Computers Crunching Computers Crunching Lipids Lipids From From - - PowerPoint PPT Presentation

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

• f Tech, and

Lab of Physics, Helsinki Univ Lab of Physics, Helsinki Univ of Tech

• f Tech

FINLAND FINLAND www.tut.fi/biophys www.fyslab.hut.fi/bio/

Cray – Helsinki – May 2008

Cholesterol Cholesterol Everyw here Everyw here

complexity complexity & scales & scales !!! !!! complexity complexity & scales & scales !!! !!!

Membrane Membrane Proteins Proteins as Biosensors as Biosensors

Macroscale: Macroscale:

• times

times ~1 s 1 s

• scales

scales ~ 1 ~ 1μ

• large

large scales cales

Atomistic Atomistic picture: icture:

• microscopic

microscopic accuracy ccuracy

• inte

interatomic ratomic forc

• rces
• intermolecular

intermolecular interactions interactions

Mesoscale: Mesoscale:

• effectiv

effective interactions nteractions

• collective

collective phenomena henomena

• long-range

long-range effects effects

Coarse graining

Multi-scale Multi-scale modeling

• deling

1. 1. Development Development of coarse- f coarse- graining graining techniques techniques for for molecules molecules and their nd their interactions interactions 2. Bridging Bridging atomistic atomistic and and CG models CG models in in applications applications to actual

• actual

problems problems

Multi-scale modeling Multi-scale modeling

0.2 mm 20 µm 2 µm 200 nm 20 nm 2 nm 0.2 nm

CELLS ORGANELLS MOLECULES

ATOMS

Naked eye Microscope Electron microscope

Scale: Experiment: Target: Simulation:

Macroscale:

• times > 1 sec
• scales > 1μ
• phase field models, FEM

Atomistic scale:

• times ~ 10–15 – 10-9 sec
• scales ~ 1 - 100 Å
• Classical MD, MC

Subatomistic scale:

• electronic structure
• ab initio
• Green’s functions

Mesoscale:

• times ~ 10–8 – 10-2 sec
• scales ~ 100 - 10000 Å
• DPD, coarse graining

Various scales, various methods

Modeler’s Modeler’s toolbox toolbox

Classical MD (Gromacs): Classical MD (Gromacs):

• 128 DPPC + Chol

128 DPPC + Chol molecules + water molecules + water

• 6 ch

6 choleste

• lesterol con

rol concentrations entrations

• Simulat

Simulated time: 100 ns each d time: 100 ns each

Phase diagram Phase diagram based on based on exper experiments: ments: Almeida et al. Almeida et al. (1992) (1992) [ Falck [ Falck et al., B t al., Biop

• phys

hys J 87, 1076 (2004) ] 87, 1076 (2004) ]

Insight Insight given iven by by atomic-scale atomic-scale mod modelin ling in complex n complex biosystems? biosystems? Example Example for a DPPC/Cholesterol for a DPPC/Cholesterol lipid lipid membrane: pros membrane: pros and cons and cons

• f atomistic

atomistic simulations imulations for syste for systems of this f this kind kind

Limits Limits of Atomistic

• f Atomistic Simulations

imulations

Chol Chol = 0% = 0% Chol Chol = 5% = 5% Chol Chol = 12% = 12% Chol Chol = 20% = 20% Chol Chol = 30% = 30% Chol Chol = 50% = 50% Cholest Cholesterol rigidifies t rol rigidifies the membrane, thus e membrane, thus decreasing the area per molecule in decreasing the area per molecule in agreement w agreement with experiments and previous experiments and previous theoretical studies. theoretical studies. DPPC + Cholest DPPC + Cholesterol binary mixture rol binary mixture Experiment: Experiment: Pur Pure DPPC DPPC 0.64 nm 0.64 nm2 Equilib Equilibration ation for 20 ns for 20 ns

[ Falck [ Falck et al., B t al., Biop

• phys

hys J 87, 1076 (2004) ] 87, 1076 (2004) ]

Area per Lipid Area per Lipid in Bilayer n Bilayer Plane lane

Chol Chol = 30% = 30% Chol Chol = 20% = 20% Chol Chol = 12% = 12% Chol Chol = 0% = 0% Chol Chol = 5% = 5% Results fully consist Results fully consistent ent wit with NMR NMR All-trans All-trans (straight “zig-zag”

(straight “zig-zag” chain) hain)

Random walk Random walk (disor

(disorder ered chain) ed chain)

Or Orde dering o ring of lipid acyl lipid acyl cha chains by choles ns by cholesterol terol

S = 3 < cos2 θ > − 1 2

The larger The larger S, the more S, the more

• rdered
• rdered the chains

he chains are. are.

θ

Bilayer Bilayer normal

• rmal

NMR order NMR order parameter parameter of acyl f acyl chains chains

MD for DPPC/Chol MD for DPPC/Chol (E. (E. Fa Falck et et a

• al. 2004)

2004) FCS measurements for FCS measurements for DLPC/Chol DLPC/Chol (Kor

• rla

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 Lateral Diffusion iffusion Coefficients Coefficients

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)

Later Lateral lipid ipid tr trajectories ajectories in a DPPC in a DPPC bilayer bilayer of 1152 lipids f 1152 lipids over

• ver a period

period

• f 30 ns
• f 30 ns
• 4 systems

4 systems with ith number umber of lipids lipids ranging 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

• bserved where

where a lipid lipid moves moves ~0.7 nm 0.7 nm in a short in a short period eriod

• f ~100 ps.
• f ~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

Lateral Lateral Lipid ipid Diffusion Diffusion Mechanism echanism

A more A more detaile tailed consid consideration ation reve eveals ls th that at all all diffusive iffusive motions motions are re collectiv collective

• nes, as nearby
• nes, as nearby lipids

lipids move move in un in unison ison as loosely as loosely defined efined clusters. clusters.

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 Lateral lipid ipid displacement displacements

• ver
• ver Δt =

t = 1 1 n ns

Lateral Lateral Lipid ipid Diffusion Diffusion Mechanism echanism

On a molecular On a molecular scale, cale, lipids lipids move move in unison in unison as loosely as loosely defined efined clusters. clusters. On larger On larger scales, the scales, the intimately intimately correlated correlated motions motions of f neighboring ighboring lipids lipids manifest manifest themsel themselves es as as 2D flow 2D flow patterns patterns

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)

Δt = t = 0 0.05 ns ns Δt = 30 ns 30 ns Δt = t = 5 5 n ns Δt = 0.5 ns 0.5 ns Lateral Lateral displacements isplacements

• f individual
• f individual lipids

lipids during during a period a period of

• f Δt

Collective Collective Diffusive Diffusive Large-Scales arge-Scales Flow s Flow s

~40 microns ~40 microns www.memphys.sdu.dk

Time scale Time scale for diffusion

• r diffusion over
• ver

a domain a domain whose whose radius is adius is L t = = L 2 / 4 / 4D In the In the flui fluid phase, hase, D ≈ 1 × 1 × 10-7

• 7 cm

cm2/s. Then /s. Then the the time time scale scale t is at least is at least t = 2.5 = 2.5 μs for s for L = 10 nm = 10 nm (nanorafts) (nanorafts) 25 ms for 25 ms for L = 1 = 1 μm (large m (large domains) domains) State-of-the-art State-of-the-art atomistic atomistic simulations imulations are are limited imited to ~0.1 to ~0.1 μs 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. .

Time Scales Time Scales of Lateral

• f Lateral Diffusion

Diffusion

bending bending stretching stretching torsion torsion

r FC

ij

cut-off cut-off

aij

How How to find

• find effective

effective interactions nteractions for the CG model? for the CG model?

Systematic Systematic coarse coarse graining graining through through Inverse Inverse Monte Carlo (IMC)

• nte Carlo (IMC)

?

Effective Effective Interactions? Interactions?

Coarse-grained model system: Coarse-grained model system: DPPC + Chol DPPC + Chol No e No explicit water plicit water Time: ~ms Time: ~ms xchol

chol = 0 –

= 0 – 50 mol% 50 mol% Speed-up: ~ 10 Speed-up: ~ 108 Ma Main fe featur ures: es: 1. 1. 3-particle 3-particle CG represent CG representation ation for DPPC

• r DPPC

2. 2. 1-particle CG 1-particle CG represent representation ation for Chol

• r Chol

3. 3. Su Surface ace tension in ension included cluded via Lag via Lagrange ange multiplie multipliers rs to match to match the area he area co comp mpressibility ressibility to the expe to the experimental rimental value value

• T. Murtola
• T. Murtola et al.,

t al., J Chem J Chem Phys 126, 075101 (2007) Phys 126, 075101 (2007) For For Inverse Mont 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).

Coarse Coarse Grained Grained Model: DPPC/Chol Model: DPPC/Chol

INVERSE INVERSE MONTE MONTE CARLO CARLO INVERSE INVERSE MONTE MONTE CARLO CARLO

DPPC - DPPC

Radial dis Radial distribution functions of the ribution functions of the atom-scale and CG model m atom-scale and CG model match, as tch, as expected expected

Chol Chol concentration 30% concentration 30% Chol Chol concentration 0% concentration 0%

g(r) from g(r) from MD MD Effective Effective potentials potentials

• T. Murtola
• T. Murtola et al.,

t al., J Chem J Chem Phys 126, 075101 (2007) Phys 126, 075101 (2007)

Chol Chol concentration 13% concentration 13% Chol Chol concentration 30% concentration 30% Snapshots f Snapshots from ab

• m above:
• ve: only posit
• nly positions of cholesterol mol
• ns of cholesterol molecules are shown here by green

ecules are shown here by green Experiments predict coexist Experiments predict coexistence ence

• f chol-rich and chol-poor domains
• f chol-rich and chol-poor domains

Experiments predict homogeneous Experiments predict homogeneous distribution distribution of chole

• f cholesterol

terol

Almeida Almeida et al. et al. (1992) (1992)

Large-Scale Large-Scale Structures tructures by CG Model G Model

• T. Murtola
• T. Murtola et al.,

t al., J Chem J Chem Phys 126, 075101 (2007) Phys 126, 075101 (2007)

Chol Chol 13 mol-% 13 mol-% Chol Chol 30 mol-% 30 mol-%

Main a Main advantage of t vantage of the CG model: e CG model: Elastic Elastic behavior ehavior in terms n terms of area f area compressibility compressibility can can be be inc incorporat rporated ed pro properly. erly. Large-scale Large-scale domain

• main ordering

rdering can an be be predicted predicted

Static Static Structure tructure Factors Factors S(k) S(k)

• T. Murtola
• T. Murtola et al.,

t al., J Chem J Chem Phys 126, 075101 (2007) Phys 126, 075101 (2007)

Scientific Scientific American American (2004) (2004)

Lipoproteins, carriers Lipoproteins, carriers of Chol f Chol

Sugges Suggestive tive views views for the structure for the structure have have been been proposed, but proposed, but the he bottom bottom line ine is that s that the structures the structures of

• f

lipoproteins lipoproteins are re not not known nown Functions Functions of f lipoproteins lipoproteins are re not not understood nderstood either either

Marrink Marrink et al., JPCB 108, 750 (2004) t al., JPCB 108, 750 (2004) Marrink Marrink et al., JPCB 111, 7812 (2007); & In press. t al., JPCB 111, 7812 (2007); & In press. Interaction Interaction parameters arameters are re chosen chosen such such that that

• il-water
• il-water partit

artitioning

• ning free

free energies energies are are described described properly roperly by the CG model he CG model wit with respec respect to ex

• exper

perime ment ntal da data. Density Density profiles rofiles of different f different components components across across the lipid the lipid membrane embrane – comparison comparison between between atomistic tomistic and CG model and CG model results. results.

Four-to-one Four-to-one mapping apping

Water Water Total tal chain hain density density PO4 PO4 NC3 NC3 Glycerol Glycerol groups groups

Ter Termina inal CH3 CH3

Classical Classical Molecular Molecular Dynamics ynamics but ut now now wit ith coarse-grained

• arse-grained beads

beads and interactions nd interactions instead instead of atomist f atomistic descriptions escriptions

Coarse-Grained Coarse-Grained MD – MD – MARTINI Model ARTINI Model

HDL – HDL – ”Good” Good” cholesterol cholesterol

Structure of spheroidal HDL particles revealed by Combined Atomistic and Coarse Grained Simulations.

• A. Catte et al., Biophys. J. 94, 2306 (2008).

Atomistic Atomistic CG CG

Model: Model: 2 ApoA-I 2 ApoA-I –proteins –proteins 56 PO 56 POPC 16 Cholesterol Cholesterol oleates leates Atomistic Atomistic simul imulations: ations: ~10 ns, CHARMM force ns, CHARMM force fields ields CG simulat CG simulations

• ns

~1 microsecond, MARTINI model ~1 microsecond, MARTINI model by Siewert-Jan iewert-Jan Marrink Marrink, L Luca ca Montic Monticelli elli et al et al.

HDL – HDL – ”Good” Good” cholesterol cholesterol

AA 10 ns at 310K (10 ns at 410K) CG 1 µs at 310K

Structure of spheroidal HDL particles revealed by Combined Atomistic and Coarse Grained Simulations.

• A. Catte et al., Biophys. J. 94, 2306 (2008).

Novel Changes in Discoidal High Density Lipoprotein Morphology: A Molecular Dynamics Study.

• A. Catte et al., Biophys. J. 90, 4345 (2006).

Atomistic Atomistic mod

• del

el for for High High Density Density Lipoprotein Lipoprotein Coa Coarse se Grained ained model model for High

• r High

Density Density Lipoprotein ipoprotein Coarse Coarse Grained Grained model

• del describes

describes HDL DL shape shape and size and size very very well well

HDL – HDL – ”Good” Good” cholesterol cholesterol

• A. Catte et al., Biophys. J. 94, 2306 (2008).

Annular Annular cholesterol holesterol esters esters (green green) in contact ) in contact with ith apoA-I: poA-I: Almost Almost 100% 100% Packing Packing of cholesterol f cholesterol esters sters (green green) within ) within POPCs POPCs Almost Almost 100% of chol 100% of chol esters esters are are annular. annular. Atomistic Atomistic and CG models nd CG models roughly roughly consistent

• nsistent regarding

egarding contacts, the differences contacts, the differences due ue to the CG nature to the CG nature of beads

• f beads

Ch Chol

• l es

esters ters stabilizing abilizing apoA-I apoA-I and thus and thus HDL HDL

Coarse-grained modeling of LDL-sized Coarse-grained modeling of LDL-sized lipid droplets wi lipid droplets with th molecular molecular composition consistent composition consistent with with experimental data experimental data – model designed

• del designed

bottom-up using extensive atomistic bottom-up using extensive atomistic simulation data of our own. simulation data of our own.

• T. Murtola, T. Vuorela
• T. Murtola, T. Vuorela et al.,

t al., work in progress work in progress (2007-2008). (2007-2008). Why Why coarse-grained

• arse-grained simulations?

simulations?

• Atomistic

Atomistic simulations imulations for LDL over for LDL over 1 1 μs would s would take ake ~100 CPU-years 100 CPU-years

• We

We need need time time scales scales > 10 > 10 μs… s…

LDL – LDL – ”Bad” Bad” Cholesterol Cholesterol

N-terminal N-terminal of apoB-100 f apoB-100 C-terminal C-terminal Complex Complex lipid ipid droplet droplet (gray) gray)

Thank you! Thank you!

Acknowledgments:

• Academy of Finland
• Center of Excellence funding
• European Union
• ESF, Nordita
• Helsinki Inst of Physics
• Bioindustry
• CSC

Collaborators (theory, examples):

Mikko Karttunen (Ontario) Roland Faller (UC Davis) Tapio Ala-Nissilä (HUT/COMP) Adam Foster (HUT/COMP) Matej Oresic et al. (VTT)

• P. Capkova (Prague)

Aatto Laaksonen et al. (Stockholm) Erik Lindahl (Stockholm) Alex Bunker (Viikki/Drug Design) Klaus Schulten et al. (Illinois) SJ Marrink (Groningen) AA Gurtovenko (UK)

Collaborators (experiments, examples):

Ole G. Mouritsen et al. (Odense) Elina Ikonen (Biomedicum, Hki) Petri Kovanen (Wihuri, Hki) Amy Rowat (Harvard) Peter Westh (Roskilde) Juha Holopainen (HUS, Hki) Susanne Wiedmert (Hki) Michael R. Morrow (Newfoundland) Filip Tuomisto (HUT) Paavo Kinnunen (Biomedicum, Hki)

Networks:

SimBioMa (ESF), MOLSIMU (COST), Nordita, Graduate Schools, etc.