论文标题
细胞极性和反应扩散和移动边界的运动：严格的建模和健壮的模拟
Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Modeling and Robust Simulations
论文作者
论文摘要
细胞极性和运动是许多生物学功能的基础。实验和理论上的研究表明，某些蛋白质的相互作用导致细胞极化，在控制细胞运动中起着关键作用。我们根据一类生物物理模型研究细胞极性和运动，这些模型由不同蛋白质的反应扩散方程组成以及运动细胞边界的动力学。这种移动的边界通常通过相关模型模拟。我们首先应用匹配的渐近分析，从相位模型中对细胞边界的夏普接口模型进行严格的推导。然后，我们开发了一种可靠的数值方法，该方法结合了级别集方法，以跟踪移动单元格的尖锐边界和精确离散化技术，以求解移动细胞区域上的反应扩散方程。我们的广泛数值模拟预测了各种刺激下的细胞极化，并长时间捕获移动细胞的线性和圆形轨迹。特别是，我们已经确定了一些控制不同细胞轨迹的关键参数，而这些参数较少的模型预测了不同的细胞轨迹。我们的工作已经连接了不同的模型，还开发了可以适应具有挑战性的三维模拟的工具。
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of moving cell boundary. Such a moving boundary is often simulated by a phase-filed model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimulus, and capture both the linear and circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.
