Biopolymers, potential energy functions

Vibrational spectroscopy has played a very important role in the development of potential functions for molecular mechanics studies of proteins. Force constants which appear in the energy expressions are heavily parameterized from infrared and Raman studies of small model compounds. One approach to the interpretation of vibrational spectra for biopolymers has been a harmonic analysis whereby spectra are fit by geometry and/or force constant changes. There are a number of reasons for developing other approaches. The consistent force field (CFF) type potentials used in computer simulations are meant to model the motions of the atoms over a large ranee of conformations and, implicitly temperatures, without reparameterization. It is also desirable to develop a formalism for interpreting vibrational spectra which takes into account the variation in the conformations of the chromophore and surroundings which occur due to thermal motions. 

Before discussing all these biopolymer applications, we first take this opportunity to remind the reader that, in general, any thermodynamic variable can be expressed as the sum of two functions, one of which depends only on the temperature and pressure, and another which depends on the system composition (expressed as the mole fraction xt of the /-component). Therefore, for example, the chemical potential fM of the /-component of the system at constant temperature T and pressure p (the general experimental conditions), /. e., partial molar Gibbs free energy (dG/dn TtP may be expressed as (Prigogine and Defay, 1954) ... 

The principle of transferability is commonly used in the construction of the intramolecular potential function of a macromolecule. It has been recently used to construct intermolecu-lar interactions or solute-solvent interaction. The main idea is to transfer the parameters describing the interaction between small molecules, e.g., methane and water, on to larger molecules, say methane-ethanol, or ethane-water. In this book we used a similar idea to extract information from small model compounds and apply it to biopolymers. The information we are interested in is the conditional solvation Gibbs energies of various groups, e.g., methyl, ethyl, hydroxyl, and so on, and intramolecular solvent-induced interactions between such groups. In this appendix we describe the methodology of this transferability principle and examine its adequacy and extent of its reliability. 

MM approach to biopolymers would be impossible without this suggestion). The studies of molecular crystals via the MM approach were important not only for the intrinsic problems of crystallography, but they enabled one to derive potential functions for nonbonded interactions and to test the fidelity and accuracy of the approach itself using extensive sets of available quantitative data on structure and energy of molecular crystals. Such justification was important for the first steps of the MM approach and for its extension to various branches of natural science. 

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