Molecular mechanics

Functional Form

The following functional abstraction, known as a potential function or force field in Chemistry, calculates the molecular system's potential energy (E) in a given conformation as a sum of individual energy terms.

where the components of the covalent and noncolvalent contributions are given by the following summations:

The exact functional form of the potential function, or force field, depends on the particular simulation program being used. Generally the bond and angle terms are modeled as harmonic potentials centered around equilibrium bond-length values derived from experiment or theoretical calculations of electronic structure performed with software which does ab-initio type calculations such as benzene rings planar).

The non-bonded terms are much more computationally costly to calculate in full, since a typical atom is bonded to only a few of its neighbors, but interacts with every other atom in the molecule. Fortunately the Lennard-Jones potential", which means that attractive forces fall off with distance as r^-6 and repulsive forces as r^-12, where r represents the distance between two atoms. Generally a cutoff radius is used to speed up the calculation so that atom pairs whose distances are greater than the cutoff have a van der Waals interaction energy of zero.

The electrostatic terms are notoriously difficult to calculate well because they do not fall off rapidly with distance, and long-range electrostatic interactions are often important features of the system under study (especially for proteins). The basic functional form is the Coulomb potential, which only falls off as r^-1. A variety of methods are used to address this problem, the simplest being a cutoff radius similar to that used for the van der Waals terms. However, this introduces a sharp discontinuity between atoms inside and atoms outside the radius. Switching or scaling functions that modulate the apparent electrostatic energy are somewhat more accurate methods that multiply the calculated energy by a smoothly varying scaling factor from 0 to 1 at the outer and inner cutoff radii. Other more sophisticated but computationally intensive methods are known as particle mesh Ewald (PME) and the multipole algorithm.

In addition to the functional form of each energy term, a useful energy function must be assigned parameters for force constants, van der Waals multipliers, and other constant terms. These terms, together with the equilibrium bond, angle, and dihedral values, partial charge values, atomic masses and radii, and energy function definitions, are collectively known as a force field. Parameterization is typically done through agreement with experimental values and theoretical calculations results. Each force field is parameterized to be internally consistent, but the parameters are generally not transferable from one force field to another.

Areas of application

The prototypical Molecular Mechanics application is energy minimization. That is, the free energy, and only this component is included during energy minimization. However, the analysis of equilibrium between different states requires also conformational entropy be included, which is possible but rarely done.

Other applications of MM include potential energy mapping and ligand docking simulations.

Molecular Mechanics and molecular modeling.

Environment and Solvation

There are several ways of defining the environment surrounding the molecule or molecules of interest in molecular mechanics. A system can be simulated in vacuum (known as a gas-phase simulation) with no surrounding environment at all, but this is usually not desirable because it introduces artifacts in the molecular geometry, especially in charged molecules. Surface charges that would ordinarily interact with solvent molecules instead interact with each other, producing molecular conformations that are unlikely to be present in any other environment. The "best" way to solvate a system is to place explicit water molecules in the simulation box with the molecules of interest and treat the water molecules as interacting particles like those in the molecule. A variety of implicit solvation, which replaces the explicitly represented water molecules with a mathematical expression that reproduces the average behavior of water molecules (or other solvents such as lipids). This method is useful for preventing artifacts that arise from vacuum simulations and reproduces bulk solvent properties well, but cannot reproduce situations in which individual water molecules have interesting interactions with the molecules under study.

Software Packages

Limited list; many more are available

• AMBER
• CHARMM
• Ghemical
• GROMOS
• GROMACS
• NAMD
• STR3DI32

See also

Force field in Chemistry
Software for molecular mechanics modeling

References

• U. Burkert and N.L. Allinger, Molecular Mechanics, 1982, ISBN 0-8412-0885-9
• Vernon G. S. Box, The Molecular Mechanics of Quantized Valence Bonds, J. Mol. Model., 3, 124, 1997
• Vernon G. S. Box, The anomeric effect of monosaccharides and their derivatives. Insights from the new QVBMM molecular mechanics force field, Heterocycles, 48, 2389 1998
• Vernon G. S. Box, Stereo-electronic effects in polynucleotides and their double helices, J. Mol. Struct., 689, 33-41 2004
• O. Becker, A.D. MacKerell, Jr., B. Roux and M. Watanabe, Editors, Computational Biochemistry and Biophysics, Marcel Dekker Inc., New York, 2001, ISBN 0-8247-0455-X
• MacKerell, A.D., Jr., Empirical Force Fields for Biological Macromolecules: Overview and Issues, Journal of Computational Chemistry, 25: 1584-1604, 2004
• Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer-Verlag, New York, NY: 2002. ISBN 0-387-95404-X.