  We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.
