CAREER: Multiscale investigation of cortical actin organization and dynamics

细胞依靠一种叫做大脑皮层的机械结构来维持自己的形状，并对环境中的化学和机械信号做出反应。皮质位于细胞外膜的正下方，主要由肌动蛋白的聚合丝组成。这些肌动蛋白细丝被各种蛋白质交叉连接，这些蛋白质可以重新定位甚至移动细丝，使皮质成为一个高度动态的结构。尽管肌动蛋白皮质对关键细胞功能很重要，但目前还不清楚小规模的相互作用如何产生与皮质相关的大规模模式和功能。这个项目将使用数学建模来连接与皮质肌动蛋白动力学相关的不同的时间和空间尺度，直接将分子水平的相互作用与细胞水平功能结构的出现联系起来。在这个项目中，将建立新的模型，利用各种数学方法，包括考虑不频繁相互作用的随机模型，以及可以跟踪皮质运动边界以及蛋白质在时间和空间上的运动的连续模型。这些基于生物学的模型的发展和分析将导致对肌动蛋白及其在细胞环境中的调节的更好的理解。这项研究还将通过开发数学建模综合本科课程，通过俄亥俄州立大学的一些现有项目招收学生，包括数学和科学领域的女性和工程领域的女性，从而招聘和留住科学、技术、工程和数学领域的女性。参与这个项目和本科课程的学生将接触到真实世界的数学应用，并将在一个支持性的跨学科环境中与其他学科的同龄人互动。数学建模是研究复杂生物系统的理想工具，在这些系统中，实验技术不可用或不可行。在宏观层面上，将使用偏微分方程组来研究生化和机械肌动蛋白动力学之间的相互作用，以及这些动力学对细胞形状的影响。渐近分析将用于明确研究曲率在肌动蛋白动力学中的作用，移动边界模拟将用于研究细胞形状的变化。在中尺度水平上，将使用积分-微分方程组来描述肌动蛋白细丝的动力学，它将被用来研究大尺度肌动蛋白细丝模式的形成，如紫锥菊、旋涡和聚集体。在微观层面上，基于个体的随机模型将被用来确定局部肌动蛋白网络的物理性质，并确定在什么条件下肌动蛋白网络表现为粘弹性材料。通过在建议的模型中实施跨多个时间和空间尺度的一致性，将揭示产生细胞结构的机制。对这些模型的分析和模拟将带来独特的挑战，导致应用数学的几个领域的技术改进，包括渐近分析、移动边界模拟、非局部模型分析和随机模拟。建议的模型将在单个实验生物体中进行激励和验证，避免将体外数据与来自多个生物体和细胞类型的体内数据相结合而产生的复杂情况。这项研究产生的综合计算和分析模型将增加我们对对正常细胞功能至关重要的基本蛋白质的理解。

Cells rely on a mechanical structure called the cortex to maintain their shape and to respond to chemical and mechanical cues in the environment. The cortex, which lies just below the outer membrane of the cell, consists primarily of polymerized filaments of the protein actin. These actin filaments are cross-linked by a variety of proteins that can reorient and even move the filaments, making the cortex a highly dynamic structure. Despite the importance of the actin cortex for critical cell functions, it is not clear how small scale interactions give rise to large scale patterns and functions associated with the cortex. This project will use mathematical modeling to bridge disparate time and space scales associated with cortical actin dynamics, directly linking molecular level interactions to the emergence of cell level functional structures. For this project, novel models will be constructed that draw on a variety of mathematical approaches, including stochastic models which take into account infrequent interactions, and continuum models which can track the moving boundary of the cortex as well movement of proteins in time and space. The development and analysis of these biologically based models will result in an improved understanding of actin and its regulation in a cellular context. This research will also be leveraged to recruit and retain women in Science, Technology, Engineering, and Mathematics fields through the development of an integrated undergraduate course in mathematical modeling, with recruitment of students through a number of existing programs at Ohio State University, including Women in Mathematics and Science and Women in Engineering. Students involved in this project, and in the undergraduate course, will be exposed to real world mathematics applications and will interact with peers from other disciplines in a supportive interdisciplinary environment.Mathematical modeling is an ideal tool for the investigation of complex biological systems, where experimental techniques are not available or are not feasible. At the macro-scale level, systems of partial differential equations will be used to investigate the interplay between biochemical and mechanical actin dynamics, and the consequence of these dynamics on cell shape. Asymptotic analysis will be used to explicitly study the role of curvature in actin dynamics, and moving boundary simulations will be used to study changes in cell shape. At the mesoscale level, integro-differential equations, which use integral kernels to describe actin filament dynamics, will be used to study the formation of large scale actin filament patterns such as asters, vortices and aggregates. At the micro-scale level, stochastic individual-based models will be used to determine physical properties of the local actin meshwork and to determine under what conditions the actin meshwork behaves as a viscoelastic material. By enforcing consistency across multiple time and space scales in the proposed models, mechanisms that give rise to cellular structures will be revealed. Analysis and simulations of these models will present unique challenges leading to improvement of techniques in several areas of applied mathematics, including asymptotic analysis, moving boundary simulations, nonlocal model analysis, and stochastic simulations. The proposed models will be motivated and validated in a single experimental organism, avoiding complications from combining in vitro data with in vivo data from multiple organisms and cell types. The integrated computational and analytical models resulting from this research will increase our understanding of a fundamental protein that is critical for proper cell function.