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Tying different knots in a molecular strand


The properties of knots are exploited in a range of applications, from shoelaces to the knots used for climbing, fishing and sailing1. Although knots are found in DNA and proteins2, and form randomly in other long polymer chains3,4, methods for tying5 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 chains6,7,8,9,10,11,12,13,14,15, 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 (01) macrocycle, a trefoil (31) knot6,7,8,9,10,11,12,13,14,15, and a three-twist (52) 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 chaperones16. 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 52 knot can bind two different metal ions simultaneously, the looser 31 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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Fig. 1: Tying molecular strand L1 into a three-twist (52) knot through metal-ion-induced folding and entanglement.
Fig. 2: Spectroscopic characterization and modelled structure of molecular knot (+52)–1•[Cu][Lu].
Fig. 3: Tying molecular strand L1 into a trefoil (31) knot.
Fig. 4: Metal-free topoisomer synthesis and characterization.

Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information, or are available from the Mendeley data repository ( at


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We thank the Engineering and Physical Sciences Research Council (EP/P027067/1), the European Research Council (Advanced Grant number 786630), the Marie Skłodowska-Curie Actions of the European Union (Individual Postdoctoral Fellowship to F.S., number EC 746993) and the East China Normal University for funding; the University of Manchester Mass Spectrometry Service Centre for mass spectrometry, the Swedish National Infrastructure for Computing at the National Supercomputer Centre at Linköping University for computational resources, and networking contributions from the COST Action CA17139, EUTOPIA (European Topology Interdisciplinary Action). We thank J.-F. Lemonnier and S. Fielden for discussions. D.A.L. is a Royal Society Research Professor.

Author information




F.S. and L.P. devised the original concept. D.P.A., L.P., F.S. and J.S. planned and carried out the synthetic work. J.H.S. performed the computational investigations. D.A.L. directed the research. All authors contributed to the analysis of the results and the writing of the manuscript.

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Correspondence to David A. Leigh.

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Leigh, D.A., Schaufelberger, F., Pirvu, L. et al. Tying different knots in a molecular strand. Nature 584, 562–568 (2020).

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