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

细胞骨架及其主要的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，我的团队已经模拟了肌动蛋白周转如何有助于细胞的运动性，以及信号传导成分（Rho家族GTP酶Cdc 42，Rac，Rho和磷酸肌醇PIP，PIP 2，PIP 3）如何调节肌动蛋白动力学。响应于分级刺激，我们的“模型细胞”产生稳定的GTP酶和PI的内部谱，并启动持续的运动，与生物学一致。(We显示GTP酶作为空间开关工作，PI过滤噪声，并定义前面与后面。相对快速的PI扩散还导致从可能的模式的集合中选择Rho GTdR分布的独特模式。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，PI和其他上游组件（2）对敲除/突变体进行进一步的计算机测试（3）添加微管与肌动蛋白，Rac和Rho的串扰，（4）在模拟复杂的粘弹性固体细胞骨架中包括肌球蛋白收缩性，被流体胞质溶胶渗透。(5)改进或重铸2D模型，以更准确地捕获力平衡，（例如，浸入边界法，具有新PDF，Mori）（5）分析Rho GTdash模块中发现的驻波和行波模式的有趣数学行为。（1-5）的意义是更好地理解正常和突变细胞的细胞运动性。在社会聚集方面，我们分析了拉格朗日模型中“完美学校”（一系列相互作用的个体以恒定的速度和相对位置移动）的存在和稳定性条件。 模拟将被用来补充和扩展我们的分析，太难的情况下，在封闭的形式进行分析。

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.