0.8 Motion planning for proteins: biophysics and applications  (Page 3/10)

Electrostatic interactions

Electrostatic interactions are usually computed using some variant of Coulomb's Law, which assumes that atoms behave as point charges located at their centers. A typical Coulombic term looks like this:

The dielectric constant is a function of the medium through which the two charges interact. The difference between the dielectric constant of water and that of pure protein is substantial, so some models attempt to take it into account. One of the simplest assumes that the farther apart two charges are, the more likely they are to have water between them. This is called a distance-dependent dielectric, because it scales with the distance between the atoms involved.

Other classes of interactions

While all of the previous terms are almost always included in energy functions, there are a handful of other terms that are common, but not present in every function. These include hydrogen bonding, solvation and cross terms.

Hydrogen bonds (which are not true bonds in the strict, electron-sharing sense) are unusually strong electrostatic interactions, usually between a hydrogen atom and an electronegative atom such as oxygen or nitrogen. They play an important role in determining and maintaining the structure of biomolecules including proteins and nucleic acids. Some energy functions account for hydrogen bonding in the electrostatic term. Other functions include a separate hydrogen bonding term which is most often a Lennard-Jones-like 12-10 potential:

The solvent that a molecule is in can have a large effect on how it moves. Explicitly representing solvent molecules, however, is a computational cost that most methods try to avoid. Usually the solvent model is separate from the energy function. There are several different ways of approximating solvent interactions including the Generalized Born Model and the Poisson-Boltzmann method. Most force fields do not have an explicit solvent term.

Other terms that describe the interaction between bonds and angles, angles and torsions and so on are included in some force fields. For example to model the interaction between bonds and angles:

Parameters

All of the terms presented above include one or more atom-type-dependent constants, or parameters. Determining these parameters is the major problem in developing a new potential function. These parameters are typically found by fitting calculated results to experimental data. Detailed quantum analysis of small molecules may also be used to set some constants. Regardless of how it is determined, it is important to remember that all potential fields are approximations, and most are best suited for some types of proteins over others.

An example: the charmm all-atom empirical potential

CHARMM (Chemistry at HARvard Macromolecular Mechanics) refers to both a program for macromolecule dynamics and mechanics and the energy function developed for use in that program. CHARMM is a popular force field used mainly for the study of macromolecules. In the most recent version, the parameters were created using experimental data and supplemented with ab initio results. The CHARMM energy function has the form: