C. Micheletti, D. Marenduzzo, E. Orlandini, D. W. Sumners
Knotting of random ring polymers in confined spaces
J. Chem. Phys. 124 064903 (2006)
Link to online article,
ABSTRACT
Stochastic simulations are used to characterize the knotting
distributions of random ring polymers confined in spheres of various
radii. The approach is based on the use of multiple Markov chains and
reweighting techniques, combined with effective strategies for
simplifying the geometrical complexity of ring conformations without
altering their knot type. By these means we extend previous studies
and characterize in detail how the probability to form a given prime
or composite knot behaves in terms of the number of ring segments,
$N$, and confining radius, $R$. For $ 50 \le N \le 450 $ we show that
the probability of forming a composite knot rises significantly with
the confinement, while the occurrence probability of prime knots are,
in general, non-monotonic functions of 1/R. The dependence of other
geometrical indicators, such as writhe and chirality, in terms of $R$
and $N$ is also characterized. It is found that the writhe
distribution broadens as the confining sphere narrows.