CFDC, Feb. 2, 2009
Mean-field model of self-assembling lipid membranes
with embedded proteins
Kang Chen
and
Glenn Fredrickson
University of California, Santa Barbara
Structure of cell membrane
Structure of
transmembrane protein
(Xanthorhodopsin)
H. Luecke, et al. PNAS
105, 16561 (2008)
•
Complex structure and many species
•
Basic structure: lipid bilayer
•
Membrane protein: biological functions
and processes
Research on membrane/protein assembly
1) Lipid-protein interaction (hydrophobic mismatch)
Membrane deformation
Protein tilting
M. Venturoli, B. Smit, M.M. Sperotto, Biophys. J. 88, 1778 (2005)
2) Membrane-mediated protein-protein interaction
P. A. Kralchevsky et al., J. Chem. Soc. Faraday Trans. 91, 3415 (1995)
Research on membrane/protein assembly
3) Assembling of proteins in the plane of membrane
Sytaxin Proteins organize in
submicrometer-sized clusters
J.J. Sieber, et al., Science 317, 1072
(2007)
Assembly of proteorhodopsin (PR)
with cationic lipids
H. Liang, et al., PNAS 104,
8212 (2007)
Goal:
develop a coarse-grained field-theoretic model of the assembling
membrane/protein system
First step:
a single membrane protein embedded in a field-theoretic description
of a lipid/water system
Outline:
•
•
•
Briefly introduce the field-theoretic method
Details of the model
Preliminary results
Field-theoretic method
Define density operators: ρˆ (r)
Express interactions in terms of density
operators: ∫ dr ∫ dr ′ρˆ (r )ν (r , r ′) ρˆ (r ′)
Decouple interactions by the typical field theoretical
technique: Hubbard-Stratonovich transformation ω (r )
∫ Dω e
− H (ω )
≈e
− H (ω * )
Self-consistent Field Theory
(mean field)
ω (r )
sampling
Field-theoretic Simulation
(complex Langevin dynamics)
• • •
Coarse-grained models of the species
• Assembling species: lipids, water and counterions
• A single immovable protein
i) Model of assembling species:
•
•
Hydrophilic head and Hydrophobic tail
•
Vh=2.8Vc
Hydrophobic tail is treat as a Gaussian
chain containing five segments
Reverse phase transition
(Neutral lipid)
Won Bo Lee, etc. PRL, 2007; JCP, 2008
+
(Free water)
(counterion)
(Cationic lipid)
charge density ∝ head density
space-filling object
negative charged; no
volume
Coarse-grained models of the species
Hydrophilic hats
ii) Model of immovable protein:
1) The protein has a cylinder shape with two
hydrophilic hats and hydrophobic body.
2) The occupation of protein is realized by
assigning density values. Incompressibility
constraint ensures the exclusion of other
species from the protein-occupied regime.
3) The hydrophilic and hydrophobic features
of the hats and body are realized by the
smooth decay of the protein density from
bulk value to zero at the interface.
Thickness of boundary ~ 1
segment length
Hydrophobic
body
Coarse-grained interactions
1) Incompressibility (excluded volume):
χ h1,t
2) Bonded interaction (Gaussian
stretching energy of lipid tail):
1
βU 0 = 2
4 Rg
dRi ( s )
∑i ∫0 ds ds
1
χ h 2, w
χ h1, w
⎛
⎞
ˆ
δ ⎜ ρ 0 − ∑ ρl ( r ) ⎟
l
⎝
⎠
χ c ,h1
χ h 2,t
χ h 2,b
χ c ,b
χ h1,b
2
χb,w
χ c,w
χt ,w
+
χ c ,t
3) Non-bonded short-range interactions (Flory-Huggins parameters):
βU1 = ρ0 ∫ dr ∑ χ l ,m ρˆl ρˆ m
l <m
4) Long-range coulomb interaction:
1 e2
dr ∫ dr ′ρˆ e (r )ν (r , r ′) ρˆ e (r ′)
βU c =
∫
2 k BT
∇ ⋅ (ε (r )∇Φ (r )) = −eρˆ e
decouple
Electric potential
field Φ (r )
ε (r ) = ∑ ε l ρˆ l (r )
l
χ c,h 2
Mean field results
Z = ∫ Dr e
−β H [r ]
HS transformation
• "Mean-field" approximation (SCFT) :
Z =e
Lipid tail density profile in the lamellar regime:
Z = ∫ Dω D ρ e − β H [ω , ρ ]
− H [ω * , ρ * ]
i.e. F ≈ H [ω * , ρ * ]
Mean field results
Lipid tail density profile in the two-phase regime:
• Isolate a single bilayer membrane
• No periodic structure; initial biased seed is needed
negative mismatch
Mean field results
positive mismatch
DPD simulations: Venturoli et al.
Biophys. J. (2004)
On-going work and future plans
•
Extending the canonical
canonical model
•
•
Lipid-induced protein tilting
•
The effect of adding salt
•
Membrane-mediated potential of mean force
between two proteins: the two proteins may be
identical or have different sizes, shapes and
charged status
•
Comparing the stability of square and hexagonal
in-plane packing of proteins
•
Full field-theoretic calculation of the assembling
multi-protein, multi-lipid system
model
to
Membrane deformation and cationic
distribution with a charged protein
Grand
lipid
Acknowledgements
•
Prof. Glenn H. Fredrickson
•
Fredrickson Group
•
Galen Stucky, Song-I Han, Evgeni Penev
•
Institute for Multiscale Materials Science (IMMS)