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 3.15061e­01 6.36386e­01
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 3.15061e­01 6.36386e­01
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. Ryckaert­Bell. LJ­14 Coulomb­14
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