Symmetries of electrostatic interaction between DNA molecules

A model for pair interaction U of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups is studied. A noncommutative group of eighth order I of symmetries that leave U invariant is found. The minima are classified with the use of group I and numerical methods are employed for finding them. The minima may correspond to several cholesteric phases, as well as to phases formed by crosslike conformations of molecules at an angle close to 90 degrees-the "snowflake phase." The results depend on the effective charge Q of the phosphate group, which can be modified by the polycations or the ions of metals. The snowflake phase could exist for Q above the threshold Q (C). Below Q (C), there could be several cholesteric phases. Close to Q (C), the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.