Flatness and intrinsic curvature of linked-ring membranes

Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations

In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.

To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers

We use computer simulations to study a system of two unlinked ring polymers, whose length and bending stiffness are systematically varied. We derive the effective potentials between the rings, calculate the areas of minimal surfaces of the same, and characterize the threading between them. When the two rings are of the same kind, threading of a one ring through the surface of the other is immanent for small ring-ring separations. Flexible rings pierce the surface of the other ring several times but only shallowly, as compared to the stiff rings which pierce less frequently but deeply. Typically, the ring that is being threaded swells and flattens up into an oblate-like conformation, while the ring that is threading the other takes a shape of an elongated prolate. The roles of the threader and the threaded ring are being dynamically exchanged. If, on the other hand, the rings are of different kinds, the symmetry is broken and the rings tend to take up roles of the threader and the threaded ring with unequal probabilities. We propose a method how to predict these probabilities based on the parameters of the individual rings. Ultimately, our work captures the interactions between ring polymers in a coarse-grained fashion, opening the way to large-scale modelling of materials such as kinetoplasts, catenanes or topological brushes.

Circular Polycatenanes: Supramolecular Structures with Topologically Tunable Properties

Polycatenanes, macrochains of topologically interlocked rings with unique physical properties have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Most of the work has been, so far, focused on linear chains and on their variety of conformational properties compared to standard polymers. Here we go beyond the linear case and show that, by circularizing such macrochains, one can exploit the topology of the local interlockings to store twist in the system, significantly altering its metric and local properties. Moreover, by properly defining the twist (Tw) and writhe (Wr) of these macrorings we show the validity of a relation equivalent to the Călugăreanu-White-Fuller theorem Tw+Wr=const, originally proved for ribbonlike structures such as double stranded DNA. Our results suggest that circular polycatenanes with storable and tunable twist can form a new category of highly designable multiscale structures with potential applications in supramolecular chemistry and material science.

Geometric Predictors of Knotted and Linked Arcs

Inspired by how certain proteins “sense” knots and entanglements in DNA molecules, here, we ask if local geometric features that may be used as a readout of the underlying topology of generic polymers exist. We perform molecular simulations of knotted and linked semiflexible polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe, and nonlocal 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the time with the shortest knotted and linked arcs. We find that this accuracy is preserved across different knot types and also under significant spherical confinement, which is known to delocalize essential crossings in knotted polymers. We further discover that nonlocal 3D writhe is the best geometric readout of the knot location. Finally, we discuss how these geometric features may be used to computationally analyze entanglements in generic polymer melts and gels.

Polycatenanes: synthesis, characterization, and physical understanding

Chemical composition and architecture are two key factors that control the physical and material properties of polymers. Some of the more unusual and intriguing polymer architectures are the polycatenanes, which are a class of polymers that contain mechanically interlocked rings. Since the development of high yielding synthetic routes to catenanes, there has been an interest in accessing their polymeric counterparts, primarily on account of the unique conformations and degrees of freedom offered by non-bonded interlocked rings. This has lead to the synthesis of a wide variety of polycatenane architectures and to studies aimed at developing structure-property relationships of these interesting materials. In this review, we provide an overview of the field of polycatenanes, exploring synthesis, architecture, properties, simulation, and modelling, with a specific focus on some of the more recent developments.