  The rupture of double-stranded DNA under stress is a key process in
biophysics and nanotechnology. In this article we consider the shear-induced
rupture of short DNA duplexes, a system that has been given new importance by
recently designed force sensors and nanotechnological devices. We argue that
rupture must be understood as an activated process, where the duplex state is
metastable and the strands will separate in a finite time that depends on the
duplex length and the force applied. Thus, the critical shearing force required
to rupture a duplex within a given experiment depends strongly on the time
scale of observation. We use simple models of DNA to demonstrate that this
approach naturally captures the experimentally observed dependence of the
critical force on duplex length for a given observation time. In particular,
the critical force is zero for the shortest duplexes, before rising sharply and
then plateauing in the long length limit. The prevailing approach, based on
identifying when the presence of each additional base pair within the duplex is
thermodynamically unfavorable rather than allowing for metastability, does not
predict a time-scale-dependent critical force and does not naturally
incorporate a critical force of zero for the shortest duplexes. Additionally,
motivated by a recently proposed force sensor, we investigate application of
stress to a duplex in a mixed mode that interpolates between shearing and
unzipping. As with pure shearing, the critical force depends on the time scale
of observation; at a fixed time scale and duplex length, the critical force
exhibits a sigmoidal dependence on the fraction of the duplex that is subject
to shearing.
