Energetic Phase-Field Methods and Biological Cell Modeling

相场的概念最近已被许多研究人员推广，并正在成为研究许多科学和工程问题的首选方法之一。研究者在本项目中关注的具体设置是其在细胞生物学中的应用，例如，细胞起泡和胞质分裂，上皮形态发生。建模、分析和计算问题非常复杂且具有挑战性。研究员在研究相场方法及其在生物学中的应用方面的先前研究经验使他为进行该项目做好了充分的准备。拟议的调查将提供新的见解，一些突出的理论问题，导致创新的计算算法，许多重要的应用和更好地了解一些基本的生物过程。该项目将为研究生和本科生提供一个独特的教育机会，他们对应用/计算数学，生物学和工程感兴趣，让他们参加一个结合数学，生物学，计算机科学和工程的跨学科研究计划。研究者将通过“FSU教学”和“定向个别研究”计划为代表性不足的本科生提供研究经验。每个本科生都将参与研究项目的各个方面。由于他们将在高中和初中阶段教育学生，让他们参与拟议的项目将对培养下一代科学家产生更广泛的影响。调查员将积极传播他的研究成果和软件，不仅在该地区的研究人员，而且通过出版物，参加会议，维护一个信息丰富的网站更广泛的社区。研究人员将利用数值模拟制作电子投影幻灯片和电影，在当地中小学展示，激发低年级学生对科学的兴趣。近年来，高能相场方法已成为一种成功的建模和模拟方法，在研究微观结构演变方面具有许多优势，包括但不限于凝固、晶粒生长和粗化，薄膜微结构、裂纹扩展、晶体生长、位错-溶质相互作用、位错动力学和电迁移。相场法的思想是引入一组相场变量来隐式跟踪微结构的运动表面，这可能是非常复杂和非线性的。在过去的几年里，研究者和他的合作者已经成功地应用相场方法来研究生物微观结构，特别是细胞膜。这些研究也扩展了相场方法的理论。本文从建模、数值方法和理论分析等方面进行了一系列的工作。该项目主要涉及相场方法的进一步研究和细胞生物学应用的拓宽;相场方法和相关概念可用作更方便和/或有效治疗的基础。在未来的几年里，研究者将研究一些理论和算法的相位场方法仍然没有解决或部分未解决的今天。这些新算法有可能大大降低计算成本，从而使相场方法成为解决复杂生物问题的最先进技术。研究者还将对膜与膜蛋白的相互作用、肌动蛋白驱动的细胞起泡、有丝分裂期间的细胞胞质分裂和上皮形态发生进行相场建模。这些都是非常具有挑战性的问题。相场方法在处理这些问题上具有比表面跟踪或表面演化方法更大的优势，特别是对于具有复杂形状变化的细胞。研究人员的数值模拟和合作者的实验室实验将帮助我们深入了解各种生物现象背后的原理。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估而被认为值得支持。

The phase field concept has recently been popularized by many researchers and is well on its way to becoming one of the methods of choice for studying many scientific and engineering problems. The specific settings the investigator focuses on in this project are its applications in cell biology, e.g., cell blebbing and cytokinesis, epithelial morphogenesis. The modeling, analytical, and computational issues are very complex and challenging. The investigator's prior research experience in studying phase field methods and its applications in biology makes him very well prepared to conduct the project. The proposed investigation will offer new insights into a number of outstanding theoretical issues leading to innovation in computational algorithms for many important applications and a better understanding of a number of fundamental biological processes. This project will offer a unique educational opportunity for both graduate and undergraduate students with interests in applied/computational mathematics, biology, and engineering by having them participate in an interdisciplinary research program that combines mathematics, biology, computer science and engineering. The investigator will provide research experience for underrepresented undergraduate students through "FSU Teach" and "Directed Individual Studies" programs. Each undergraduate will participate in each and every aspect of the research project. Because they will be teaching students at the high- and middle-school levels, involving them in the proposed project will produce a broader impact on training scientists of the next generation. The investigator will actively disseminate his research results and software not only to researchers in the area but also to a much broader community through publications, attending meetings, maintaining an informative web-site. The investigator will make electronic projection slides and movies from the numerical simulations to present in local elementary and middle schools to stimulate interest in science among younger students.During recent years, the energetic phase field approach has emerged as a successful modeling and simulation method having many advantages in the study of micro structure evolution, including but not limited to solidification, grain growth and coarsening, thin film micro structure, crack propagation, crystal growth, dislocation-solute interactions, dislocation dynamics, and electromigration. The idea of phase field methods is to introduce a set of phase field variables to implicitly track the moving surfaces of micro structures, which can be very complex and nonlinear. In the past few years, the investigator and his collaborators have successfully applied phase field methods to study biological micro structures, especially cell membranes. These studies also extended the theory of phase field methods. A series of efforts have been carried out on modeling, numerical methods and theoretical analysis. The proposed project is mainly concerned with further studies on phase field methods and the broadening of applications for the cell biology; phase field methods and related concepts can be used as a basis for more convenient and/or efficient treatments. In the next few years, the investigator will investigate some theoretical and algorithmic problems on phase field methods that still remained unsolved or are partly unsolved today. Those new algorithms have the potential to dramatically lower the computational cost and thus make phase field method a state-of-art technique for solving complex biology problems. The investigator will also perform phase field modeling on membrane interaction with membrane proteins, acto-myosin driven cell blebbing, cell cytokinesis during mitosis, and epithelial morphogenesis. Those are very challenging problems. Phase field methods have the advantages in handling those problems compared to surface tracking or surface evolving methods, especially for cells with complex shape changes. The investigator's numerical simulations together with his collaborator's lab experiments will help us gain insight into the principles behind various biological phenomena.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.