Cytoplasmic streaming and amoeboid cell motility: Mathematical models and computational methods

最近通过三维纤维基质进行的细胞运动实验对细胞运动的基本机制提出了新的问题。特别是，他们已经证明了一些细胞使用压力驱动的突起（称为气泡）来挤压基质中的间隙，并且已经假设这种运动方法可以在不与周围环境相互作用的情况下实现。这个项目的目标是建立一个全面的气泡细胞的数学模型，并使用这个建模框架来探索细胞如何利用细胞质流进行运动。这个模型将是第一个提供局部机械和化学因素如何共同推动定向细胞运动的综合图片。这些模型将涉及细胞骨架、细胞质、细胞膜、细胞外液和周围固体结构之间的机械化学相互作用。这个项目的一个必要组成部分是计算细胞几何形状的变化。考虑到问题的复杂性，需要有效的数值模拟来探索模型。研究人员开发了一种新的混合欧拉-拉格朗日框架来统一这些复杂相互作用材料的数学描述。利用这一框架，开发了求解模型中出现的耦合方程的新的有效方法。生物学中的许多问题涉及力学、复杂多相流体、化学反应和变形结构之间的相互作用。例如，细菌生物膜生长的动力学和呼吸系统中粘液的运输就是两个这样的过程。我们的模型和数值方法可以适用于探索这些重要的复杂系统。作为这个研究项目的一部分，将训练一名研究生。这个项目非常适合培养具有数学生物学和科学计算研究所需的广泛背景的研究生。学生将直接与参与项目的实验合作者接触，学习跨学科交流思想的基本技能。

Recent experiments on cell locomotion through three-dimensional fibrous matrices have raised new questions about the basic mechanisms of cell locomotion. In particular, they have shown that some cells use pressure-driven protrusions called blebs to squeeze their way through the gaps in the matrix, and it has been hypothesized that this method of locomotion can be achieved without adhesive interactions with the surrounding environment. The goal of this project is to develop a comprehensive mathematical model of a blebbing cell and use this modeling framework to explore how cells use cytoplasmic streaming for locomotion. This model will be the first to provide an integrative picture of how local mechanical and chemical factors work together to drive directed cell locomotion. These models will involve the mechanochemical chemical interactions between the cytoskeleton, cytosol, cell membrane, extracellular fluid, and the surrounding solid structures. A necessary component to this project is accounting for the changing geometry of the cells. Given the complexity of the problem, efficient numerical simulations are needed to explore the models. The investigators develop a new mixed Eulerian-Lagrangian framework to unify the mathematical description of these complex interacting materials. Using this framework, new and efficient methods for solving the coupled equations that arise in the model are developed.Many problems in biology involve interactions between mechanics complex multiphase fluids, chemical reactions, and deforming structures. For example, the dynamics of growing bacterial biofilms and the transport of mucus in the respiratory system are two such processes. Our models and numerical methods can be adapted to explore these important complex systems. A graduate student will be trained as part of this research project. This project is ideally suited for training graduate students with the broad background necessary for research in mathematical biology and scientific computation. The student will interface directly with the experimental collaborators involved in the project to learn the essential skill of communicating ideas across disciplines.