Collision-free configuration-spaces in macromolecular crystals

• Published in: Robotica Vol. 34; no. 8; pp. 1679 - 1704
• Main Authors: Chirikjian, Gregory S., Shiffman, Bernard
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.08.2016
• Subjects: Collision avoidance; Crystals; Feasibility; Placement; Proteins; Searching; Special Section: Robotics Methods for Structural and Dynamic Modeling of Molecular Systems; Symmetry; Two dimensional
• ISSN: 0263-5747; 1469-8668
• DOI: 10.1017/S0263574715001046

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.