Mathematical Modeling and Computational Analysis of Cell and Tissue Movement

细胞运动在多细胞生物体的胚胎发育、血管生成、组织再生、免疫应答和伤口愈合过程中起着重要作用。 运动是一个非常复杂的过程，涉及空间和时间的控制和许多子过程的整合，包括来自环境的化学或机械信号的转导，细胞内生化反应，以及将细胞内和细胞外信号转化为机械反应。 突起的力来自于单体肌动蛋白局部聚合成片状伪足中肌动蛋白丝的交联网络或丝状伪足或伪足中的成束细丝。 为了产生定向的细胞运动，肌动蛋白子网络的相互作用和力传递到基底必须在空间和时间上适当地整合。 理解所涉及的过程之间的相互作用需要一个数学模型，该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，但是如何制定将微观步骤整合到宏观模型中的多尺度模型在这种情况下知之甚少。 这项研究将集中在一些简单的问题，将导致组件模块在一个综合模型顺序。 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）粘着斑结构和寿命的作用的模型和分析，以及运动活动水平和底物的粘附如何决定细胞速度，（iii）分析简单系统的全细胞模型，以了解各种组分之间的机械平衡如何产生肌动蛋白周转的稳定稳态，运动活动和细胞形状，以及在没有外部信号的情况下，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体生命周期各个阶段的重要过程。 多细胞生物体的早期发育涉及个体和集体细胞运动，白细胞必须向感染部位迁移作为免疫应答的一部分，并且在癌症中定向运动涉及侵袭和转移。 本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，以及调节细胞运动中所涉及的细胞骨架结构的机械特性的相关控制机制。 理解所涉及的过程之间的相互作用需要一个数学模型，该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，但是如何制定将微观步骤整合到宏观模型中的多尺度模型在这种情况下知之甚少。 发展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.