  The time-dependent transverse response of stiff polymers, represented as
weakly-bending wormlike chains (WLCs), is well-understood on the linear level,
where transverse degrees of freedom evolve independently from the longitudinal
ones. We show that, beyond a characteristic time scale, the nonlinear coupling
of transverse and longitudinal motion in an inextensible WLC significantly
weakens the polymer response compared to the widely used linear response
predictions. The corresponding feedback mechanism is rationalized by scaling
arguments and quantified by a multiple scale approach that exploits an inherent
separation of transverse and longitudinal correlation length scales. Crossover
scaling laws and exact analytical and numerical solutions for characteristic
response quantities are derived for different experimentally relevant setups.
Our findings are applicable to cytoskeletal filaments as well as DNA under
tension.
