Energetic Phase-Field Methods and Biological Cell Modeling

相场概念最近得到了许多研究人员的推广，并正在成为研究许多科学和工程问题的首选方法之一。在这个项目中，研究者关注的具体设置是它在细胞生物学中的应用，例如细胞起泡和细胞分裂，上皮形态发生。建模、分析和计算问题是非常复杂和具有挑战性的。研究者在研究相场方法及其在生物学中的应用方面的研究经验使他为开展该项目做好了充分的准备。拟议的研究将为许多突出的理论问题提供新的见解，从而导致许多重要应用的计算算法的创新，并更好地理解一些基本的生物过程。该项目将为对应用/计算数学、生物学和工程学感兴趣的研究生和本科生提供一个独特的教育机会，让他们参与一个结合数学、生物学、计算机科学和工程学的跨学科研究项目。研究员将通过“FSU教学”和“定向个人研究”项目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每一个方面。因为他们将教授高中和初中水平的学生，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。研究者将积极地传播他的研究成果和软件，不仅向该领域的研究人员传播，而且通过出版物、参加会议、维护一个信息丰富的网站向更广泛的社区传播。研究人员将根据数值模拟制作电子投影幻灯片和电影，在当地小学和中学播放，以激发年轻学生对科学的兴趣。近年来，高能相场方法作为一种成功的建模和模拟方法，在微观组织演变研究中具有许多优点，包括但不限于凝固、晶粒生长和粗化、薄膜微观组织、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。相场方法的思想是引入一组相场变量来隐式跟踪微观结构的运动表面，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法的理论。在建模、数值方法和理论分析方面进行了一系列的努力。本项目主要研究相场方法的进一步研究和扩大相场方法在细胞生物学中的应用；相场方法和相关概念可以作为更方便和/或有效处理的基础。在接下来的几年中，研究者将研究一些目前尚未解决或部分解决的相场方法的理论和算法问题。这些新算法有可能大大降低计算成本，从而使相场法成为解决复杂生物学问题的最先进技术。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。相对于表面跟踪或表面演化方法，相场方法在处理这些问题方面具有优势，特别是对于具有复杂形状变化的细胞。研究者的数值模拟和他的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。该奖项反映了美国国家科学基金会的法定使命，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，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.