Several authors have proposed a direct interference between the extracellular membrane layers of two adjacent cells as a so-called "electrical field effect" (ephaptic coupling) or due to local changes of ionic concentrations. Up to now, experimental methods hardly allow to analyze in vivo what happens inside the cleft space of the intercalated disks (ID), so a theoretical approach is required.

Methods: 

First, we performed a high resolution simulation of electrodiffusion in the intercellular cleft in order to get insights into local changes of ionic concentrations. We used a spatial resolution of 0.25nm and a temporal stepsize of 0.02ns for solving Poisson-Nernst-Planck equations dynamically. We evaluated our results by comparing steady state values with analytical solutions of the static case. Second, we used the obtained results and incorporated them into a 3D cell model taking into account subtle geometrical inhomogeneities, such as discrete connexin distribution. Transmembrane currents where calculated according to the Hodgkin-Huxley kinetics. We varied cleft widths (2 to 20nm), distribution of GJ and Na⁺ channels, GJ conductance (g_GJ, 1nS to 500nS) and investigated the effects on conduction velocity (CV).

Results: 

First, we analyzed a control simulation similar to conventional cell models finding disagreements with experimental measurements of g_GJ: when using 50–100nS, which are common values, we obtained too low CV (<25cm/s). When increasing g_GJ up to 500nS, CV reached normal values (40–50cm/s). Simulations showed local increases of Na⁺ when the cleft width was smaller than 4nm leading to a strong driving force for the fast Na⁺ current with an increased overshoot potential (60–80mV) and increased CV. We could show that a higher density of Na⁺ channels at the ID and the presence of GJ clusters enhanced this effect resulting in normal CV together with normal values of g_GJ. Distributing GJs randomly slowed CV. Second, we investigated the proposed modes of ephaptic coupling. We could not find an electrical field effect because the membranes surface charge was insulated by counter ions within microseconds. It was not possible to obtain AP propagation when g_GJ was set to zero. Finally, we simulated the K⁺ accumulation in the cleft, which lead to a slight depolarization of the adjacent membrane, but could not facilitate fast AP propagation.

Conclusion: 

There seems to be low evidence for an electrical field effect. Yet, we could show that local increases of Na⁺ together with the clustered arrangement of GJ and Na⁺ channels facilitate the maintenance of AP propagation. By incorporating these geometrical inhomogeneities, we could reproduce realistic CV together with realistic g_GJ, indicating their importance for maintaing high CV. This could explain observed alterations of CV when cell geometry is changed, e.g. in heart failure.