Monotone dynamics of two cells dynamically coupled by a voltage-dependent gap junction

Peter Donnell (1) , Stephen A. Baigent (2) , Murad Banaji (3)

1 Department of Medical Physics and Bioengineering
2 Department of Mathematics
3 Department of Biological Sciences

We introduce and analyse a simple model for two non-excitable cells that are dynamically coupled by a gap junction, a plaque of aqueous channels that electrically couple the cells. The gap junction channels have a low and high conductance state, and the transition rates between these states are voltage-dependent. We show that the number and stability of steady states of the system has a simple relationship with the determinant of the Jacobian matrix. For the case that channel opening rates decrease with increasing trans-junctional voltage, and closing rates increase with increasing trans-junctional voltage, we show that the system is monotone, with tridiagonal Jacobian matrix, and hence every initial condition evolves to a steady state, but that there may be multiple steady

Mots clés: Dynamic coupling; Monotone dynamics; Gap junction

Peter Donnell, Stephen A. Baigent, Murad Banaji. Monotone dynamics of two cells dynamically coupled by a voltage-dependent gap junction. Journal of Theoretical Biology, 2009, 261 (1), pp.120. ⟨10.1016/j.jtbi.2009.07.012⟩. ⟨hal-00554637⟩