2R v. R v. R l c. Reminder: self assembly. Packing parameter (shape factor): v/a 0. spherical micelles : v/a 0 <1/3 <1/2

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1 Reminder: self assembly a 0 Packing parameter (shape factor): v/a 0 l c spherical micelles : v/a 0 l c <1/3 v non-spherical micelles : 1/3 < v/a 0 l c <1/ R l c vesicles or bilayers : 1/ < v/a 0 l c < 1 w inverted structures : v/a 0 l c >1 oil What makes the lipids form vesicles instead of sheets? Answer: edge tension, λ (units: J/m) Experimental values: for lecithin bilayers -- 4x10-11 J/m for pure SOPC -- 9x10-1 J/m Will the sphere always win? R v R v radius of disk = R v in order to conserve surface area Small head-group and bulky chains v/a 0 l c 1 Two chains 1) hydrophobicity CMC CMC (micelle-form.) = M CMC (bilayer-form.) = M ) residence time, τ R : τ R(micelles) 55 x 10-9 / s τ R(bilayers) 55 x 10-7 / s For the same a 0 and l c, the HC chain volume, v, is to be twice the volume of micelle forming surfactant where 1/3< v/a 0 l c <1/ two chains 3) flip-flop times, τ fl τ fl s (depends more on the head-group rather than the chain)

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6 Differential scanning calorimetry (DSC): measures heat uptake Features: directly measures a thermodynamic property observes a different signal - just about every reaction has an enthalpic component measurable quantities: H, S, C P Def: monitor heat adsorbed vs. temperature: titrate with heat Microcalorimeters: insulation heaters cell with buffer thermocouples cell with sample Features: heat is supplied at the same rate to the cells (applied current to heaters) solution cell generally absorbs more T feedback loop supply Q to the solution cell, to equalize T calculate (dh/dt) from difference in power to maintain the same T C P endothermic Heat capacity C P = Q/ T Def: heat required to change the temperature of a substance with 1K, [cal/k] heat flow is equivalent to enthalpy changes: (dq/dt) P = dh/dt time or T (dh/dt) = (dh/dt) sample - (dh/dt) reference

7 DSC Isotherms endothermic exothermic C P : shift in the baseline at the starting transient glass transitions: cause a baseline shift Def: a rapid change of the specific heat, the coefficient of thermal expansion, the free volume, the dielectric constant no enthalpy associated with it called a second order transition C P = Q/ T

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10 Membrane Functions Define the external boundary & internal compartments of cells Regulate molecular traffic into & out of cells and organelles. biological energy conservation (ion gradients). cell-cell communication (receptors, etc.) Membrane Composition Proteins: 30-75% (usually 50%) Lipid (5-70%), carbohydrate up to 10% (glycolipids and glycoproteins) Compositions vary between species, and between cells & tissues of same species Note: Biological membranes have asymmetric distributions of lipid & protein (external internal) external PLA cleaves sn-

11 Molecular motions of lipids 1. Lateral Diffusion Diffusion coefficients range from 10-7 (fast) to (slow) cm /s. orders of magnitude faster than diffusion across the membrane Problem: for D=10-8 cm /s, what is the distance (in µm) a lipid can traverse in 4s?. Transbilayer movement (flip-flop) Very slow process (energetically unfavorable to move headgroup into hydrophobic interior), unless aided by a translocase For PC t 1/ = several days Flip-flop of some PL (PA and PG) and FA can be induced by a transmembrane ph gradient Cholesterol will flip-flop by passive diffusion Proteins not at all Membrane permeability next lecture

12 Membrane mechanics Topics overview: 1) Classical modes of deformation ) Membrane elasticity (essential for lipid-protein interactions, behavior of mixtures, lyotropic phase transitions e.g. bilayer -> inverted hexagonal) stretching elasticity membrane curvature, bending elasticity lysis membrane elasticity measurements micropipettes, fluctuation analysis, measurements on red blood cells effect of cholesterol 3) Shear viscosity of membranes (essential for mobility and activity of membrane proteins, membrane diffusion) Classical modes of deformation bilayer membrane Stretching Bending Shear stretching elasticity [dyn/cm] dilatational surf.viscosity [sp] bending stiffness [erg] bending surf. viscosity [sp] shear elastic modulus [dyn/cm] shear surface viscosity [sp] Intermonolayer slip, - essential for elasticity of membranes in fluid state,,, - to be considered when dealing with erythrocytes, membranes from polymerized lipids intermonolayer friction [dyn.s/cm 3 ]

13 τ τ A τ τ A+δA Stretching elasticity of membranes Isotropic lateral extension: Elastic energy density: Mean tension: g ext = 1 K ( δa A) K area compressibility modulus τ = K δa A Methods for measuring K : - micropipette technique - photon correlation spectroscopy, cryoelectron microscopy and DLS of small vesicles subjected to osmotic stress - NMR and X-ray diffraction of strongly dehydrated multibilayer arrays Cells under tension: Pressure can come from osmotic effects: π=rtσc s Or from mechanical effect such as microtubili polymerisation during cell division

14 Micropipette technique: best resolution (better than 0.1% for δa); can test reversibility, instantaneous tension area dilation at rupture R v Increase suction pressure, P τ = PR R p p R v 5µm δ A π Rp 1 R R p v L Evans, Rawvicz, PRL, 64, 094 (1990) Helfrich, Servus, Nuovo Cimento, D3, 137 (1984) R p Example: (polymer membrane) L 0 τ, dyn/cm 10 Red blood cell in a pipette at different pressures δa A Typical values for lipids: K = dyn/cm For cholesterol containing membranes: e.g. SOPC:cholesterol=1:1 K 850 dyn/cm erythrocyte lipid extract (50% cholesterol) 750 dyn/cm For sheets (5nm thick) of rubber: 100 dyn/cm polyethylene: 5000 dyn/cm steel: 10 7 dyn/cm

15 Bending elasticity of membranes h M 1) Bending a bilayer with free ends (freely sliding monolayers) = splay of a single smectic layer: κ= Κ 11 h 1 u u Elastic energy density: g bend = κ + C 0 x y 1 R x Bending moment: M M M 1 1 M = κ + C 0 Rx Ry κ - bending elastic modulus u 1 u = ; = - principal radii of curvature C 0 spontaneous curvature: x R y y z expansion compression Π(z) M d / = zπ( z) dz C0 = M 0 ; d / 0 κ Example for creating intrinsic bending moment ) Bending closed bilayer i.e. vesicle additional constraints: fixed volume V constant average area A fixed monolayer area difference A 1 1 A h da + R x R y bilayer coupling constraint global bending modulus, κ (similar to κ) Basic concepts for calculating shapes and shape transitions of vesicles and cells Gaussian curvature: G = 1 R R - constant for closed vesicles ignored Important for lyotropic phase transitions and for torus-shaped vesicles, high genus vesicles C x y Mutz, Bensimon PRA,43,455 (1991)

16 Bending elasticity of membranes (cont.) Methods for measuring κ : - micropipette technique (most versatile, difficult) - electric field deformation technique (cells, vesicles) - cell poking - fluctuation spectroscopy (measures forces in the femto-newton range) - new: with differential confocal miccroscopy Micropipette technique: aspiration at low tensions (entropic regime) δa A k BT = 8πκ Crossover tension: τ x 1dyn/cm ln τ τ x = K B k T 8π κ ln(τ) 3 0 Typical value for κ 0 k B T Red-blood cell: 1 k B T (?enigma?) δa A Membrane lysis: Rupture tension (τ lysis ) < 10 dyn/cm (cholesterol increases τ lysis ) Maximum area expansion: between and 5% Fluctuation spectroscopy: τ lysis K Fourier expansion of the deviations from spherical shape with equivalent radius R 0 R ( ϕ) = R 1+ a cos( nπϕ) + b sin( nπϕ) 0 n n n n 0.4 Döbereiner, et al, PRE, 55, 4458 (1997) R(ϕ) ϕ a n a - elipticity a 3 - assymetry 0.0 k B κ T a n time, sec

17 Differential confocal microscopy (Lee, Ling, Wang 001) Deformation < 1µm Vesicle at the bottom L Undulation forces: membrane close to a surface d For d < L the long wavelength undulations freeze out interaction potential: V ( d) kbt κd Reflection interference contrast microscopy Radler, et al. PRE, 51,456 (1995) Intercorrelation of the elastic parameters: K κ = cm - stays constant From theory of elasticity (for d shells) K κ h Effects of various factors on the elastic properties: Cholesterol increases both K and κ Small molecules e.g. peptides, short bipolar lipid ( bola ) decrease the bending stiffness (possibly due to creating variation in h)

18 Shear surface viscosity τ s = η constant area s ln t ( λ) Energy and force representation of Hook s law: g sh ( λ ) 1 = µ λ λ - lateral extension ratio Viscous dissipation in the bilayer - difficult to measure: deformation response is dominated by dissipation in water Shear surface viscosity measurement: diffusion of molecular probes (unreliable for frozen bilayers; large scattering of the data) e.g. FRAP tether formation experiments (gives upper bound) optical dynamometry vesicle tether Fluorescence photobleaching recovery (FRP or FRAP) D diffusion in cell membranes or in concentrated solutions Fluorophores: green fluorescent protein (GFP) fluorescent label bound to a protein, nucleic acid, lipid spot bleached by a laser Recovered fluorescence fraction: time ω Gaussian beam waist

19 Optical dynamometry latex particle g vesicle 1. Falling-ball viscosimetry : measure friction coefficient calculate viscosity Membrane shear surface viscosity contribution to friction: free bulk bulk + membrane. Brownian motion D = k B T ζ η S η ζ = 6πηR b ζ = 6πηR b ηs +.93η s ηr b 0.1 k B T 3. Optical trap dynamometry Typical value for η s : 3 x 10-6 dyn.s/cm (SOPC) units: [bulk viscosity] x [thickness] ~ 150 cp ~ 5 nm (water: 1 cp) 0 = k RP x ζ x& F RP radiation pressure force