Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada.
PLoS Comput Biol. 2012;8(12):e1002793. doi: 10.1371/journal.pcbi.1002793. Epub 2012 Dec 27.
Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction-diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a "free-boundary" problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.
真核细胞的运动涉及信号分子、细胞骨架、细胞膜和力学在空间和时间上的复杂相互作用。这些成分共同被细胞用来解释和响应外部刺激，导致极化、突起、黏附形成和肌球蛋白介导的收缩。当这些过程被正确编排时，就会产生形状变化和运动。大量的实验数据已经确定了许多参与这些过程的分子成分，但它们相互作用和空间组织的复杂性使得理解这一问题具有挑战性。这促使人们采用简化的细胞结构和行为的理论和计算方法，旨在更好地理解某些类型的细胞和/或行为组合。反应-扩散（RD）方程和粘弹性流动方程已被用于描述运动机制。在这篇综述中，我们描述了一些最近的细胞运动计算模型，重点是模拟细胞形状的变化（主要是在二维和三维）。这个问题不仅具有挑战性，因为抽象和简化生物复杂性具有难度，而且还因为在变形区域中计算 RD 或流体流动方程，这是应用数学中的一个极其具有挑战性的问题，称为“自由边界”问题。在这里，我们描述了不同的方法，比较了它们的优缺点，以及它们能够解决的生物学问题的类型。
