  DNA and other biopolymers differ from classical polymers due to their
torsional stiffness. This property changes the statistical character of their
conformations under tension from a classical random walk to a problem we call
the `torsional directed walk'. Motivated by a recent experiment on single
lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the
torsional directed walk problem and solve it analytically in the appropriate
force regime. Our technique affords a direct physical determination of the
microscopic twist stiffness C and twist-stretch coupling D relevant for DNA
functionality. The theory quantitatively fits existing experimental data for
relative extension as a function of overtwist over a wide range of applied
force; fitting to the experimental data yields the numerical values C=120nm and
D=50nm. Future experiments will refine these values. We also predict that the
phenomenon of reduction of effective twist stiffness by bend fluctuations
should be testable in future single-molecule experiments, and we give its
analytic form.
