Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell.
Mathematical modelling and numerical simulations of actin dynamics in the eukaryotic cell.
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真核细胞肌动蛋白动力学的数学建模和数值模拟。
DOI：
10.1007/s00285-012-0521-1
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发表时间：
2013
影响因子：
1.9
通讯作者：
George UZ
中科院分区：
文献类型：
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作者：
George UZ
本文的目的是研究细胞变形和细胞运动，同时考虑到肌动蛋白丝及其浓度的皮质网络的机械和生物化学性质。肌动蛋白是可以以丝状形式（F-肌动蛋白）或以单体形式（G-肌动蛋白）存在的聚合物（Chen et al. in Trends Biochem Sci 25：19-23，2000），并且丝状形式以两个原丝的成对螺旋排列（Ananthakrishnan et al.在Recent Res Devel Biophys 5：39-69，2006中）。通过假设细胞变形是细胞骨架中皮质肌动蛋白动力学的结果，我们考虑了一个连续体数学模型，该模型将肌动蛋白丝网络的力学与其生化动力学耦合起来。采用移动网格有限元法（Madzvamuse et al. J Comput Phys 190：478-500，2003）。此外，通过假设细胞的缓慢变形，我们使用线性稳定性理论来验证数值模拟结果接近分叉点。远离分叉点，我们表明，数学模型是能够描述复杂的细胞变形通常观察到的实验结果。我们的数值结果说明细胞膨胀，细胞收缩，细胞平移和细胞搬迁以及细胞突起。在所有这些结果中，由肌动蛋白丝与肌球蛋白II马达蛋白的结合形成的收缩张力被确定为关键的分叉参数。
The aim of this article is to study cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical network of actin filaments and its concentration. Actin is a polymer that can exist either in filamentous form (F-actin) or in monometric form (G-actin) (Chen et al. in Trends Biochem Sci 25:19–23, 2000) and the filamentous form is arranged in a paired helix of two protofilaments (Ananthakrishnan et al. in Recent Res Devel Biophys 5:39–69, 2006). By assuming that cell deformations are a result of the cortical actin dynamics in the cell cytoskeleton, we consider a continuum mathematical model that couples the mechanics of the network of actin filaments with its bio-chemical dynamics. Numerical treatment of the model is carried out using the moving grid finite element method (Madzvamuse et al. in J Comput Phys 190:478–500, 2003). Furthermore, by assuming slow deformations of the cell, we use linear stability theory to validate the numerical simulation results close to bifurcation points. Far from bifurcation points, we show that the mathematical model is able to describe the complex cell deformations typically observed in experimental results. Our numerical results illustrate cell expansion, cell contraction, cell translation and cell relocation as well as cell protrusions. In all these results, the contractile tonicity formed by the association of actin filaments to the myosin II motor proteins is identified as a key bifurcation parameter.