Mesoscopic simulations of lipid membranes -...
Transcript of Mesoscopic simulations of lipid membranes -...
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Mesoscopic simulations of lipidmembranes
Mingyang Hu, Patrick Diggins, and Markus Deserno
Department of Physics, Carnegie Mellon University, Pittsburgh PA, USA
October 11, 2012
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
IntroductionLipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 3: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/3.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
OutlineIntroduction
Lipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 4: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/4.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
What’s a lipid membrane?
I forms continuous barriers around cells, cell nucleiI made of two layers of lipid moleculesI controls the diffusion of molecules in and out of the cell
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Building blocks: Lipid molecules
I amphiphilic moleculeI hydrophilic head (polar: “attracted” by water)I hydrophobic tails (apolar: “repelled” by water)
I membranes form by spontaneous aggregation of lipidsI self-assembly process
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Building blocks: Lipid molecules
I amphiphilic moleculeI hydrophilic head (polar: “attracted” by water)I hydrophobic tails (apolar: “repelled” by water)
I membranes form by spontaneous aggregation of lipidsI self-assembly process
![Page 7: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/7.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Why coarse-graining?
Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations inlipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433(2000)
All-atom lipid bilayer20 nm× 20 nm, 1024 lipidssimulation time: 10 ns
What if we want a boxlength of L = 200nm?
How does computing effort scale with L?
effort ∼ L2︸︷︷︸geometry
![Page 8: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/8.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Why coarse-graining?
Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations inlipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433(2000)
All-atom lipid bilayer20 nm× 20 nm, 1024 lipidssimulation time: 10 ns
What if we want a boxlength of L = 200nm?
How does computing effort scale with L?
effort ∼ L2︸︷︷︸geometry
![Page 9: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/9.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Why coarse-graining?
Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations inlipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433(2000)
All-atom lipid bilayer20 nm× 20 nm, 1024 lipidssimulation time: 10 ns
What if we want a boxlength of L = 200nm?
How does computing effort scale with L?
effort ∼ L2︸︷︷︸geometry
× L4︸︷︷︸equilibration
∼ L6
![Page 10: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/10.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Efficiency
20 nm −→ 200 nmMillion times more
computationally expensive!
I amount of material ∼ membrane area A = L2.I domain decomposition scheme:
I increase # CPUs ∼ AI but simulation time ∼ A3
I uncompensated factor of A2
![Page 11: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/11.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Efficiency
20 nm −→ 200 nmMillion times more
computationally expensive!
I CG helps to understand the essence of the problemsI CG reduces the number of DOFI CG allows larger time stepsI CG smoothens the free energy surface⇒ Better sampling
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
OutlineIntroduction
Lipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 13: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/13.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
The CG model1
Coarse-grain in order to probe themesoscopic regime of lipid bilayersI generic top-down bead-springI 3 beads: reasonable aspect ratioI only pair forcesI solvent free
I Note: several other similar models exist.I Here I’ll talk about the one used in our groupI It has been implemented in ESPResSo.
1I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005)I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
![Page 14: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/14.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
The CG model1
Coarse-grain in order to probe themesoscopic regime of lipid bilayersI generic top-down bead-springI 3 beads: reasonable aspect ratioI only pair forcesI solvent free
I Note: several other similar models exist.I Here I’ll talk about the one used in our groupI It has been implemented in ESPResSo.
1I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005)I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
![Page 15: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/15.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
The CG model1
Coarse-grain in order to probe themesoscopic regime of lipid bilayersI generic top-down bead-springI 3 beads: reasonable aspect ratioI only pair forcesI solvent free
I Note: several other similar models exist.I Here I’ll talk about the one used in our groupI It has been implemented in ESPResSo.
1I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, 011506 (2005)I.R. Cooke and M. Deserno, J. Chem. Phys. 123, 224710 (2005).
![Page 16: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/16.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Why is “solvent free” good?
membrane
solvent
surface
bulk
Examplea
I 16,000 DPD lipids, 4 beads per lipid.I 64,000 particles for lipids.I But in total 1,536,000 particles in box!
96% simulation time spent with solvent.
aM. Laradji & P.B. Sunil Kumar, Phys. Rev. Lett. 93, 198105 (2004).
![Page 17: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/17.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Why is “solvent free” good?
membrane
solvent
surface
bulk
Examplea
I 16,000 DPD lipids, 4 beads per lipid.I 64,000 particles for lipids.I But in total 1,536,000 particles in box!
They had a good reason for doing this:study of the dynamics of domain growth,where hydrodynamics is an important factor.
aM. Laradji & P.B. Sunil Kumar, Phys. Rev. Lett. 93, 198105 (2004).
![Page 18: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/18.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Difficulties
I Implicit solvent models are incredibly common and usefulin polymer physics.
I Why has it taken so long for them to appear in the field ofmembrane research?
I Polymers don’t first have to self assemble!I One needs additional cohesion to make the lipids come
together.I Fluidity has proven to be the major challenge.
Lennard-Jones interactions:I weak attraction→ gas phaseI no fluid phase in between?!I strong attraction→ solid (gel) phase
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Model
I link three beads Vbond(r) = − 12 kbondr2
∞ ln[1− (r/r2
∞)]
I make lipid stiff Vbend(r13) = 12 kbend(r13 − 4σ)2
I nonbonded Vrep(r) = 4ε[( rc
r
)12 −( rc
r
)6+ 1
4
]Θ(rc−r)
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Overall phase behavior
I long-range attractions “save” the system some entropy!
![Page 21: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/21.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Self-assembly
movies/self_assembly_1.mpg
![Page 22: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/22.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
OutlineIntroduction
Lipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 23: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/23.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Implementation
I mbtools architecture:I engine (C)
I interactions (lj-cos2 interaction implemented as a FEATURE)I several analysis routines (e.g. modes, stress tensor)
I user-interface (Tcl)I system generation (e.g. initial particle positions)I parameters (configuration files)I register particles in ESPResSo (e.g. topology, interactions)I call to integrate commandI analysis/output
Program structure located in:
ESPRESSO/packages/mbtools
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Program structure
I mbtools is a Tcl package.I set of Tcl functionsI (crude) version control
I load package to get access to enclosed functionspackage require mbtools [1.0.0]
I ESPResSo loads mbtools during initialization (fileESPRESSO/scripts/init.tcl)lappend auto_path "[pwd]/packages/mbtools/"
I auto_path contains the list of (sub)directories checkedby the package loader
I use namespaces to avoid defining two functions with thesame name
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Program structure
# Espresso/packages/mbtools/mbtools.tcl#
package require ::mbtools::utilspackage require ::mbtools::system_generationpackage require ::mbtools::analysis
package provide mbtools 1.0.0
namespace eval mbtools {
}
# Espresso/packages/mbtools/utils/setup.tcl#
proc ::mbtools::utils::readcheckpoint { dir }
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Config file example (incomplete...)
# .../mbtools/examples/simplebilayer.tcl#
# define geometryset geometry { geometry "flat -fixz" }# time stepset main_time_step 0.01# analysislappend analysis_flags pressure
From command line:
Espresso scripts/main.tcl simplebilayer.tcl
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
OutlineIntroduction
Lipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 28: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/28.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Membrane elasticity
I Model membrane as a 2D elastic sheet (continuum theory)
E =
∫dA{
12κK2 + σ
}' 1
2
∫dxdy
{κ(∇2h)2 + σ(∇h)2}
I κ: bending modulusI K: total curvatureI σ: surface tensionI h(x, y): height function (Monge gauge)
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Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Bending modulus
I Model membrane as a 2D elastic sheet (continuum theory)
E =
∫dA{
12κK2 + σ
}' 1
2
∫dxdy
{κ(∇2h)2 + σ(∇h)2}
I κ: bending modulusI K: total curvatureI σ: surface tensionI h(x, y): height function (Monge gauge)
I Fourier expansion and equipartition theorem
〈|hq|2〉 =kBT
L2[κq4 + σq2︸︷︷︸set to 0
]=
kBTL2κ
q−4
I determine bending modulus κ
![Page 30: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/30.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Fluctuation spectrum from continuum theory
![Page 31: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/31.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Fluctuation spectrum from continuum theory
![Page 32: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/32.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
However...
I Equilibration time of Fourier modes scales like q−4
I Large bending modulus κ from small perturbation (kBT)→ small signal!
h(x) = hqeiqx → K = −h′′(x) = hqq2eiqx
〈K2〉 = 〈|h′′(x)|2〉 = q4〈|hq|2〉 =kBTL2κ
R̄ =1
〈K2〉1/2 =
√κ
kBTL ' 3 . . . 5L
I Result relevant for strong bending?
![Page 33: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/33.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
κ from actively bent membranes
I first implementation:W.K. den Otter and W.J. Briels, J. Chem. Phys.118, 4712 (2003)
I Enforce large undulation mode,measure constraining force.
Simpler way: stretch a membrane tether!2
2V. A. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
![Page 34: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/34.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
κ from actively bent membranes3
I Area:A = 2πRL
I Energy:
E =κ
2× 1
R2 × A
I Force:
F =
(∂E∂L
)A
= · · · = 2πκR
I Bending modulus:
κ =FR2π' F R
2π
3V. A. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
![Page 35: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/35.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
κ from actively bent membranes4
4V. A. Harmandaris and M. Deserno, J. Chem. Phys. 125, 204905 (2006)
![Page 36: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/36.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Simpler way of extracting the line tension
I simulate a periodicallyhalf-connected bilayer in abox
I stress tensor will beimbalanced precisely bytwice the line tension!
![Page 37: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/37.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Simpler way of extracting the line tension
![Page 38: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/38.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
OutlineIntroduction
Lipid MembraneWhy coarse-graining?
Solvent-free CG ModelSolvent-freeModel
Code Implementation
PropertiesMembrane elasticityBendingLine tension
ApplicationsVesiclesProtein-induced buddingLipid A-B–mixturesstretching
![Page 39: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/39.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Vesicles
I competition between bending rigidity and line tension 5
I sonicate vesicle solution: rip vesicles into bits and pieces!I these (flat) pieces will merge and grow biggerI at what point will they again close up and form vesicles?
5“The size of bilayer vesicles generated by sonication”, W. Helfrich, Physics LettersA, Vol 50, Issue 2, p. 115-116
![Page 40: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/40.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Vesicles
movies/c16sa.mpg
![Page 41: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/41.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Vesicles
Evesicle = 4πR2 ·
[12κ
(1R
+1R
)2
+ κ1R· 1
R
]= 4π(2κ+ κ)
![Page 42: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/42.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Vesicles
What values do we expect?
I κ = 20 kBT ' 80 pN · nmI κ ' −κ (very little is known about κ, come back tomorrow!)I γ ' 10 pN
I Rpancake =4(2κ+κ)
γ' 4κ
γ' 320 pNnm
10 pN = 32 nm
I This is then also the diameter of vesicles we expect to find!
![Page 43: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/43.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Protein-induced budding
Intuitive, but no physical justification!
![Page 44: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/44.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Protein-induced budding6
I 36 curved caps, ∼50,000 lipidsI 160nm side-length, total time ∼1msI no lateral tensionI no explicit interaction between caps
6B.J. Reynwar et al., Nature 447, 461 (2007)
![Page 45: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/45.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Protein-induced budding7
movies/caps.avi
7B.J. Reynwar et al., Nature 447, 461 (2007)
![Page 46: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/46.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Protein-induced budding8
8B.J. Reynwar et al., Nature 447, 461 (2007)
![Page 47: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/47.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Protein-induced budding9
9B.J. Reynwar et al., Nature 447, 461 (2007)
![Page 48: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/48.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Lipid A-B–mixtures
![Page 49: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/49.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Lipid A-B–mixtures
wAB < wAA = wBB
![Page 50: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/50.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Lipid A-B–mixtures10
movies/budding.mpg
10B.J. Reynwar & M. Deserno, Biointerphases 3, FA118 (2009)
![Page 51: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/51.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Lipid A-B–mixtures11
movies/spinodal.avi
11from Sarah Veatch
![Page 52: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/52.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
Lipid A-B–mixtures
wAB < wAA = wBB
![Page 53: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/53.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
stretching modulus12
12i.r. cooke and m. deserno, j. chem. phys. 123, 224710 (2005)
![Page 54: Mesoscopic simulations of lipid membranes - ESPResSoespressomd.org/html/ess2012/Day4/T1-02-mbtools/talk_mb...lipid bilayers from molecular dynamics simulations. Biophys. J. 79, 426-433](https://reader034.fdocuments.net/reader034/viewer/2022051901/5ff08d220d9356606a5b2f9b/html5/thumbnails/54.jpg)
Mesoscopicmembranes
Mingyang [email protected]
IntroductionLipid Membrane
Why coarse-graining?
Solvent-free CG ModelSolvent-free
Model
Code Implementation
PropertiesMembrane elasticity
Bending
Line tension
ApplicationsVesicles
Protein-induced budding
Lipid A-B–mixtures
stretching
stretching modulus
simple theory:farago, jcp, 2003; tolpekina/den otter/briels, jcp 2004; cooke/deserno, jcp 2005
membrane stretching plus line energy
rescaling of energy
equilibrium condition for pore radius
e =12
m(a− as − πr2)2
as+ 2πγr
λ3 =γas
πm, r̃ =
rλ, b =
a− as
πλ2
r̃3 − br̃ + 1 = 0