  The twisting deformation of mechanically stretched DNA molecules is studied
by a coarse grained Hamiltonian model incorporating the fundamental
interactions that stabilize the double helix and accounting for the radial and
angular base pair fluctuations. The latter are all the more important at short
length scales in which DNA fragments maintain an intrinsic flexibility. The
presented computational method simulates a broad ensemble of possible molecule
conformations characterized by a specific average twist and determines the
energetically most convenient helical twist by free energy minimization. As
this is done for any external load, the method yields the characteristic
twist-stretch profile of the molecule and also computes the changes in the
macroscopic helix parameters i.e. average diameter and rise distance. It is
predicted that short molecules under stretching should first over-twist and
then untwist by increasing the external load. Moreover, applying a constant
load and simulating a torsional strain which over-twists the helix, it is found
that the average helix diameter shrinks while the molecule elongates, in
agreement with the experimental trend observed in kilo-base long sequences. The
quantitative relation between percent relative elongation and superhelical
density at fixed load is derived. The proposed theoretical model and
computational method offer a general approach to characterize specific DNA
fragments and predict their macroscopic elastic response as a function of the
effective potential parameters of the mesoscopic Hamiltonian.
