Symmetry laws for interaction between helical macromolecules

The power of symmetry laws is applied in many scientific areas from elementary particle physics to structural biology. The structures of many biological helices, including DNA, were resolved with the use of pertinent symmetry constraints, It was not recognized, however, that similar constraints determine cardinal features of helix-helix interactions vital for many recognition and assembly reactions in living cells. We now formulate such symmetry-determined interaction laws and apply them to explain DNA "over-winding" from 10.5 base pairs per turn in solution to 10 in hydrated fibers, counterion specificity in DNA condensation, and forces observed over the last 15 Angstrom of separation between DNA, collagen, and four-stranded guanosine helices.