Symmetrical rigid body parameterization for biomolecular structures

Assessing preferred relative rigid-body position and orientation is important in the description of biomolecular structures (such as proteins) and their interactions. For that purpose, techniques from the kinematics community are often used. In this paper, we review parameterization methods that are widely used to describe relative rigid body motions (in particular, orientations). Then we present the extended and updated review of a ‘symmetrical parameterization’ which was newly introduced in the kinematics community. This parameterization is useful in describing the relative biomolecular rigid body motions, where the parameters are symmetrical in the sense that the subunits of a complex biomolecular structure are described in the same way for the corresponding motion and its inverse. The properties of this new parameterization, singularity analysis and inverse kinematics, are also investigated in more detail. Finally the parameterization is applied to real biomolecular structures to show the efficacy of the symmetrical parameterization in the field of computational structural biology.