title: Symmetry of helicoidal biopolymers in the frameworks of algebraic geometry: α-helix and DNA structures.
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.
authors.affiliation: Central Scientific Research Institute of Technology `Technomash', Ivan Franko Street 4, Moscow, 121108, Russian Federation.
authors.forename: Mikhail
authors.initials: M
authors.lastname: Samoylovich
authors.affiliation: A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences, Vavilova Street 28, Moscow, 119991, Russian Federation.
authors.forename: Alexander
authors.initials: A
authors.lastname: Talis
mesh_terms: D004247:DNA / Q000737:chemistry*; D043542:DNA, Z-Form / Q000737:chemistry; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D017433:Protein Structure, Secondary
chemical_list: D043542:DNA, Z-Form; D004247:DNA
keywords: algebraic geometry; eight-dimensional lattice E8; helical axis 40/11; polytopes; structures; topology; α-helix