Sedimentation of knotted polymers

We investigate the sedimentation of knotted polymers by means of stochastic rotation dynamics, a molecular dynamics algorithm that takes hydrodynamics fully into account. We show that the sedimentation coefficient s, related to the terminal velocity of the knotted polymers, increases linearly with the average crossing number n(c) of the corresponding ideal knot. This provides direct computational confirmation of this relation, postulated on the basis of sedimentation experiments by Rybenkov et al. [J. Mol. Biol. 267, 299 (1997)]. Such a relation was previously shown to hold with simulations for knot electrophoresis. We also show that there is an accurate linear dependence of s on the inverse of the radius of gyration R(g)(-1), more specifically with the inverse of the R(g) component that is perpendicular to the direction along which the polymer sediments. When the polymer sediments in a slab, the walls affect the results appreciably. However, R(g)(-1) remains to a good precision linearly dependent on n(c). Therefore, R(g)(-1) is a good measure of a knot's complexity.