Before revision:  We show that such coupling induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature . The periodicity is close to that of the double helix and depends on the degree of overtwisting. From a simple elastic energy minimization ansatz we derive an analytical expression of the minicircle shape which matches very well the results obtained from simulations of various coarse-grained models of DNA. Finally, the calculation of the twist and bending energy of minicircles shows how these are governed by renormalized stiffness constants, not the bare ones.
After revision:  We show that such coupling induces minimal energy shapes of overtwisted DNA minicircles resembling rounded polygons, with a periodic alternance of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energy of minicircles shows how these are governed by renormalized stiffness constants, not the bare ones.