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Structural regularities of helicoidally-like biopolymers in the framework of algebraic topology: II. α-Helix and DNA structures

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Abstract

The developed apparatus of the “structural application” of algebraic geometry and topology makes it possible to determine topologically stable helicoidally-like packings of polyhedra (clusters). A packing found is limited by a minimal surface with zero instability index; this surface is set by the Weierstrass representation and corresponds to the bifurcation point. The symmetries of the packings under consideration are determined by four-dimensional polyhedra (polytopes) from a closed sequence, which begins with diamondlike polytope {240}. One example of these packings is a packing of tetrahedra, which arises as a result of the multiplication of a peculiar starting aggregation of tetrahedra by a fractional 40/11 axis with an angle of helical rotation of 99°. The arrangement of atoms in particular positions of this starting aggregation allows one to obtain a model of the α-helix. This apparatus makes it possible to determine a priori the symmetry parameters of DNA double helices.

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Authors and Affiliations

  1. Central Research Technological Institute “Technomash”, ul. Ivana Franko 4, Moscow, 121108, Russia

    M. I. Samoylovich

  2. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, ul. Vavilova 28, Moscow, 119991, Russia

    A. L. Talis

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  1. M. I. Samoylovich
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  2. A. L. Talis
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Correspondence to M. I. Samoylovich.

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Original Russian Text © M.I. Samoylovich, A.L. Talis, 2013, published in Kristallografiya, 2013, Vol. 58, No. 5, pp. 639–651.

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Samoylovich, M.I., Talis, A.L. Structural regularities of helicoidally-like biopolymers in the framework of algebraic topology: II. α-Helix and DNA structures. Crystallogr. Rep. 58, 651–662 (2013). https://doi.org/10.1134/S106377451305009X

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  • DOI: https://doi.org/10.1134/S106377451305009X

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