Helical Repeat and Linking Number of Surface-Wrapped DNA

The geometric properties of duplex DNA are systematically altered when the DNA is wrapped on a protein surface. The linking number of surface-wrapped closed circular DNA is the sum of two integers: the winding number, $\Phi $, a function of the helical repeat; and the surface linking number, SLk, a newly defined geometric constant that accounts for the effects of surface geometry on the twist and writhe of DNA. Changes in the helical repeat, h, and in the winding number can be deduced solely from surface geometry and superhelix density, $\sigma $. This treatment relates the theoretically important properties twist and writhe to the more experimentally accessible quantities $\Phi $, h, SLk, and $\sigma $. The analysis is applied to three biologically important cases: interwinding of DNA in a plectonemic superhelix, catenated DNA, and minichromosomes.