This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomechanical forces. We propose a mechanobiochemical model which considers the actin filament network as a viscoelastic and contractile gel. The mechanical properties are modelled by a force balancing equation for the displacements, the pressure and concentration forces are driven by actin and myosin dynamics, and these are in turn modelled by a system of reaction-diffusion equations on a moving cell domain. The biophysical model consists of highly non-linear partial differential equations whose analytical solutions are intractable. To obtain approximate solutions to the model system, we employ the moving grid finite element method. The numerical results are supported by linear stability theoretical results close to bifurcation points during the early stages of cell migration. Numerical simulations exhibited show both simple and complex cell deformations in 3-dimensions that include cell expansion, cell protrusion and cell contraction. The computational framework presented here sets a strong foundation that allows to study more complex and experimentally driven reaction-kinetics involving actin, myosin and other molecular species that play an important role in cell movement and deformation.

中文翻译：

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移动网格有限元方法应用于 3D 细胞迁移的机械生化模型。

这项工作介绍了 3D 细胞变形和运动的生物物理模型的开发、分析和数值模拟，该模型将生化反应和生物力学力耦合在一起。我们提出了一种机械生化模型，该模型将肌动蛋白丝网络视为粘弹性和收缩凝胶。机械特性由位移的力平衡方程建模，压力和集中力由肌动蛋白和肌球蛋白动力学驱动，而这些又由移动细胞域上的反应扩散方程系统建模。生物物理模型由高度非线性的偏微分方程组成，其解析解是难以处理的。为了获得模型系统的近似解，我们采用移动网格有限元方法。在细胞迁移的早期阶段，接近分叉点的线性稳定性理论结果支持了数值结果。展示的数值模拟显示了 3 维的简单和复杂的细胞变形，包括细胞扩张、细胞突出和细胞收缩。此处介绍的计算框架奠定了坚实的基础，可以研究更复杂和实验驱动的反应动力学，涉及肌动蛋白、肌球蛋白和其他在细胞运动和变形中起重要作用的分子种类。