Ephaptic coupling of cardiac cells through the junctional electric potential

Cardiac cells are electrically coupled through gap junction channels, which allow ionic current to spread intercellularly from one cell to the next. In addition, it is possible that cardiac cells are coupled through the electric potential in the junctional cleft space between neighboring cells. We develop and analyze a mathematical model of two cells coupled through a common junctional cleft potential. Consistent with more detailed models, we find that the coupling mechanism is highly parameter dependent. Analysis of our model reveals that there are two time scales involved, and the dynamics of the slow subsystem provide new mathematical insight into how the coupling mechanism works. We find that there are two distinct types of propagation failure and we are able to characterize parameter space into regions of propagation success and the two different types of propagation failure.