Abstract:  Living cells are enveloped by membranes, made up of lipid molecules arranged in a bilayer configuration. These lipid bilayers are composed of different types of lipid molecules and, rather than being a homogeneous mixture, the lipids exhibit partial "phase separation", with the formation of cholesterol- and sphingomyelin-enriched microdomains (also known as "lipid rafts") within the membrane. It is thought that certain proteins or other reactants are preferentially associated with these phase-separated microdomains, and thus that ``rafts'' can act to prevent interactions with other reactants in the rest of the membrane, or conversely, bring desired reactants into close proximity to promote certain reactions. Lipid rafts are therefore thought to play many very important roles in cell biology, but the basic principles that govern their formation and function remain poorly understood.

To shed light on these fundamental issues, experiments have been conducted on simple in vitro systems, with microdomains forming in membranes composed of controlled lipid mixtures (e.g. 20% cholesterol and 80% phosphatidylcholine (PC)). This talk will briefly outline the background biology and the experimental measurements, and then describe how a mathematical model can be built to explain the experimental findings. The model relies on the Smoluchowski theory of coagulation and fragmentation, applied to an idealised system in which a large number of cholesterol molecules in 2D clusters of varying sizes (the ``rafts'') are diffusing around in an otherwise inert 2D fluid (the PC bilayer). The key step in the modelling lies in studying the physics of the cluster interactions to deduce how the rate coefficients for the coagulation and fragmentation events depend on the cluster size, something on which the model results depend sensitively. We find remarkably good agreement with the experiments and, moreover, the model provides us with a large amount of information that the experiments cannot measure.