Dynamics of Biological Interfaces

Northwestern University, Evanston IL

Investigators

Abstract

This project is concerned with a numerical and analytical investigation of the dynamics of biological interfaces. Our interest will be directed to lipid bilayers, which are the basic component of cell membranes. Our aim is to develop solution methods and to investigate the behavior of the mathematical models governing the dynamics of these biological interfaces. Mathematically we will be dealing with a complex free boundary problem. Continuum theory will be used to model the motion of these interfaces. The dynamics of the liquids surrounding the interface will be governed by a set of partial differential equations. These equations will be coupled to a system of partial differential equations along the interface. A boundary integral numerical method will be used to solve these complicated three-dimensional free-boundary problems. Recent experimental work will be used as a guide in selecting our mathematical models. A computational investigation beyond the parameter ranges of current experimental results will be done in order to fully understand our models. Several limiting cases will be investigated analytically using perturbation methods. The dynamics of biological interfaces is an important and relatively unexplored field. It is central to cellular activities and especially in vesicle transport and delivery processes. A number of diseases are related to a malfunction of vesicle transport in cells; hence the results of this research could lead to new treatments and drugs. This project will use methods from applied mathematics and ideas from continuum theory and applied them in a biological setting. The project is interdisciplinary and hence will enhance the education and development of the students associated with the project.