Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, BC, Canada.
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK.
J Math Biol. 2021 Mar 4;82(4):28. doi: 10.1007/s00285-021-01550-0.
The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.
真核细胞的极化和运动取决于肌动蛋白细胞骨架的组装和收缩，以及其调节蛋白 GTP 酶的作用。GTP 酶的活性导致丝状肌动蛋白的组装（由 GTP 酶 Cdc42、Rac 引起），从而导致细胞边缘的突出。用于 GTP 酶动力学的数学模型解决了此类蛋白质在细胞中自发形成模式和非均匀空间分布的问题。在这里，我们重新审视了 GTP 酶诱导的细胞极化的波钉模型，以及文献中提出的一些扩展。这些扩展包括引入活性和非活性 GTP 酶的源和汇（由 A. Champneys 小组提出），以及 F-肌动蛋白对 GTP 酶活性的负反馈。我们单独和组合地在 1D 和 2D 静态域中讨论了这些扩展。然后，我们展示了形成的模式（斑点、波和螺旋）如何与细胞边界相互作用，以创建各种有趣和动态的细胞形状和运动。
