The small-amplitude conformational changes in macromolecules can be described by the changes in bond lengths and bond angles. The descriptors of large scale changes are torsions. We present a recursive algorithm, in which a bond vector is explicitly written in terms of these internal, or polyspherical coordinates, in a local frame defined by two other bond vectors and their cross product. Conformations of linear and branched molecules, as well as molecules containing rings can be described in this way. The orientation of the molecule is described by the orientation of a body frame. It is parametrized by the instantaneous rotation angle, and the two angles that parametrize the orientation of the instantaneous rotation axis. The reason not to use more conventional Euler angles is due to the fact that Euler angles are not well-defined in gimbal lock (i.e., when a body axis becomes aligned with its space fixed counter part). The position of the molecule is parametrized by its center of mass. Original and calculated positions are compared for several proteins, containing up to about 100,000 atoms.
Copyright 2010 Wiley Periodicals, Inc.