  DNA supercoils are generated in genome regulation processes such as
transcription and replication, and provide mechanical feedback to such
processes. Under tension, DNA supercoil can present a coexistence state of
plectonemic (P) and stretched (S) phases. Experiments have revealed the dynamic
behaviors of plectoneme, e.g. diffusion, nucleation and hopping. To represent
these dynamics with computational changes, we demonstrated first the fast
dynamics on the DNA to reach torque equilibrium within the P and S phases, and
then identified the two-phase boundaries as collective slow variables to
describe the essential dynamics. According to the time scale separation
demonstrated here, we accordingly developed a two-phase model on the dynamics
of DNA supercoiling, which can capture physiologically relevant events across
time scales of several orders of magnitudes. In this model, we systematically
characterized the slow dynamics between the two phases, and compared the
numerical results with that from the DNA polymer physics-based worm-like chain
model. The supercoiling dynamics, including the nucleation, diffusion, and
hopping of plectoneme, have been well represented and reproduced, using the
two-phase dynamic model, at trivial computational costs. Our current
developments, therefore, can be implemented to explore multi-scale physical
mechanisms of the DNA supercoiling-dependent physiological processes.
