A molecular strand can be knotted and unknotted into three different topologies, depending on the complexing metal ion used (copper or lanthanide or none). The properties of knots are exploited in a range of applications, from shoelaces to the knots used for climbing, fishing and sailing(1). Although knots are found in DNA and proteins(2), and form randomly in other long polymer chains(3,4), methods for tying(5)different sorts of knots in a synthetic nanoscale strand are lacking. Molecular knots of high symmetry have previously been synthesized by using non-covalent interactions to assemble and entangle molecular chains(6-15), but in such instances the template and/or strand structure intrinsically determines topology, which means that only one type of knot is usually possible. Here we show that interspersing coordination sites for different metal ions within an artificial molecular strand enables it to be tied into multiple knots. Three topoisomers-an unknot (0(1)) macrocycle, a trefoil (3(1)) knot(6-15), and a three-twist (5(2)) knot-were each selectively prepared from the same molecular strand by using transition-metal and lanthanide ions to guide chain folding in a manner reminiscent of the action of protein chaperones(16). We find that the metal-ion-induced folding can proceed with stereoinduction: in the case of one knot, a lanthanide(iii)-coordinated crossing pattern formed only with a copper(i)-coordinated crossing of particular handedness. In an unanticipated finding, metal-ion coordination was also found to translocate an entanglement from one region of a knotted molecular structure to another, resulting in an increase in writhe (topological strain) in the new knotted conformation. The knot topology affects the chemical properties of the strand: whereas the tighter 5(2)knot can bind two different metal ions simultaneously, the looser 3(1)isomer can bind only either one copper(i) ion or one lutetium(iii) ion. The ability to tie nanoscale chains into different knots offers opportunities to explore the modification of the structure and properties of synthetic oligomers, polymers and supramolecules.

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Fast radio bursts (FRBs) are millisecond-duration radio transients(1,2) of unknown origin. Two possible mechanisms that could generate extremely coherent emission from FRBs invoke neutron star magnetospheres(3-5) or relativistic shocks far from the central energy source(6-8). Detailed polarization observations may help us to understand the emission mechanism. However, the available FRB polarization data have been perplexing, because they show a host of polarimetric properties, including either a constant polarization angle during each burst for some repeaters(9,10) or variable polarization angles in some other apparently one-off events(11,12). Here we report observations of 15 bursts from FRB 180301 and find various polarization angle swings in seven of them. The diversity of the polarization angle features of these bursts is consistent with a magnetospheric origin of the radio emission, and disfavours the radiation models invoking relativistic shocks.

One of the key challenges for nuclear physics today is to understand from first principles the effective interaction between hadrons with different quark content. First successes have been achieved using techniques that solve the dynamics of quarks and gluons on discrete space-time lattices(1,2). Experimentally, the dynamics of the strong interaction have been studied by scattering hadrons off each other. Such scattering experiments are difficult or impossible for unstable hadrons(3-6) and so high-quality measurements exist only for hadrons containing up and down quarks(7). Here we demonstrate that measuring correlations in the momentum space between hadron pairs(8-12) produced in ultrarelativistic proton-proton collisions at the CERN Large Hadron Collider (LHC) provides a precise method with which to obtain the missing information on the interaction dynamics between any pair of unstable hadrons. Specifically, we discuss the case of the interaction of baryons containing strange quarks (hyperons). We demonstrate how, using precision measurements of proton-omega baryon correlations, the effect of the strong interaction for this hadron-hadron pair can be studied with precision similar to, and compared with, predictions from lattice calculations(13,14). The large number of hyperons identified in proton-proton collisions at the LHC, together with accurate modelling(15) of the small (approximately one femtometre) inter-particle distance and exact predictions for the correlation functions, enables a detailed determination of the short-range part of the nucleon-hyperon interaction.