markus deserno carnegie mellon university coarse-grained simulation studies of mesoscopic membrane...
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Markus DesernoMarkus Deserno
Carnegie Mellon University Carnegie Mellon University
Coarse-grained simulation studies of
mesoscopic membrane phenomena
Coarse-grained simulation studies of
mesoscopic membrane phenomenaDepartment of PhysicsDepartment of Physics
with: Ira R. Cooke, Gregoria Illya, Benedict J. Reynwar, Vagelis A. Harmandaris, Kurt Kremer @ MPI-P
IMA Workshop on the Development and Analysis of Multiscale MethodsIMA Workshop on the Development and Analysis of Multiscale Methods
November 5, 2008November 5, 2008
Quick motivationMembranes
http://www.animalport.com/img/Animal-Cell.jpg
Typical illustration of an animal cell
Typical illustration of an animal cell
Quick motivationMembranes
Almost everything you see here are
membranes!
Almost everything you see here are
membranes!
http://www.animalport.com/img/Animal-Cell.jpg
Typical illustration of an animal cell
Typical illustration of an animal cell
Quick motivationMembranes
Almost everything you see here are
membranes!
Almost everything you see here are
membranes!
http://www.animalport.com/img/Animal-Cell.jpg
Notice the many changes in
morphology!
Notice the many changes in
morphology!
Membranes need to be constantly reshaped in order to do their task.
The available energy is (bio)chemical;typically coming from ATP hydrolysis.
Eavailable ~ 20 kBT (physiol. cond.)
Quick motivation
Membranes need to be constantly reshaped in order to do their task.
The available energy is (bio)chemical;typically coming from ATP hydrolysis.
The elasticity of membranes needs to match the available deformation energies!
Eavailable ~ 20 kBT (physiol. cond.)
Quick motivation
3121
B20 hYTk Membrane
bending modulus
3121
B20 hYTk Membrane
bending modulus
3121
B20 hYTk
Young’s modulusYoung’s modulus
thicknessthickness
Membrane bending modulus
3121
B20 hYTk
Young’s modulusYoung’s modulus
thicknessthicknessEnergy matchEnergy match
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
thicknessthicknessEnergy matchEnergy match
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
Pa107Y
thicknessthicknessEnergy matchEnergy match
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
Pa107Y
thicknessthicknessEnergy matchEnergy match
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
Pa107Y
thicknessthicknessEnergy matchEnergy match
Let’s hypothesize…
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
Pa107Y
…and insist on metal!…and insist on metal!
thicknessthicknessEnergy matchEnergy match
3121
B20 hYTk
nm5h
Young’s modulusYoung’s modulus
Pa1011Y
thicknessthicknessEnergy matchEnergy match
…and insist on metal!…and insist on metal!
3121
B20 hYTk
Young’s modulusYoung’s modulus
Pa1011Y
thicknessthickness
2h Å
Energy matchEnergy match
…and insist on metal!…and insist on metal!
3121
B20 hYTk
Young’s modulusYoung’s modulus
Pa1011Y
thicknessthickness
2h Å
Energy matchEnergy match
Fail!Fail!
…and insist on metal!…and insist on metal!
Membranes must be made from soft materials!
Moral:
We will invariably encounter long time scales!
Quick motivation (II)Long time scales – How bad is it?
Long time scales – How bad is it?Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayersfrom molecular dynamics simulations.Biophys. J. 79, 426-433 (2000).
All-atom lipid bilayer20nm20nm, 1024 lipids, 10ns
Quick motivation (II)
Long time scales – How bad is it?Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayersfrom molecular dynamics simulations.Biophys. J. 79, 426-433 (2000).
All-atom lipid bilayer20nm20nm, 1024 lipids, 10ns
What if we want a boxlength of L=200nm?
How does computing effort scale with L?
Quick motivation (II)
Long time scales – How bad is it?Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayersfrom molecular dynamics simulations.Biophys. J. 79, 426-433 (2000).
All-atom lipid bilayer20nm20nm, 1024 lipids, 10ns
What if we want a boxlength of L=200nm?
How does computing effort scale with L?
effort ~ L2
Amount of material
Quick motivation (II)
Long time scales – How bad is it?Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayersfrom molecular dynamics simulations.Biophys. J. 79, 426-433 (2000).
All-atom lipid bilayer20nm20nm, 1024 lipids, 10ns
What if we want a boxlength of L=200nm?
How does computing effort scale with L?
effort ~ L2 L4
Equilibration timeAmount of material
Quick motivation (II)
Long time scales – How bad is it?Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayersfrom molecular dynamics simulations.Biophys. J. 79, 426-433 (2000).
All-atom lipid bilayer20nm20nm, 1024 lipids, 10ns
What if we want a boxlength of L=200nm?
How does computing effort scale with L?
effort ~ L2 L4 ~ L6
Equilibration timeAmount of material
Quick motivation (II)
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
206 210
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
206 210 20 doublings of computer power!
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
206 210 20 doublings of computer power!
20 x 2 years (Moore’s law)
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
206 210 20 doublings of computer power!
20 x 2 years
40 years
(Moore’s law)
Long time scales – How bad is it?Quick motivation (II)
20nm20nm 200nm200nmMillion times more
computationally expensive!
Million times more computationally
expensive!
206 210 20 doublings of computer power!
20 x 2 years
40 years
I’ll be retired by then!
(Moore’s law)
(best case scenario)
This is why
we all love
coarse graining
Today:
I’ll illustrate a way to
efficiently treat the
~100nm regime.
• Generic top-down bead-spring• solvent free• only pair forces• robust & physically meaningful
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005);I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
attraction range
tem
per
atu
re
unstableunstable
fluid phasefluid phase
gel-phase(s)gel-phase(s)
Today:
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005);I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
attraction range
tem
per
atu
re
unstableunstable
fluid phasefluid phase
gel-phase(s)gel-phase(s)
Today:
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005);I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
Long-ranged attractions “save” the system some entropy!
attraction range
tem
per
atu
re
unstableunstable
fluid phasefluid phase
gel-phase(s)gel-phase(s)
Today:
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005);I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
Long-ranged attractions “save” the system some entropy!
A.P. Gast, C.K. Hall, and W.B. Russel,J. Coll. Interface Sci. 96, 251 (1983);
M.H.J. Hagen, D. Frenkel,J. Chem. Phys. 101, 4093 (1994);A.A. Louis, Phil. Trans. R. Soc.
Lond. A 359, 939 (2001).
A.P. Gast, C.K. Hall, and W.B. Russel,J. Coll. Interface Sci. 96, 251 (1983);
M.H.J. Hagen, D. Frenkel,J. Chem. Phys. 101, 4093 (1994);A.A. Louis, Phil. Trans. R. Soc.
Lond. A 359, 939 (2001).
attraction range
tem
per
atu
re
unstableunstable
fluid phasefluid phase
gel-phase(s)gel-phase(s)
Today:
I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005);I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
Long-ranged attractions “save” the system some entropy!
Shape of CG potential is qualitatively important!
A.P. Gast, C.K. Hall, and W.B. Russel,J. Coll. Interface Sci. 96, 251 (1983);
M.H.J. Hagen, D. Frenkel,J. Chem. Phys. 101, 4093 (1994);A.A. Louis, Phil. Trans. R. Soc.
Lond. A 359, 939 (2001).
A.P. Gast, C.K. Hall, and W.B. Russel,J. Coll. Interface Sci. 96, 251 (1983);
M.H.J. Hagen, D. Frenkel,J. Chem. Phys. 101, 4093 (1994);A.A. Louis, Phil. Trans. R. Soc.
Lond. A 359, 939 (2001).
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Material properties
Material propertiesProbably most important: bending modulus
Material properties
Can be determined in two very different ways
From fluctuations From deformations
Probably most important: bending modulus
Material properties
From fluctuations From deformations
Probably most important: bending modulus
Material properties
From fluctuations From deformations
energy of cylinder
force tohold it
Probably most important: bending modulus
V. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
Material properties
From fluctuations From deformations
energy of cylinder
force tohold it
Probably most important: bending modulus
V. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
Both ways give the same answer
Shows that Helfrich theory worksup to extremely large curvature
Material properties
From fluctuations From deformations
energy of cylinder
force tohold it
Probably most important: bending modulus
V. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
Both ways give the same answer
Shows that Helfrich theory worksup to extremely large curvature
~ 3…30 kBT ~ 3…30 kBT
Other Material properties
I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
Expansion modulus
Line tension
~ 100 dyn/cm
~ 10 pN
Other Material propertiesExpansion modulus
Line tension
thermal expansivity
~ 100 dyn/cm
~ 10 pN
~ 2×10-3 K-1
I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Adsorption to a substrate
bilayersubstrate
M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
picture:M.I. Hoopes
Adsorption to a substrate
proximal leaflet
distal leaflet
z
bilayersubstrate
M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
picture:M.I. Hoopes
Adsorption to a substrate
bilayer
proximal leaflet
distal leaflet
zp i(z
) free
z
p i(z) supported
z
substrate
M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
picture:M.I. Hoopes
Adsorption to a substratep i(z
) free
z
p i(z) supported
z
Major suppression of perpendicular lipid fluctuations in the proximal leaflet.
Entropy loss, since
Reduction of free energy of binding (here: ~25%)
)(log)(dB zpzpzkS ii
M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
area/lipid
bila
yer
pres
sure
freesupported
substrate interactions excluded
substrate interactions included
Adsorption to a substrate• “Zero tension case” needs to be precisely defined• Compressibility increases, since fluctuations are damped
M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Lipid curvature effects
The model of Israelachvili, Mitchell and NinhamJ. Chem. Soc., Faraday Trans. 272 1525 (1976)
LA
VP
packing parameter
V = lipid volumeL = lipid lengthA = lipid head area
Lipid curvature effects
The model of Israelachvili, Mitchell and NinhamJ. Chem. Soc., Faraday Trans. 272 1525 (1976)
0 1/3 1/2 1
P
LA
VP
packing parameter
V = lipid volumeL = lipid lengthA = lipid head area
Lipid curvature effects
The model of Israelachvili, Mitchell and NinhamJ. Chem. Soc., Faraday Trans. 272 1525 (1976)
0 1/3 1/2 1
P
LA
VP
packing parameter
V = lipid volumeL = lipid lengthA = lipid head area
Lipid curvature effects
50:50mixture
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
Lipid curvature effects
50:50mixture
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
R
Lipid curvature effects
50:50mixture
Simple model gives:
Density of big headed lipids in the outer monolayer
Density of big headed lipids in the inner monolayer
Linear in bilayer
curvature!
R
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
in
outln
K
Lipid curvature effects
50:50mixture
Simple model gives:
Density of big headed lipids in the outer monolayer
Density of big headed lipids in the inner monolayer
Linear in bilayer
curvature!
R
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
in
outln
K
Lipid curvature effects
50:50mixture
R
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
nm50R
0.03
That’s small !
…for realistic membranecurvatures the effect is
not enough to drive sorting!
in
outln
K
Lipid curvature effects
50:50mixture
R
I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
nm50R
0.03
That’s small !
…for realistic membranecurvatures the effect is
not enough to drive sorting!
Tian & Baumgart, preprint
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Peptide-induced pore formation
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
AntimicrobialPeptide
“magainin”
Peptide-induced pore formation
Example above:
Peptides:
n
bead
s
m beadsm
nP – peptide
28P
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
Example above:
Peptides:
n
bead
s
m beadsm
nP – peptide
28P
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
Surface adsorbed
Monolayer contact
Sliding in
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
breakthrough
Surface adsorbed
Monolayer contact
Sliding in
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
Binding strength kBT=1.7 kBT=1.9
1.5 stray stray1.6 bound bound/inserted1.7 inserted inserted1.8 inserted inserted
1.4 stray stray1.5 bound inserted1.6 inserted inserted1.7 inserted inserted1.8 inserted inserted
26P
28P
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
Binding strength kBT=1.7 kBT=1.9
1.5 stray stray1.6 bound bound/inserted1.7 inserted inserted1.8 inserted inserted
1.4 stray stray1.5 bound inserted1.6 inserted inserted1.7 inserted inserted1.8 inserted inserted
26P
28P
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Let us now look at this system consisting of
many of these peptides
Let us now look at this system consisting of
many of these peptides
Peptide-induced pore formation
• Stronger joint perturbation• Sliding in very efficient
…of a peptide which alone does not insert within 25000
c) g) 3000G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
08P 1
8P 28P 3
8P
5.1c w
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
08P 1
8P 28P 3
8P
5.1c w
6.1c w2
6P
No peptide attraction
Some peptide attraction
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Peptide-induced pore formation
08P 1
8P 28P 3
8P
5.1c w
6.1c w2
6P
No peptide attraction
Some peptide attraction
toroidal
barrel-stave
G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
attraction range
tem
per
atu
re
Lipid A-B–mixtures
B.J. Reynwar & M. Deserno, Biointerphases (accepted)
attraction range
tem
per
atu
re
heterotypic homotypic
Lipid A-B–mixtures
BBAAAB www B.J. Reynwar & M. Deserno, Biointerphases (accepted)
BBAAAB www
Lipid A-B–mixtures
B.J. Reynwar & M. Deserno, Biointerphases (accepted)
ideal lipid mixture non-ideal lipid mixture
Composition-induced protein aggregation
Lipid A-B–mixtures+proteinsProteins only adsorb on blue lipids
B.J. Reynwar & M. Deserno, Biointerphases (accepted)
Pair potentials can be fittedby simple ground state theory.
Lipid A-B–mixtures+proteins
B.J. Reynwar & M. Deserno, Biointerphases (accepted)
Illustrations:
• Material properties
• Adsorption to a substrate
• Lipid curvature effects
• Peptide-induced pore formation
• Lipid mixtures
• Protein-induced budding
Protein-induced buddingB. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006)
Protein-induced buddingB. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006)
Membrane-curving proteins can attract and drive
membrane vesiculation
Membrane-curving proteins can attract and drive
membrane vesiculation
Protein-induced buddingB. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006)
Membrane-curving proteins can attract and drive
membrane vesiculation
Membrane-curving proteins can attract and drive
membrane vesiculation
Intuitive, but no physical justification!
Protein-induced budding
36 curved caps, ~50000 lipids,160nm side-length, total time ~1msno lateral tensionno explicit interaction between caps
36 curved caps, ~50000 lipids,160nm side-length, total time ~1msno lateral tensionno explicit interaction between caps
many caps
B.J. Reynwar et al., Nature 447, 461 (2007)
(“contact lens”)
Protein-induced budding
B.J. Reynwar et al., Nature 447, 461 (2007)
Protein-induced budding
B.J. Reynwar et al., Nature 447, 461 (2007)
Some observations:
• Caps attract collectively• Attractive pair-forces exist• No crystalline structure• Cooperative vesiculation• No “scaffolding”• 50-100nm length scales• several milliseconds
Some observations:
• Caps attract collectively• Attractive pair-forces exist• No crystalline structure• Cooperative vesiculation• No “scaffolding”• 50-100nm length scales• several milliseconds
Protein-induced budding
Blood and Voth, PNAS 103, 15068 (2006)
Protein-induced budding
Blood and Voth, PNAS 103, 15068 (2006)
G.S. Ayton, P.D. Blood, and G.A. Voth, Biophys. J. 92, 3595 (2007)
Protein-induced budding
Blood and Voth, PNAS 103, 15068 (2006)
G.S. Ayton, P.D. Blood, and G.A. Voth, Biophys. J. 92, 3595 (2007)
A. Arkhipov,Y. Yin,K. Schulten. Biophys. J. 95, 2806 (2008)
Summary
CG membrane model can efficiently treat many mesoscopic membrane processes.
Physical properties turn out reasonable
Link to finer scale ought to be possible!
Link to continuum elastic level works
(under way)
GregoriaGregoria
VagelisVagelis
(me)(me)DavoodDavood
MartinMartinIraIra
BenBen
Acknowledgements
MPI-PMPI-P
Kurt Kremer, Eva Sinner,Jemal Guven
Matt Hoopes, Roland FallerTristan Bereau, Zunjing Wang
…and many more
Kurt Kremer, Eva Sinner,Jemal Guven
Matt Hoopes, Roland FallerTristan Bereau, Zunjing Wang
…and many more
Material properties
From fluctuations From deformations
Probably most important: bending modulus
V. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
/ kBT 11.70.2 / kBT 12.51