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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. Classical Newtonian Dynamics Electrons are in the ground state Force fields are approximate

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force field of biological system
Force Field of Biological System



研究生院《分子建模与模拟导论》课堂 2009年10月21日

1 force fields
1. Force Fields
  • 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


  • 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“
  • Takao Yoda, et al, “Comparisons of force field for proteins by generalized-ensemble simulations”
2 commonly used force fields
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


  • 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
3. Functional forms

Basic functionals

4 differences for bonded interactions
4. Differences for bonded interactions

Valence Angles

Improper Dihedral Angles

  • AMBER:
  • CHARMM: +
  • OPLS-AA:

maintain chirality or planarity

Urey- Bradly angle term

  • AMBER: +
  • CHARMM: +
  • OPLS-AA: +
  • GROMOS: +
5 differences for nonbonded interactions
5. Differences for nonbonded interactions
  • Handling of 1,4-nonbonded interactions between A, D in dihedral A-B-C-D
  • AMBER: LJ ½ Coulomb 1/1.2
  • CHARMM: not scaling except some special pairs
  • OPLS-AA: LJ ½ Coulomb ½
  • GROMOS: case by case
6 how to construct a force field
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.


  • 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


  • Key idea:
  • Balancing water-protein, water-water, and protein-protein interaction energies in the condensed phase
  • Difference:
  • Dimerization energies, molecule-water minimum-energy distances



6 comparison of force field in realization
6. Comparison of force field in realization


  • 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