Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Symmetry of helicoidal biopolymers in the frameworks of algebraic geometry: α‐helix and DNA structures

Symmetry of helicoidal biopolymers in the frameworks of algebraic geometry: α‐helix and DNA... The chain of algebraic geometry and topology constructions is mapped on a structural level that allows one to single out a special class of discrete helicoidal structures. A structure that belongs to this class is locally periodic, topologically stable in three‐dimensional Euclidean space and corresponds to the bifurcation domain. Singular points of its bounding minimal surface are related by transformations determined by symmetries of the second coordination sphere of the eight‐dimensional crystallographic lattice E8. These points represent cluster vertices, whose helicoid joining determines the topology and structural parameters of linear biopolymers. In particular, structural parameters of the α‐helix are determined by the seven‐vertex face‐to‐face joining of tetrahedra with the E8 non‐integer helical axis 40/11 having a rotation angle of 99°, and the development of its surface coincides with the cylindrical development of the α‐helix. Also, packing models have been created which determine the topology of the A, B and Z forms of DNA. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

Symmetry of helicoidal biopolymers in the frameworks of algebraic geometry: α‐helix and DNA structures

Loading next page...
 
/lp/wiley/symmetry-of-helicoidal-biopolymers-in-the-frameworks-of-algebraic-HGva4ZOiTa

References (25)

Publisher
Wiley
Copyright
Copyright © 2014 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S2053273313033822
pmid
24572320
Publisher site
See Article on Publisher Site

Abstract

The chain of algebraic geometry and topology constructions is mapped on a structural level that allows one to single out a special class of discrete helicoidal structures. A structure that belongs to this class is locally periodic, topologically stable in three‐dimensional Euclidean space and corresponds to the bifurcation domain. Singular points of its bounding minimal surface are related by transformations determined by symmetries of the second coordination sphere of the eight‐dimensional crystallographic lattice E8. These points represent cluster vertices, whose helicoid joining determines the topology and structural parameters of linear biopolymers. In particular, structural parameters of the α‐helix are determined by the seven‐vertex face‐to‐face joining of tetrahedra with the E8 non‐integer helical axis 40/11 having a rotation angle of 99°, and the development of its surface coincides with the cylindrical development of the α‐helix. Also, packing models have been created which determine the topology of the A, B and Z forms of DNA.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Mar 1, 2014

Keywords: ; ; ; ; ; ;

There are no references for this article.