Eur. Phys. J. E (2010) 31: 59-67
https://doi.org/10.1140/epje/i2010-10549-7

Regular Article

Symmetry of electrostatic interaction between pyrophosphate DNA molecules

¹ Department of Mechanics and Mathematics, the Lomonosov Moscow State University, 119 992 GSP-2, Moscow, Russia
² Institute Laue-Langevin Grenoble, Grenoble, France
³ L.D. Landau Institute for Theoretical Physics, Moscow, Russia
⁴ Department of Chemistry, the Lomonosov Moscow State University, 119 992 GSP-2, Moscow, Russia

^* e-mail: voislav.golo@gmail.com
^** e-mail: kats@ill.fr
^*** e-mail: svetlana@belozersky.msu.ru
^**** e-mail: yu.volkov@gmail.com

Received: 24 August 2009
Accepted: 26 November 2009
Published online: 20 January 2010

Abstract

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.