lipid membranes between nano and micro: markus deserno max-planck-institut für polymerforschung,...
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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
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