具有反应扩散和移动边界的细胞极性和运动:严格的模型分析和鲁棒模拟

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Shuang Liu, Li-Tien Cheng, Bo Li
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引用次数: 0

摘要

SIAM应用数学杂志,出版前。摘要。细胞极性和运动是许多生物功能的基础。实验和理论研究表明,某些蛋白质的相互作用导致细胞极化,并在控制细胞运动中起着关键作用。我们研究细胞极性和运动基于一类生物物理模型,包括不同蛋白质的反应-扩散方程和移动细胞边界的动力学。这种移动边界通常用相场模型来模拟。我们首先应用匹配渐近分析从相场模型推导出细胞边界的锐界面模型。然后,我们开发了一种鲁棒的数值方法,该方法结合了水平集方法来跟踪移动细胞的尖锐边界和精确的离散化技术来求解移动细胞区域上的反应扩散方程。我们广泛的数值模拟预测了各种刺激下的细胞极化,并捕获了长时间运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,这些参数通过简化模型预测的准确性较低。我们的工作将不同的模型联系起来,并开发了能够适应具有挑战性的三维模拟的工具。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations
SIAM Journal on Applied Mathematics, Ahead of Print.
Abstract. Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical 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 a moving cell boundary. Such a moving boundary is often simulated by a phase-field 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 stimuli and capture both the linear and the 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.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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