Simple Solvent-Free Molecular Modelto Simulate Bilayer Membrane

Hiroshi Noguchi
ISSP, University of Tokyo
ISSP/SOFT2010

・ Biomembrane
CellPlasma membrane

10nm
~10µm
Large scale gap

http://upload.wikimedia.org/wikipedia/commons/1/10/Illu_cell_structure.jpg

Membrane models∼ µm

curved surface( no bilayer structure）

Numericallyfastergo down
molecular model

length andtime scalecoarse grained
molecule
atomistic model
bottom up

More detailed
information

Shinoda etc.
Tieleman, et al. BBA 1331, 225 (1997)~ nm

● curved surface● theory: continuous surface

C1, C2:principal curvatures、C0:spontaneous curvature● simulation: discretized surface● mesh methods ● meshless methods

A particle represents
a membrane patch.

● mesh method
degrees of freedom: positions and connections of particles
fluid membraneby bond flip (Monte Carlo)

for fixed topology
works very well
Ochanomizu Lecture (Aug. 23)
by G. Gompper
disadvantage
dynamics with topological changes

● meshless methods
1) degrees of freedom: positions and orientation
Drouffe, Maggs, S. Leibler Science 254, 1353 (1991).
Del Popolo (2008); T. Kohyama (2009);
P. Liu (2009); H. Yuan (2010).

2) degrees of freedom: only positions
Noguchi and Gompper Phys. Rev. E 73, 021903 (2006).

Advantage:
Naturally applied to the topological changes

21.5

A0 /Nσ2

1.4

A0 /Nσarea oftensionlessmembranekα and ε dependence

1.45

1.2

KAσ / T

A22K σ /T402020κ/ T4020

Γσ / TΓσ / T

19180line tension

4020

κ/ T

bending
rigidityarea
compressmodulus60

4ε /T=462d4kα/T=102010kα / T20κ and Γ can be independently varied.

24ε/T

6

Vesicle formation

Very large membrane Rdis/σ >> 8kα/ε
Buckling into two vesicles is also possible.

● rupture

ε/T= 1.5 -> 1.3<t rup >D 0 /σ 2

10000

1000

BD
MPC

100

1.2

1.3

ε /k BT

Noguchi and Gompper J. Chem. Phys. 125, 164908 (2006).

1.4

curved surface

1 particle or segment>~ 100 lipid moleculesσ~> thickness
molecular model

length scale >10times~

1 coarse-grained molecule= 1~4 lipid molecules

・Coarse-graining of lipids

with explicit solvent
atomistic models

without explicit solvent

coarse-grained models?

Klein et al.

0.1nm

0.4 nm1nm

solvent-free molecular model for bilayer membrane
H. Noguchi, M. Takasu (2001)

modifications
O. Farago (2003)
G. Brannigan, F.L.H. Brown (2004)
G. Brannigan, P.F. Philips, F.L.H. Brown (2005)
I.R. Cooke, K. Kremer, M. Deserno (2005)
Z.J. Wang, D. Frenkel (2005)
J.D. Revalee, M. Laradji, P.B.S.Kumar (2008).
M. Hoemberg, M. Mueller (2010).

Only narrow parameter range
Aim 1: make a model for wide parameter range

Aim 2: Coarse graining more to simulate larger scale

3 spheres

1 sphereContinuum theory
for bilayer membrane

Membrane bending, area dilation,
molecular tilt, chain stretching.
Fournier, EPL 43, 725 (1998).

Tilt + bending of membranetilt + bendingu=ntilt onlyunbending onlyu
Kozlovsky and Kozlov, Biophys. J. 2002n

● Our new model

local density

● Self-assembly

Vesicle formation

surface tension
tensionless membrane

bilayer structurebending rigidity κ

linear dependenceon ktilt and kbend

line tension
line tension

line tension ofmembrane edge

● ruptureCʼ0 = 0 -> 0.85

● droplet-vesicle transition

Bilayer is metastable at ktilt = 0.

Preliminary simulation: Membrane fusion

Optical tweezers
External force

Fusion!

2.5mm
Dai et al., J. Neurosci. 18, 6681 (1998).

Experimental studies

Quick-freezing Electron
microscopy images Bars, 100 nm.
Kanaseki et al. J. Cell Biol. 137, 1041 (1997).

Electric resistance measurement
V.A. Frolov et al. Biophys. J. 85, 1725 (2003).

fusion pathways found by simulations
Solvent-free models
Noguchi et al. 2001
Lattice MC
Mueller, et al. 2002
LJ modelMarrink et al. 2003
Stevens et al. 2003
Smeijers, et al. 2006
Kasson et al. 2007
DPD model
Li and Liu 2005
Shillcock et al. 2005
Atomistic model
Knecht and Marrink 2007

Membrane fusion by mechanical force

Pathway of modified stalk model

Distance between
nanoparticles Xnp

My previous simulation
nm30

20

1005000

10000 ns

Time step t

StochasticallyNoguchi J. Chem. Phys. 117, 8130 (2002).

Summary○ A new CG model is proposed.
・ Minimum molecular size: a sphere and orientation
・ Membrane properties can be varied in wide range(including metastable bilayer).
・ Application:
membrane fusion etc.

uoykhanruoyfor!
noit
atten

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Supported by KAKENHI (Grant-in-Aid for Scientific Research)

ISSP Supercomputer

http://fujibakama.issp.u-tokyo.ac.jp/supercom/