Special Session 22: Modeling and Analysis of Multi-Phase Lipid Bilayer Membranes Tim Healey, Cornell University, USA Qiang Du, Penn State University, USA Of domains and boundaries: lipid bilayer membranes with phase coexistence Tobias Baumgart University of Pennsylvania, USA baumgart@sas.upenn.edu Aiwei Tian and Sovan Das Lipid bilayer membranes of biological cells are likely to be non-random mixtures of membrane com- ponents. Lateral membrane domain formation is thought to be involved in essential functions of the membrane, including signaling, sorting, and traffick- ing. In order to elucidate the physical, mechani- cal, and physico-chemical basis and consequences of membrane heterogeneity, model systems have been developed. These typically consist of ternary lipid mixtures that under suitable conditions segregate into two fluid phases, a liquid ordered, and a liquid disordered phase. Of particular interest to us are the boundaries of domains in membranes with phase coexistence due to interfacial tension (line tension) at fluid phase boundaries. We find that this line ten- sion couples to three dimensional membrane shape, modulating biologically relevant phenomena, includ- ing vesicle budding and fission. Line tension is also a control parameter regulating domain size and growth kinetics. We are therefore developing methods to pre- cisely measure line tension as a function of membrane composition, using micropipette aspiration of giant vesicles, as well as capillary wave spectroscopy of thermal boundary fluctuations. We demonstrate that these two complementary techniques probe different line tension regimes. Furthermore, we are developing experimental methods to investigate the partitioning of both lipids and proteins among curvature gradi- ents. We find that lipids are not detectably sorted among membrane with steep curvature difference, whereas peripherally membrane binding proteins are efficiently sorted. We discuss the biological relevance of our findings. −→∞⋄∞←− A boundary layer analysis for two-phase lipid bilayer vesicle and vesicle adhesion Sovan Das Department of Mathematics, Penn State University, USA sld36@psu.edu James T. Jenkins and Qiang Du Lipid bilayer vesicles with two coexisting phases are promising model systems for cell membranes and pro- mote the understanding of mechanical and physico- chemical aspects of biological membrane functions. They consist of many of the same phospholipids that, in association with cholesterol, form cell membranes. They are fluid-like, spontaneously form in aqueous solution, resist bending, and have a large variety of shapes. The shapes are characterized locally by their mean and Gaussian curvatures. We present approximate solutions to the equa- tions that govern the shape of two-phase lipid bilayer vesicles obtained via a boundary layer analysis. The equations involve a dimensionless small parameter re- lated to the resistance to changes in mean curvature. We determine a relationship between the tangent an- gle at the interface and the difference in the Gaus- sian curvature stiffnesses of the co-existing phases. This relationship demonstrates that a difference in the Gaussian curvature stiffnesses moves the phase boundary, as determined in previous numerical stud- ies. The analytical expression for the tangent angle obtained can be used to determine elastic parame- ters for the membranes from experimental data. We also describe a boundary layer analysis for the vesi- cle or cell adhesion which is a key mechanism for the survival of cells. −→∞⋄∞←− Derivation of a new free energy for biological membranes Luca Deseri SAVA Dept.-Div. Engineering-Univ. Molise-Italy & DIMS-Trento, Italy deseril@ing.unitn.it M. D. Piccioni and G. Zurlo A new free energy for thin biomembranes depend- ing on chemical composition, degree of order and membranal-bending deformations is derived in this paper. This is a result of constitutive and geometric