Driven Translocation of Linked Ring Polymers through a Pore

Shape and size tunability of sheets of interlocked ring copolymers

Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials. In this context, two open questions regard the large-scale reverberations of the heterogeneous composition of the rings and the inequivalent modes of interlocking neighboring rings. We address these questions with Langevin dynamics simulations of chainmails with honeycomb-lattice connectivity, where the rings are block copolymers with two segments of different rigidity. We considered various combinations of the relative lengths of the two segments and the patterns of the over- and under-passes linking neighboring rings. We find that varying ring composition and linking patterns have independent and complementary effects. While the former sets the overall size of the chainmail, the latter defines the shape, enabling the selection of starkly different conformation types. Notably, one of the considered linking patterns favors saddle-shaped membranes, providing a first example of spontaneous negative Gaussian curvature in mechanically bonded sheets. The results help establish the extent to which mechanically bonded membranes can differ from conventional elastic ones, particularly for the achievable shape and size tunability.

Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers

We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.

Topological Entanglement of Linear Catenanes: Knots and Threadings

We used molecular dynamics simulations to investigate the self-entanglements of the collapsed linear catenanes. We found two different types of topologically complex states. First, we observed numerous long-lived knotting events of the catenane backbone. However, comparison with conventional polymers reveals that knots are suppressed in catenanes. Next, we observed topologically complex states with no analogue in polymers, where a concatenated ring was threaded by other near or distal rings sliding through it. Differently from knots, these threaded states can disentangle by becoming fully tightened. A detailed thermodynamic and microscopic analysis is employed to rationalize the persistence of threaded states, which can survive significant internal reorganizations of the entire catenane. We finally discuss the broader implications of these previously unreported types of entanglements for other systems, such as noncollapsed and interacting catenanes.

Constraints on Knot Insertion, Not Internal Jamming, Control Polycatenane Translocation Dynamics through Crystalline Pores

The translocation of polymers through pores and channels is an archetypal process in biology and is widely studied and exploited for applications in bio- and nanotechnology. In recent times, the translocation of polymers of various different topologies has been studied both experimentally and by computer simulation. However, in some cases, a clear understanding of the precise mechanisms that drive their translocation dynamics can be challenging to derive. Experimental methods are able to provide statistical details of polymer translocation, but computer simulations are uniquely placed to uncover a finer level of mechanistic understanding. In this work, we use high-throughput molecular simulations to reveal the importance that knot insertion rates play in controlling translocation dynamics in the small pore limit, where unexpected nonpower law behavior emerges. This work both provides new predictive understanding of polycatenane translocation and shows the importance of carefully considering the role of the definition of translocation itself.

Nanopore translocation of topologically linked DNA catenanes

The electrical signal associated with a biopolymer translocating through a nanoscale pore depends on the size, topology, and configuration of each molecule. Building upon recent interest in using solid-state nanopores for studying the topology of knotted and supercoiled DNA, we present experimental observations of topologically linked catenanes translocating through a solid-state nanopore. Using restriction enzymes, linked circular molecules were isolated from the mitochondrial DNA of Crithidia fasciculata, a structure known as a kinetoplast that comprises thousands of topologically interlocked minicircles. Digested kinetoplasts produce a spectrum of catenane topologies, which are identified from their nanopore translocation signals by spikes in the blockade current associated with the topological linkages. We attribute the different patterns of the measured electrical signals to 2-catenanes, linear and triangular 3-catenanes, and several types of 4- and 5-catenanes as well as more complex structures. Measurements of the translocation time of signals consistent with 2- and 3-catenanes suggest that topological friction between the linkages and the pore slows the translocation time of these structures, as predicted in recent simulations.

Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers

We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

RNA Pore Translocation with Static and Periodic Forces: Effect of Secondary and Tertiary Elements on Process Activation and Duration

We use MD simulations to study the pore translocation properties of a pseudoknotted viral RNA. We consider the 71-nucleotide-long xrRNA from the Zika virus and establish how it responds when driven through a narrow pore by static or periodic forces applied to either of the two termini. Unlike the case of fluctuating homopolymers, the onset of translocation is significantly delayed with respect to the application of static driving forces. Because of the peculiar xrRNA architecture, activation times can differ by orders of magnitude at the two ends. Instead, translocation duration is much smaller than activation times and occurs on time scales comparable at the two ends. Periodic forces amplify significantly the differences at the two ends, for both activation times and translocation duration. Finally, we use a waiting-times analysis to examine the systematic slowing downs in xrRNA translocations and associate them to the hindrance of specific secondary and tertiary elements of xrRNA. The findings provide a useful reference to interpret and design future theoretical and experimental studies of RNA translocation.