Cells coupled by voltage-dependent gap junctions: the asymptotic dynamical limit.
We study the steady state and dynamical properties of a pair of cells coupled by a voltage-dependent gap junction. The cells have linear membrane properties, and the gap junction is modelled using a simple Markov chain with a voltage-dependent transition matrix. We first show that the voltage-independent case is globally convergent using energy dissipation as a Lyapunov function for the cells, and standard results on the convergence of homogeneous Markov chains for the junction. For the voltage-dependent case, we use the difference in cell and gap junction time scales to reduce the coupled equations for cells and the gap junction to a single equation for the gap junction, but with a transition matrix that depends upon the current gap junction state. We identify cooperativity as key property behind the global convergence of Markov chains and investigate convergence of the voltage-dependent system by establishing some conditions under which cooperativity is preserved.
Baigent
Stephen
S
Centre for Non-linear Dynamics and Its Applications, University College London, Gower Street, London WC1E 6BT, UK. s.baigent@ucl.ac.uk
D002450:Cell Communication / Q000502:physiology*; D017629:Gap Junctions / Q000502:physiology*; D008390:Markov Chains