An Empirical Potential Energy Function for Phospholipids: Criteria for Parameter Optimization and Applications

Abstract

Theoretical studies of biological molecules permit the study of the relationships between structure, function and dynamics at the atomic level. Since many of the problems that one would like to address in biological systems involve many atoms, it is not yet feasible to treat these systems using quantum mechanics. However, the problems become much more tractable when turning to empirical potential energy functions, which are much less computationally demanding than quantum mechancis; but this comes at a cost. Numerous approximations are introduced which lead to certain limitations. These are discussed below. Current generation force fields (or potential energy functions) provide a reasonably good compromise between accuracy and computational efficiency. They are often calibrated to experimental results and quantum mechanical calculations of small model compounds. Their ability to reproduce physical properties measurable by experiment is tested; these properties include structural data obtained from x-ray crystallography and NMR, dynamic data obtained from spectroscopy and inelastic neutron scattering and thermodynamic data. The development of parameter sets is a very laborious task, requiring extensive optimization. This is an area of continuing research and many groups have been working over the past two decades to derive functional forms and parameters for potential energy functions of general applicability to biological molecules. Among the most commonly used potential energy functions are the AMBER, CHARMM, GROMOS and OPLS/AMBER force fields. The continuing development of force fields remains an intense area of research with implications for both fundamental research as well as for applied research in the pharmaceutical industry. As mentioned above, there are certain limitations of empirical force fields. One of the most important is that no drastic changes in electronic structure are allowed, i.e., no events like bond making or breaking can be modeled. To address this limitation, mixed quantum mechanical-molecular mechanical force fields are under development in a number of laboratories. We will not cover these force fields in the current manual. Complete potential functions are now available for macromolecular simulations; one particular example is the CHARMM22 all atom potential function for proteins (MacKerell et al 1998), nucleic acids (MacKerell et al. 1995), lipids (Schlenkrich et al. 1996) and carbohydrates (Ha et al. 1988). References A revised potential-energy surface for molecular mechanics studies of carbohydrates, Carbohydr. Res. (1988), 180(2), 207-221. The CHARMM potential energy function The energy, E, is a function of the atomic positions, R, of all the atoms in the system, these are usually expressed in term of Cartesian coordinates. The value of the energy is calculated as a sum of internal, or bonded, terms Ebonded, which describe the bonds, angles and bond rotations in a molecule, and a sum of external or nonbonded terms, Enon-bonded, These terms account for interactions between nonbonded atoms or atoms separated by 3 or more covalent bonds.