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Development of a New Computaional Approach to the Prediction of Nucleic Acid
Structure by Potential Energy Methods: I. Deoxyribose

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We discuss the three fundamental issues of a computational approach
in structure prediction by potential energy minimization, and examine 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. Our approach consists of 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 function is nonconvex and is directed quickly toward
physically interesting regions.

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