平滑肌细胞模型中起搏器动力学的数值分岔分析
Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells
AI总结：
针对平滑肌细胞的起搏器动力学问题，将相关模型简化为等价于简化Morris-Lecar模型的二维系统，聚焦跨壁压响应参数开展数值分岔分析，揭示了无外加电流时I型与II型兴奋性的转变及分岔机制。
摘要：
实验研究证据表明，平滑肌细胞内可自发产生由机电耦合引发的振荡，这类细胞动力学被称为起搏器动力学。本文研究了平滑肌细胞膜上钙离子（$\text{Ca}^{2+}$）与钾离子（$\text{K}^+$）通量相互作用相关的起搏器动力学。首先，我们将一个起搏器模型简化为等价于简化Morris-Lecar模型的二维系统，随后对该简化模型开展详细的数值分岔分析。现有Morris-Lecar模型的分岔分析多聚焦于外加电流，而我们关注的是表征细胞对跨壁压变化响应的参数。研究揭示了无需外加电流即可发生的I型与II型兴奋性之间的转变，还计算了双参数分岔图，阐明了分岔结构如何解释这一转变过程。
英文摘要：
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.
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