  We develop a continuum elastic approach to examining the bending mechanics of
semiflexible filaments with a local internal degree of freedom that couples to
the bending modulus. We apply this model to study the nonlinear mechanics of a
double stranded DNA oligomer (shorter than its thermal persistence length)
whose free ends are linked by a single standed DNA chain. This construct,
studied by Qu et al. [Europhys. Lett., $\bf{94}$, 18003, 2011], displays
nonlinear strain softening associated with the local melting of the double
stranded DNA under applied torque and serves as a model system with which to
study the nonlinear elasticity of DNA under large energy deformations. We show
that one can account quantitatively for the observed bending mechanics using an
augmented worm-like chain model, the helix coil worm-like chain. We also
predict that the highly bent and partially molten dsDNA should exhibit
particularly large end-to-end fluctuations associated with the fluctuation of
the length of the molten region, and propose appropriate experimental tests. We
suggest that the augmented worm-like chain model discussed here is a useful
analytic approach to the nonlinear mechanics of DNA or other biopolymer
systems.
