  By combining analytical results and simulations of various coarse-grained
models we investigate the minimal energy shape of DNA minicircles which are
torsionally constrained by an imposed over or undertwist. We show that
twist-bend coupling, a cross interaction term discussed in the recent DNA
literature, induces minimal energy shapes 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 energies of minicircles are governed by renormalized
stiffness constants, not the bare ones. This has important consequences for the
analysis of experiments involving circular DNA meant to determine DNA elastic
constants.
