Computing and Updating Molecular Conformations Using the Atomgroup Local Frames Method

Abstract

Efficiently maintaining molecular conformations is important for molecular modeling and protein engineering. This paper reviews the widely used simple rotations scheme, simple local frames method, and introduces a new atom group local frames method for maintaining the molecular conformation changes due to the changes of torsional angles. The simple rotations scheme applies a sequence of rotations to update all atom positions. The order of the updates is important and some bookkeeping of the atom positions is necessary. Numeric errors can accumulate as rotations around the bonds are repeated. The simple local frames method builds local frames at the bonds, and relational matrices between parents and children frames are constructed. The atom positions are computed by chaining series of such matrices. No bookkeeping is necessary and numeric errors do not accumulate upon rotations. Multiple local frames are needed at a bond if it has more than one child. This paper introduces a new atom group local frames method to efficiently maintain molecular conformations. A single local frame is attached to each atom group. Bookkeeping is not necessary and numeric errors do not accumulate upon rotations. This method also provides lazy evaluations for atom positions. Thus, the conformational maintenance cost is greatly reduced, especially when many conformations are generated and updated such as in a minimization process.