Mathematical Modeling and Computational Analysis of Cell and Tissue Movement

在多细胞生物体中，细胞运动在胚胎发育、血管生成、组织再生、免疫反应和伤口愈合等过程中起着至关重要的作用。运动是一个非常复杂的过程，涉及许多子过程的时空控制和整合，包括来自环境的化学或机械信号的转导，细胞内的生化反应，以及将细胞内和细胞外的信号转化为机械反应。突起的力量是由于单体肌动蛋白局部聚合成片状肌动蛋白细丝的交联网络或细丝或伪足中的细丝束所致。为了产生定向的细胞运动，肌动蛋白亚网络的相互作用和向底物的力传递必须在空间和时间上适当地整合。要理解所涉及的过程之间的相互作用，需要一个数学模型，将分子水平的行为与对所施加的力、细胞形状和细胞速度的宏观观察联系起来，但如何制定一个多尺度模型，将微观步骤整合到宏观模型中，在这种情况下理解得很少。这项研究将集中在一些更简单的问题上，这些问题将导致一个集成模型中的组件模块顺序。要解决的主要问题是(I)细胞前沿肌动蛋白网络的动态控制，(Ii)焦点黏附结构和寿命的作用的模型和分析，以及运动活动的水平和底物的黏附如何决定细胞速度，(Iii)分析简单系统的全细胞模型，以期了解不同组件之间的机械平衡如何产生肌动蛋白周转、运动活动和细胞形状的稳定稳定状态，以及在没有外界信号的情况下，这种稳定状态的扰动是否会导致极化和运动。细胞运动是大多数生物生命周期不同阶段的一个基本过程。多细胞生物体的早期发育涉及个体和集体细胞的运动，作为免疫反应的一部分，白细胞必须向感染部位迁移，而在癌症中，定向运动参与了侵袭和转移。这项研究涉及细胞骨架动力学的各个方面，这些动力学与肌动蛋白结合和细胞信号蛋白的反应网络的整合，以及调节细胞运动所涉及的细胞骨架结构的机械特性的相关控制机制。要理解所涉及的过程之间的相互作用，需要一个数学模型，将分子水平的行为与对所施加的力、细胞形状和细胞速度的宏观观察联系起来，但如何制定一个多尺度模型，将微观步骤整合到宏观模型中，在这种情况下理解得很少。开发这样的描述是我们研究工作的一个主要组成部分。

Cell locomotion plays an essential role during embryonic development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms. Movement is a very complex process that involves the spatial and temporal control and integration of a number of sub-processes, including the transduction of chemical or mechanical signals from the environment, intracellular biochemical responses, and translation of the intra- and extracellular signals into a mechanical response. The force for protrusion results from localized polymerization of monomeric actin into cross-linked networks of actin filaments in lamellipodia or bundles of filaments in filopdia or pseudopodia. In order to produce directed cell movement the interaction of the actin sub-networks and force transmission to the substrate must be properly integrated in space and time. Understanding the interplay between the processes involved requires a mathematical model that links molecular-level behavior with macroscopic observations on forces exerted, cell shape, and cell speed, but how to formulate a multiscale model that integrates the microscopic steps into a macroscopic model is poorly understood in this context. This study will focus on a number of simpler problems that will lead to the component modules in an integrated model sequentially. The major issues to be addressed are (i) the dynamic control of the actin network at the leading edge of a cell, (ii) models and analysis of the role of focal adhesion construction and lifetime, and how the level of motor activity and the adhesiveness of the substrate determines the cell speed, (iii) analysis of whole-cell models of simple systems with a view toward understanding how the mechanical balances between various components produces stable steady states of actin turnover, motor activity and cell shape, and whether perturbations of this steady state can lead to polarization and movement in the absence of external signals.Cell movement is an essential process at various stages in the life cycle of most organisms. Early development of multicellular organisms involves individual and collective cell movement, leukocytes must migrate toward sites of infection as part of the immune response, and in cancer directed movement is involved in invasion and metastasis. This research addresses various aspects of cytoskeleton dynamics, the integration of these dynamics with the reaction network of actin-binding and cell-signaling proteins, and the related control mechanisms regulating the mechanical properties of cytoskeletal structures involved in cell motility. Understanding the interplay between the processes involved requires a mathematical model that links molecular-level behavior with macroscopic observations on forces exerted, cell shape, and cell speed, but how to formulate a multiscale model that integrates the microscopic steps into a macroscopic model is poorly understood in this context. Developing such descriptions is a major component of our research effort.