Markus Deserno Carnegie Mellon University Coarse-grained simulation studies of mesoscopic membrane...

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