Pyrophosphate Groups in Liquid Crystalline Phases of the DNA

We study electrostatic interaction between molecules of the DNA 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 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 potential $U$. The symmetries form a noncommutative group of 8-th order, ${\cal S}$. Using the group ${\cal S}$ we suggest a classification of liquid crystalline phases of the DNA, which allows of several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the part played by charges in its liquid crystalline phases, and make for experimental research, important for nano-technological and bio-medical applications.