Continuum model of cell adhesion and migration
Continuum model of cell adhesion and migration
复制标题
DOI：
10.1007/s00285-008-0179-x
复制
发表时间：
2009-01-01
影响因子：
1.9
通讯作者：
Alt, Wolfgang
中科院分区：
文献类型：
--
作者：
Kuusela, Esa;Alt, Wolfgang
细胞在基质上爬行的运动起源于一种叫做薄片的薄细胞器官。我们提出了一个二维连续体模型板层动力学缓慢迁移的细胞，如人类角质形成细胞。该模型的核心组成部分是能够产生收缩和膨胀应力的粘性细胞骨架的动力学，以及质细胞膜上细胞骨架片和基质粘附位点之间的粘附键的形成。我们将展示一个简单的机制模型，忽略活细胞复杂的信号通路和调节过程，能够捕捉到片层动力学的最突出方面，如移动尖端的准周期性突起和收缩，细胞骨架的逆行流动以及迁移细胞前沿的黏附复合物的相关积累。所建立的模型框架由不同分子浓度的双曲方程、抛物方程和常微分方程组成的非线性耦合系统，以及高粘性两相流中细胞骨架速度和动水压力的两个椭圆方程组成，并在运动边界处设置适当的等式和不等式。为了对这种混合连续体模型进行数值模拟分析，我们在固定三角网上采用合适的有限元和有限体积格式，并结合自适应水平集方法描述自由边界动力学。
The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.