Knots may ultimately prove just as versatile and useful at the nanoscale as at the macroscale. However, the lack of synthetic routes to all but the simplest molecular knots currently prevents systematic investigation of the influence of knotting at the molecular level. We found that it is possible to assemble four building blocks into three braided ligand strands. Octahedral iron(II) ions control the relative positions of the three strands at each crossing point in a circular triple helicate, while structural constraints on the ligands determine the braiding connections. This approach enables two-step assembly of a molecular 819 knot featuring eight nonalternating crossings in a 192-atom closed loop ~20 nanometers in length. The resolved metal-free 819 knot enantiomers have pronounced features in their circular dichroism spectra resulting solely from topological chirality.
Molecular knots remain difficult to produce using the current synthetic methods of chemistry because of their topological complexity. We report here the near-quantitative self-assembly of a trefoil knot from a naphthalenediimide-based aqueous disulfide dynamic combinatorial library. The formation of the knot appears to be driven by the hydrophobic effect and leads to a structure in which the aromatic components are buried while the hydrophilic carboxylate groups remain exposed to the solvent. Moreover, the building block chirality constrains the topological conformation of the knot and results in its stereoselective synthesis. This work demonstrates that the hydrophobic effect provides a powerful strategy to direct the synthesis of entwined architectures.
The use of ureteral stents has become a routine urological practice. There are many different complications with ureteral stent use. One rare complication is knotting, which can be a very difficult condition to treat. We report a case in which a complete knot was found in the proximal part of an indwelling ureteral stent with a proximal ureteral stone.
OBJECTIVE: To compare the ergonomics and workload of the surgeon during single-site suturing while using the magnetic anchoring and guidance system (MAGS) camera vs a conventional laparoscope. METHODS: Seven urologic surgeons were enrolled and divided into an expert group (n = 2) and a novice group (n = 5) according to their laparoendoscopic single-site (LESS) experience. Each surgeon performed 2 conventional LESS and 2 MAGS camera-assisted LESS vesicostomy closures in a porcine model. A Likert scale (scoring 1-5) questionnaire assessing workload, ergonomics, technical difficulty, visualization, and needle handling, as well as a validated National Aeronautics and Space Administration Task Load Index (NASA-TLX) questionnaire were used to evaluate the tasks and workloads. RESULTS: MAGS LESS suturing was universally favored by expert and novice surgeons compared with conventional LESS in workload (3.4 vs 4.2), ergonomics (3.4 vs 4.4), technical challenge (3.3 vs 4.3), visualization (2.4 vs 3.3), and needle handling (3.1 vs 3.9 respectively; P <.05 for all categories). Surgeon NASA-TLX assessments found MAGS LESS suturing significantly decreased the workload in physical demand (P = .004), temporal demand (P = .017), and effort (P = .006). External instrument clashing was significantly reduced in MAGS LESS suturing (P <.001). The total operative time of MAGS LESS suturing was comparable to that of conventional LESS (P = .89). CONCLUSION: MAGS camera technology significantly decreased surgeon workload and improved ergonomics. Nevertheless, LESS suturing and knot tying remains a challenging task that requires training, regardless of which camera is used.
We describe theory and simulations of a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton’s orbital angular momentum and spatial twist, tangle on propagation to form links and knots. We anticipate similar spontaneous knot topology to be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.
- Surgical laparoscopy, endoscopy & percutaneous techniques
- Published over 3 years ago
The aim of this study was to evaluate the efficacy and feasibility of a novel pusher device for performing extracorporeal knot tying. Each of the 3 laparoscopists randomly performed 10 device-assisted double sheet bends (the device group), ten 4s modified Roeder sliding knots (the sliding group), and 10 laparoscopic traditional extracorporeal static surgeon’s knots (the static group). All knots and 5 unknotted threads were measured for strength. The device group had higher knot strength, lower knotting failure rate, and shorter knotting time compared with the sliding group. The knot strengths of the successful knots in the device group were consistent with those obtained in the static group, and higher than the sliding group. Our laparoscopic novel pusher device should be an effective device in assisting knot tying with the advantages of steady and strong knot strength, lower failure rate, and shorter knotting time.
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important.
- Proceedings of the National Academy of Sciences of the United States of America
- Published over 3 years ago
We use an accurate coarse-grained model for DNA and stochastic molecular dynamics simulations to study the pore translocation of 10-kbp-long DNA rings that are knotted. By monitoring various topological and physical observables we find that there is not one, as previously assumed, but rather two qualitatively different modes of knot translocation. For both modes the pore obstruction caused by knot passage has a brief duration and typically occurs at a late translocation stage. Both effects are well in agreement with experiments and can be rationalized with a transparent model based on the concurrent tensioning and sliding of the translocating knotted chains. We also observed that the duration of the pore obstruction event is more controlled by the knot translocation velocity than the knot size. These features should advance the interpretation and design of future experiments aimed at probing the spontaneous knotting of biopolymers.
Tangles of string typically become knotted, from macroscopic twine down to long-chain macromolecules such as DNA. Here, we demonstrate that knotting also occurs in quantum wavefunctions, where the tangled filaments are vortices (nodal lines/phase singularities). The probability that a vortex loop is knotted is found to increase with its length, and a wide gamut of knots from standard tabulations occur. The results follow from computer simulations of random superpositions of degenerate eigenstates of three simple quantum systems: a cube with periodic boundaries, the isotropic three-dimensional harmonic oscillator and the 3-sphere. In the latter two cases, vortex knots occur frequently, even in random eigenfunctions at relatively low energy, and are constrained by the spatial symmetries of the modes. The results suggest that knotted vortex structures are generic in complex three-dimensional wave systems, establishing a topological commonality between wave chaos, polymers and turbulent Bose-Einstein condensates.
Large-scale and high-efficient water collection of microfibers with long-term durability still remains challenging. Here we present well-controlled, bioinspired spindle-knot microfibers with cavity knots (named cavity-microfiber), precisely fabricated via a simple gas-in-water microfluidic method, to address this challenge. The cavity-microfiber is endowed with unique surface roughness, mechanical strength, and long-term durability due to the design of cavity as well as polymer composition, thus enabling an outstanding performance of water collection. The maximum water volume collected on a single knot is almost 495 times than that of the knot on the cavity-microfiber. Moreover, the spider-web-like networks assembled controllably by cavity-microfibers demonstrate excellent large-scale and high-efficient water collection. To maximize the water-collecting capacity, nodes/intersections should be designed on the topology of the network as many as possible. Our light-weighted yet tough, low-cost microfibers with high efficiency in directional water transportation offers promising opportunities for large-scale water collection in water-deficient areas.