Force Field of Biological System
中国科学院理论物理研究所
张小虎
研究生院《分子建模与模拟导论》课堂
2009年10月21日
Why do we need force field?
1. Force Fields
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•
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Classical Newtonian Dynamics
Electrons are in the ground state
Force fields are approximate
Nonbonded force fields for biological systems are effective pair potentials
No Explicit term for hydrogen bonding
References
H. J. C. Berendsen, et al, Gromacs User Manual version 4.0
A. D. MacKerell, Jr. , et al, "Comparison of Protein Force Fields for
Molecular Dynamics Simulations“
A. D. Mackerell, Jr. , et al, "Empirical Force Fields for Biological
Macromolecules: Overview and Issues“
J. W. Ponder, et al, "FORCE FIELDS FOR PROTEIN SIMULATIONS“
Takao Yoda, et al, “Comparisons of force field for proteins by
generalized-ensemble simulations”
2. Commonly used force fields
• Amber: Assisted Model Building with Energy Refinement
• CHARMM: Chemistry at HARvard Macromolecular Mechanics
• OPLS-AA: Optimized Potentials for Liquid Simulations- All Atom
• GROMOS: GROningen MOlecular Simulation
References
W. D. Cornell, et al (1995) ”A second generation force field for the
simulation of proteins, nucleic acids, and organic molecules”
A. D. MacKerell, et al (1998) ”All-atom empirical potential for molecular
modeling and dynamics studies of proteins”
W. L. Jorgensen, et al (1996) ” Development and Testing of the OPLS
All-Atom Force Field on Conformational Energetics and Properties of
Organic Liquids”
C. Oostenbrink, et al (2004) “A biomolecular force field based on the
free enthalpy of hydration and solvation: The GROMOS force-field
parameter sets 53A5 and 53A6”
3. Functional forms
Basic functionals
Vtotal  Vbonded  Vnonbonded
Vbonded 
 K (b  b )
b
bonds
Vnonbonded
0
2

 K (  )
0
2
angles
  R
min,ij
    ij 
 rij
nonbonded 

pairs ij 
12



 Rmin,ij
  2* 

 rij
K  [1  cos(n   )]
dihedrals



6
 qq
 i j
 rij





4. Differences for bonded interactions
Valence Angles
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•
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AMBER:
k
2
CHARMM: + ( r  r 0 )
2
OPLS-AA:
GROMOS:
Improper Dihedral Angles
maintain chirality or planarity
Urey- Bradly angle term
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•
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AMBER: +
CHARMM: +
OPLS-AA: +
GROMOS: +
k (1  cos 2w)
k 2 / 2
k (1  cos 2w)
k 2 / 2
5. Differences for nonbonded interactions
 Handling of 1,4-nonbonded interactions between
A, D in dihedral A-B-C-D
•
•
•
•
AMBER:
CHARMM:
OPLS-AA:
GROMOS:
LJ ½ Coulomb 1/1.2
not scaling except some special pairs
LJ ½ Coulomb ½
case by case
6. How to construct a force field?
Adjusting parameter values until the force
field is able to reproduce a set of target data
to within a prescribed threshold
; name bond_type mass charge ptype sigma
epsilon
amber99_0 H0 0.0000 0.0000 A 2.47135e-01 6.56888e-02
amber99_1 BR 0.0000 0.0000 A 0.00000e+00 0.00000e+00
amber99_2 C
0.0000 0.0000 A 3.39967e-01 3.59824e-01
amber99_3 CA 0.0000 0.0000 A 3.39967e-01 3.59824e-01
amber99_4 CB 0.0000 0.0000 A 3.39967e-01 3.59824e-01
amber99_5 CC 0.0000 0.0000 A 3.39967e-01 3.59824e-01
amber99_6 CK 0.0000 0.0000 A 3.39967e-01 3.59824e-01
amber99_7 CM 0.0000 0.0000 A 3.39967e-01 3.59824e-01
Target data
 Experimental: vibrational spectra; heats of vaporization; densities;
solvation free energies; microwave, electron, or X-ray diffraction
structure; and relative conformational energies and barrier heights.
 QM: vibrational spectra; minimum energy geometries; dipole
moments; conformational energies and barrier heights; electrostatic
potentials; and dimerization energies
The Amber,
CHARMM, GROMOS, and OPLS-AA force field for
proteins each target a different subset of the possible experimental and
QM data, although there is substantial overlap between the subsets.
AMBER

AMBER84: Polar hydrogens + united atoms ( hydrogens bonded to
carbon)

AMBER86: All- atom model
• Based on experimental with gas phase simulation
• Key ideas:
 ESP
partial charge ( qi , qj )
 ( Kb , b0 , Ksita , Sita0 ) from crystal structures, match NMF for peptide
fragments
 VDW fits amide crystal data
 Dihedral match torsional barriers from experiments and quantum
calculations

AMBER94: Aimed to better perform Condensed phase simulations
• Partial charges:
 Dependency on environments: RESP
 Dependency on conformations: fit simultaneously with multiple
configurations
• More accurate electron correlation method and larger basis set to
determine torsional terms

AMBER96,99
• Account long-range effects
• Fit tetrapeptide + dipeptide

AMBER03
• More accurate electron correlation method and larger
basis set to determine torsional terms and partial charges
• Continuum solvent models instead of vacuum
CHARMM
Key
idea:
Balancing water-protein, water-water, and protein-protein interaction
energies in the condensed phase
Difference:
Dimerization
OPLS-AA
GROMOS
energies, molecule-water minimum-energy distances
6. Comparison of force field in realization
Favor
Alpha-helix: Amber 94, 99
Beta-hairpin: GROMOS96
Intermediate: CHARMM22, AMBER96, OPLS-AA/L
Experimental agreement
Alpha-helix:
• Remarkable agreement: Amber 99, CHARMM22
• Consistent with some experiments: AMBER96, OPLS-AA/L
• Disagreement: AMBER94, GROMOS96
Beta-hairpin:
• Remarkable agreement: OPLS-AA/L, GROMOS96
• Consistent with some experiments: AMBER96
• Disagreement: AMBER94, AMBER99, CHARMM22
THANK YOU