Force field (chemistry)




 

In the context of proteins, provide even more abstracted representations for increased computational efficiency.

The usage of the term "force field" in chemistry and computational biology differs from the standard usage in physics. In chemistry usage a force field is defined as a potential function, while the term is used in physics to denote the negative gradient of a scalar potential.

Functional form

Further information: Molecular mechanics

The basic functional form of a force field encapsulates both van der Waals forces. The specific decomposition of the terms depends on the force field, but a general form for the total energy can be written as \ E_{total} = E_{covalent} + E_{noncovalent} where the components of the covalent and noncolvalent contributions are given by the following summations:

\ E_{covalent} = E_{bond} + E_{angle} + E_{dihedral}

\ E_{noncovalent} = E_{electrostatic} + E_{van der Waals}

The bond and angle terms are usually modeled as harmonic oscillators in force fields that do not allow bond breaking. The functional form is highly variable. It can include potentials for Lennard-Jones potential and the electrostatic term with Coulomb's law, although both can be buffered or scaled by a constant factor to produce better agreement with experimental observation.

Parameterization

In addition to the functional form of the potentials, a force field defines a set of parameters for each type of atom. For example, a force field would include distinct parameters for an polarizability, in which a particle's charge is influenced by electrostatic interactions with its neighbors. For example, polarizability can be approximated by the introduction of induced dipoles; it can also be represented by Drude particles, or massless, charge-carrying virtual sites attached by a springlike harmonic potential to each polarizable atom. The introduction of polarizability into force fields in common use has been inhibited by the high computational expense associated with calculating the local electrostatic field.

Although many molecular simulations involve biological enthalpy of sublimation (CFF), dipole moments, or various spectroscopic parameters (CFF).

Parameter sets and functional forms are defined by force field developers to be self-consistent. Because the functional forms of the potential terms vary extensively between even closely related force fields (or successive versions of the same force field), the parameters from one force field should never be used in conjunction with the potential from another.

Deficiencies

All force fields are based on numerous approximations and derived from different types of experimental data. Therefore they are called empirical. Some existing force fields usually do not account for electronic dielectric constant is questionable in the highly heterogeneous environments of proteins or biological membranes, and the nature of the dielectric depends on the model used [3].

All types of Jacob Israelachvili in his book "Intermolecular and surface forces". It was concluded that "the interaction between hydrocarbons across water is about 10% of that across vacuum" [4]. Such effects are unaccounted in the standard molecular mechanics.

Another round of criticism came from practical applications, such as protein structure refinement. It was noted that protein design [14] [15] [16], and modeling of proteins in membranes [17].

There is also an opinion that molecular mechanics may operate with energy which is irrelevant to protein folding or ligand binding [18]. The parameters of typical force fields reproduce Lennard-Jones potentials derived from protein engineering data were also smaller than in typical force fields and followed the “like dissolves like” rule, as predicted by McLachlan theory [18].

Popular force fields

Different force fields are designed for different purposes.

MM2 was developed primarily for conformational analysis of small organic molecules. It is designed to reproduce the equilibrium covalent geometry of molecules as precisely as possible. It implements a large set of parameters that is continuously refined and updated for many different classes of organic compounds (MM3 and MM4).

CFF was developed by Warshel, Lifson and coworkers as a general method for unifying studies of energies, structures and vibration of general molecules and molecular crystals. The CFF program, developed by Levitt and Warshel, is based on the Cartesian representation of all the atoms, and it served as the basis for many subsequent simulation programs.

ECEPP was developed specifically for modeling of peptides and proteins. It uses fixed geometries of amino acid residues to simplify the potential energy surface. Thus, the energy minimization is conducted in the space of protein torsion angles. Both MM2 and ECEPP include potentials for H-bonds and torsion potentials for describing rotations around single bonds. ECEPP/3 was implemented (with some modifications) in Internal Coordinate Mechanics and FANTOM [25].

molecular dynamics of macromolecules, although they are also commonly applied for energy minimization. Therefore, the coordinates of all atoms are considered as free variables.

Classical force fields

  • AMBER (Assisted Model Building and Energy Refinement) - widely used for proteins and DNA
  • CHARMM - originally developed at Harvard, widely used for both small molecules and macromolecules
  • Accelrys
  • CVFF - also broadly used for small molecules and macromolecules
  • GROMACS - The force field optimized for the package of the same name
  • GROMOS - A force field that comes as part of the GROMOS (GROningen MOlecular Simulation package), a general-purpose molecular dynamics computer simulation package for the study of biomolecular systems. GROMOS force field (A-version) has been developed for application to aqueous or apolar solutions of proteins, nucleotides and sugars. However, a gas phase version (B-version) for simulation of isolated molecules is also available
  • OPLS-AA, OPLS-UA, OPLS-2001, OPLS-2005 - Members of the OPLS family of force fields developed by William L. Jorgensen at the Yale University Department of Chemistry.
  • ENZYMIX – A general polarizable force field for modeling chemical reactions in biological molecules. This force field is implemented with the empirical valence bond (EVB) method and is also combined with the semimacroscopic PDLD approach in the program in the MOLARIS package.
  • ECEPP/2 - First force field for polypeptide molecules - developed by F.A.Momany, H.A.Scheraga and colleagues.
  • QCFF/PI – A general force field for conjugated molecules. [26]. [27]

Second-generation force fields

  • CFF - a family of forcefields adapted to a broad variety of organic compounds, includes forcefields for polymers, metals, etc.
  • MMFF - developed at Merck, for a broad range of chemicals
  • MM2, MM3, MM4 - developed by Norman L. Allinger, for a broad range of chemicals

Polarizable force field based on induced dipole

  • -CFF/ind and ENZYMIX – The first polarizable force field [28] which has subsequently been used in many applications to biological systems.[2].

Polarizable Force Fields based on point charges

  • - PFF (Polarizable Force Field) developed by Richard A. Friesner and coworkers
  • - DRF90 developed by P. Th. van Duijnen and coworkers.
  • - SP-basis Chemical Potential Equalization (CPE) approach developed by R. Chelli and P. Procacci
  • - CHARMM polarizable force field developed by B. Brooks and coworkers.
  • - AMBER polarizable force field developed by Jim Caldwell and coworkers.

Polarizable Force Fields based on distributed multipoles

  • - The SIBFA (Sum of Interactions Between Fragments Ab initio computed) force field for small molecules and flexible proteins, developed by Nohad Gresh (Paris V, René Descartes University) and Jean-Philip Piquemal (Paris VI, Pierre & Marie Curie University). SIBFA is a molecular mechanics procedure formulated and calibrated on the basis of ab initio supermolecule computations. Its purpose is to enable the simultaneous and reliable computations of both intermolecular and conformational energies governing the binding specificities of biologically and pharmacologically relevant molecules. This procedure enables an accurate treatment of transition metals. The inclusion of a ligand field contribution allows computations on "open-shell" metalloproteins.
  • - AMOEBA force field. developed by Pengyu Ren (University of Texas at Austin) and Jay W. Ponder (Washington University).
  • - ORIENT procedure developed by Anthony J. Stone (Cambridge University) and coworkers.
  • - Non-Empirical Molecular Orbital (NEMO) procedure developed by Gunnar Karlström and coworkers at Lund University (Sweden).

Polarizable Force Fields based on density

  • - Gaussian Electrostatic Model (GEM), a polarizable force field based on Density Fitting developed by Thomas A. Darden and G. Andrés Cisneros at NIEHS; and Jean-Philip Piquemal (Paris VI University).
  • - Polarizable procedure based on the Kim-Gordon approach developed by Jürg Hutter and coworkers (University of Zurick)

Reactive Force Fields

  • ReaxFF - reactive force field developed by Adri van Duin, William Goddard and coworkers. It is fast, transferable and is the computational method of choice for atomistic-scale dynamical simulations of chemical reactions.
  • EVB (empirical valence bond) – This reactive force field, introduced by Warshel and coworkers, is probably the most reliable and physically consistent way of using force fields in modeling chemical reactions in different environments. The EVB facilitates calculations of actual activation free energies in condensed phases and in enzymes.

Other

Water Models

Main article: water model

The set of parameters used to model water or aqueous solutions (basically a force field for water) is called a water model. Water has attracted a great deal of attention due to its unusual properties and its importance as a solvent. Many water models have been proposed; some examples are TIP3P, TIP4P, SPC, and ST2.

See also

References

  1. ^ Ponder JW and Case DA. (2003) Force fields for protein simulations. Adv. Prot. Chem. 66: 27-85.
  2. ^ a b Warshel A, Sharma PK, Kato M and Parson WW (2006) Modeling Electrostatic Effects in Proteins. Biochim. Biophys. Acta 1764:1647-1676.
  3. ^ Schutz CN. and Warshel A. 2001. What are the dielectric "constants" of proteins and how to validate electrostatic models? Proteins 44: 400-417.
  4. ^ a b c d Israelachvili, J.N. 1992. Intermolecular and surface forces. Academic Press, San Diego.
  5. ^ Leckband, D. and Israelachvili, J. (2001) Intermolecular forces in biology. Quart. Rev. Biophys. 34: 105-267.
  6. ^ Koehl P. and Levitt M. (1999) A brighter future for protein structure prediction. Nature Struct. Biol. 6: 108-111.
  7. ^ Brunger AT and Adams PD. (2002) Molecular dynamics applied to X-ray structure refinement. Acc. Chem. Res. 35: 404-412.
  8. ^ Guntert P. (1998) Structure calculation of biological macromolecules from NMR data. Quart. Rev. Biophys. 31: 145-237.
  9. ^ Tramontano A. and Morea V. 2003. Assessment of homology-based predictions in CASP5. Proteins. 53: 352-368.
  10. ^ Gohlke H. and Klebe G. (2002) Approaches to the description and prediction of the binding affinity of small-molecule ligands to macromolecular receptors. Angew. Chem. Internat. Ed. 41: 2644-2676.
  11. ^ Edgcomb SP. and Murphy KP. (2000) Structural energetics of protein folding and binding. Current Op. Biotechnol. 11: 62-66.
  12. ^ Lazaridis T. and Karplus (2000) Effective energy functions for protein structure prediction. Curr. Op. Struct. Biol. 10: 139-145
  13. ^ Levitt M. and Warshel A. (1975) Computer Simulations of Protein Folding, Nature 253: 694-698
  14. ^ Gordon DB, Marshall SA, and Mayo SL (1999) Energy functions for protein design. Curr. Op. Struct. Biol. 9: 509-513.
  15. ^ Mendes J., Guerois R, and Serrano L (2002) Energy estimation in protein design. Curr. Op. Struct. Biol. 12: 441-446.
  16. ^ Rohl CA, Strauss CEM, Misura KMS, and Baker D. (2004) Protein structure prediction using Rosetta. Meth. Enz. 383: 66-93.
  17. ^ Lomize AL, Pogozheva ID, Lomize MA, Mosberg HI (2006) Positioning of proteins in membranes: A computational approach. Protein Sci. 15, 1318-1333.
  18. ^ a b Lomize A.L., Reibarkh M.Y. and Pogozheva I.D. (2002) Interatomic potentials and solvation parameters from protein engineering data for buried residues. Protein Sci., 11:1984-2000.
  19. ^ Murphy K.P. and Gill S.J. 1991. Solid model compounds and the thermodynamics of protein unfolding. J. Mol. Biol., 222: 699-709.
  20. ^ Shakhnovich, E.I. and Finkelstein, A.V. (1989) Theory of cooperative transitions in protein molecules. I. Why denaturation of globular proteins is a first-order phase transition. Biopolymers 28: 1667-1680.
  21. ^ Graziano, G., Catanzano, F., Del Vecchio, P., Giancola, C., and Barone, G. (1996) Thermodynamic stability of globular proteins: a reliable model from small molecule studies. Gazetta Chim. Italiana 126: 559-567.
  22. ^ Myers J.K. and Pace C.N. (1996) Hydrogen bonding stabilizes globular proteins, Biophys. J. 71: 2033-2039.
  23. ^ Scholtz J.M., Marqusee S., Baldwin R.L., York E.J., Stewart J.M., Santoro M., and Bolen D.W. (1991) Calorimetric determination of the enthalpy change for the alpha-helix to coil transition of an alanine peptide in water. Proc. Natl. Acad. Sci. USA 88: 2854-2858.
  24. ^ Gavezotti A. and Filippini G. (1994) Geometry of intermolecular X-H...Y (X,Y=N,O) hydrogen bond and the calibration of empirical hydrogen-bond potentials. J. Phys. Chem. 98: 4831-4837.
  25. ^ Schaumann, T., Braun, W. and Wutrich, K. (1990) The program FANTOM for energy refinement of polypeptides and proteins using a Newton-Raphson minimizer in torsion angle space. Biopolymers 29: 679-694.
  26. ^ Warshel A (1973). Quantum Mechanical Consistent Force Field (QCFF/PI) Method: Calculations of Energies, Conformations and Vibronic Interactions of Ground and Excited States of Conjugated Molecules, Israel J. Chem. 11: 709.
  27. ^ Warshel A and Levitt M (1974). QCFF/PI: A Program for the Consistent Force Field Evaluation of Equilibrium Geometries and Vibrational Frequencies of Molecules, QCPE 247, Quantum Chemistry Program Exchange, Indiana University.
  28. ^ Warshel A. and Levitt M. (1976) Theoretical Studies of Enzymatic Reactions: Dielectric Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme, J. Mol. Biol. 103: 227-249

Further reading

  1. Schlick T. (2000). Molecular Modeling and Simulation: An Interdisciplinary Guide Interdisciplinary Applied Mathematics: Mathematical Biology. Springer-Verlag New York, NY.
  2. Israelachvili, J.N. (1992) Intermolecular and surface forces. Academic Press, San Diego.
  3. Warshel A (1991). "Computer Modeling of Chemical Reactions in Enzymes and Solutions" John Wiley & Sons New York.
 
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