Collision-free configuration-spaces in macromolecular crystals - Chirikjian, Gregory S.; Shiffman, Bernard (Robotica, 2016)
Molecular replacement (MR) is a well-established computational method for phasing in macromolecular crystallography. In MR searches, spaces of motions are explored for determining the appropriate placement of rigid single-body (or articulated multi-rigid-body) models of macromolecules. By determining a priori which portions of motion space correspond to non-physical packing arrangements with symmetry mates in collision, it becomes feasible to construct more efficient MR techniques which avoid searching in these non-realizable regions of motion space. This paper investigates which portion of the motion space is physically realizable, given that packing of protein molecules in a crystal are subject to the constraint that they cannot interpenetrate, and gives explicit expressions for the volume of the non-realizable regions for crystals in two-dimensions.