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.

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.

Percolation and dissolution of Borromean networks.

Inspired by experiments on topologically linked DNA networks, we consider the connectivity of Borromean networks, in which no two rings share a pairwise-link, but groups of three rings form inseparable triplets. Specifically, we focus on square lattices at which each node is embedded a loop which forms a Borromean link with pairs of its nearest neighbors. By mapping the Borromean link network onto a lattice representation, we investigate the percolation threshold of these networks (the fraction of occupied nodes required for a giant component), as well as the dissolution properties: the spectrum of topological links that would be released if the network were dissolved to varying degrees. We find that the percolation threshold of the Borromean square lattice occurs when approximately 60.75% of nodes are occupied, slightly higher than the 59.27% typical of a square lattice. Compared to the dissolution of Hopf-linked networks, a dissolved Borromean network will yield more isolated loops, and fewer isolated triplets per single loop. Our simulation results may be used to predict experiments from Borromean structures produced by synthetic chemistry.

Flatness and intrinsic curvature of linked-ring membranes.

Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.

Trapping in self-avoiding walks with nearest-neighbor attraction.

The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a square lattice. Here, we consider the effect of nearest-neighbor attractive interactions on isolated growing self-avoiding walks, and we examine the effect that self-attraction has both on the statistics of trapping as well as on chain statistics through the transition between expanded and collapsed walks at the theta point. We find that the trapping length increases exponentially with the nearest-neighbor contact energy, but that there is a local minimum in trapping length for weakly self-attractive walks. While it has been controversial whether growing self-avoiding walks have the same asymptotic behavior as traditional self-avoiding walks, we find that the theta point is not at the same location for growing self-avoiding walks, and that the persistence length converges much more rapidly to a smaller value.

Equilibrium structure and deformation response of 2D kinetoplast sheets.

The considerable interest in two-dimensional (2D) materials and complex molecular topologies calls for a robust experimental system for single-molecule studies. In this work, we study the equilibrium properties and deformation response of a complex DNA structure called a kinetoplast, a 2D network of thousands of linked rings akin to molecular chainmail. Examined in good solvent conditions, kinetoplasts appear as a wrinkled hemispherical sheet. The conformation of each kinetoplast is dictated by its network topology, giving it a unique shape, which undergoes small-amplitude thermal fluctuations at subsecond timescales, with a wide separation between fluctuation and diffusion timescales. They deform elastically when weakly confined and swell to their equilibrium dimensions when the confinement is released. We hope that, in the same way that linear DNA became a canonical model system on the first investigations of its polymer-like behavior, kinetoplasts can serve that role for 2D and catenated polymer systems.

Long-Lived Self-Entanglements in Ring Polymers.

The entanglement of ring polymers remains mysterious in many aspects. In this Letter, we use electric fields to induce self-entanglements in circular DNA molecules, which serve as a minimal system for studying chain entanglements. We show that self-threadings give rise to entanglements in ring polymers and can slow down polymer dynamics significantly. We find that strongly entangled circular molecules remain kinetically arrested in a compact state for very long times, thereby providing experimental evidence for the severe topological constraints imposed by threadings.

Conformational State Hopping of Knots in Tensioned Polymer Chains.

We use Brownian dynamics simulations to study the conformational states of knots on tensioned chains. Focusing specifically on the 81 knot, we observe knot conformational state hopping and show that the process can be described by a two-state kinetic model in the presence of an external force. The distribution of knot conformational states depends on the applied chain tension, which leads to a force-dependent distribution of knot untying pathways. We generalize our findings by considering the untying pathways of other knots and find that the way knots untie is generally governed by the force applied to the chain. From a broader perspective, being able to influence how a knot unties via external force can potentially be useful for applications of single-molecule techniques in which knots are unwanted.

Motion of Knots in DNA Stretched by Elongational Fields.

Knots in DNA occur in biological systems, serve as a model system for polymer entanglement, and affect the efficacy of modern genomics technologies. We study the motion of complex knots in DNA by stretching molecules with a divergent electric field that provides an elongational force. We demonstrate that the motion of knots is nonisotropic and driven towards the closest end of the molecule. We show for the first time experimentally that knots can go from a mobile to a jammed state by varying an applied strain rate, and that this jamming is reversible. We measure the mobility of knots as a function of strain rate, demonstrating the conditions under which knots can be driven towards the ends of the molecule and untied.

Knots modify the coil-stretch transition in linear DNA polymers.

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.

Nanoconfinement greatly speeds up the nucleation and the annealing in single-DNA collapse.

Manipulating and measuring single-molecule dynamics and reactions in nanofluidics is a rapidly growing field with broad applications in developing new biotechnologies, understanding nanoconfinement effects in vivo, and exploring new phenomena in confinement. In this work, we investigate the kinetics of DNA collapse in nanoslits using single T4-DNA (165.6 kbp) and λ-DNA (48.5 kbp), with particular focus on the measurement of the nucleation and annealing times. Fixing the ethanol concentration at 35% and varying the slit height from 2000 to 31 nm, the nucleation time dramatically decreases from more than 1 hour to a few minutes or less. The increased collapsed rate results from the larger free energy experienced by coiled DNA in confinement relative to compacted DNA. Our results also shed light on other conformational transitions in confinement, such as protein folding.

Steady-State and Transient Behavior of Knotted Chains in Extensional Fields.

Recently, there has been a push to understand how molecular topology alters the nonequilibrium dynamics of polymer systems. In this paper, we probe how knotted polymers evolve in planar extensional fields using Brownian dynamics simulations and single-molecule experiments. In the first part of the study, we quantify the extension versus strain-rate curves of polymers and find that knots shift these curves to larger strain-rates. These trends can be quantitatively explained by Rouse-like scaling theories. In the second half of the study, we examine the consequences of knot untying on the time-dependent conformations of polymers in these external fields. We find that knot untying creates significant, transient changes in chain extension. If the topology is complex, the chain undergoes a wide range of time-dependent conformations since knot untying proceeds through many different stages. We provide examples of such untying trajectories over time.

Waves of DNA: Propagating excitations in extended nanoconfined polymers.

We use a nanofluidic system to investigate the emergence of thermally driven collective phenomena along a single polymer chain. In our approach, a single DNA molecule is confined in a nanofluidic slit etched with arrays of embedded nanocavities; the cavity lattice is designed so that a single chain occupies multiple cavities. Fluorescent video-microscopy data shows fluctuations in intensity between cavities, including waves of excess fluorescence that propagate across the cavity-straddling molecule, corresponding to propagating fluctuations of contour overdensity in the cavities. The transfer of DNA between neighboring pits is quantified by examining the correlation in intensity fluctuations between neighboring cavities. Correlations grow from an anticorrelated minimum to a correlated maximum before decaying, corresponding to a transfer of contour between neighboring cavities at a fixed transfer time scale. The observed dynamics can be modeled using Langevin dynamics simulations and a minimal lattice model of coupled diffusion. This study shows how confinement-based sculpting of the polymer equilibrium configuration, by renormalizing the physical system into a series of discrete cavity states, can lead to new types of dynamic collective phenomena.

Temperature change near microbubbles within a capillary network during focused ultrasound.

Preformed gas bubbles can increase energy absorption from an ultrasound beam and therefore they have been proposed for an enhancer of ultrasound treatments. Although tissue temperature measurements performed in vivo using invasive thermocouple probes and MRI thermometry have demonstrated increased tissue temperature, the microscopic temperature distribution has not been investigated so far. In this study the transfer of heat between bubbles and tissue during focused ultrasound was simulated. Microbubble oscillations were simulated within a rat cortical microvascular network reconstructed from in vivo dual-photon microscopy images and the power density of these oscillations was used as an input term in the Pennes bioheat transfer equation. The temperature solution from the bioheat transfer equation was mapped onto vascular data to produce a three-dimensional temperature map. The results showed high temperatures near the bubbles and slow temperature rise in the tissue. Heating was shown to increase with increasing bubble frequency and insonation pressure, and showed a frequency-dependent peak. The goal of this research is to characterize the effect of various parameters on bubble-enhanced therapeutic ultrasound to allow better treatment planning. These results show that the induced temperature elevations have nonuniformities which may have a significant impact on the bio-effects of the exposure.