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Polymers exposed to shear flow exhibit a rich tumbling dynamics. While rigidrods rotate on Jeffery orbits, flexible polymers stretch and coil up duringtumbling. Theoretical results show that in both of these asymptotic regimes thetumbling frequency f_c in a linear shear flow of strength \gamma scales as apower law Wi^(2/3) in the Weissenberg number Wi=\gamma \tau, where \tau is acharacteristic time of the polymer's relaxational dynamics. For flexiblepolymers these theoretical results are well confirmed by experimental singlemolecule studies. However, for the intermediate semiflexible regime thesituation is less clear. Here we perform extensive Brownian dynamicssimulations to explore the tumbling dynamics of semiflexible polymers over abroad range of shear strength and the polymer's persistence length l_p. We findthat the Weissenberg number alone does not suffice to fully characterize thetumbling dynamics, and the classical scaling law breaks down. Instead, both thepolymer's stiffness and the shear rate are relevant control parameters. Basedon our Brownian dynamics simulations we postulate that in the parameter rangemost relevant for cytoskeletal filaments there is a distinct scaling behaviorwith f_c \tau*=Wi^(3/4) f_c (x) with Wi=\gamma \tau* and the scaling variablex=(l_p/L)(Wi)^(-1/3); here \tau* is the time the polymer's center of massrequires to diffuse its own contour length L. Comparing these results withexperimental data on F-actin we find that the Wi^(3/4) scaling law agreesquantitatively significantly better with the data than the classical Wi^(2/3)law. Finally, we extend our results to single ring polymers in shear flow, andfind similar results as for linear polymers with slightly different power laws.

Dynamics of a Semiflexible Polymer or Polymer Ring in Shear Flow