Coarse-grained simulation studies of mesoscopic membrane phenomena
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1 Coarse-grained simulation studies of mesoscopic membrane phenomena Markus Deserno Department of Physics Carnegie Mellon University with: Ira R. Cooke, Gregoria Illya, Benedict J. Reynwar, Vagelis A. Harmandaris, Kurt MPI-P IMA Workshop on the Development and Analysis of Multiscale Methods November 5, 2008
2 Quick motivation Membranes Typical illustration of an animal cell
3 Quick motivation Membranes Typical illustration of an animal cell Almost everything you see here are membranes!
4 Quick motivation Membranes Notice the many changes in morphology! Almost everything you see here are membranes!
5 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. E available ~ 20 k B T (physiol. cond.)
6 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. E available ~ 20 k B T (physiol. cond.) The elasticity of membranes needs to match the available deformation energies!
7 Membrane bending B modulus k T Yh 3
8 Membrane bending B modulus k T Yh 3
9 Membrane bending B modulus k T Yh Young s modulus 3 thickness
10 Energy match Young s modulus thickness B k T Yh 3
11 Energy match Young s modulus thickness B k T Yh 3 h 5nm
12 Energy match Young s modulus thickness B k T Yh 3 h 5nm Y 10 7 Pa
13 Energy match Young s modulus thickness B k T Yh 3 h 5nm Y 10 7 Pa
14 Energy match Young s modulus thickness B k T Yh 3 Let s hypothesize h 5nm Y 10 7 Pa
15 Energy match Young s modulus thickness B k T Yh 3 h 5nm Y 10 7 Pa and insist on metal!
16 Energy match Young s modulus thickness B k T Yh 3 h 5nm Y Pa and insist on metal!
17 Energy match Young s modulus thickness B k T Yh 3 h 2Å Y Pa and insist on metal!
18 Energy match Young s modulus thickness B k T Yh 3 Fail! h 2Å Y Pa and insist on metal!
19 Moral: Membranes must be made from soft materials! We will invariably encounter long time scales!
20 Quick motivation (II) Long time scales How bad is it?
21 Quick motivation (II) Long time scales How bad is it? Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79, (2000). All-atom lipid bilayer 20nm 20nm, 1024 lipids, 10ns
22 Quick motivation (II) Long time scales How bad is it? Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79, (2000). All-atom lipid bilayer 20nm 20nm, 1024 lipids, 10ns What if we want a boxlength of L=200nm? How does computing effort scale with L?
23 Quick motivation (II) Long time scales How bad is it? Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79, (2000). All-atom lipid bilayer 20nm 20nm, 1024 lipids, 10ns What if we want a boxlength of L=200nm? How does computing effort scale with L? effort ~ L 2 Amount of material
24 Quick motivation (II) Long time scales How bad is it? Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79, (2000). All-atom lipid bilayer 20nm 20nm, 1024 lipids, 10ns What if we want a boxlength of L=200nm? How does computing effort scale with L? effort ~ L 2 L 4 Amount of material Equilibration time
25 Quick motivation (II) Long time scales How bad is it? Lindahl, E. & Edholm, O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 79, (2000). All-atom lipid bilayer 20nm 20nm, 1024 lipids, 10ns What if we want a boxlength of L=200nm? How does computing effort scale with L? effort ~ L 2 L 4 ~ L 6 Amount of material Equilibration time
26 Quick motivation (II) Long time scales How bad is it? 20nm 200nm Million times more computationally expensive!
27 Quick motivation (II) Long time scales How bad is it? 20nm nm Million times more computationally expensive!
28 Quick motivation (II) Long time scales How bad is it? 20nm nm Million times more computationally expensive! 20 doublings of computer power!
29 Quick motivation (II) Long time scales How bad is it? 20nm nm Million times more computationally expensive! 20 doublings of computer power! 20 x 2 years (Moore s law)
30 Quick motivation (II) Long time scales How bad is it? 20nm nm Million times more computationally expensive! 20 doublings of computer power! 20 x 2 years 40 years (Moore s law)
31 Quick motivation (II) Long time scales How bad is it? 20nm nm Million times more computationally expensive! 20 doublings of computer power! 20 x 2 years 40 years (Moore s law) I ll be retired by then! (best case scenario)
32 This is why we all love coarse graining
33 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, (2005); I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
34 temperature Today: unstable fluid phase gel-phase(s) attraction range I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, (2005); I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
35 temperature Today: unstable fluid phase gel-phase(s) attraction range Long-ranged attractions save the system some entropy! I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, (2005); I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
36 temperature Today: 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). unstable fluid phase gel-phase(s) attraction range Long-ranged attractions save the system some entropy! I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, (2005); I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
37 temperature Today: 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). unstable fluid phase gel-phase(s) I.R. Cooke, K. Kremer, M. Deserno, Phys. Rev. E 72, (2005); I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005). attraction range Long-ranged attractions save the system some entropy! Shape of CG potential is qualitatively important!
38 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
39 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
40 Material properties
41 Material properties Probably most important: bending modulus
42 Material properties Probably most important: bending modulus From fluctuations From deformations Can be determined in two very different ways
43 Material properties Probably most important: bending modulus From fluctuations From deformations
44 Material properties Probably most important: bending modulus From fluctuations From deformations energy of cylinder force to hold it V. Harmandaris and M. Deserno, J. Chem. Phys. 125, (2006)
45 Material properties Probably most important: bending modulus From fluctuations From deformations energy of cylinder Both ways give the same answer Shows that Helfrich theory works up to extremely large curvature force to hold it V. Harmandaris and M. Deserno, J. Chem. Phys. 125, (2006)
46 Material properties Probably most important: bending modulus From fluctuations From deformations energy of cylinder Both ways give the same answer Shows that Helfrich theory works up to extremely large curvature force to hold it ~ 3 30 k B T V. Harmandaris and M. Deserno, J. Chem. Phys. 125, (2006)
47 Other Material properties Expansion modulus ~ 100 dyn/cm Line tension ~ 10 pn I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
48 Other Material properties Expansion modulus ~ 100 dyn/cm Line tension ~ 10 pn thermal expansivity ~ K -1 I.R. Cooke and M. Deserno, J. Chem. Phys. 123, (2005).
49 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
50 Adsorption to a substrate picture: M.I. Hoopes substrate bilayer M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
51 Adsorption to a substrate z picture: M.I. Hoopes substrate bilayer M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press)
52 p i (z) p i (z) Adsorption to a substrate z picture: M.I. Hoopes substrate bilayer free supported M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press) z z
53 p i (z) p i (z) Adsorption to a substrate Major suppression of perpendicular lipid fluctuations in the proximal leaflet. Entropy loss, since S k B dz p i ( z)log p i ( z) Reduction of free energy of binding (here: ~25%) free supported M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press) z z
54 bilayer pressure Adsorption to a substrate Zero tension case needs to be precisely defined Compressibility increases, since fluctuations are damped free supported substrate interactions excluded substrate interactions included M.I. Hoopes, M. Deserno, M.L. Longo, and R. Faller, J. Chem. Phys. (in press) area/lipid
55 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
56 Lipid curvature effects The model of Israelachvili, Mitchell and Ninham packing parameter P V LA J. Chem. Soc., Faraday Trans (1976) V = lipid volume L = lipid length A = lipid head area
57 Lipid curvature effects The model of Israelachvili, Mitchell and Ninham packing parameter P V LA J. Chem. Soc., Faraday Trans (1976) V = lipid volume L = lipid length A = lipid head area P 0 1/3 1/2 1
58 Lipid curvature effects The model of Israelachvili, Mitchell and Ninham packing parameter P V LA J. Chem. Soc., Faraday Trans (1976) V = lipid volume L = lipid length A = lipid head area P 0 1/3 1/2 1
59 Lipid curvature effects 50:50 mixture I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
60 Lipid curvature effects 50:50 mixture R I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
61 Lipid curvature effects 50:50 mixture R Density of big headed lipids in the outer monolayer Simple model gives: Density of big headed lipids in the inner monolayer Linear in bilayer curvature! I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
62 Lipid curvature effects 50:50 mixture ln out in R Density of big headed lipids in the outer monolayer K Simple model gives: Density of big headed lipids in the inner monolayer Linear in bilayer curvature! I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
63 Lipid curvature effects 50:50 mixture ln out in R for realistic membrane curvatures the effect is not enough to drive sorting! K R 50nm 0.03 That s small! I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
64 Lipid curvature effects 50:50 mixture ln out in R for realistic membrane curvatures the effect is not enough to drive sorting! Tian & Baumgart, preprint K R 50nm 0.03 That s small! I.R. Cooke and M. Deserno, Biophys. J. 91, 487 (2006)
65 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
66 Peptide-induced pore formation Antimicrobial Peptide magainin G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
67 n beads Peptide-induced pore formation Peptides: m beads P m n peptide Example above: 2 P 8 G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
68 n beads Peptide-induced pore formation Peptides: m beads P m n peptide Example above: 2 P 8 G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
69 Peptide-induced pore formation Surface adsorbed Monolayer contact G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008) Sliding in
70 Peptide-induced pore formation breakthrough Surface adsorbed Monolayer contact G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008) Sliding in
71 Peptide-induced pore formation Binding strength k B T=1.7 k B T=1.9 2 P 6 2 P stray stray 1.6 bound bound/inserted 1.7 inserted inserted 1.8 inserted inserted 1.4 stray stray 1.5 bound inserted 1.6 inserted inserted 1.7 inserted inserted 1.8 inserted inserted G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
72 Peptide-induced pore formation Binding strength k B T=1.7 k B T=1.9 2 P 6 2 P stray stray 1.6 bound bound/inserted 1.7 inserted inserted 1.8 inserted inserted Let us now look 1.4 stray at this stray system 1.5 bound consisting insertedof 1.6 inserted manyinserted of these 1.7 inserted peptides inserted 1.8 inserted inserted G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
73 Peptide-induced pore formation of a peptide which alone does not insert within Stronger joint perturbation Sliding in very efficient c) g) 3000 G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
74 Peptide-induced pore formation w c P 8 1 P 8 2 P 8 3 P 8 G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
75 Peptide-induced pore formation w c P 8 1 P 8 2 P 8 3 P 8 No peptide attraction Some peptide attraction 2 P 6 w c 1.6 G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
76 Peptide-induced pore formation w c P 8 1 P 8 2 P 8 3 P 8 No peptide attraction toroidal Some peptide attraction 2 P 6 w c 1.6 barrel-stave G. Illya & M. Deserno, Biophys. J. 95, 4163 (2008)
77 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
78 temperature Lipid A-B mixtures attraction range B.J. Reynwar & M. Deserno, Biointerphases (accepted)
79 temperature Lipid A-B mixtures heterotypic homotypic attraction range w AB w AA w BB B.J. Reynwar & M. Deserno, Biointerphases (accepted)
80 Lipid A-B mixtures w AB w AA w BB B.J. Reynwar & M. Deserno, Biointerphases (accepted)
81 Lipid A-B mixtures+proteins Proteins only adsorb on blue lipids ideal lipid mixture non-ideal lipid mixture Composition-induced protein aggregation B.J. Reynwar & M. Deserno, Biointerphases (accepted)
82 Lipid A-B mixtures+proteins Pair potentials can be fitted by simple ground state theory. B.J. Reynwar & M. Deserno, Biointerphases (accepted)
83 Illustrations: Material properties Adsorption to a substrate Lipid curvature effects Peptide-induced pore formation Lipid mixtures Protein-induced budding
84 Protein-induced budding B. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006)
85 Protein-induced budding Membrane-curving proteins can attract and drive membrane vesiculation B. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006)
86 Protein-induced budding Membrane-curving proteins can attract and drive membrane vesiculation B. Antonny, Curr. Opin. Cell Biol. 18, 386 (2006) Intuitive, but no physical justification!
87 Protein-induced budding many caps ( contact lens ) 36 curved caps, ~50000 lipids, 160nm side-length, total time ~1ms no lateral tension no explicit interaction between caps B.J. Reynwar et al., Nature 447, 461 (2007)
88 Protein-induced budding B.J. Reynwar et al., Nature 447, 461 (2007)
89 Protein-induced budding Some observations: Caps attract collectively Attractive pair-forces exist No crystalline structure Cooperative vesiculation No scaffolding nm length scales several milliseconds B.J. Reynwar et al., Nature 447, 461 (2007)
90 Protein-induced budding Blood and Voth, PNAS 103, (2006)
91 Protein-induced budding G.S. Ayton, P.D. Blood, and G.A. Voth, Biophys. J. 92, 3595 (2007) Blood and Voth, PNAS 103, (2006)
92 Protein-induced budding 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) Blood and Voth, PNAS 103, (2006)
93 Summary CG membrane model can efficiently treat many mesoscopic membrane processes. Link to continuum elastic level works Physical properties turn out reasonable Link to finer scale ought to be possible! (under way)
94 Acknowledgements MPI-P Gregoria Vagelis (me) Davood Martin Ira Ben Kurt Kremer, Eva Sinner, Jemal Guven Matt Hoopes, Roland Faller Tristan Bereau, Zunjing Wang and many more
95
96 Material properties Probably most important: bending modulus From fluctuations From deformations / k B T / k B T V. Harmandaris and M. Deserno, J. Chem. Phys. 125, (2006)
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