Writhing geometry of open DNA

Motivated by recent experiments on DNA torsion-force-extension characteristics we consider the writhing geometry of open stiff molecules. We exhibit a cyclic motion which allows arbitrarily large twisting of the end of a molecule via an activated process. This process is suppressed for forces larger than femtonewtons which allows us to show that experiments are sensitive to a generalization of the Călugăreanu–White formula for the writhe. Using numerical methods we compare this formulation of the writhe with recent analytic calculations.