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• 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 4.0A. 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

total bonded nonbondedV V V

2 20 0( ) ( ) [1 cos( )]bonded b

bonds angles dihedrals

V K b b K K n

12 6

min, min,2*ij ij i jnonbonded ij

nonbonded ij ij ijpairs ij

R R q qV

r r r

Basic functionals

4. Differences for bonded interactions

• AMBER: • CHARMM: + • OPLS-AA: • GROMOS:

20( )

2

kr r

Valence Angles

maintain chirality or planarity

Improper Dihedral Angles

Urey- Bradly angle term

(1 cos 2 )k w2 / 2k(1 cos 2 )k w2 / 2k

• AMBER: + • CHARMM: + • OPLS-AA: +• GROMOS: +

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

; name bond_type mass charge ptype sigma epsilonamber99_0 H0 0.0000 0.0000 A 2.47135e-01 6.56888e-02amber99_1 BR 0.0000 0.0000 A 0.00000e+00 0.00000e+00amber99_2 C 0.0000 0.0000 A 3.39967e-01 3.59824e-01amber99_3 CA 0.0000 0.0000 A 3.39967e-01 3.59824e-01amber99_4 CB 0.0000 0.0000 A 3.39967e-01 3.59824e-01amber99_5 CC 0.0000 0.0000 A 3.39967e-01 3.59824e-01amber99_6 CK 0.0000 0.0000 A 3.39967e-01 3.59824e-01amber99_7 CM 0.0000 0.0000 A 3.39967e-01 3.59824e-01

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

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

AMBER

• 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 cal

culations

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 energies, molecule-water minimum-energy distances

OPLS-AA

GROMOS

6. Comparison of force field in realization

Favor Alpha-helix: Amber 94, 99Beta-hairpin: GROMOS96Intermediate: CHARMM22, AMBER96, OPLS-AA/L

Experimental agreement

Alpha-helix: • Remarkable agreement: Amber 99, CHARMM22• Consistent with some experiments: AMBER96, OPLS-AA/L• Disagreement: AMBER94, GROMOS96Beta-hairpin:• Remarkable agreement: OPLS-AA/L, GROMOS96• Consistent with some experiments: AMBER96• Disagreement: AMBER94, AMBER99, CHARMM22

THANK YOU