When
Where
This is a joint colloquium with the University of Arizona Physics Department. The meeting location for this colloquium will be in PAS 201.
Speaker: Patrick Shipman, Mathematics Department, University of Arizona College of Science
Title: Membrane Geometry and the Role of Curvature in Lipid-Protein Interactions: From Elastic Free Energies to Pattern Formation
Abstract: Membrane proteins operate within a lipid bilayer whose composition profoundly influences their structure, conformational equilibria, and biological function. The physical mechanisms underlying this lipid regulation remain incompletely understood. One prevailing view assumes that chemically specific binding of individual lipids to the protein modulates its activity. The alternative we examine is that the bilayer acts as a continuum elastic medium, transmitting the effects of lipid composition through a small set of collective physical variables including the monolayer spontaneous curvature and the bending rigidity. We describe a variational Flexible Surface Model, an approach being developed with the group of Michael Brown at UA. The model is based on the Helfrich curvature energy, in which the cost of the membrane deformation induced by a protein contributes directly to its conformational free energy. In this picture, chemically distinct lipid mixtures with the same elastic properties produce the same protein response. We apply techniques from the Calculus of Variations, pattern formation theory, and differential geometry to predict how protein responses depend on the membrane energy landscape. Conformational equilibria of individual proteins are linked to the collective organization of protein properties and ultimately to the three-dimensional lipid phases governed by the same elastic energy. The model is calibrated against spectroscopy.