Mathematical Modeling of Biomembranes

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Miksis1312935 The objective of the project is the development of an effective zero-thickness model for a fluid-embedded lipid bilayer membrane. The predictions of the model equations are applied to explain observed features of membrane behavior such as the appearance of sharp edges, vesicle bursting, and stability of the thin liquid film between membranes undergoing electrofusion. The dynamics of a compound vesicle are also considered. Generalizations of the lipid bilayer model to account for pores are studied. Mathematically, these are challenging free boundary problems exhibiting complex dynamics. Continuum theory is used to model the motion of the lipid membrane interface and the surrounding liquids, e.g., the Stokes equations for the flow in the bulk and a coupled system of partial differential equations describing the interface evolution and membrane charging. The interface conditions are related to the jump in stress and electric potential across the interface and they depend on the geometry of the interface and several physical constants, e.g., the bending rigidity and membrane capacitance. A computational method is developed to solve these complicated transient three-dimensional free-boundary problems. Limiting cases are investigated analytically, using asymptotic and perturbation methods. Recent experimental work is used as a guide in selecting our mathematical models. An investigation beyond the range of the experimental situations is done to fully understand the models and as a guide to the development of more realistic models of cells. The dynamics and stability of biomembranes is at the heart of cellular function. The electromechanics of biomembranes is an area that is largely unexplored. This project uses methods from applied mathematics and ideas from continuum theory, and applies them in a biological setting. This expands the frontiers of these disciplines. The outcomes of this project directly impact biomedical technologies that employ membrane electroporation (e.g. gene transfection) or cell fusion. The interconversion of electric and mechanical energies, one example being the membrane flexoelectricity (bending in response to electric fields), could be exploited for novel micro- and nano-fluidic designs. The project is interdisciplinary and this is very beneficial for the education and development of the undergraduate and graduate students associated with the project.