### Concept: Ropework

#### 43

##### Braiding a molecular knot with eight crossings

- Science (New York, N.Y.)
- Published over 2 years ago
- Discuss

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.

#### 23

##### Optimizing Laparoscopically Extracorporeal Knot Tying Using a Novel Pusher Device

- Surgical laparoscopy, endoscopy & percutaneous techniques
- Published over 2 years ago
- Discuss

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.

#### 0

##### A nanofluidic knot factory based on compression of single DNA in nanochannels

- OPEN
- Nature communications
- Published over 1 year ago
- Discuss

Knots form when polymers self-entangle, a process enhanced by compaction with important implications in biological and artificial systems involving chain confinement. In particular, new experimental tools are needed to assess the impact of multiple variables influencing knotting probability. Here, we introduce a nanofluidic knot factory for efficient knot formation and detection. Knots are produced during hydrodynamic compression of single DNA molecules against barriers in a nanochannel; subsequent extension of the chain enables direct assessment of the number of independently evolving knots. Knotting probability increases with chain compression as well as with waiting time in the compressed state. Using a free energy derived from scaling arguments, we develop a knot-formation model that can quantify the effect of interactions and the breakdown of Poisson statistics at high compression. Our model suggests that highly compressed knotted states are stabilized by a decreased free energy as knotted contour contributes a lower self-exclusion derived free energy.

#### 0

Coronary angiography and percutaneous coronary intervention using the radial approach are becoming more frequent. Pronounced guide catheter manipulation in cases with tortuous access routes may lead to severe catheter kinking or knotting. The purpose of this review article is to present several techniques to resolve radial access catheter knots and kinks. First, simple maneuvers such as gentle traction, rotation, and guidewire advancement can often resolve minor kinking; however, complex loops and kinks are often not reversible with these simple maneuvers. Second, fixing the distal catheter tip using external compression, encasing the knot with a larger sheath, or untwisting the knot with hydraulic pressure can be useful. Finally, internal fixation by grasping the kinked catheter with a snare introduced via the femoral artery allows both ends of the catheter to be rotated in opposite directions to untwist the catheter for safe removal.

#### 0

##### Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains

- Soft matter
- Published about 3 years ago
- Discuss

We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.

#### 0

##### Subknots in ideal knots, random knots, and knotted proteins

- OPEN
- Scientific reports
- Published over 4 years ago
- Discuss

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots.

#### 0

##### Cotranslational folding of deeply knotted proteins

- Journal of physics. Condensed matter : an Institute of Physics journal
- Published about 4 years ago
- Discuss

Proper folding of deeply knotted proteins has a very low success rate even in structure-based models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.

#### 0

##### Characteristic length of the knotting probability revisited

- Journal of physics. Condensed matter : an Institute of Physics journal
- Published about 4 years ago
- Discuss

We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(-N/NK), where the estimates of parameter NK are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius rex, i.e. the screening length of double-stranded DNA.

#### 0

##### Knotting dynamics of DNA chains of different length confined in nanochannels

- Journal of physics. Condensed matter : an Institute of Physics journal
- Published about 4 years ago
- Discuss

Langevin dynamics simulations are used to characterize the typical mechanisms governing the spontaneous tying, untying and the dynamical evolution of knots in coarse-grained models of DNA chains confined in nanochannels. In particular we focus on how these mechanisms depend on the chain contour length, Lc, at a fixed channel width D = 56 nm corresponding to the onset of the Odijk scaling regime where chain backfoldings and hence knots are disfavoured but not suppressed altogether. We find that the lifetime of knots grows significantly with Lc, while that of unknots varies to a lesser extent. The underlying kinetic mechanisms are clarified by analysing the evolution of the knot position along the chain. At the considered confinement, in fact, knots are typically tied by local backfoldings of the chain termini where they are eventually untied after a stochastic motion along the chain. Consequently, the lifetime of unknots is mostly controlled by backfoldings events at the chain ends, which is largely independent of Lc. The lifetime of knots, instead, increases significantly with Lc because knots can, on average, travel farther along the chain before being untied. The observed interplay of knots and unknots lifetimes underpins the growth of the equilibrium knotting probability of longer and longer chains at fixed channel confinement.

#### 0

##### Influence of Rigidity and Knot Complexity on the Knotting of Confined Polymers

- Macromolecules
- Published over 5 years ago
- Discuss

We employ computer simulations and thermodynamic integration to analyze the effects of bending rigidity and slit confinement on the free energy cost of tying knots, ΔF knotting, on polymer chains under tension. A tension-dependent, nonzero optimal stiffness κmin exists, for which ΔF knotting is minimal. For a polymer chain with several stiffness domains, each containing a large amount of monomers, the domain with stiffness κmin will be preferred by the knot. A local analysis of the bending in the interior of the knot reveals that local stretching of chains at the braid region is responsible for the fact that the tension-dependent optimal stiffness has a nonzero value. The reduction in ΔF knotting for a chain with optimal stiffness relative to the flexible chain can be enhanced by tuning the slit width of the 2D confinement and increasing the knot complexity. The optimal stiffness itself is independent of the knot types we considered, while confinement shifts it toward lower values.