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 15 4575 (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 transitionOne dimensional periodicityLiquid-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. 60 813 (1988)

NN NNN Arb.

The sub-gel phaseOccurs below the gel phase on long incubationSlow transition kineticsAppearance of a few additional peaks in the diffraction pattern

Molecular superlatticeAdvantage 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

DHPC

DMPCUsed for orienting macromolecules inHigh-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)

0.0025 0.01 0.05 0.1 0.15 0.25

ULV

Bilayers

Bicelles

T(oC)

55

45

35

25

10

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-1

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 SANSNo 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