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Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells

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Abstract

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of \({\text {Ca}}^{2+}\) and \(\text {K}^+\) fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris–Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris–Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

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Acknowledgements

We thank Prof. Hinke M. Osinga (University of Auckland, New Zealand) for the support provided and useful discussion.

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  1. School of Fundamental Sciences, Massey University, Palmerston North, New Zealand

    H. O. Fatoyinbo, R. G. Brown, D. J. W. Simpson & B. van Brunt

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  1. H. O. Fatoyinbo
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Fatoyinbo, H.O., Brown, R.G., Simpson, D.J.W. et al. Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells. Bull Math Biol 82, 95 (2020). https://doi.org/10.1007/s11538-020-00771-6

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