Mathematical models of actin in cell motility and of swarms/schools in social aggregation

细胞骨架及其主要生物聚合物肌动蛋白负责动物细胞的形状、运动和许多方面的功能。近年来，我的团队模拟了肌动蛋白周转如何促进突起细胞运动，以及信号组件(Rho家族GTP酶CDc42、Rac、Rho和肌醇磷脂PIP、PIP2、PIP3)如何调节肌动蛋白动力学。作为对分级刺激的反应，我们的“模型细胞”产生稳定的GTP酶和PI的内部轮廓，并启动与生物学一致的持续运动。(我们证明了GTP酶作为空间开关发挥作用，PI过滤噪声，并定义前后。相对快速的PI扩散还导致从一组可能的模式中选择Rho GTP酶分布的唯一模式)。我们还组装了爬行细胞的初步2D模拟。我建议通过以下方式继续这项研究：(1)更新当前的2D模型，以包括细胞表面受体结合、Pis和其他上游组件(2)进一步进行基因敲除/突变的计算机测试(3)添加与肌动蛋白、RAC和Rho的微管串扰，(4)在模拟复杂的粘弹性固体细胞骨架时包括肌球蛋白收缩性能，这些细胞骨架由液体胞浆相互渗透。(5)改进或重铸2D模型以更准确地捕捉力平衡(例如，沉浸边界法，带有新的PDF，Mori)(5)分析Rho GTPase模块中发现的驻波和行波模式的有趣的数学行为。(1-5)的意义是更好地理解正常细胞和突变细胞中的细胞运动性。在社会聚集上，我们解析地探索拉格朗日模型中存在和稳定“完美学派”的条件(一组以恒定速度和相对位置移动的相互作用的个体)。我们的模拟将被用来补充和扩展我们的理论分析到那些太难以封闭形式分析的案例。

The cytoskeleton, and its major biopolymer, actin are responsible for the shape, motility, and many aspects of animal cell function.  In recent years, my group has modelled how actin turnover contributes to protrusive cell motility, and how signalling components (Rho family GTPases Cdc42, Rac, Rho, and phosphoinositides PIP, PIP2, PIP3), regulate actin dynamics. In response to a graded stimulus, our "model cell" produces stable internal profiles of GTPases and PIs, and initiates persistent motility, consistent with the biology. (We showed that GTPases work as a spatial switch, PIs filter noise, and define the front vs. back. Relatively fast PI diffusion also leads to selection of a unique pattern of Rho GTPase distribution from a collection of possible patterns). We also assembled  preliminary 2D simulations of a crawling cell.  I propose to continue this research by (1) updating the current 2D model to include cell-surface receptor binding,  PIs and other upstream components (2) conducting further in silico tests on knockouts/mutants (3) adding microtubule crosstalk with actin, Rac and Rho, (4) including myosin contractility in simulations of complex visco-elastic solid cytoskeleton, interpenetrated by fluid cytosol. (5) improving or recasting the 2D model to capture force balance more accurately, (e.g. immersed boundary method, with new PDF, Mori) (5) analyzing  interesting math behaviour of standing and travelling wave patterns found in the Rho GTPase module. Significance of (1-5) is a better understanding of cell motility in normal and mutant cells.On social aggregation we analytically explore conditions for the existence and stability of a "perfect school"  (an array of interacting individuals moving with constant speed and relative positions) in Lagrangian models.  Simulations will be used to complement and extend our  analysis to cases that are too difficult to analyze in closed form.