Topologically Linked Chains in Confinement

Abstract

We examine how channel confinement affects the equilibrium properties of topologically linked ring polymers and, by contrast, of equivalent unlinked rings, too. By performing extensive simulations of semiflexible rings of different chain length, N, and channel diameter, D, we discover three notable properties purely due to linking. First, upon entering the weak confinement regime, the length of the physically linked portion, The, becomes independent of chain length. Next, even when confinement is strong enough to pull apart and segregate unlinked rings, stays much larger than in the highly stretched limit. Finally, at fixed N, varies approximately as D 0.5, and we provide a simple scaling argument for this power–law behavior. These properties, which may hold for different link topologies, can be tested by current experimental setups on DNA rings confined in microchannels. Moreover, they could be relevant for the efficient in vivo unlinking of newly replicated bacterial chromosomes.

Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement

“…Second, we neglect any entropic contribution from the intramolecular topological constraints within each kinetoplast. This is supported by recent work demonstrating that the size of the overlap region of topologically linked rings adjusts to the blob size for all degrees of confinement and always remains much larger than the highly stretched limit …”

“…This is supported by recent work demonstrating that the size of the overlap region of topologically linked rings adjusts to the blob size for all degrees of confinement and always remains much larger than the highly stretched limit. 49 We fit the experimental data for h < 2 μm, over which there is a notable change in R G , and obtain a scaling exponent of −0.23 ± 0.13 (95% confidence interval). Remarkably, despite the simplified representation of the kinetoplast and mean-field approximation of the Flory approach, the data appear to follow the expected scaling prediction.…”

Stimuli‐responsive polyurethane bionanocomposites of poly(ethylene glycol)/poly(ε‐caprolactone) and [poly(ε‐caprolactone)‐grafted‐] cellulose nanocrystals

“…Figure 4F shows an intense increase in crystallization of the soft segments, as indicated by appearance of sharp and intense peaks at 2 θ = 19.3, 21.9, and 23.7°, which are main characteristic peaks of PCL and PEG 10,15 . The reason for overlapping of these three peaks is due to presence of a broad base peak, which is a characteristic of PUs with low crystallization extent due to the presence of hard segments (covalently bonded to soft segments) with negative and repulsive interaction toward soft segments reducing the conformational states and entropy of the soft domain chains 4,25 . The tendency of covalently bonded soft and hard segments to phase segregate causes stretching of soft segments and for the far excluded soft segments, the repulsive interaction weakens 26 .…”

“…CNCs, cellulose nanocrystals; PU, polyurethane presence of hard segments (covalently bonded to soft segments) with negative and repulsive interaction toward soft segments reducing the conformational states and entropy of the soft domain chains. 4,25 The tendency of covalently bonded soft and hard segments to phase segregate causes stretching of soft segments and for the far excluded soft segments, the repulsive interaction weakens. 26 The stretched state of the soft segments reduces the number of conformational states they can obtain, reducing their entropy and limiting their mobility to form stable crystalline structures.…”

Flatness and Intrinsic Curvature of Linked-Ring Membranes

“…12 In this study, we use Monte Carlo simulations to investigate the equilibrium statistical properties of catenated membranes. While other recent simulation studies have examined the statistical and dynamical properties of similar systems, including catenane dimers, 24,25 polycatenanes, [26][27][28][29][30] Olympic gels, [31][32][33] as well as the linking statistics of ring polymers under confinement, [34][35][36] this is the first simulation study of a catenated membrane, to our knowledge. The model membrane consists of identical rigid circular rings connected in 2D lattices.…”