A New Method for Fast and Accurate Derivation of Molecular Conformations

During molecular simulations, three-dimensional conformations of biomolecules are calculated from the values of their bond angles, bond lengths, and torsional angles. In this paper we study how to efficiently derive three-dimensional molecular conformations from the values of torsional angles. This case is of broad interest as torsional angles greatly affect molecular shape and are always taken into account during simulations. We first review two widely used methods for deriving molecular conformations, the simple rotations scheme and the Denavit-Hartenberg local frames method. We discuss their disadvantages which include extensive bookkeeping, accumulation of numerical errors, and redundancies in the local frames used. Then we introduce a new, fast, and accurate method called the atomgroup local frames method. This new method not only eliminates the disadvantages of earlier approaches but also provides lazy evaluation of atom positions and reduces the computational cost. Our method is especially useful in applications where many conformations are generated or updated such as in energy minimization and conformational search.