  Here we present a systematic study of supercoil formation in DNA minicircles
under varying linking number by using molecular dynamics simulations of a
two-bead coarse-grained model. Our model is designed with the purpose of
simulating long chains without sacrificing the characteristic structural
properties of the DNA molecule, such as its helicity, backbone directionality
and the presence of major and minor grooves. The model parameters are extracted
directly from full-atomistic simulations of DNA oligomers via Boltzmann
inversion, therefore our results can be interpreted as an extrapolation of
those simulations to presently inaccessible chain lengths and simulation times.
Using this model, we measure the twist/writhe partitioning in DNA minicircles,
in particular its dependence on the chain length and excess linking number. We
observe an asymmetric supercoiling transition consistent with experiments. Our
results suggest that the fraction of the linking number absorbed as twist and
writhe is nontrivially dependent on chain length and excess linking number.
Beyond the supercoiling transition, chains of the order of one persistence
length carry equal amounts of twist and writhe. For longer chains, an
increasing fraction of the linking number is absorbed by the writhe.
