www.nobelprize.org 108-2,936 μs K. Lindorff-Larsen, S. Piana, R.O. Dror, D.E. Shaw, How fast-folding proteins fold. Science 334, 517-520 (2011). 100 ns, 64,000,000 atoms 3.2 ps, < 1,000 atoms J.A. McCammon, B.R. Gelin & M. Karplus, Dynamics of folded proteins. Nature 267, 585-590 (1977). G. Zhao et al. Mature HIV1 capsid structure by cryoelectron microscopy and all-atom molecular dynamics. Nature, 497, 643-646 (2013).
Molecular Dynamics Simulation 1957 hard spheres - Alder & Waiinwright 1964 argon? Rahman 1971 water 2.2 ps Rahman & Stillinger 1977 BPTI 8 ps 1988 phospholipid bilayer 200 ps Egberts & Berendsen 1993 biotin-streptavidin 108 ps Myiamoto & Kollman 1995 bacteriorhodopsin 300 ps Edholm et al. 1998 porin 1 ns Tieleman & Berendsen 1998 peptide folding 1 μs Duan & Kollman 2011 small protein folding 2.9 ms Shaw et al. 2013 virus capsid 100 ns Schulten et al. McCammon et al.
BIOMOLECULAR SIMULATIONS - 4D structures - molecular microscopy - explanation of structural phenomena - predictions
BIOMOLECULAR SIMULATIONS - protein stability in different environments effect of covalent modifications on protein structures protein folding validation of predicted protein structures protein-ligand, protein-protein interactions membrane structures structures of other biopolymers mechanics of biopolymers and their complexes signal transition in biomolecular systems virtual experiments assistance of experimental methods
Newton's equation of motion 2 mi ri t 2 =Fi V Fi = ri
Software for biomolecular simulation free GROMACS http://www.gromacs.org cheap AMBER http://ambermd.org GROMOS http://www.gromos.net CHARMM http://www.charmm.org expensive
Potential energy good structure low energy bad structure high energy
Force fields 1 1 2 2 V = k r r r 0 k 0 bonds 2 angles 2 k 1 cos n s torsions pairs [ 12 ij 12 ij qi q j C 1 4 0 r r ij r 2 4 1 3 5 6 C 6 ij 6 ij r ]
Force fields 1 1 2 2 V = k r r r 0 k 0 bonds 2 angles 2 k 1 cos n s torsions pairs [ 12 ij 12 ij qi q j C 1 4 0 r r ij r 7 2 8 1 3 4 5 6 C 6 ij 6 ij r ]
Partial charges
Force fields Proteins, nucleic acids, lipids: AMBER GROMOS OPLS CHARMM general molecules: GAFF MM2 MM3 MMFF Special: Glycam (carbohydrates) Martini (coarse grained)
Force fields all atom united atom coarse grained
[ atomtypes ] ;name bond_type mass charge ptype sigma epsilon opls_111 OW 8 15.99940 0.834 A 3.15061e 01 6.36386e 01 opls_112 HW 1 1.00800 0.417 A 0.00000e+00 0.00000e+00 [ moleculetype ] ; molname nrexcl SOL 2 [ atoms ] ; id at type res nr residu name at name cg nr charge 1 opls_111 1 SOL OW 1 0.834 2 opls_112 1 SOL HW1 1 0.417 3 opls_112 1 SOL HW2 1 0.417 [ bonds ] ; i j funct length force.c. 1 2 1 0.09572 502416.0 1 3 1 0.09572 502416.0 [ angles ] ; i j k funct angle force.c. 2 1 3 1 104.52 628.02
Water (TIP3P model) [ atomtypes ] ;name bond_type mass charge ptype sigma epsilon opls_111 OW 8 15.99940 0.834 A 3.15061e 01 6.36386e 01 opls_112 HW 1 1.00800 0.417 A 0.00000e+00 0.00000e+00 [ moleculetype ] ; molname nrexcl SOL 2 [ atoms ] ; id at type res nr residu name at name cg nr charge 1 opls_111 1 SOL OW 1 0.834 2 opls_112 1 SOL HW1 1 0.417 3 opls_112 1 SOL HW2 1 0.417 [ bonds ] ; i j funct length force.c. 1 2 1 0.09572 502416.0 1 3 1 0.09572 502416.0 [ angles ] ; i j k funct angle force.c. 2 1 3 1 104.52 628.02
How to obtain (missing) force field parameters? 1. Other force fields (with caution) 2. Experiment infrared spectroscopy, crystallography,... 3. Molecular modelling quantum chemistry
Newton's equation of motion Forces 2 Masses mi ri t 2 =Fi V Fi = ri Potential energy
Molecular dynamics simulation vs geometry optimization & geometry search r r
Chemical reactions - quantum chemistry - combination of molecular mechanics with quantum chemistry (QM/MM) - molecular mechanics trained by quantum chemistry (empirical valence bond) - special reactive force fields
Water Why is water important? + +
QM/MM M. Krupička, I. Tvaroška: J Phys Chem B (2009) 113, 11314-9.
Constraints
Periodic boundary condition
Other issues: Temperature control - Berendsen, Nose-Hoover, V-rescale thermostat - initial velocity Pressure control - Berendsen, Parrinello-Rahman barostats Control of surface tension
Output analysis temporary development of structural parameters: - energy, temperature - distances, angles, torsions - number of native contacts - secondary structure - radius of gyration - root mean square deviations (RMSD) RMSD RMSD time time
Output analysis - root mean square fluctuations (RMSF) RMSF residue number
Output analysis - essential dynamics trajectory molecule CV2 collective motions CV1
S-peptide demo
S-peptide GROMACS 1. initial coordinates 2. topology 3. instructions for the program
S-peptide GROMACS convert speptide.pdb to topology and coordinates, add hydrogens $ pdb2gmx -f speptide -o speptide -p speptide + chose the right force field create a box with the protein in the centre $ editconf -f speptide -o box -c -d 1 fill the box with water $ genbox -cp box -cs -p speptide -o solvated add counterions if necessary
S-peptide GROMACS 1. initial coordinates (speptide.gro) Go Rough, Oppose Many Angry Chinese Serial killers 286 1LYS N 1 2.497-0.065 2.231 1LYS H1 2 2.581-0.048 2.180 1LYS H2 3 2.519-0.086 2.326 1LYS H3 4 2.448-0.142 2.190... 19ALA C 284 2.846 3.022 2.056 19ALA OC1 285 2.919 3.015 1.954 19ALA OC2 286 2.713 3.020 2.055 1.79949 3.37953 1.37997 S-peptide (19 amino acids, 286 atoms, C86H140N27O32S, 1 Cl-, 859 H2O)
S-peptide GROMACS 2. topology (speptide.top) 22 atom types 286 atoms 287 bonds, 733 1 4 interactions 513 valence angles 798 torsions + water and ion topology
S-peptide GROMACS 3. instructions for the program (md.mdp) integrator = constraints = constraint_algorithm = dt = nsteps = nstcomm = nstxout = nstvout = nstfout = nstlog = nstenergy = nstlist = ns_type = coulombtype = rlist = rcoulomb = rvdw = Use molecular dynamics md Fixed length of all bonds all-bonds lincs 0.002 ; ps! 500000 ; total 1 ns. 1 Simulated time 250 (500 000 times 2 fs = 1 ns) 1000 0 100 100 Frequency of data storage 10 grid PME 1.0 Set-up of non-covalent 1.0 interaction treatment 1.0
S-peptide GROMACS 3. instructions for the program (speptide.top) ; Berendsen temperature coupling is on in two groups Tcoupl = berendsen tc-grps = Protein SOL Temperature control tau_t = 0.1 0.1 ref_t = 300 300 ; Energy monitoring energygrps = Protein SOL ; Isotropic pressure coupling is now on Pcoupl = berendsen Pcoupltype = isotropic tau_p = 0.5 Pressure control compressibility = 4.5e-5 ref_p = 1.0 ; Generate velocites is off at 300 K. gen_vel = no gen_temp = 300.0 Temperature at t=0 gen_seed = 173529
S-peptide run energy minimization $ grompp -f em -c solvated -p speptide -o em1 $ mdrun -s em1 -o em1 -e em1 -g em1 -c after_em1 run molecular dynamics simulation $ grompp -f md -c after_em1 -p speptide -o md1 $ mdrun -s md1 -o md1 -e md1 -g md1 -c after_md1 Step Time Lambda 2800 5.60000 0.00000 Rel. Constraint Deviation: Max between atoms RMS Before LINCS 0.058424 247 248 0.007393 After LINCS 0.000082 180 182 0.000029 Energies (kj/mol) Angle Proper Dih. Ryckaert Bell. LJ 14 Coulomb 14 6.22621e+02 5.32697e+01 7.29416e+02 2.94892e+02 3.86087e+03 LJ (SR) Coulomb (SR) Potential Kinetic En. Total Energy 4.62848e+03 4.71919e+04 3.70024e+04 7.47176e+03 2.95306e+04 Temperature Pressure (bar) 3.14265e+02 2.02309e+02
S-peptide NODE (s) Real (s) (%) Time: 573.400 580.000 98.9 9:33 (Mnbf/s) (GFlops) (ns/day) (hour/ns) Performance: 11.327 1.597 15.068 1.593 Finished mdrun on node 0 Sun Sep 20 11:21:17 2011
Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:485-497.
Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:485-497.
Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:485-497.
Sampling
Sampling A B
Sampling A Vpot,A B Vpot,B Comparison of Vpot does not (usually) work: - many degrees of freedom - water - temperature, entropy
Sampling A B A B time
Sampling A B A B time We can really simulate
Computers Clusters
Supercomputers http://www.top500.org #1: Tianhe-2 (MilkyWay-2), 3,120,000 cores, China
Supercomputers http://www.top500.org #40: Salomon, 76,896 cores, IT4Innovation, CZ
GPU computing
Special purpose computers
Příklady simulací 2-adrenergní receptor Dror et al. (2009) Proc Natl Acad Sci USA, 106, 4689 4694
Distributed computing http://folding.stanford.edu/
Sampling problem algorithmic solutions Metadynamics Herbert C. et al. Molecular Mechanism of SSR128129E, an Extracellularly Acting, Small-Molecule, Allosteric Inhibitor of FGF Receptor Signaling. Cancer Cell 23, 489501 (2013). SSR128129E - Allosteric inhibitor of fibroblast growth factor receptor, which does not compete with FGF, but inhibits FGF signalling.
Sampling problem algorithmic solutions Metadynamics Iduronic acid 4 C1 1 C4 2 SO P. Oborský, I. Tvaroška, B. Králová, V. Spiwok, Toward an Accurate Conformational Modeling of Iduronic Acid. J Phys Chem B 117, 1003-1009 (2013).
Sampling problem algorithmic solutions Metadynamics Iduronic acid 4 C1 4 C1 SO 2 population (%) 100 1 80 60 +30 kj/mol C4 SO 2 100 60 40 40 20 20 0 0 C4 4 C1 +30 kj/mol 80 α-l-idoa2s-ome 1 C4 1 2 SO others α-l-idoa-ome 1 C4 4 C1 2 SO others P. Oborský, I. Tvaroška, B. Králová, V. Spiwok, Toward an Accurate Conformational Modeling of Iduronic Acid. J Phys Chem B 117, 1003-1009 (2013).
Metadynamika Spiwok et al. (2015) J Chem Phys, 113, 9589 9594