x-ray and neutron diffraction studies of lipid bilayers v a raghunathan raman research institute,...
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X-ray and Neutron diffraction studies of lipid bilayers
V A Raghunathan
Raman Research Institute, Bangalore
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Phospholipids
Major component of cell membranes
Amphiphilic molecules Self-assemble to form bilayers
Critical micellar concentration (CMC) ~ 1 n M
Phosphatidylcholine (PC)
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Morphologies of lipid bilayers
Unilamellar vesicles (ULV)
Multilamellar vesicles (MLV) liposomes
Multilamellar stacks (on a substrate)
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Phase diagram of DPPC-water
Janiak et al., Biochemistry 15 4575 (1976)
Chain melting transition
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Diffraction geometries
1. Unaligned samples (MLV)
2. Multilayers on a substrate
Geometric corrections
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The fluid phase
Occurs above the chain melting transitionOne dimensional periodicityLiquid-like in-plane order
d - bilayer thickness - lipid volume fraction
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The gel phase
phase – no chain tilt
phase – tilted chains
No trans-bilayer correlation of tilt direction
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Phase diagram of hydrated DMPC
Smith et al., Phys. Rev. Lett. 60 813 (1988)
NN NNN Arb.
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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)
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Intensity of the scattered beam
Structure factor
Form factor
density-density correlation function
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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
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Paracrystalline model
Stack of parallel layers with mean separation D
mean square fluctuation –
Uncorrelated fluctuations
Decreasing peak height with increasing order
Tails
(A. Guinier)
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Thermal fluctuations in the lamellar phase (de Gennes & Prost; Chaikin & Lubensky)
Density
Fluctuations in the phase
Normal modes - equipartition of energy
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Landau – Peierls instability
No long-range order
Power-law decay of correlations – quasi-long-range order
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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
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Unoriented (powder) samples
Safinya et al., Phys. Rev. Lett. (1986)
Rounding due to finite size
Power-law decay
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A better approximation for S(q)
Zhang et al., Phys. Rev. E (1994)
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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)
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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)
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Modeling I(q)
Calculate S(q) and f(q) from models Model parameters from the best fit
Pabst et al., Phys. Rev. E (2000)
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Determination of K and B
Oriented samples
Parameters
In-plane correlation length ~ K/B
Lyatskaya et al., Phys. Rev. E (2000)
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The ripple phase
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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?
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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
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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
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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
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Bicelles
Dilute solutions Below chain melting transition
Nieh et al., Biohys J. (2001)
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Monodisperse unilamellar vesicles
Very dilute solutions
Above chain melting transition
Nieh et al., Langmuir (2001)
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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)
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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
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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)
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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
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SANS studies of pores in bilayers
In-plane scattering
Solvent – heavy water
He et al., Biophys. J. (1996)
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The form factor
He et al., Biophys. J. (1996)
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The structure factor
Lipid /peptide ~ 10
Determined from simulations
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Effect of contrast variation
He et al., Biophys. J. (1996)
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The structure of the pore