Protein association with circular DNA: rate enhancement by nonspecific binding

An analytical solution for the nonspecific-binding-facilitated diffusion-controlled rate of association of a protein with a specific site on a circular DNA is derived. Nonspecific binding is modeled by a short-range attractive surface potential. The protein undergoes diffusion in the bulk solution and in the surface layer. The association rate for a circular DNA is compared to the counterpart for a linear DNA, in which the ends of the surface layer are treated as reflecting. As expected, when the DNA length is long, the shape of the DNA does not affect the association rate. For a shorter length, the association rate for the linear DNA is modestly higher than the circular counterpart. The higher rate of the linear DNA is possibly due to its more open shape, which affords it a higher ability to draw the protein from the bulk to its surface. The analytical solution is verified by Brownian dynamics simulations.