论文标题
平滑肌细胞模型中的起搏器动力学的数值分叉分析
Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells
论文作者
论文摘要
实验研究的证据表明，由于电机耦合引起的振荡可以在平滑肌细胞中自发产生。这种细胞动力学被称为\ textit {Pacemaker Dynamics}。在本文中，我们解决了与$ \ text {ca}^{2+} $和$ \ text {k}^+$ fluxes在平滑肌细胞的细胞膜中的相互作用相关的Pacemaker动力学。首先，我们将起搏器模型减少到相当于莫里斯 - 莱卡模型的二维系统，然后对还原模型进行详细的数值分叉分析。 Morris-Lecar模型的现有分叉分析集中在外部应用电流上，而我们集中于对细胞对透壁压力变化的响应进行建模的参数。我们揭示了I型和II型兴奋性之间的过渡，而无需外部电流。我们还计算一个两参数分叉图，并显示如何通过分叉结构解释过渡。
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 \textit{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.
