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Collision-free configuration-spaces in macromolecular crystals

Published online by Cambridge University Press:  22 January 2016

Gregory S. Chirikjian  and
Bernard Shiffman
Gregory S. Chirikjian*
Affiliation:
Department of Mechanical Engineering. E-mail: gregc@jhu.edu Johns Hopkins University, 3400 N. Charles St., Baltimore, Maryland, 21218, USA
Bernard Shiffman
Affiliation:
Department of Mathematics. E-mail: shiffman@math.jhu.edu Johns Hopkins University, 3400 N. Charles St., Baltimore, Maryland, 21218, USA
*
*Corresponding author.
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Summary

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.

Type
Articles
Information
Robotica , Volume 34 , Issue 8 , August 2016 , pp. 1679 - 1704
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

(1) This paper is an expanded version of a paper delivered at the Workshop on Robotics Methods for Structural and Dynamic Modeling of Molecular Systems in July 2014 at Berkeley, CA (cs.unm.edu/amprg/rss14workshop/PAPERS/Chirikjian.pdf).

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