This work builds a basis for understanding electrostatic and solvation forces between various types of helical molecules by explicitly incorporating the helical structure and symmetries into the theory. We derive exact expressions for interaction between molecules with cylindrical inner cores and arbitrary distribution of discrete surface charges and analyze forces between single-stranded, double-stranded, and multistranded helices. For example, we demonstrate that the traditional approximation by a homogeneously charged rod becomes inappropriate when even less than a third of the strand charge on a single-stranded helix is neutralized by countercharges (adsorbed or intrinsic to the helix by their nature). The traditionally expected force is then complemented by helix-specific interactions. These helix-specific forces allow commensurate helices (with the ratio of pitches equal to a rational number) to recognize each other at a distance and self-assemble into an aggregate. Under certain conditions, these forces may induce a spontaneous symmetry loss, e.g., two DNA-type double helices rotate around their long axes to a separation-dependent angle when the molecules come closer than a critical interaxial separation. In general, while a longer-range helix-specific attraction induces the self-assembly, a shorter-range helix-specific repulsion prevents the tight molecular contact creating a force balance responsible for a nonzero surface separation in equilibrium. The decay rates and the amplitudes of the attraction and of the repulsion depend on the helical pitch and on the number and relative disposition of the helical strands. The theory of these forces allows us to explain a number of puzzling features of interactions measured between biological helices, including DNA, collagen, and four-stranded guanosine macromolecules.

Kornyshev, A. A., & Leikin, S. (1997). Theory of interaction between helical molecules. The Journal of Chemical Physics, 107(9), 3656–3674.