A Topological Selection of Folding Pathways from Native States of Knotted Proteins

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.

Spatially Multiplexing of Metasurface for Manipulating the Focused Trefoil and Cinquefoil Vector Light Field

The trefoil and cinquefoil vector field are of essential significance for fundamental topology properties as the Hopf link and trefoil knots in the light field. The spatially multiplexing metasurfaces were designed with two sets of periodical nanoslits arranged alternately, each had independent geometric spiral phases and metalens phases to produce and focus vortex of the corresponding circular polarized (CP) light. By arranging the orientations of the two slit sets, the two CP vortices of the desired topological charges were obtained, the superposition of the vortices were realized to generate the vector field. With the topological charges of the vortices set to one and two, and three and two, respectively, the focused trefoil and cinquefoil vector light fields were acquired. The work would be important in broadening the applications of metasurface in areas as vector beam generations and topology of light field.

Same knot, longer rope: altering ligand geometry provides control over nuclearity in self-assembled trefoil knots

Selective constructions of Cp*Rh(iii)-based hexanuclear and octanuclear trefoil knots are realized using two ester bipyridyl ligands bearing minor differences in geometry.

Construction of organometallic trefoil knots and one-dimensional chains featuring half-sandwich Cp*Rh corner units and an abnormal zwitterion ligand

An abnormal flexible O-coordinated zwitterion ligand L shows self-adaptive conformation behaviour in chemical self-assembly. Two trefoil knots were obtained with C-shaped ligand L and two novel 1D chains were obtained with Z-shaped ligand L.

Design and synthesis of a bis-macrocyclic host and guests as building blocks for small molecular knots

The thread–link–cut (TLC) approach has previously shown promise as a novel method to synthesize molecular knots. The modular second-generation approach to small trefoil knots described herein involves electrostatic interactions between an electron-rich bis-macrocyclic host compound and electron-deficient guests in the threading step. The bis-macrocyclic host was synthesized in eight steps and 6.6% overall yield. Ammonium and pyridinium guests were synthesized in 4–5 steps. The TLC knot-forming sequence was carried out and produced a product with the expected molecular weight, but, unfortunately, further characterization did not produce conclusive results regarding the topology of the product.