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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


  1. Ashley, C. The Ashley Book of Knots (Doubleday, 1994).

  2. Lim, N. C. H. & Jackson, S. E. Molecular knots in biology and chemistry. J. Phys. Condens. Matter 27, 354101 (2015).

    Article  Google Scholar 

  3. Tubiana, L., Rosa, A., Fragiacomo, F. & Micheletti, C. Spontaneous knotting and unknotting of flexible linear polymers: equilibrium and kinetic aspects. Macromolecules 46, 3669–3678 (2013).

    Article  ADS  CAS  Google Scholar 

  4. Amin, S., Khorshid, A., Zeng, L., Zimny, P. & Reisner, W. A nanofluidic knot factory based on compression of single DNA in nanochannels. Nat. Commun. 9, 1506 (2018).

    Article  ADS  Google Scholar 

  5. Arai, Y. et al. Tying a molecular knot with optical tweezers. Nature 399, 446–448 (1999).

    Article  ADS  CAS  Google Scholar 

  6. Dietrich-Buchecker, C. O. & Sauvage, J.-P. A synthetic molecular trefoil knot. Angew. Chem. Int. Edn Engl. 28, 189–192 (1989).

    Article  Google Scholar 

  7. Safarowsky, O., Nieger, M., Fröhlich, R. & Vögtle, F. A molecular knot with twelve amide groups—one-step synthesis, crystal structure, chirality. Angew. Chem. Int. Ed. 39, 1616–1618 (2000).

    Article  CAS  Google Scholar 

  8. Feigel, M., Ladberg, R., Engels, S., Herbst-Irmer, R. & Fröhlich, R. A trefoil knot made of amino acids and steroids. Angew. Chem. Int. Ed. 45, 5698–5702 (2006).

    Article  CAS  Google Scholar 

  9. Adams, H. et al. Knot tied around an octahedral metal centre. Nature 411, 763 (2001).

    Article  ADS  CAS  Google Scholar 

  10. Barran, P. E. et al. Active metal template synthesis of a molecular trefoil knot. Angew. Chem. Int. Ed. 50, 12280–12284 (2011).

    Article  CAS  Google Scholar 

  11. Ponnuswamy, N., Cougnon, F. B. L., Clough, J. M., Pantos, G. D. & Sanders, J. K. M. Discovery of an organic trefoil knot. Science 338, 783–785 (2012).

    Article  ADS  CAS  Google Scholar 

  12. Prakasam, T. et al. Simultaneous self-assembly of a [2]catenane, a trefoil knot, and a Solomon link from a simple pair of ligands. Angew. Chem. Int. Ed. 52, 9956–9960 (2013).

    Article  CAS  Google Scholar 

  13. Ayme, J.-F. et al. Lanthanide template synthesis of a molecular trefoil knot. J. Am. Chem. Soc. 136, 13142–13145 (2014).

    Article  CAS  Google Scholar 

  14. Cougnon, F. B. L., Caprice, K., Pupier, M., Bauza, A. & Frontera, A. A strategy to synthesize molecular knots and links using the hydrophobic effect. J. Am. Chem. Soc. 140, 12442–12450 (2018).

    Article  CAS  Google Scholar 

  15. Segawa, Y. et al. Topological molecular nanocarbons: all-benzene catenane and trefoil knot. Science 365, 272–276 (2019).

    Article  ADS  CAS  Google Scholar 

  16. Hartl, F. U., Bracher, A. & Hayer-Hartl, M. Molecular chaperones in protein folding and proteostasis. Nature 475, 324–332 (2011).

    Article  CAS  Google Scholar 

  17. Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (W. H. Freeman, 1994).

  18. Eliel, E. L. & Wilen, S. H. Stereochemistry of Organic Compounds (Wiley, 1994).

  19. Gawley, R. E. & Aubé, J. Principles of Asymmetric Synthesis 2nd edn (Elsevier, 2012).

  20. Marenda, M., Orlandini, E. & Micheletti, C. Discovering privileged topologies of molecular knots with self-assembling models. Nat. Commun. 9, 3051 (2018).

    Article  ADS  Google Scholar 

  21. Ayme, J.-F. et al. A synthetic molecular pentafoil knot. Nat. Chem. 4, 15–20 (2012).

    Article  CAS  Google Scholar 

  22. Ponnuswamy, N., Cougnon, F. B. L., Pantos, G. D. & Sanders, J. K. M. Homochiral and meso figure eight knots and a Solomon link. J. Am. Chem. Soc. 136, 8243–8251 (2014).

    Article  CAS  Google Scholar 

  23. Danon, J. J. et al. Braiding a molecular knot with eight crossings. Science 355, 159–162 (2017).

    Article  ADS  CAS  Google Scholar 

  24. Zhang, L. et al. Stereoselective synthesis of a composite knot with nine crossings. Nat. Chem. 10, 1083–1088 (2018).

    Article  CAS  Google Scholar 

  25. Jackson, S. E., Suma, A. & Micheletti, C. How to fold intricately: using theory and experiments to unravel the properties of knotted proteins. Curr. Opin. Struct. Biol. 42, 6–14 (2017).

    Article  CAS  Google Scholar 

  26. Flapan, E., He, A. & Wong, H. Topological descriptions of protein folding. Proc. Natl Acad. Sci. USA 116, 9360–9369 (2019).

    Article  MathSciNet  CAS  Google Scholar 

  27. Mallam, A. L. & Jackson, S. E. Knot formation in newly translated proteins is spontaneous and accelerated by chaperonins. Nat. Chem. Biol. 8, 147–153 (2012).

    Article  CAS  Google Scholar 

  28. Zhao, Y., Dabrowski-Tumanski, P., Niewieczerzal, S. & Sulkowska, J. I. The exclusive effects of chaperonin on the behavior of proteins with 52 knot. PLoS Comput. Biol. 14, e1005970 (2018).

    Article  ADS  Google Scholar 

  29. Virnau, P., Mirny, L. A. & Kardar, M. Intricate knots in proteins: function and evolution. PLoS Comput. Biol. 2, e122 (2006).

    Article  ADS  Google Scholar 

  30. Hill, D. J., Mio, M. J., Prince, R. B., Hughes, T. S. & Moore, J. S. A field guide to foldamers. Chem. Rev. 101, 3893–4012 (2001).

    Article  CAS  Google Scholar 

  31. Hecht, S. & Huc, I. (eds) Foldamers: Structure, Properties, And Applications (Wiley-VCH, 2007).

  32. Maayan, G. & Albrecht, M. (eds) Metallofoldamers: Supramolecular Architectures From Helicates To Biomimetics (Wiley-VCH, 2013).

  33. Girvin, Z. C., Andrews, M. K., Liu, X. & Gellman, S. H. Foldamer-templated catalysis of macrocycle formation. Science 366, 1528–1531 (2019).

    Article  ADS  CAS  Google Scholar 

  34. Garber, S. B., Kingsbury, J. S., Gray, B. L. & Hoveyda, A. H. Efficient and recyclable monomeric and dendritic Ru-based metathesis catalysts. J. Am. Chem. Soc. 122, 8168–8179 (2000).

    Article  CAS  Google Scholar 

  35. Forgan, R. S., Sauvage, J.-P. & Stoddart, J. F. Chemical topology: complex molecular knots, links, and entanglements. Chem. Rev. 111, 5434–5464 (2011).

    Article  CAS  Google Scholar 

  36. Fielden, S. D. P., Leigh, D. A. & Woltering, S. L. Molecular knots. Angew. Chem. Int. Ed. 56, 11166–11194 (2017).

    Article  CAS  Google Scholar 

  37. Conway, J. H. An enumeration of knots and links, and some of their algebraic properties. In Computational Problems in Abstract Algebra (ed. Leech, J.) 329–358 (Pergamon Press, 1970).

  38. Leigh, D. A., Pirvu, L. & Schaufelberger, F. Stereoselective synthesis of molecular square and granny knots. J. Am. Chem. Soc. 141, 6054–6059 (2019).

    Article  CAS  Google Scholar 

  39. Sauvage, J.-P. From chemical topology to molecular machines (Nobel lecture). Angew. Chem. Int. Ed. 56, 11080–11093 (2017).

    Article  CAS  Google Scholar 

  40. Barry, D. E., Caffrey, D. F. & Gunnlaugsson, T. Lanthanide-directed synthesis of luminescent self-assembly supramolecular structures and mechanically bonded systems from acyclic coordinating organic ligands. Chem. Soc. Rev. 45, 3244–3274 (2016).

    Article  CAS  Google Scholar 

  41. Kotova, O., Kitchen, J. A., Lincheneau, C., Peacock, R. D. & Gunnlaugsson, T. Probing the effects of ligand isomerism in chiral luminescent lanthanide supramolecular self-assemblies: a europium “Trinity Sliotar” study. Chem. Eur. J. 19, 16181–16186 (2013).

    Article  CAS  Google Scholar 

  42. Gil-Ramírez, G. et al. Tying a molecular overhand knot of single handedness and asymmetric catalysis with the corresponding pseudo-D3-symmetric trefoil knot. J. Am. Chem. Soc. 138, 13159–13162 (2016).

    Article  Google Scholar 

  43. Rapenne, G., Dietrich-Buchecker, C. & Sauvage, J.-P. Resolution of a molecular trefoil knot. J. Am. Chem. Soc. 118, 10932–10933 (1996).

    Article  CAS  Google Scholar 

  44. Shen, T. & Wolynes, P. G. Statistical mechanics of a cat’s cradle. New J. Phys. 8, 273 (2006).

    Article  ADS  Google Scholar 

  45. de Gennes, P. G. Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55, 572–579 (1971).

    Article  ADS  Google Scholar 

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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.

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Authors and Affiliations



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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