Modelling the Effect of Gap Junction Nonlinearities in Systems of Coupled Cells

A general model for the transfer of ions and molecules between two cells via a gap junction is presented. This constitutes a dynamical system consisting of two connected parts: the dynamics of intracellular concentrations and electrical potentials, and the dynamics of the gating in the gap junction. The analysis focuses on a particular approximation in which the concentration changes are assumed negligible, so that the dynamics then describes the evolution of the potential differences across the cell membranes. This matches the conditions of voltage clamp experiments on Xenopus cell pairs. It is argued that the cell pair is unlikely to possess oscillatory behaviour; rather every initial state of the system evolves towards a stable steady state. It is shown that, in theory, coupled Xenopus cell pairs can demonstrate hysteretic behaviour for certain cell and junctional parameter ranges. The model fits data from recent electrophysiological experiments on Xenopus cell pairs. It is argued that cell pairs could operate under conditions in which hysteretic changes take place and we show that the hysteretic behaviour is more likely when the gap junction displays a residual conductance.