1. 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

2. Why do we need force field?

3. 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 4.0  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”

4. 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”

5. 3. Functional forms Basic functionals

6. 4. Differences for bonded interactions AMBER: CHARMM: + OPLS-AA: GROMOS: Valence Angles maintain chirality or planarity Improper Dihedral Angles Urey- Bradly angle term AMBER: + CHARMM: + OPLS-AA: + GROMOS: +

7. 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

8. ; 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 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

9. 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.

10.  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 ( q i, q j )  ( K b, b 0, K sita, Sita 0 ) from crystal structures, match NMF for peptide fragments  VDW fits amide crystal data  Dihedral match torsional barriers from experiments and quantum calculations

11.  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

12. 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

13. 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

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