Computers Crunching Computers Crunching Lipids Lipids – From From Cell Cell Membranes Membranes to to Lipoproteins Lipoproteins Ilpo Ilpo Vattulainen Vattulainen Biological Physics & Soft Matter Team Biological Physics & Soft Matter Team Institu Institute of Physics, Tampere e of Physics, Tampere Univ Univ of Tech, and of Tech, and Lab of Physics, Helsinki Univ Lab of Physics, Helsinki Univ of Tech of Tech FINLAND FINLAND www.tut.fi/biophys www.fyslab.hut.fi/bio/ Cray – Helsinki – May 2008
Cholesterol Cholesterol Everyw here Everyw here complexity complexity complexity complexity & scales & scales !!! !!! & scales & scales !!! !!!
Proteins as Biosensors as Biosensors Membrane Proteins Membrane
Multi-scale modeling Multi-scale modeling Mesoscale: Mesoscale: Macroscale: Macroscale: • effectiv effective interactions nteractions • times times ~1 s 1 s ~ 1 μ • collective collective phenomena henomena • scales scales ~ 1 • large large scales cales • long-range long-range effects effects Coarse graining Multi-scale modeling Multi-scale odeling 1. 1. Development of coarse- Development f coarse- graining techniques graining techniques for for molecules and their molecules nd their interactions interactions 2. Bridging atomistic Bridging atomistic and and CG models in CG models in applications applications to actual o actual problems problems Atomistic picture: Atomistic icture: • microscopic microscopic accuracy ccuracy • inte interatomic ratomic forc orces • intermolecular intermolecular interactions interactions
Modeler’s toolbox Modeler’s toolbox Various scales, various methods Macroscale: Simulation: Experiment: Scale: Target: •times > 1 sec •scales > 1 μ Naked eye 0.2 mm •phase field models, FEM CELLS 20 µm Mesoscale: • times ~ 10 – 8 – 10 -2 sec ORGANELLS • scales ~ 100 - 10000 Å 2 µm • DPD, coarse graining 200 nm Microscope Atomistic scale: • times ~ 10 – 15 – 10 -9 sec MOLECULES 20 nm • scales ~ 1 - 100 Å • Classical MD, MC 2 nm Subatomistic scale: 0.2 nm Electron •electronic structure ATOMS microscope •ab initio •Green’s functions
Limits of Atomistic Limits of Atomistic Simulations imulations Example for a DPPC/Cholesterol Example for a DPPC/Cholesterol lipid lipid membrane: pros membrane: pros and cons and cons of atomistic atomistic simulations imulations for syste for systems of this f this kind kind Classical MD (Gromacs): Classical MD (Gromacs): •128 DPPC + Chol 128 DPPC + Chol molecules + water molecules + water •6 ch 6 choleste olesterol con rol concentrations entrations •Simulat Simulated time: 100 ns each d time: 100 ns each Phase diagram Phase diagram based on based on experiments: exper ments: Almeida et al. Almeida et al. (1992) (1992) Insight given Insight iven by by atomic-scale atomic-scale mod modelin ling in complex n complex biosystems? biosystems? [ Falck et al., B [ Falck t al., Biop ophys hys J 87, 1076 (2004) ] 87, 1076 (2004) ]
Area per Lipid in Bilayer Area per Lipid n Bilayer Plane lane DPPC + Cholesterol binary mixture DPPC + Cholest rol binary mixture Chol = 0% Chol = 0% Experiment: Experiment: Chol Chol = 5% = 5% Pure DPPC Pur DPPC Chol Chol = 12% = 12% 0.64 nm 2 0.64 nm Chol = 20% Chol = 20% Chol Chol = 30% = 30% Chol = 50% Chol = 50% Cholesterol rigidifies t Cholest rol rigidifies the membrane, thus e membrane, thus Equilib Equilibration ation decreasing the area per molecule in decreasing the area per molecule in agreement with experiments and previous agreement w experiments and previous for 20 ns for 20 ns theoretical studies. theoretical studies. [ Falck [ Falck et al., B t al., Biop ophys hys J 87, 1076 (2004) ] 87, 1076 (2004) ]
NMR order parameter NMR order parameter of acyl f acyl chains chains Orde Or dering o ring of lipid acyl lipid acyl cha chains by choles ns by cholesterol terol Results fully consist Results fully consistent ent wit with NMR NMR S = 3 < cos 2 θ > − 1 All-trans All-trans (straight “zig-zag” (straight “zig-zag” chain) hain) Chol = 30% Chol = 30% 2 Chol Chol = 20% = 20% The larger S, the more The larger S, the more ordered the chains ordered he chains are. are. Chol = 12% Chol = 12% Chol Chol = 5% = 5% θ Chol Chol = 0% = 0% Random walk (disor Random walk (disorder ered chain) ed chain) Bilayer normal Bilayer ormal
Lateral Diffusion Lateral iffusion Coefficients Coefficients FCS measurements for FCS measurements for MD for DPPC/Chol MD for DPPC/Chol DLPC/Chol DLPC/Chol (E. (E. Fa Falck et et a al. 2004) 2004) (Kor orla lach ch et et a al, PN PNAS 1999) AS 1999) [ Falck [ Falck et al., BJ 87, 1076 (2004) ] t al., BJ 87, 1076 (2004) ]
Lateral Lipid Lateral ipid Diffusion Diffusion Mechanism echanism Later Lateral lipid ipid tr trajectories ajectories in a DPPC in a DPPC bilayer bilayer of 1152 lipids f 1152 lipids over over a period period of 30 ns of 30 ns •4 systems 4 systems with ith number umber of lipids ranging lipids ranging between etween 128 – 128 – 4096 4096 •Time scale Time scale 10 – 10 – 100 ns 00 ns Less ss than than 10 ev events ents observed observed where where a lipid moves lipid moves ~0.7 nm 0.7 nm in a short in a short period eriod of ~100 ps. of ~100 ps. That That is, the simulations is, the simulations indicate ndicate that that there there are re no single-particle no single-particle jumps umps Falck, Rog, K Falck, Rog, Karttu rttune nen, Vattula n, Vattulainen, J Am Chem inen, J Am Chem Soc Soc 130, 44 (2008) 30, 44 (2008)
Lateral lipid Lateral ipid Lateral Lipid Lateral ipid Diffusion Diffusion Mechanism echanism displacements displacement over Δ t = over t = 1 1 n ns A more detaile A more tailed consid consideration ation reve eveals ls th that at all all diffusive iffusive motions motions are re collectiv collective ones, as nearby lipids ones, as nearby lipids move move in un in unison ison as loosely as loosely defined efined clusters. clusters. Falck, Rog, Karttu Falck, Rog, K rttune nen, Vattula n, Vattulainen, J Am Chem inen, J Am Chem Soc Soc 130, 44 (2008) 30, 44 (2008)
Collective Collective Diffusive Diffusive Large-Scales arge-Scales Flow s Flow s Δ t = Δ t = 0.5 ns Lateral displacements Lateral isplacements t = 0 0.05 0.5 ns of individual lipids of individual lipids ns ns of Δ t during during a period a period of On a molecular scale, On a molecular cale, lipids lipids move move in unison in unison as loosely as loosely defined efined Δ t = Δ t = 30 ns t = 5 5 n ns 30 ns clusters. clusters. On larger scales, the On larger scales, the intimately intimately correlated correlated motions of motions f neighboring ighboring lipids lipids manifest manifest themsel themselves es as 2D flow as 2D flow patterns patterns Falck, Rog, Karttu Falck, Rog, K rttune nen, Vattula n, Vattulainen, J Am Chem inen, J Am Chem Soc Soc 130, 44 (2008) 30, 44 (2008)
Time Scales of Lateral Time Scales of Lateral Diffusion Diffusion ~40 microns ~40 microns Time scale for diffusion Time scale or diffusion over over a domain a domain whose whose radius is adius is L = L 2 / 4 t = / 4 D In the In the flui fluid phase, hase, D ≈ 1 × 1 × 10 -7 -7 cm cm 2 /s. Then /s. Then the the time scale time scale t is at least is at least t = 2.5 = 2.5 μ s for s for L = 10 nm = 10 nm (nanorafts) (nanorafts) 25 ms for 25 ms for L = 1 = 1 μ m (large m (large domains) domains) www.memphys.sdu.dk State-of-the-art atomistic State-of-the-art atomistic simulations imulations are are limited imited to ~0.1 to ~0.1 μ s and 10 nm. s and 10 nm. Long time Long time scales scales & the la & the large rge system ystem sizes izes call call for for coarse-grained coarse-grained models models. .
Effective Interactions? Effective Interactions? How How to find o find effective effective interactions nteractions for the CG model? for the CG model? Systematic Systematic coarse coarse graining graining through through Inverse Monte Carlo (IMC) Inverse onte Carlo (IMC) ? bending bending F C ij a ij torsion torsion stretching stretching r cut-off cut-off
Coarse Grained Coarse Grained Model: DPPC/Chol Model: DPPC/Chol INVERSE INVERSE INVERSE INVERSE MONTE MONTE MONTE MONTE CARLO CARLO CARLO CARLO For Inverse Mont For verse Monte Carlo e Carlo (IMC (IMC), see Lyubartse ), see Lyubartsev and d Laaksonen, PRE 52, 3730-3737 (1995). Laaksonen, PRE 52, 3730-3737 (1995). Main fe Ma featur ures: es: Coarse-grained model system: Coarse-grained model system: 1. 1. 3-particle CG represent 3-particle CG representation ation for DPPC or DPPC DPPC + Chol DPPC + Chol 2. 2. 1-particle CG 1-particle CG represent representation ation for Chol or Chol No e No explicit water plicit water 3. 3. Surface Su ace tension in ension included cluded via Lag via Lagrange ange Time: ~ms Time: ~ms multiplie multipliers rs to match to match the area he area co comp mpressibility ressibility to the expe to the experimental rimental value value x chol chol = 0 – = 0 – 50 mol% 50 mol% Speed-up: ~ 10 Speed-up: ~ 10 8 T. Murtola et al., T. Murtola t al., J Chem J Chem Phys 126, 075101 (2007) Phys 126, 075101 (2007)
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