Rigid-Body Parameters for Molecular Docking Applications

In mechanisms and robotics it is common to describe motions relative to a ground link, or robot base, and the position and orientation of the distal link (or robot hand) is viewed as a rigid-body motion relative to this fixed world frame. Assessing preferred relative rigid-body position and orientation in interacting biomolecules (such as proteins) often uses this approach as well by artificially calling one molecule the ground, and considering the motions of another molecule relative to it. But since both molecules are floating, it is not as natural to take this perspective as it is in the field of mechanisms and robotics. Therefore, this paper introduces a ‘symmetrical’ parameterization of relative biomolecular motions in which the structure of the equations is the same when each molecule views the other. In this way, there is no bias in terms of labeling one molecule as being fixed and the other as moving. The properties of this new parameterization are evaluated and compared with traditional ones known to the kinematics community.