  By combining analytical theory and Molecular Dynamics simulations we study
the relaxation dynamics of DNA circular plasmids that initially undergo a local
twist perturbation. We identify three distinctive time scales; (I) a rapid
relaxation of local bending, (II) the slow twist spreading, and (III) the
buckling transition taking place in a much longer time scale. In all of these
stages, the twist-bend coupling arising from the groove asymmetry in DNA double
helix clearly manifests. In particular, the separation of time scales allows to
deduce an effective diffusion equation in stage (II), with a diffusion
coefficient influenced by the twist-bend coupling. We also discuss the mapping
of the realistic DNA model to the simplest isotropic twistable worm-like chain
using the renormalized bending and twist moduli; although useful in many cases,
it fails to make a quantitative prediction on the instability mode of buckling
transition.
