While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we present a framework that couples an active gel model of the cell mechanical scaffold with the complex cell metabolic system stochastically delivering the chemical energy needed to sustain an active stress in the scaffold. Our closure assumption setting the magnitude of the fluctuations is that the chemo-mechanical free energy of the cell is controlled at a target homeostatic value. Our model rationalizes the experimental observation that the cell shape fluctuations depend on the mechanical environment that constraints the cell. We apply our framework to the simple case of a cell migrating on a one dimensional track to successfully capture the different regimes of the cell mean square displacement along the track as well as the magnitude of the long time scale effective diffusive motion of the cell.

尽管通常观察到哺乳动物细胞的形状动力学会经历较大的随机波动，但旨在捕获细胞力学的理论模型通常侧重于运动的确定性部分。在本文中，我们提出了一个框架，该框架将细胞机械支架的主动凝胶模型与复杂的细胞代谢系统耦合，随机地传递维持支架中主动应力所需的化学能。我们设定波动幅度的闭合假设是将细胞的化学机械自由能控制在目标稳态值。我们的模型合理化了实验观察，即单元格形状的波动取决于约束单元格的机械环境。