Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the ``natural'' frame of space curves, we formulate an intrinsic dynamics of a twisted elastic filament in a viscous fluid. Coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density capture the dynamic interplay of twist and writhe. These equations are used to illustrate a remarkable nonlinear phenomenon: geometric untwisting of open filaments, whereby twisting strains relax through a transient writhing instability without axial rotation. Experimentally observed writhing motions of fibers of the bacterium B. subtilis [N. H. Mendelson et al., J. Bacteriol. 177, 7060 (1995)] may be examples of this untwisting process.