Interactive Graphical Optimization of Potential Energy Function Parameters in the Consistent Force Field

The performance of a molecular mechanics force field depends on the form of its potential energy function as well as on their parametrization. In the consistent force field (CFF), the fundamentallv empirical nature of potential energy functions is recognized by their refinement through optimization which is an integral part of the CFF concept. A graphical interface to the optimization algorithm has been developed with the dual purposes of compressing large amounts of nu&rical data into one intuitive comprehensible picture of the residue functions and giving the user interactive control of the optimization process. The principles of force field optimization are outlined, with emphasis on the design and realization of the graphical interface. iNTRODUCTION FORCE FIELDS IN MOLECULAR MECHANICS The concept of the Consistent Force Field (CFF) was founded by Lifson (Lifson & Warshel, 1968; Lifson, 1983). It is, in short, a computational cycle in which properties of matter are calculated using potential functions (PEFs), results are compared to experimental data, and potential energy function parameters are iteratively optimized to fit the experimental data. The Lyngby version of CFF (Niketic and Rasmussen, 1977; Rasmussen, 1985) was developed since 1970 from the original program of Warshel (Lifson & Warshel, 1968) independent of the CHARMM program (Brooks et al., 1983) which has the same genesis. While CHARMM has become a highly sophisticated calculational and analytical tool for macromolecules, CFF has remained true to the CFF concept and put emphasis on the optimization process necessary in empirical force field development. Although molecular systems are governed by quantum laws, molecular mechanics has given results which are reasonable both from a qualitative and a quantitative point of view. The basis of molecular mechanics is to construct a set of potential energy functions representing the different energy contributions of molecular subsystems and optimize the parameters (“constants”) of the potential energy functions in order to be able to reproduce, as closely as possible, experimental data of model compounds, with the selected set of potential energy functions. In this way, carefully optimized potential energy functions can be designed, for specific functional groups, which possess good predictive power for large molecular systems made by combining functional groups, and which therefore are suitable for extrapolation. The present paper describes the optimization algorithm and a new interactive interface which has found its main use in exploratory optimizations aiming at the development of new potential energy functions and new parameter sets. A series of papers will document the first parameter sets developed with the new methods. The first application of the new results, to the bacterial cell-wall disaccharide /?-gentiobiose, was published recently (Engelsen and Rasmussen, 1993). Since CFF is a tool for development of force fields it has a number of different potential energy functions built-in, representing different interand intramolecular forces, and the user will find it easy to model new functional terms from the already existing ones. For an overview over readily available potential energy functions in CFF see Table 1. The source code of CFF is written in ANSI FORTRAN 77 whereas the graphical interface GOPT to which this paper is dedicated is written in ANSI C working under the X-Windows system and invoked as a child process From the CFF program. Minimization of energy in Cartesian space requires, in addition to the potential energy functions, at least their first derivatives, and preferably also the second derivatives. These are anyway necessary for calculation of normal modes. The present version of CFF employs three different minimization algorithms intended for different initial situations; the quite elaborate formulas are documented elsewhere (Niketic and Rasmussen, 1977; Engelsen, 1991). Energy minimization of molecules is a necessary prerequisite to *Author for correspondence.