaptic coupling between neurons: a systematic review of mathematical models

Ephaptic coupling is a relatively underexplored mechanism of neuronal interaction mediated by perturbations of the extracellular electric potential without the formation of conventional chemical or electrical synapses. Although the first theoretical accounts of ephaptic interactions appeared as early as the 1940s, computational approaches to this phenomenon have been actively developed only since the late 1990s and early 2000s, based on classical models of neuronal activity and cable theory. Both simplified phenomenological and biophysically detailed models have been developed. The former capture only essential features of large-scale neuronal dynamics and offer high computational efficiency, whereas the latter incorporate more complex characteristics, such as the properties of myelinated and unmyelinated fibers, the spatial distribution of nodes of Ranvier, axonal diameter heterogeneity, and the dynamics of extracellular ion concentrations. Recent studies highlight a growing interest in ephaptic interactions, particularly in their potential roles in neuronal synchronization, sensory coding, the propagation of epileptic seizures, and the development of neurodegenerative as well as demyelinating disorders. This work presents the systematic review dedicated to mathematical models of ephaptic coupling. The review aims to consolidate the diverse computational approaches used to study ephaptic coupling and to outline the main mechanisms of this phenomenon explored in modeling studies. The reviewed models were classified by type, tested hypotheses, and availability of open-source implementations. We surveyed nearly seventy mathematical models of ephaptic coupling. The review highlights how ephaptic interactions may contribute not only to normal brain function—such as synchronization and sensory processing—but also to pathological conditions, including epilepsy, demyelination, neuropathic pain, and neurodegeneration. By bringing together disparate studies, we aim to make the modeling of ephaptic coupling comprehensible to a broad scientific audience, including researchers with little prior experience in this area, stimulate further integration of computational and experimental approaches, and promote investigation of ephaptic mechanisms in both health and disease. This review serves both as a reference point for researchers developing new computational models and as a resource for those seeking to understand how ephaptic interactions may shape neuronal dynamics.