1. Chapter 5 of Yeagle Structure of Biological Membranes Non-lamellar phases Spontaneous curvature Actual curvature What is the physical basis of non-lamellar phase structures? Can we understand the competing forces that stabilize a lamellar versus a non-lamellar phase? Bilayer thickness Surface charge Dielectric constant Lipid composition In cells, primarily lamellar structures are found, yet lipids extracted from cells will form non-lamellar phases in vitro.

2. POLYMORPHISM MESOMORPHISM

3. General Motivation: (1) by studying structural polymorphism/mesomorphism, one gaines an understanding of the forces that are “locked-up” in biomembranes that can affect the organization and function of membrane proteins (2) Generally extended to surfactant/detergent chemistry This chapter is interested in phase changes that change the CURVATURE of the lipid-water interface. These phases occur at temperatures above the gel-liquid transition, but below the transition temperature to an isotropic liquid.

4. Why do we care about CURVATURE? Cell division Endocytosis Membrane fusion Structure organelles

5. X-ray diffraction and NMR EPR, UV-VIS, IR, Calorimetry, Neutron diffraction

6. GOAL: INTUITIVE UNDERSTANDING OF THE FORCESTHAT DRIVE THE FORMATION OF CURVATURE ALTERING PHASE TRANSITIONS TERMINOLOGY: NON-BILAYER PHASE: really means non-lamellar, but still a bilayer of phospholipids INVERTED/WATER-IN-OIL PHASE: H II phase, possess a net concave curvature when viewed from the water domain. NONINVERTED/OIL-IN-WATER PHASE: H I phase, possesses a net convex curvature when viewed from the water domain OIL-WATER SURFACTANT MICELLES What happens when you have detergents and a small amount of oil in water? What happens when the oil is the majority constituent? THERMOTROPISM and LYOTROPISM

7. Phenomenological Approach: like Hooke’s Law – the force required to stretch an elastic object is linearly proportional to displacement from equilibrium position. This disregards the molecular forces at play For lipid bilayers: the fundamental unit of all lipid mesomorphs is the lipid monolayer, and that this monolayer may be endowed with a spontaneous tendency to curl. C o = 1/R o C o = spontaneous curvature R o = radius of spontaneous curvature Rigidity of object  E = 0 when R = R 0 Parabolic dependence

9. Perform X-ray crystallography and obtain d-spacing and reflections

10. By adding 16%(w) tetradecane, it is possible to minimize the unfavorable packing of the acylchains, thus lowering the phase transition temperature to the hex phase As you raise the Temperature, the tube radius becomes smaller

14. Inverted Hex phase is a cylinder

18. Bending membranes using: 1)Lipids themselves 2)Molecular motors 3)Protein binding

19. Bending by proteins: Scaffolding Mechanism The protein coats that cover budding membrane surfaces function as “scaffolds” to curve the membrane. Constraint is that protein must be curved and rigid for the membrane to “follow”. There must also be a tight binding examples: dynamin and BAR-domain proteins Local Spontaneous Curvature Mechanism. Spontaneous curvature is generated by the penetration of a protein into the membrane. Example is the ENTH domain of epsin. It is involved in clathrin mediated endocytosis. The ENTH domain binds to PIPs (PI-4,5 biphosphate) Amphiphysin is another protein example. Both have amphipathic helices that insert into the bilayer which may cause a local curvature strain.

21. Sensing by proteins: A new concept in cell trafficing and membrane curvature is that proteins can sense curvature. Proteins have been discovered that have binding affinities that are dependent upon the radius of membrane curvature.