108-2,936 μs K. Lindorff-Larsen, S. Piana, R.O. Dror, D.E. Shaw, How fast-folding proteins fold. Science 334, (2011). 100 ns, 64,000,000 atoms
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1 ,936 μs K. Lindorff-Larsen, S. Piana, R.O. Dror, D.E. Shaw, How fast-folding proteins fold. Science 334, (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, (1977). G. Zhao et al. Mature HIV1 capsid structure by cryoelectron microscopy and all-atom molecular dynamics. Nature, 497, (2013).
2 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 porin 1 ns Tieleman & Berendsen 1998 peptide folding 1 μs Duan & Kollman 2011 small protein folding 2.9 ms Shaw et al virus capsid 100 ns Schulten et al. McCammon et al.
3 BIOMOLECULAR SIMULATIONS - 4D structures - molecular microscopy - explanation of structural phenomena - predictions
4 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
5 Newton's equation of motion 2 mi ri t 2 =Fi V Fi = ri
6
7 Software for biomolecular simulation free GROMACS cheap AMBER GROMOS CHARMM expensive
8 Potential energy good structure low energy bad structure high energy
9 Force fields 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 r r ij r C 6 ij 6 ij r ]
10 Force fields 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 r r ij r C 6 ij 6 ij r ]
11 Partial charges
12 Force fields Proteins, nucleic acids, lipids: AMBER GROMOS OPLS CHARMM general molecules: GAFF MM2 MM3 MMFF Special: Glycam (carbohydrates) Martini (coarse grained)
13 Force fields all atom united atom coarse grained
14 [ atomtypes ] ;name bond_type mass charge ptype sigma epsilon opls_111 OW A e e 01 opls_112 HW A e e+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 opls_112 1 SOL HW opls_112 1 SOL HW [ bonds ] ; i j funct length force.c [ angles ] ; i j k funct angle force.c
15 Water (TIP3P model) [ atomtypes ] ;name bond_type mass charge ptype sigma epsilon opls_111 OW A e e 01 opls_112 HW A e e+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 opls_112 1 SOL HW opls_112 1 SOL HW [ bonds ] ; i j funct length force.c [ angles ] ; i j k funct angle force.c
16 How to obtain (missing) force field parameters? 1. Other force fields (with caution) 2. Experiment infrared spectroscopy, crystallography, Molecular modelling quantum chemistry
17 Newton's equation of motion Forces 2 Masses mi ri t 2 =Fi V Fi = ri Potential energy
18 Molecular dynamics simulation vs geometry optimization & geometry search r r
19 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
20 Water Why is water important? + +
21 QM/MM M. Krupička, I. Tvaroška: J Phys Chem B (2009) 113,
22 Constraints
23 Periodic boundary condition
24 Other issues: Temperature control - Berendsen, Nose-Hoover, V-rescale thermostat - initial velocity Pressure control - Berendsen, Parrinello-Rahman barostats Control of surface tension
25 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
26 Output analysis - root mean square fluctuations (RMSF) RMSF residue number
27 Output analysis - essential dynamics trajectory molecule CV2 collective motions CV1
28 S-peptide demo
29 S-peptide GROMACS 1. initial coordinates 2. topology 3. instructions for the program
30 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
31 S-peptide GROMACS 1. initial coordinates (speptide.gro) Go Rough, Oppose Many Angry Chinese Serial killers 286 1LYS N LYS H LYS H LYS H ALA C ALA OC ALA OC S-peptide (19 amino acids, 286 atoms, C86H140N27O32S, 1 Cl-, 859 H2O)
32 S-peptide GROMACS 2. topology (speptide.top) 22 atom types 286 atoms 287 bonds, interactions 513 valence angles 798 torsions + water and ion topology
33 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 ; ps! ; total 1 ns. 1 Simulated time 250 ( times 2 fs = 1 ns) Frequency of data storage 10 grid PME 1.0 Set-up of non-covalent 1.0 interaction treatment 1.0
34 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 = ref_t = ; 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 = Temperature at t=0 gen_seed =
35 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 Rel. Constraint Deviation: Max between atoms RMS Before LINCS After LINCS Energies (kj/mol) Angle Proper Dih. Ryckaert Bell. LJ 14 Coulomb e e e e e+03 LJ (SR) Coulomb (SR) Potential Kinetic En. Total Energy e e e e e+04 Temperature Pressure (bar) e e+02
36 S-peptide NODE (s) Real (s) (%) Time: :33 (Mnbf/s) (GFlops) (ns/day) (hour/ns) Performance: Finished mdrun on node 0 Sun Sep 20 11:21:
37 Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:
38 Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:
39 Example study V. Spiwok, P. Lipovová, T. Skálová, J. Dušková, J. Dohnálek, J. Hašek, N.J. Russell, B. Králová: J. Mol. Model. (2007) 13:
40 Sampling
41 Sampling A B
42 Sampling A Vpot,A B Vpot,B Comparison of Vpot does not (usually) work: - many degrees of freedom - water - temperature, entropy
43 Sampling A B A B time
44 Sampling A B A B time We can really simulate
45 Computers Clusters
46 Supercomputers #1: Tianhe-2 (MilkyWay-2), 3,120,000 cores, China
47 Supercomputers #40: Salomon, 76,896 cores, IT4Innovation, CZ
48 GPU computing
49 Special purpose computers
50 Příklady simulací 2-adrenergní receptor Dror et al. (2009) Proc Natl Acad Sci USA, 106,
51 Distributed computing
52 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, (2013). SSR128129E - Allosteric inhibitor of fibroblast growth factor receptor, which does not compete with FGF, but inhibits FGF signalling.
53 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, (2013).
54 Sampling problem algorithmic solutions Metadynamics Iduronic acid 4 C1 4 C1 SO 2 population (%) kj/mol C4 SO 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, (2013).
55 Metadynamika Spiwok et al. (2015) J Chem Phys, 113,
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