## Understanding the stability of lipid bilayers

- Date: 07/18/2007

Mark Peletier (Technische Universiteit Eindhoven)

University of British Columbia

Lipid bilayers demonstrate an intriguing combination of properties: at

a microscopic scale they consist of individual molecules without

covalent bonding, but at larger scales they show behaviour reminiscent

of elastic solids. Energy-based models, going back to Helfrich, are

often used to describe this macroscopic behaviour; in these models the

bilayer is represented as a smooth surface, and the energy functional

penalizes the curvature of this surface.

In this talk I describe our work to understand, mathematically, the

connection between a microscopic, diffusion-based model of the lipids

on one hand and the macroscopic Helfrich-type surface model on the

other. This is too complex a task to do in full generality: instead we

consider a simplified continuum lipid model that is derived from

Density Functional Theory, in which volume exclusion effects are

represented by a mean field. For this simplified model we can

investigate the connection in detail, and rigorously, resulting in an

expansion of the microscopic energy in terms of the layer thickness.

The terms of this expansion represent macroscopic quantities, such as

the preferred thickness, the penalty to breakage, and the bending

stiffness. This gives an interesting insight into the relative

importances of these quantities.

PIMS Distinguished Lecture 2007