Lipid membranes between nano and

micro:

Lipid membranes between nano and

micro:

Markus DesernoMax-Planck-Institut für Polymerforschung, Mainz

Cells and Materials, Workshop I: Membrane Protein Science and Engineering

http://www.mpip-mainz.mpg.de/~desernohttp://www.mpip-mainz.mpg.de/~deserno

IPAM, Los Angeles, California, USA

deserno@mpip-mainz.mpg.dedeserno@mpip-mainz.mpg.de

A solvent-free coarse-grained simulation model

A solvent-free coarse-grained simulation model

(and what we can learn from it)(and what we can learn from it)

Motivation

Motivation

Cells !

Motivation

Cells & Materials !

Motivation

Cells & Materials?

Some simple scaling

Some simple scaling

Thickness: 5 nm

Some simple scaling

Thickness: 5 nm

Lipids ~ dense hydrocarbons ~ typical length scale: 5 nm ~ between rubber and plastic ~ Young modulus: Pa107

Some simple scaling

Pa107Y

3121 hY

nm5h

Some simple scaling

Pa107Y

3121 hY

Young’s modulusbending modulus

membrane

thickness

nm5h

Some simple scaling

Pa107Y

3121 hY

Young’s modulusbending modulus

membrane

thickness

nm5h

TkB25

Some simple scaling

Pa107Y

3121 hY

Young’s modulusbending modulus

membrane

thickness

nm5h

TkB25 That’s about right!

ImplicationsBending modulus of phospholipid bilayers:

a few tens of kT

Why’s that such an interesting value?

ImplicationsBending modulus of phospholipid bilayers:

a few tens of kT

Why’s that such an interesting value?• bigger than thermal energy

Bilayer doesn’t fluctuate into pieces!

ImplicationsBending modulus of phospholipid bilayers:

a few tens of kT

Why’s that such an interesting value?• bigger than thermal energy

Bilayer doesn’t fluctuate into pieces!

• not much bigger than thermal energy

Nano-sources of energy can deform it!

ImplicationsBending modulus of phospholipid bilayers:

a few tens of kT

Why’s that such an interesting value?

Ideal material for nano-technology !

• bigger than thermal energy

Bilayer doesn’t fluctuate into pieces!

• not much bigger than thermal energy

Nano-sources of energy can deform it!

But front-cover “NanoTech” seems to be shiny metal stuff!

But front-cover “NanoTech” seems to be shiny metal stuff!

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

TkB25

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

TkB25 Pa1010

(metal)

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

TkB25 Pa1010

nm5.0h

(metal)

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

TkB25 Pa1010

nm5.0h

falls apart !(metal)

But front-cover “NanoTech” seems to be shiny metal stuff!

Just turn the argument around:

3121 hY

TkB25 Pa1010

nm5.0h

falls apart !

Nanotechnology

invariably means

soft matter!

Nanotechnology

invariably means

soft matter!

(metal)

Nature has found out first!

Membranes everywhere !

A closer look…Lipid bilayers show interesting physics on many different length scales.

Self-assembly

Protein-embeddingFluidity

Pressure-profilesBending-deformations

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

A closer look…Lipid bilayers show interesting physics on many different length scales.

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

Lipid bilayers show interesting physics on many different length scales.

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

any

A closer look…

Lipid bilayers show interesting physics on many different length scales.

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

Theory

any

A closer look…

Lipid bilayers show interesting physics on many different length scales.

Simulation

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

Theory

any

A closer look…

Lipid bilayers show interesting physics on many different length scales.

Simulation

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

Experiment

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

Theory

any

A closer look…

Lipid bilayers show interesting physics on many different length scales.

Simulation

J. G

ould

and W

. K

eeto

n,

Bio

logic

al Sci

ence

,6

th e

d.

(W.W

. N

ort

on,

New

York

, 1

99

6)

Experiment

When studying this system, one’s approach should be tuned towards the length scale one intends to probe.

Theory

any

A closer look…

Simulation of lipid membranes

i n c r e a s i n g l y c o a r s e g r a i n e d

much detail little detail

atomistic models triangulated surfacesbead-spring models

“standard”Lennard-Jones

DPD solvent free

increasing numerical efficiencymatter of debate…

Marrink; Klein, Sansom; Scott; Voth; …

Gompper&Kroll,…

Goetz&Lipowsky;Stevens; …

Groot&Rabone;Shillcock&Lipowsky;Laradji&Kumar, …

Drouffe&Maggs&Leibler;Noguchi&Takasu; Farago;

Brannigan&Brown

Simulation of lipid membranes

i n c r e a s i n g l y c o a r s e g r a i n e d

much detail little detail

atomistic models triangulated surfacesbead-spring models

“standard”Lennard-Jones

DPD solvent free

increasing numerical efficiencymatter of debate…

Marrink; Klein, Sansom; Scott; Voth; …

Gompper&Kroll,…

Goetz&Lipowsky;Stevens; …

Groot&Rabone;Shillcock&Lipowsky;Laradji&Kumar, …

Drouffe&Maggs&Leibler;Noguchi&Takasu; Farago;

Brannigan&Brown

Why is “solvent free” good?

Why is “solvent free” good?

membrane surface

Why is “solvent free” good?

membrane surface

solvent bulk

Why is “solvent free” good?

membrane surface

solvent bulk

Why is “solvent free” good?

membrane surface

solvent bulk

Studying membranes may well become the study of a finite size

effect!

Studying membranes may well become the study of a finite size

effect!

Illustrative examplemembrane surface

solvent bulk

M. Laradji, P. B. Sunil Kumar,Phys. Rev. Lett. 93, 198105 (2004)

16000 (DPD) lipids times 4 beads per lipid 64000 degrees of freedom for lipids

But in total: 1536000 particles in box

96% of simulation time spent with solvent!

“No solvent” is difficult. Why?Implicit solvent models are very commonand incredibly useful in polymer physics.

Why are they not so common in the membrane field?

“No solvent” is difficult. Why?Implicit solvent models are very commonand incredibly useful in polymer physics.

Why are they not so common in the membrane field?

Polymers don’t first have to self-assemble

“No solvent” is difficult. Why?Implicit solvent models are very commonand incredibly useful in polymer physics.

Why are they not so common in the membrane field?

Polymers don’t first have to self-assemble

One needs to introduce additional cohesive energy for the lipid tails!

kBT, not eV!

“No solvent” is difficult. Why?Implicit solvent models are very commonand incredibly useful in polymer physics.

Why are they not so common in the membrane field?

Polymers don’t first have to self-assemble

One needs to introduce additional cohesive energy for the lipid tails!

kBT, not eV!

“No solvent” is difficult. Why?Implicit solvent models are very commonand incredibly useful in polymer physics.

Why are they not so common in the membrane field?

Fluidity has proven to be the main challenge

Polymers don’t first have to self-assemble

One needs to introduce additional cohesive energy for the lipid tails!

DifficultiesPolymers don’t first have to self-assemble

Fluidity has proven to be the main challenge

“gas” phase

solid bilayer

weak attraction

strong attraction

Empirical observation:

no fluid phase

inbetween!

no fluid phase

inbetween!

DifficultiesPolymers don’t first have to self-assemble

Fluidity has proven to be the main challenge

“gas” phase

solid bilayer

weak attraction

strong attraction

Empirical observation:

no fluid phase

inbetween!

no fluid phase

inbetween!

DifficultiesPolymers don’t first have to self-assemble

Fluidity has proven to be the main challenge

“gas” phase

solid bilayer

weak attraction

strong attraction

Empirical observation:

This observation is incorrect.But we’ll later see where it came from!

Previous and current solutions• J.-M. Drouffe, A. C. Maggs, and S. Leibler, Science 254, 1353 (1991)• H. Noguchi and M. Takasu, Phys. Rev. E 64, 041913 (2001)• Z.J. Wang and D. Frenkel, J. Chem. Phys. 122, 234711 (2005)• H. Noguchi and G. Gompper, Phys. Rev. E 72, 021903 (2006)

• O. Farago, J. Chem. Phys. 119, 396 (2003)

• G. Brannigan and F.L.H. Brown, J. Chem. Phys. 120, 1059 (2004)

• G. Ayton and G.A. Voth, Biophys. J. 83, 3357 (2002)

• I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005)• G. Brannigan, P.F. Philips, and F.L.H. Brown, Phys. Rev. E 72, 011915, (2005)

Previous and current solutions• J.-M. Drouffe, A. C. Maggs, and S. Leibler, Science 254, 1353 (1991)• H. Noguchi and M. Takasu, Phys. Rev. E 64, 041913 (2001)• Z.J. Wang and D. Frenkel, J. Chem. Phys. 122, 234711 (2005)• H. Noguchi and G. Gompper, Phys. Rev. E 72, 021903 (2006)

• O. Farago, J. Chem. Phys. 119, 396 (2003)

• G. Brannigan and F.L.H. Brown, J. Chem. Phys. 120, 1059 (2004)

• G. Ayton and G.A. Voth, Biophys. J. 83, 3357 (2002)

• I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005)• G. Brannigan, P.F. Philips, and F.L.H. Brown, Phys. Rev. E 72, 011915, (2005)

Multibody interactions

Tethered membrane

Highly tuned Lennard-Jones

Angle-dependent potentials

Pair-potentials

Our own model

Three bead lipid

I.R. Cooke, K. Kremer, M. Deserno,Phys. Rev. E 72, 011506 (2005)

Our own model

Three bead lipid

Only three beads

?

I.R. Cooke, K. Kremer, M. Deserno,Phys. Rev. E 72, 011506 (2005)

Our own model

Three bead lipid

Only three beads

?

I.R. Cooke, K. Kremer, M. Deserno,Phys. Rev. E 72, 011506 (2005)

Look at the aspect ratio for real lipids:

3nm0.7

nm5.2

moleculeper area

icknessbilayer th2

21

Our own model

Three bead lipidhead

tail}

[I. R. Cooke, K. Kremer, M. Deserno, 2005)]

Linked by two bonds

Stiffened by (effective) bending potential

Our own model

Three bead lipid

Stiffened by (effective) bending potential

Tail attraction via some generic potential with tunable range

Linked by two bonds

[I. R. Cooke, K. Kremer, M. Deserno, 2005)]

Our own model

Three bead lipid

Stiffened by (effective) bending potential

Tail attraction via some generic potential with tunable range

Linked by two bonds

2 parameters!

[I. R. Cooke, K. Kremer, M. Deserno, 2005)]

Simulation

• Molecular Dynamics• Langevin thermostat• constant volume/area or constant pressure/tension• Simulation software: ESPResSo

http://www.espresso.mpg.dehttp://www.espresso.mpg.de

c-core controlled via tcl scripts

or: pairwise(DPD

thermostat)

Self-assembly

Example of a self-assembly run

4000 lipids, 100LJ between frames (1000), 10kBT

Tensionless phase diagram

gel-phase(s)gel-phase(s)

fluid phasefluid phase

unstableunstable

The tragedy of Lennard-JonesLJ potential with artificially “stretched” minimum

gel-phase(s)gel-phase(s)

fluid phasefluid phase

unstableunstable

Bending modulusFluctuation spectrum from continuum Helfrich theory:

Bending modulusFluctuation spectrum from continuum Helfrich theory:

extrinsiccurvature

surfacetension

“Linearized Monge”

Bending modulusFluctuation spectrum from continuum Helfrich theory:

Fourier expansion plus equipartition theorem:

extrinsiccurvature

surfacetension

“Linearized Monge”

Bending modulusFluctuation spectrum from continuum Helfrich theory:

Fourier expansion plus equipartition theorem:

zero tension

extrinsiccurvature

surfacetension

“Linearized Monge”

Bending modulusFluctuation spectrum from continuum Helfrich theory:

Fourier expansion plus equipartition theorem:

zero tension

extrinsiccurvature

surfacetension

“Linearized Monge”

Bending modulus

determinebendingmodulus

Fluctuation spectrum from continuum Helfrich theory:

Fourier expansion plus equipartition theorem:

zero tension

extrinsiccurvature

surfacetension

“Linearized Monge”

Bending modulus

=0

tunable within experimentally relevant range!

Bending modulus

Worries: We’re only probing very weak bending!

Bending modulus

Worries: We’re only probing very weak bending!

Bending modulus

Worries: We’re only probing very weak bending!

Bending modulus

Worries: We’re only probing very weak bending!

Bending modulus

Worries: We’re only probing very weak bending!

This is much weaker bending than what we’d typically like to do in a

simulation!

Bending modulusAlternative: measure response to bending deformation!

Bending modulusAlternative: measure response to bending deformation!

First imple-mentation:

W.K. den Otter and W.J. Briels,J. Chem. Phys. 118, 4712 (2003)

(Impose undulation mode,measure constraining force bending modulus)

Bending modulusAlternative: measure response to bending deformation!

First imple-mentation:

W.K. den Otter and W.J. Briels,J. Chem. Phys. 118, 4712 (2003)

Easier method: Stretch a membrane tether!

(Impose undulation mode,measure constraining force bending modulus)

[V. Harmandaris and M. Deserno, in preparation]

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:RR

LL

Bending modulus

Energy:

Force:

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:

Force:

Bending modulus:

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:

Force:

Bending modulus:

What about fluctuations?

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:

Force:

Bending modulus:

What about fluctuations?

goes up

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:

Force:

Bending modulus:

What about fluctuations?

goes up goes down

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Energy:

Force:

Bending modulus:

What about fluctuations?

goes up goes down

(plane waveapproximation)

RR

LL

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Simulation:

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Simulation:

Result fromfluctuations

Bending modulus

[V. Harmandaris and M. Deserno, in preparation]

Simulation:

Result fromfluctuations

Within our resolution no “stiffening” of the membrane at

large curvatures is observed!

Within our resolution no “stiffening” of the membrane at

large curvatures is observed!

Domain induced budding

mixed-lipidmembrane

demixing budding

time

Domain induced budding

mixed-lipidmembrane

demixing budding

time

T. Baumgart, S.T. Hess, W.W. Webb, Nature 425, 821 (2003)

5m

5m

sphingomyelin & cholesterol, Lo

DOPC & cholesterol, Ld

Domain induced budding

mixed-lipidmembrane

demixing budding

Balance between• line tension• curvature energy

[R. Lipowsky, (1993)]

time

8 patch2 r

Bud-size: nm50/2bud R

TkB25 nm/1 BTk

Good range for coarse-

grained simulations!

Movie of domain induced budding

16000 lipids, 50LJ between first 50 frames, then 500LJ for next 100 frames; 10kBT

Vice versa…

pancakepancakeR

Vice versa…

holeholeR

frame tension

line tension

RRE 22 Energy for constant frame tension: (Litster, 1975)

Energy for constant frame area:

R

A

RAAKE 2

)(

0

220

21

(Farago 2003; Tolpekina et al., 2004)

nucleation scenario

wc=1.6, kBT=1.1, =15kBT

Membranes under tensionMeasure tension as a function of frame size (NAT ensemble)

wc=1.6, kBT=1.1, =15kBT

Membranes under tensionMeasure tension as a function of frame size (NAT ensemble)

pore opens

membrane buckles

Membranes under tensionMeasure tension as a function of frame size (NAT-ensemble)

wc=1.6, kBT=1.1, =15kBT

Simplest possible theory for pore opening: Harmonic extensibility plus line tension.O. Farago, J. Chem. Phys. 119, 596 (2003);T. V. Tolpekina, W. K. den Otter, and W. J. Briels, J. Chem. Phys. 121, 8014 (2004)

Three fit-parameter:

zero tension area

compressibility

rupture tension

6 mN/m3 kT/nm

Lipid sorting in nature

Different cellular membranes are linked by many trafficking processes.

Yet, different membranes have distinctly different lipid compositions!

Why doesn’t the trafficking mess up the compositional gradients?

Idea: trafficking creates the gradient!

Lipid sorting by curvature

50:50mixture

I. R. Cooke and M. Deserno, to appear in Biophys. J.

Lipid sorting by curvature

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, to appear in Biophys. J.

Lipid sorting by curvature

50:50mixture

Simple model gives:

Density of big headed lipids in the inner

monolayer

Linear in bilayer

curvature!

in

outln

KDensity of big headed

lipids in the outer monolayer

R

I. R. Cooke and M. Deserno, to appear in Biophys. J.

in

outln

K

How big is this effect?

45.0lnin

out

6.1in

out

21

21

in

out6.1 2

1out

21

in }

nm12R

0.11R

I. R. Cooke and M. Deserno, to appear in Biophys. J.

in

outln

K

How big is this effect?

45.0lnin

out

6.1in

out

21

21

in

out6.1 2

1out

21

in }

nm12R

0.11

)(21e

1e 3/2

/2

21

RRkT

KkTKK

kTKK

OlMl

l

M

M

R

I. R. Cooke and M. Deserno, to appear in Biophys. J.

in

outln

K

How big is this effect?

45.0lnin

out

6.1in

out

21

21

in

out6.1 2

1out

21

in }

nm12R

0.11

)(21e

1e 3/2

/2

21

RRkT

KkTKK

kTKK

OlMl

l

M

M

nm50R

0.03

That’s small !

R

I. R. Cooke and M. Deserno, to appear in Biophys. J.

Neck regionsWhat happens in the highly curved regions where a bud is forming?

H.T. McMahon, J.L. Gallop, Nature 438, 590 (2005)

I. R. Cooke and M. Deserno, to appear in Biophys. J.

Neck regionsWhat happens in the highly curved regions where a bud is forming?

H.T. McMahon, J.L. Gallop, Nature 438, 590 (2005)

I. R. Cooke and M. Deserno, to appear in Biophys. J.

Neck regionsWhat happens in the highly curved regions where a bud is forming?

H.T. McMahon, J.L. Gallop, Nature 438, 590 (2005)

I. R. Cooke and M. Deserno, to appear in Biophys. J.

Neck regionsWhat happens in the highly curved regions where a bud is forming?

Density map of big-headed

lipids

Reason:mean curvature

is zero!Hardly any effect in the neck region! I. R. Cooke and M. Deserno, to appear in Biophys. J.

Mediated interactions

Colloid

ColloidMembrane (=30kT)

B. Reynolds, G. Illya, V. Harmandaris, M. Deserno, in preparation

Mediated interactions

does not stickto membranedoes not stickto membrane

sticks to membranesticks to membrane

zero lateral tension

zero lateral tension

Janus-colloids{}

B. Reynolds, G. Illya, V. Harmandaris, M. Deserno, in preparation

Mediated interactionsFix horizontal separation by

“computational laser tweezers”

Force on tweezer equalsforce between particles!

B. Reynolds, G. Illya, V. Harmandaris, M. Deserno, in preparation

Force-distance-curves

distance

forc

e

B. Reynolds, G. Illya, V. Harmandaris, M. Deserno, in preparation

Four-colloid-interaction

8000 lipids, 4 colloids; 50LJ between frames (448), 12kBT

Four-colloid-interaction

8000 lipids, 4 colloids, 12kBT ; rotation of “final” configuration

Summary

Simple solvent-free coarse-grained lipid model with pair interactions

Physics is correct, values are tunable

There are many more such questions!

Biological questions accessible, such as budding, coarsening, sorting

GregoriaGregoria

VagelisVagelis(me)(me)

DavoodDavood

MartinMartinIraIra

BenBen

Acknowledgements

Kurt KremerKurt Kremer

Andreas Janshoff, Siegfried SteltenkampAndreas Janshoff, Siegfried Steltenkamp

Olaf Lenz, Friederike SchmidOlaf Lenz, Friederike Schmid

Oded Farago, Hiroshi NoguchiOded Farago, Hiroshi Noguchi

Jemal GuvenJemal Guven