Monotone dynamics of two cells dynamically coupled by a voltage-dependent gap junction |
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Authors: | Peter Donnell Murad Banaji |
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Institution: | a Department of Medical Physics and Bioengineering, UCL, Gower Street, London WC1E 6BT, UK b Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK c Department of Biological Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK |
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Abstract: | 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 states. |
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Keywords: | Dynamic coupling Monotone dynamics Gap junction |
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