| Abstract: | We discuss the three fundamental issues of a computational approach in structure prediction by potential energy minimization, and analyze them for the nucleic acid component deoxyribose. Predicting the conformation of deoxyribose is important not only because of the molecule's central conformational role in the nucleotide backbone, but also because energetic and geometric discrepancies from experimental data have exposed some underlying uncertainties in potential energy calculations. The three fundamental issues examined here are: (i) choice of coordinate system to represent the molecular conformation; (ii) construction of the potential energy function; and (iii) choice of the minimization technique. For our study, we use the following combination. First, the molecular conformation is represented in cartesian coordinate space with the full set of degrees of freedom. This provides an opportunity for comparison with the pseudorotation approximation. Second, the potential energy function is constructed so that all the interactions other than the nonbonded terms are represented by polynomials of the coordinate variables. Third, two powerful Newton methods that are globally and quadratically convergent are implemented: Gill and Murray's Modified Newton method and a Truncated Newton method, specifically developed for potential energy minimization. These strategies have produced the two experimentally-observed structures of deoxyribose with geometric data (bond angles and dihedral angles) in very good agreement with experiment. More generally, the application of these modeling and minimization techniques to potential energy investigations is promising. The use of cartesian variables and polynomial representation of bond length, bond angle and torsional potentials promotes efficient second-derivative computation and, hence, application of Newton methods. The truncated Newton, in particular, is ideally suited for potential energy minimization not only because the storage and computational requirements of Newton methods are made manageable, but also because it contains an important algorithmic adaptive feature: the minimization search is diverted from regions where the function is nonconvex and is directed quickly toward physically interesting regions. |
