Force field (chemistry)

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In the context of molecular mechanics, a force field (also called a forcefield) refers to the functional form and parameter sets used to describe the potential energy of a system of particles (typically but not necessarily atoms). Force field functions and parameter sets are derived from both experimental work and high-level quantum mechanical calculations. "All-atom" force fields provide parameters for every atom in a system, including hydrogen, while "united-atom" force fields treat the hydrogen and carbon atoms in methyl and methylene groups as a single interaction center. "Coarse-grained" force fields, which are frequently used in long-time simulations 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.

Contents 1 Functional form 2 Parameterization 3 Deficiencies 4 Popular force fields 5 See also 6 References 7 Further reading

[edit] Functional form

Further information: Molecular mechanics

The basic functional form of a force field encapsulates both bonded terms relating to atoms that are linked by covalent bonds, and nonbonded (also called "noncovalent") terms describing the long-range electrostatic and 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

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 hydrogen bonds, an "improper torsion" term to account for the planarity of aromatic rings and other conjugated systems, and "cross-terms" that describe coupling of different internal variables, such as dihedral angles and bond lengths. The nonbonded terms are most computationally intensive because they include many more pairwise interactions per atom. The van der Waals term is usually computed with a 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.

[edit] 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 oxygen atom in a carbonyl functional group and in a hydroxyl group. The parameter set includes polarizability, atomic mass, and partial charge for individual atoms, and equilibrium values of bond lengths and angles for pairs, triplets, and quadruplets of bonded atoms. Although many molecular simulations involve biological macromolecules such as proteins, DNA, and RNA, the parameters for given atom types are generally derived from observations on small organic molecules that are more tractable for experimental studies and quantum calculations. Different force fields can be derived from dissimilar types of experimental data, such as enthalpy of vaporization (OPLS), enthalpy of sublimation (CFF), dipole moments, or various spectroscopic parameters.

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.

[edit] Deficiencies

All force fields are based on numerous approximations and derived from different types of experimental data. Therefore they are called empirical. The existing force fields usually do not account for electronic polarization of the environment, an effect that can significantly reduce electrostatic interactions of partial atomic charges. This problem was addressed by developing “polarizable force fields” ^[1] or using macroscopic dielectric constant. However, application of a single value of dielectric constant is questionable in the highly heterogeneous environments of proteins or biological membranes ^[2].

All types of van der Waals forces are also strongly environment-dependent, because these forces originate from interactions of induced and “instantaneous” dipoles (see Intermolecular force). The original Fritz London theory of these forces can only be applied in vacuum. A more general theory of van der Waals forces in condensed media was developed by A. D. McLachlan in 1963 (this theory includes the original London’s approach as a special case) ^[3]. The McLachlan theory predicts that van der Waals attractions in media are weaker than in vacuum and follow the "like dissolves like" rule, which means that different types of atoms interact weaker than identical types of atoms. ^[4]. This is in contrast to “combinatorial rules” or Slater-Kirkwood equation applied for development of the classical force fields. The “combinatorial rules” state that interaction energy of two dissimilar atoms (e.g. C…N) is an average of the interaction energies of corresponding identical atom pairs (i.e. C…C and N…N). According to McLachlan theory, the interactions of particles in a media can even be completely repulsive, as observed for liquid helium ^[3]. The conclusions of McLachlan theory are supported by direct measurements of attraction forces between different materials (Hamaker constant), as explained by 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" ^[3]. 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 CASP participants did not try to refine their models to avoid "a central embarrassment of molecular mechanics, namely that energy minimization or molecular dynamics generally leads to a model that is less like the experimental structure". ^[5] Actually, the force fields have been successfully applied for protein structure refinement in different X-ray crystallography and NMR spectroscopy applications, especially using program XPLOR ^[6] However, such refinement is driven primarily by a set of experimental constraints, whereas the force fields serve merely to remove interatomic hindrances. The results of calculations are practically the same with rigid sphere potentials implemented in program DYANA ^[7] (calculations from NMR data), or with programs for crystallographic refinement that do not use any energy functions. The deficiencies of the force fields remain a major bottleneck in homology modeling of proteins ^[8] Such situation gave rise to development of alternative empirical scoring functions specifically for ligand docking ^[9], protein folding ^{[10] [11]}, computational protein design ^{[12] [13] [14]}, and modeling of proteins in membranes. ^[15]

There is also an opinion that molecular mechanics may operate with energy which is irrelevant to protein folding or ligand binding ^[16]. The parameters of typical force fields reproduce enthalpy of sublimation, i.e. energy of evaporation of molecular crystals. However, it was recognized that protein folding and ligand binding are thermodynamically very similar to crystallization, or liquid-solid transitions, because all these processes represent “freezing” of mobile molecules in condensed media ^{[17] [18] [19]}. Therefore, free energy changes during protein folding or ligand binding are expected to represent a combination of an energy similar to heat of fusion (energy absorbed during melting of molecular crystals), a conformational entropy contribution, and solvation free energy. The heat of fusion is significantly smaller than enthalpy of sublimation ^[3]. . Hence, the potentials describing protein folding or ligand binding must be weaker than potentials in molecular mechanics. Indeed, the energies of H-bonds in proteins are ~ -1.5 kcal/mol when estimated from protein engineering or alpha helix to coil transition data ^{[20] [21]}, but the same energies estimated from sublimation enthalpy of molecular crystals were -4 to -6 kcal/mol ^[22]. The depths of modified 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^[16].

[edit] 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).

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 ^[23].

AMBER, CHARMM and GROMOS have been developed primarily for 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
• CHARMm - commercial version of CHARMM, available through 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 Yale Department of Chemistry.
• ECEPP/2 - First force field for polypeptide molecules - developed by F.A.Momany, H.A.Scheraga and colleagues.

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

Reactive force fields

• ReaxFF - reactive force field developed by William Goddard and coworkers. It is fast, transferable and is the computational method of choice for atomistic-scale dynamical simulations of chemical reactions.

[edit] See also

• Comparisons and Evaluations of various forcefields
• Molecular dynamics
• Molecular modelling

[edit] References

[edit] 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.