Microscopic modelling of the non-linear gap junction channels

The usual way to model the propagation of the action potential through the cardiac tissue is to assume passive diffusive intracellular and extracellular domains, and ion channel dynamics on the cells' membrane. Gap junctions (GJ) are localised clusters of gap junction channels (GJCs) that connects electrically adjacent cells. The importance of GJCs and their modifications in the signal propagation has been demonstrated in the experimental studies (e.g. Beauchamp et al 2012). But, in the current mathematical models the behaviour of the GJCs is either neglected or assumed to be passive, i.e the conductance of GJCs is taken as a steady constant. On the other hand, the experimental results, obtained by the dual-voltage clamp technique, show that GJCs are time and voltage dependent. Here we focus on describing ventricular GJCs made of connexin Cx43 and Cx45. We use the Hodgkin-Huxley formalism to describe GJC conductance via one gating variable. We incorporate the non-linear GJC voltage dependence into the microscopic model of the tissue as a new boundary condition on specific parts of the cells' membranes.