DNA enclosing forms from scaled growth forms of snow crystals

Abstract

The same structural principles based on scale-rotational symmetries observed in snow crystals also occur in nucleic acids with helical structure. Due to the axial symmetry, a point group characterization implies a 2-dimensional description in the projected axial view. This allows a comparison with snow crystals. Three aspects are involved in the present approach: a geometric one, based on the polygrammal symmetries of scaled forms (growth forms and enclosing forms, respectively); an arithmetic one, allowing an assignment of rational indices to planes (or lines) and to special points of the scaled forms and to a selected set of atomic positions; and an algebraic group-theoretical one, by means of a scale-rotation group relating the planes (or lines) and the special points of the scaled forms and the selected atomic positions involved in the structural relations.