Deformation, Phase Segregation and Adhesion of Lipid-Bilayer Vesicles

California Institute Of Technology, Pasadena CA

Investigators

Abstract

Bhattacharya DMS-0606667 The investigator seeks to study partial differential equations that describe the equilibrium and evolution of the shape, phase distribution, and adhesion of lipid bilayer membranes. An intricate interaction between the shape, the composition distribution, and pressure enable these membranes to undergo a variety of composition- and ordering-related phase transformations resulting in complex microstructure. These in turn affect the function of the membrane. The experimental study of the mechanics, phase segregation, and adhesion of bilayer membranes is an extremely active and fascinating field. A number of theoretical models and studies that consider different aspects and different approximations are beginning to emerge. This has set the stage for a systematic mathematical analysis that examines the relationship between the different models, understands the status of the various approximations, and yields a mapping of the different parameter and behavioral regimes. This mathematical analysis is the aim of this project. The investigator seeks not only to catalog and reconcile available experimental observations but hopes to motivate new experiments and the discovery of new phenomena by pointing out potentially interesting regions. The project builds on and extends the class of mathematical problems involving diffusion, phase transformation, and pattern formation that has been studied in flat spaces, motivated by issues in materials science, to a new class of problems that involve these phenomena on deformable manifolds. The investigator starts with an energetic formulation of the single phase membrane and derives limiting theories using both formal (matched asymptotic) and rigorous (Gamma convergence) methods. He then considers multi-species membranes and identifies circumstances when there is strong phase separation, studies nucleation from stability considerations, and derives sharp interface models. Evolutionary problems are treated as gradient flows of appropriate energy. Finally, he studies the implications of this analysis for cell adhesion. Lipid bilayer membranes are ubiquitous in living organisms as cell walls, mitochondria, golgi apparatus, and numerous other important organelles. They play a critical role in biology as they protect, regulate flow, and host many metabolic functions by forming a variety of complicated shapes and structures. This project seeks to advance our understanding of the factors that govern the shape and composition distribution of these membranes. It does so by building mathematical models based on existing observations and using mathematical analysis to explore the full implications of these models. The project provides for the training of a doctoral student in this critical and emerging interdisciplinary area. The student is trained in and uses contemporary methods of mathematical analysis, but also is exposed to experiments in biology and theories in mechanics and materials science. The project also trains three summer undergraduate research students.