Energetic Phase-Field Methods and Biological Cell Modeling

Florida State University, Tallahassee FL

Investigators

Abstract

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.