Effects of Topological Constraints on Penetration Structures of Semi-Flexible Ring Polymers

Abstract

The effects of topological constraints on penetration structures of semi-flexible ring polymers in a melt are investigated using molecular dynamics simulations, considering simultaneously the effects of the chain stiffness. Three topology types of rings are considered: 01-knot (the unknotted), 31-knot and 61-knot ring polymers, respectively. With the improved algorithm to detect and quantify the inter-ring penetration (or inter-ring threading), the degree of ring threading does not increase monotonously with the chain stiffness, existing a peak value at the intermediate stiffness. It indicates that rings interpenetrate most at intermediate stiffness where there is a balance between coil expansion (favoring penetrations) and stiffness (inhibiting penetrations). Meanwhile, the inter-ring penetration would be suppressed with the knot complexity of the rings. The analysis of effective potential between the rings provides a better understanding for this non-monotonous behavior in inter-ring penetration.

Topological and threading effects in polydisperse ring polymer solutions

“…Another interesting static property of the ensemble of unknotted ring conformations is the minimal area of a surface spanned by the ring's contour. The (minimal) surfaces, typically constrained to disk-like topology, have been found useful to investigate static, dynamic and threading properties in entangled regimes of systems of nonconcatenated rings in equilibrium [10,[26][27][28], out of equilibrium [13,[29][30][31], tadpole-shaped polymers [32,33] or 'lasso' proteins [34]. A threading, as we define it here, is a conformation for which a polymer segment pierces through the minimal surface spanned on a ring segment of another polymer.…”

Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers

“…In practice, we consider M polymers N beads long in a cubic box of size L 3 , with ρ = M / L 3 denoting the concentration of chains and at monomer density c = MN / L 3 = 0.1σ –3 (σ is the size of one bead). The polymers are semiflexible, that is, have persistence length l p = 5σ, chosen to lower the typical entanglement length (found to be N e = 40 beads) and to promote inter-ring threading. , A summarizing table with the key parameters is given in the SI.…”

Topological Tuning of DNA Mobility in Entangled Solutions of Supercoiled Plasmids

“…It should be highlighted that the dynamical exponent found here is expected for longer and more flexible rings, and that for shorter flexible ring polymers (smaller L / l p and comparable with the rings studied here) the dynamical exponent is about 1.5 ( 26 ). We speculate that this more severe dependence on plasmid length may be due to the large persistence length of DNA ( l p = 20 σ b ≃ 50 nm) which can both, reduce the effective entanglement length ( 27 ) and also increase the number of threadings between plasmids ( 51 ). In agreement with this argument, entangled solutions of semi-flexible and stiff ring polymers vitrify in certain concentration regimes ( 52 ) implying that large stiffness and large concentrations may exacerbate threading constraints ( 28, 53–55 ).…”