Overhand Knot Research Articles

Folding a Molecular Strand into a Trefoil Knot of Single Handedness with Co(II)/Co(III) Chaperones.

We report the synthesis of a right-handed (Δ-stereochemistry of strand crossings) trefoil knot from a single molecular strand containing three pyrazine-2,5-dicarboxamide units adjacent to point-chiral centers and six pyridine moieties. The oligomeric ligand strand folds into an overhand (open-trefoil) knot through the assistance of coordinatively dynamic Co(II) "chaperones" that drive the formation of a three-metal-ion circular helicate. The entangled structure is kinetically locked by oxidation to Co(III) and covalently captured by ring-closing olefin metathesis to generate a trefoil knot of single topological handedness. The stereochemistry of the strand crossings in the metal-coordinated overhand knot is governed by the stereochemistry of the point-chiral carbon centers in the ligand strand. The overhand and trefoil knots were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography. Removal of the metal ions from the knot, followed by hydrogenation of the alkene, yielded the wholly organic trefoil knot. The metal-free knot and parent ligand were investigated by circular dichroism (CD) spectroscopy. The CD spectra indicate that the topological stereochemistry of the knot has a greater effect on the asymmetry of the chromophore environment than do the point-chiral centers of the strand.

Increasing polymer scission rate by tying an overhand knot

Increasing polymer scission rate by tying an overhand knot

Mechanical scission of a knotted polymer

Molecular knots and entanglements form randomly and spontaneously in both biological and synthetic polymer chains. It is known that macroscopic materials, such as ropes, are substantially weakened by the presence of knots, but until now it has been unclear whether similar behaviour occurs on a molecular level. Here we show that the presence of a well-defined overhand knot in a polymer chain substantially increases the rate of scission of the polymer under tension (≥2.6× faster) in solution, because deformation of the polymer backbone induced by the tightening knot activates otherwise unreactive covalent bonds. The fragments formed upon severing of the knotted chain differ from those that arise from cleavage of a similar, but unknotted, polymer. Our solution studies provide experimental evidence that knotting can contribute to higher mechanical scission rates of polymers. It also demonstrates that entanglement design can be used to generate mechanophores that are among the most reactive described to date, providing opportunities to increase the reactivity of otherwise inert functional groups.

Snap Buckling in Overhand Knots

Abstract When an overhand knot tied in an elastic rod is tightened, it can undergo a sudden change in shape through snap buckling. In this article, we use a combination of discrete differential geometry (DDG)-based simulations and tabletop experiments to explore the onset of buckling as a function of knot topology, rod geometry, and friction. In our setup, two open ends of an overhand knot are slowly pulled apart, which leads to snap buckling in the knot loop. We call this phenomenon “inversion” since the loop appears to move dramatically from one side of the knot to the other. This inversion occurs due to the coupling of elastic energy between the braid (the portion of the knot in self-contact) and the loop (the portion of the knot with two ends connected to the braid). A numerical framework is implemented that combines discrete elastic rods with a constraint-based method for frictional contact to explore inversion in overhand knots. The numerical simulation robustly captures inversion in the knot and is found to be in good agreement with experimental results. In order to gain physical insight into the inversion process, we also develop a simplified model of the knot that does not require simulation of self-contact, which allows us to visualize the bifurcation that results in snap buckling.

An approximation method for the prevention of knot formation during catheterization in children

Knotting during urethral catheterization in children is an unpleasant situation. We aimed to minimize this risk. To prevent knot formation, we must understand its nature. We focused on the simplest, and most fundamental, known as overhand knot. Calculating the maximum length of catheter inserted in the bladder without risk of knotting, we estimated the minimum length of catheter needed for an overhand knot. This theoretical approach provides a rough estimation which may contribute to secure catheterization. Adding the calculated length to the appropriate for gender and age urethral length, may reduce knotting risk.

Effects of turn-structure on folding and entanglement in artificial molecular overhand knots.

The length and constitution of spacers linking three 2,6-pyridinedicarboxamide units in a molecular strand influence the tightness of the resulting overhand (open-trefoil) knot that the strand folds into in the presence of lanthanide(iii) ions. The use of β-hairpin forming motifs as linkers enables a metal-coordinated pseudopeptide with a knotted tertiary structure to be generated. The resulting pseudopeptide knot has one of the highest backbone-to-crossing ratios (BCR)—a measure of knot tightness (a high value corresponding to looseness)—for a synthetic molecular knot to date. Preorganization in the crossing-free turn section of the knot affects aromatic stacking interactions close to the crossing region. The metal-coordinated pseudopeptide knot is compared to overhand knots with other linkers of varying tightness and turn preorganization, and the entangled architectures characterized by NMR spectroscopy, ESI-MS, CD spectroscopy and, in one case, X-ray crystallography. The results show how it is possible to program specific conformational properties into different key regions of synthetic molecular knots, opening the way to systems where knotting can be systematically incorporated into peptide-like chains through design.

Rat model and validation of a modified single-armed suture technique for microsurgical vasoepididymostomy: Guo's SA-LIVE.

Double-armed suture longitudinal intussusception vasoepididymostomy (DA-LIVE) has been widely adopted owing to its simplicity and high success rate; however, specialized double-armed microsutures are required. To provide a novel single-armed suture longitudinal intussusception vasoepididymostomy (SA-LIVE) technique using only two single-armed sutures, named Guo's SA-LIVE. Four weeks after vasectomy in male adult Wistar rats, vasoepididymostomies were performed using DA-LIVE, SA-LIVE, or Guo's SA-LIVE. After 12weeks, functional patency was functionally assessed by evaluating for motile spermatozoa distal to the anastomosis. If no motile spermatozoa were visible, the mechanical patency of the anastomosis was tested by the ability of methylene blue to pass through the surgical anastomosis. The key procedure in Guo's SA-LIVE was cutting each needle with over 1cm attaching suture and making a flat overhand bend knot to tie the needle to the other end of the suture, after the needles were passed through the epididymal tubule and then the vasal lumen in an inside-out fashion, and then, the needles were passed through the vasal lumen in an inside-out fashion. The proportions of functional patency were 50.0% (3/6), 33.3% (2/6), and 50% (3/6) for the DA-LIVE, SA-LIVE, and Guo's SA-LIVE groups, respectively (P=.799). The proportions of mechanical plus functional patency for the three methods were 83.3% (5/6), 66.7% (4/6), and 83.3% (5/6), respectively (P=.725). The mean anastomosis times for the three LIVE techniques and the proportions of complications were similar (P=.150 and .758, respectively). Guo's single-armed suture technique is a potentially effective alternative to perform vasoepididymostomy when specialized double-armed microsutures are not available based on the current animal experiment.

Knotting a molecular strand can invert macroscopic effects of chirality.

Transferring structural information from the nanoscale to the macroscale is a promising strategy for developing adaptive and dynamic materials. Here we demonstrate that the knotting and unknotting of a molecular strand can be used to control, and even invert, the handedness of a helical organization within a liquid crystal. An oligodentate tris(2,6-pyridinedicarboxamide) strand with six point-chiral centres folds into an overhand knot of single handedness upon coordination to lanthanide ions, both in isotropic solutions and in liquid crystals. In achiral liquid crystals, dopant knotted and unknotted strands induce supramolecular helical organizations of opposite handedness, with dynamic switching achievable through in situ knotting and unknotting events. Tying the molecular knot transmits information regarding asymmetry across length scales, from Euclidean point chirality (constitutional chirality) via molecular entanglement (conformation) to liquid-crystal (centimetre-scale) chirality. The magnitude of the effect induced by the tying of the molecular knots is similar to that famously used to rotate a glass rod on the surface of a liquid crystal by synthetic molecular motors.

8-0 Polypropylene Suture Looping and Overhand Knot: Transconjunctival Approach to Four-Point Scleral Fixation of an Akreos Adapt Intraocular Lens.

To evaluate a novel surgical technique for transscleral fixation of the intraocular lens (IOL) with four hollow haptics using 8-0 polypropylene suture looping and overhand knot. An 8-0 polypropylene suture was tied to a 10-0 polypropylene suture with an overhand knot. One set of 8-0 polypropylene suture was then passed through the IOL four haptics. The suture knot was buried by rotating into the sclera tunnel. Best-corrected visual acuity, intraocular pressure, and complications were determined. The IOLs were fixed with using an 8-0 polypropylene suture in 13 eyes of 11 patients with aphakia and dislocated crystalline lens. The mean preoperative corrected distance visual acuity was 0.71 ± 0.58 logarithm of the minimum angle of resolution (Snellen 20/103), and it improved to 0.24 ± 0.25 logarithm of the minimum angle of resolution (Snellen 20/35) at the final follow-up ( P < 0.05). No vitreous hemorrhage, hypotony, suture exposed, and pupillary capture of the IOL were observed in any of the patients. The authors have developed a new technique for transscleral IOL fixation with one set of an 8-0 polypropylene suture tied to a 10-0 polypropylene suture with an overhand knot. The overhand knot offers the opportunity to use an 8-0 polypropylene suture for the long-term safety and may not require the surgeon to learn any new technique.

Intrascleral sewing-machine technique: A Grooveless/flapless cyclopexy technique for large traumatic Cyclodialysis cleft repairs in pars plana vitrectomy.

To describe a minimally invasive technique for the repair of large traumatic cyclodialysis clefts using intrascleral sewing machine suture and overhand friction knot techniques in pars plana vitrectomy. This prospective, noncomparative, interventional case series included seven eyes of seven patients with a large traumatic cyclodialysis cleft. The sewing machine technique was modified by an intrascleral approach. The procedure was transconjunctival or subconjunctival performed without scleral flaps/grooves. An overhand friction knot was used to lead the cutting ends of the suture buried in the scleral tunnel. The closure of the cyclodialysis cleft was achieved in seven eyes. The mean follow-up duration was 49.1 ± 15.6 weeks (range, 30-70 weeks). The intraocular pressure increased from 7.3 ± 2.1 mm Hg (range, 5-11 mmHg) preoperatively to 13.6 ± 2.4 mm Hg (range, 10-17 mmHg) postoperatively ( P < 0.01). The best-corrected visual acuity improved from a mean of 2.76 ± 2.77 logarithm of the minimum angle of resolution preoperatively to 0.63 ± 0.82 logarithm of the minimum angle of resolution at the final follow-up ( P < 0.01). In conclusion, the present technique is safe and effective in the treatment of large traumatic cyclodialysis clefts with minimal surgical trauma and a decreased surgical duration.

Stereoselective Synthesis of Molecular Square and Granny Knots.

We report on the stereoselective synthesis of both molecular granny and square knots through the use of lanthanide-complexed overhand knots of specific handedness as three-crossing “entanglement synthons”. The composite knots are assembled by combining two entanglement synthons (of the same chirality for a granny knot; of opposite handedness for a square knot) in three synthetic steps: first, a CuAAC reaction joins together one end of each overhand knot. Ring-closing olefin metathesis (RCM) then affords the closed-loop knot, locking the topology. This allows the lanthanide ions necessary for stabilizing the entangled conformation of the synthons to subsequently be removed. The composite knots were characterized by 1H and 13C NMR spectroscopy and mass spectrometry and the chirality of the knot stereoisomers compared by circular dichroism. The synthetic strategy of combining building blocks of defined stereochemistry (here overhand knots of Λ- or Δ-handed entanglement) is reminiscent of the chiron approach of using minimalist chiral synthons in the stereoselective synthesis of molecules with multiple asymmetric centers.

Development of a Tying Tool to Bind a Wire Harness

This paper describes the development of a prototype tool to be used to tie a clove hitch in order to bind a wire harness. The wire harnesses which are installed in airplanes are bound with belt-like strings. The binding process, which involves tying a clove hitch and then a double overhand knot, is still performed by human workers. To promote efficiency, simplifying the process by using tools is more practical than automating it with robots. We propose a tool that has a groove through which a string is pushed to form a clove hitch. The shape of the bottom of the groove is very important in order to ensure that the belt-like string goes through the groove without jamming. We formulated the bottom's shape based on the theory of surfaces and designed the shape to minimize changes in its curvature and torsion. We made a physical model of the prototype tool and confirmed its performance with tying experiments. As a result of the experiments, we found that there was a 93% probability of a successful tie occurring.

Securing a Supramolecular Architecture by Tying a Stopper Knot.

We report on a rotaxane‐like architecture secured by the in situ tying of an overhand knot in the tris(2,6‐pyridyldicarboxamide) region of the axle through complexation with a lanthanide ion (Lu3+). The increase in steric bulk caused by the knotting locks a crown ether onto the thread. Removal of the lutetium ion unties the knot, and when the axle binding site for the ring is deactivated, the macrocycle spontaneously dethreads. When the binding interaction is switched on again, the crown ether rethreads over the 10 nm length of the untangled strand. The overhand knot can be retied, relocking the threaded structure, by once again adding lutetium ions.

Securing a Supramolecular Architecture by Tying a Stopper Knot

AbstractWe report on a rotaxane‐like architecture secured by the in situ tying of an overhand knot in the tris(2,6‐pyridyldicarboxamide) region of the axle through complexation with a lanthanide ion (Lu3+). The increase in steric bulk caused by the knotting locks a crown ether onto the thread. Removal of the lutetium ion unties the knot, and when the axle binding site for the ring is deactivated, the macrocycle spontaneously dethreads. When the binding interaction is switched on again, the crown ether rethreads over the 10 nm length of the untangled strand. The overhand knot can be retied, relocking the threaded structure, by once again adding lutetium ions.

Planning of Knotting Based on Manipulation Skills with Consideration of Robot Mechanism/Motion and Its Realization by a Robot Hand System

This paper demonstrates the relationship between the production process of a knot and manipulation skills. First, we define the description (rope intersections, grasp type and fixation positions) of a knot. Second, we clarify the characteristics of the manipulation skills from the viewpoint of the knot description. Next, in order to obtain the production process of the knot, we propose an analysis method based on the structure of the knot and the characteristics of the manipulation skills. Using the proposed analysis method, we analyzed eight kinds of knots, formed with a single rope, two ropes or a single rope and an object. Finally, in order to validate the production process obtained by the proposed analysis method, we show experimental results of an overhand knot and a half hitch produced by using a robot hand system.

Hair-on-hair static friction coefficient can be determined by tying a knot

Characterizing the tribological properties of the hair–hair interface is important to quantify the manageability of hair and to assess the performance of hair care products. Audoly et al. (Phys. Rev. Lett. 99, 164301, 2007) derived an equation relating the self-friction coefficient of an elastic fiber to the dimensions of a simple, relaxed overhand knot made from this fiber. I experimentally tested and validated their equation using nylon thread and an independent measurement of its self-friction coefficient. I show that this methodology can be applied to provide high-throughput data on the static self-friction coefficient of single hair fibers in various conditions and to quantitatively assess how hair care treatments (conditioner, relaxant) alter frictional properties. I find that treatment of hair with 1M sodium hydroxide leads to a quick, irreversible self-friction coefficient increase; the resulting fine frictional fibers can be used to form very small knots for microsurgical vessel and organ ligature in medicine or embryology. The relaxed overhand knot method can more generally be used to measure the self-friction coefficients of a wide range of elastic fibers from the nano- (e.g. proteins, nanotubes) to the macro-scale (e.g. textile fiber, fiberglass).

A moray’s many knots: knot tying behaviour around bait in two species of Gymnothorax moray eel

Being able to tie their body into a knot is beneficial to some moray eels and other cylindrical vertebrates for various reasons, although not all morays’ tie knots. Knot tying can generate leverage for feeding activity by moving the knot up the body, and this leverage may be affected by knot type. Three types of knots are known to have been used by morays’ and this study further elucidates this behaviour and ability. Baited Remote Underwater Videos (BRUVs) were used to compare knot tying between the moray eels Gymnothorax prasinus and Gymnothorax prionodon in the Solitary Islands region, eastern Australia. Gymnothorax prasinus tied more knots overall and more types of knot than G. prionodon (five types vs one type, respectively). Both tied the overhand knot and this was the most common knot used by G. prasinus. The figure of eight knot was used two times more than the double overhand knot, being relatively wider and likely easier to move up the body. Gymnothorax prasinus also tied two undescribed knots, now called the ‘moray knot’ and the ‘morays banana knot’, which have more crossings and are bulkier, increasing potential for generating leverage. However, their uncommon use indicates costs may outweigh benefits of these more complex knots. Lower habitat complexity in deeper waters may influence differences in knot tying as G. prasinus were only recorded shallower than 40 m and G. prionodon mainly deeper. These findings further reveal the utility and complexity of knot tying in moray species and cylindrical vertebrates generally.

Tying a Molecular Overhand Knot of Single Handedness and Asymmetric Catalysis with the Corresponding Pseudo-D3-Symmetric Trefoil Knot.

We report the stereoselective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer with six chiral centers using a lanthanide(III) ion template. The oligomer folds around the lanthanide ion to form an overhand knot complex of single handedness. Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis affords a single enantiomer of the trefoil knot in 90% yield. The knot topology and handedness were confirmed by NMR spectroscopy, mass spectrometry, and X-ray crystallography. The pseudo-D3-symmetric knot was employed as an asymmetric catalyst in Mukaiyama aldol reactions, generating enantioselectivities of up to 83:17 er, which are significantly higher than those obtained with a comparable unknotted ligand complex.

Accidental uvulectomy after removal of a nasogastric tube

SummaryThe formation of a knot in a gastric tube is a rare event, but it can lead to complications. We describe a case in which an accidental uvulectomy occurred after retraction of a nasogastric feeding tube with an overhand knot in it. This knot probably formed in the pharynx of the patient and entangled the uvula on removal. This complication might have been avoided if the gastric tube was placed under direct vision or if it was removed more carefully. We recommend measuring the required tube length in order to prevent looping and knotting in the stomach.

Knotted nasoenteric feeding tube in an infant

This is a case report, with review of the literature, of an infant in the neonatal intensive care unit (NICU) with the complication of a nasoenteric weighted feeding tube that assumed an overhand knot configuration. Knotting of the feeding tube is a rare occurrence related to the use of feeding tubes, and should be considered if the tube becomes nonfunctional, if there are clinical factors that might lead to displacement or malposition of the tube, or if there is excessive resistance or sudden onset of respiratory distress in association with attempted removal.