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

点击翻译按钮获取中文摘要

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.