X-ray and Neutron diffraction studies of lipid bilayers V A Raghunathan Raman Research Institute, Bangalore

Phospholipids Major component of cell membranes Amphiphilic molecules Self-assemble to form bilayers Critical micellar concentration (CMC) ~ 1 n M Phosphatidylcholine (PC)

Morphologies of lipid bilayers Unilamellar vesicles (ULV) Multilamellar vesicles (MLV) liposomes Multilamellar stacks (on a substrate)

Phase diagram of DPPC-water Janiak et al., Biochemistry (1976) Chain melting transition

Diffraction geometries 1. Unaligned samples (MLV) 2. Multilayers on a substrate Geometric corrections

The fluid phase Occurs above the chain melting transition One dimensional periodicity Liquid-like in-plane order d   - bilayer thickness  - lipid volume fraction

The gel phase phase – no chain tilt phase – tilted chains No trans-bilayer correlation of tilt direction

Phase diagram of hydrated DMPC Smith et al., Phys. Rev. Lett (1988) NN NNN Arb.

The sub-gel phase Occurs below the gel phase on long incubation Slow transition kinetics Appearance of a few additional peaks in the diffraction pattern Molecular superlattice Advantage of oriented samples VAR & J Katsaras Phys Rev Lett (1995)

Intensity of the scattered beam Structure factor Form factor density-density correlation function

Models for the lamellar structure factor 1D crystal f(q) sampled at the reciprocal lattice points bilayer - center of symmetry – f(q) real determination of |f(q)| from swelling expts equal weight for all reflections

Paracrystalline model Stack of parallel layers with mean separation D mean square fluctuation – Uncorrelated fluctuations Decreasing peak height with increasing order Tails (A. Guinier)

Thermal fluctuations in the lamellar phase (de Gennes & Prost; Chaikin & Lubensky) Density Fluctuations in the phase Normal modes - equipartition of energy

Landau – Peierls instability No long-range order Power-law decay of correlations – quasi-long-range order

The structure factor = 0, 0.1, 0.2 Nallet et al., J. Phys. II (1993) Broadening – resolution function - finite size Caille, C.R. Hebdo. Acad. Sci. Paris (1972) Approximate relation valid far from the peaks

Unoriented (powder) samples Safinya et al., Phys. Rev. Lett. (1986) Rounding due to finite size Power-law decay

A better approximation for S(q) Zhang et al., Phys. Rev. E (1994)

Electron density profiles |F(h)| obtained from integrating the data over a q-range about the peak Correct it by integrating S(q) over the same range Phases from trial and error or modeling Corrections not too important Nagle et al., Biophys. J. (1996)

Modeling the electron density Models with a few adjustable parameters Their values from the best fit between calculated and observed |F(h)| Also gives the phases Data from different samples with differing water contents can be used No truncation errors (Fourier wiggles) Nagle et al., Biophys. J. (1996)

Modeling I(q) Calculate S(q) and f(q) from models Model parameters from the best fit Pabst et al., Phys. Rev. E (2000)

Determination of K and B Oriented samples Parameters In-plane correlation length ~ K/B Lyatskaya et al., Phys. Rev. E (2000)

The ripple phase

Electron density map of the ripple phase Sun et al., PNAS (1996); Sengupta et al. Phys. Rev. Lett. (01) Vary the model parameters to get the best fit with observed data Center of symmetry – phases 0 or  Calculated phases, observed magnitudes Packing of chains in the bilayer?

Small angle neutron scattering I (q) ~ |f (q)|² S(q) Systems with short-range order High dilution S(q) ~ 1 Neutrons – scattering cross section different for isotopes contrast variation deuterated chains and solvent

The “bicelle” mixture Mixtures of long-chain and short-chain lipids: DMPC-DHPC DMPC DHPC DMPC Used for orienting macromolecules in High-resolution NMR studies Sanders and Prosser, Structure 6, 1227 (1998) Bicelle – disc-like micelle Different morphologies preferred by the two DMPC – bilayers DHPC – micelles Leads to novel behavior of the mixtures

The Magnetically Alignable Phase Ф = 20 wt % I - isotropic B - ? Aligns in a field L – fluid lamellar Raffard et al, Langmuir 16, 7655 (2000) DMPC-DHPC Phase diagram from NMR

Bicelles Dilute solutions Below chain melting transition Nieh et al., Biohys J. (2001)

Monodisperse unilamellar vesicles Very dilute solutions Above chain melting transition Nieh et al., Langmuir (2001)

Phase behaviour – dilute regime Lipid Con. (g/mL) ULV Bilayers Bicelles T( o C) Charged ‘bicelle’ mixture - DMPC+ DHPC + DMPG M.-P. Nieh, et al. Biophys. J., 82, 2487 (2002)

Concentrated solutions [DMPC]/[DHPC] = 3.2 I (q) ~ |f (q)|² S(q) Linear aggregate: |f (q)|² ~ q Bicelles (disc-like micelles) Nieh et al., Biophys. J. 82, 2487 (2002) High viscosity - ribbons (worm-like micelles) Porod’s law

The phase diagram [DMPC]/[DHPC] = 3.2 From microscopy and SANS No bicelles at higher T Nematic phase of ribbons - high viscosity - magnetic field induced alignment M.-P. Nieh et al., Langmuir (2004)

Antimicrobial peptides in bilayers Brogden, Nature (2005) Alamethicin – 20 amino acid peptide - produced by a fungus Amphipathic – hydrophilic on one side and hydrophobic on the other

SANS studies of pores in bilayers In-plane scattering Solvent – heavy water He et al., Biophys. J. (1996)

The form factor He et al., Biophys. J. (1996)

The structure factor Lipid /peptide ~ 10 Determined from simulations

Effect of contrast variation He et al., Biophys. J. (1996)

The structure of the pore