Knotting a molecular strand can invert macroscopic effects of chirality


Transferring structural information from the nanoscale to the macroscale is a promising strategy for developing adaptive and dynamic materials. Here we demonstrate that the knotting and unknotting of a molecular strand can be used to control, and even invert, the handedness of a helical organization within a liquid crystal. An oligodentate tris(2,6-pyridinedicarboxamide) strand with six point-chiral centres folds into an overhand knot of single handedness upon coordination to lanthanide ions, both in isotropic solutions and in liquid crystals. In achiral liquid crystals, dopant knotted and unknotted strands induce supramolecular helical organizations of opposite handedness, with dynamic switching achievable through in situ knotting and unknotting events. Tying the molecular knot transmits information regarding asymmetry across length scales, from Euclidean point chirality (constitutional chirality) via molecular entanglement (conformation) to liquid-crystal (centimetre-scale) chirality. The magnitude of the effect induced by the tying of the molecular knots is similar to that famously used to rotate a glass rod on the surface of a liquid crystal by synthetic molecular motors.

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Fig. 1: Doping nematic liquid crystals with molecular strands and knots.
Fig. 2: Entanglement of molecular strands into overhand knots.
Fig. 3: Solution-phase characterization of ligand strands and overhand knots.
Fig. 4: Polarized optical microscopy image of a strand-doped liquid crystal.
Fig. 5: The in situ tying and untying of a molecular overhand knot dopant reversibly inverts the handedness of a chiral nematic liquid crystal.

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 ( under


  1. 1.

    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).

    CAS  PubMed  Google Scholar 

  2. 2.

    Wasserman, S. A. & Cozzarelli, N. R. Biochemical topology: applications to DNA recombination and replication. Science 232, 951–960 (1986).

    CAS  PubMed  Google Scholar 

  3. 3.

    Frank-Kamenetskii, M. D., Lukashin, A. V. & Vologodskii, A. V. Statistical mechanics and topology of polymer chains. Nature 258, 398–402 (1975).

    CAS  PubMed  Google Scholar 

  4. 4.

    Sułkowska, J. I., Sułkowski, P., Szymczak, P. & Cieplak, M. Stabilizing effect of knots on proteins. Proc. Natl Acad. Sci. USA 105, 19714–19719 (2008).

    PubMed  Google Scholar 

  5. 5.

    Saitta, A. M., Soper, P. D., Wasserman, E. & Klein, M. L. Influence of a knot on the strength of a polymer strand. Nature 399, 46–48 (1999).

    CAS  PubMed  Google Scholar 

  6. 6.

    Caraglio, M., Micheletti, C. & Orlandini, E. Stretching response of knotted and unknotted polymer chains. Phys. Rev. Lett. 115, 188301 (2015).

    PubMed  Google Scholar 

  7. 7.

    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).

    PubMed  PubMed Central  Google Scholar 

  8. 8.

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

    CAS  Google Scholar 

  9. 9.

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

    CAS  PubMed  Google Scholar 

  10. 10.

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

    CAS  Google Scholar 

  11. 11.

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

    PubMed  Google Scholar 

  12. 12.

    Goujon, A. et al. Hierarchical self-assembly of supramolecular muscle-like fibers. Angew. Chem. Int. Ed. 55, 703–707 (2016).

    CAS  Google Scholar 

  13. 13.

    Yamaguchi, H. et al. Photoswitchable gel assembly based on molecular recognition. Nat. Commun. 3, 603 (2012).

    PubMed  PubMed Central  Google Scholar 

  14. 14.

    Cantekin, S. et al. The effect of isotopic substitution on the chirality of a self-assembled helix. Nat. Chem. 3, 42–46 (2011).

    CAS  PubMed  Google Scholar 

  15. 15.

    Berná, J. et al. Macroscopic transport by synthetic molecular machines. Nat. Mater. 4, 704–710 (2005).

    PubMed  Google Scholar 

  16. 16.

    Zhu, K., O’Keefe, C. A., Vukotic, V. A., Schurko, R. W. & Loeb, S. J. A molecular shuttle that operates inside a metal–organic framework. Nat. Chem. 7, 514–519 (2015).

    CAS  PubMed  Google Scholar 

  17. 17.

    Danowski, W. et al. Unidirectional rotary motion in a metal–organic framework. Nat. Nanotechnol. 14, 488–494 (2019).

    CAS  PubMed  Google Scholar 

  18. 18.

    Eelkema, R. et al. Nanomotor rotates microscale objects. Nature 440, 163 (2006).

    CAS  PubMed  Google Scholar 

  19. 19.

    Sakuda, J., Yasuda, T. & Kato, T. Liquid-crystalline catenanes and rotaxanes. Isr. J. Chem. 52, 854–862 (2012).

    CAS  Google Scholar 

  20. 20.

    Baranoff, E. D. et al. A liquid-crystalline [2]catenane and its copper(I) complex. Angew. Chem. Int. Ed. 46, 4680–4683 (2007).

    CAS  Google Scholar 

  21. 21.

    Aprahamian, I. et al. A liquid-crystalline bistable [2]rotaxane. Angew. Chem. Int. Ed. 46, 4675–4679 (2007).

    CAS  Google Scholar 

  22. 22.

    Lancia, F., Ryabchun, A. & Katsonis, N. Life-like motion driven by artificial molecular machines. Nat. Rev. Chem. 3, 536–551 (2019).

    CAS  Google Scholar 

  23. 23.

    Morrow, S. M., Bissette, A. J. & Fletcher, S. P. Transmission of chirality through space and across length scales. Nat. Nanotechnol. 12, 410–419 (2017).

    CAS  PubMed  Google Scholar 

  24. 24.

    Yashima, E. et al. Supramolecular helical systems: helical assemblies of small molecules, foldamers, and polymers with chiral amplification and their functions. Chem. Rev. 116, 13752–13990 (2016).

    CAS  PubMed  Google Scholar 

  25. 25.

    Katsonis, N., Lacaze, E. & Ferrarini, A. Controlling chirality with helix inversion in cholesteric liquid crystals. J. Mater. Chem. 22, 7088–7097 (2012).

    CAS  Google Scholar 

  26. 26.

    Tai, J.-S. B. & Smalyukh, I. I. Three-dimensional crystals of adaptive knots. Science 365, 1449–1453 (2019).

    CAS  PubMed  Google Scholar 

  27. 27.

    Alexander, G. P. Knot your regular crystal of atoms. Science 365, 1377 (2019).

    CAS  PubMed  Google Scholar 

  28. 28.

    Tkalec, U., Ravnik, M., Čopar, S., Žumer, S. & Muševič, I. Reconfigurable knots and links in chiral nematic colloids. Science 333, 62–66 (2011).

    CAS  PubMed  Google Scholar 

  29. 29.

    Dang, L.-L. et al. Coordination-driven self-assembly of a molecular figure-eight knot and other topologically complex architectures. Nat. Commun. 10, 2057 (2019).

    PubMed  PubMed Central  Google Scholar 

  30. 30.

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

    CAS  PubMed  Google Scholar 

  31. 31.

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

    Google Scholar 

  32. 32.

    Guo, J., Mayers, P. C., Breault, G. A. & Hunter, C. A. Synthesis of a molecular trefoil knot by folding and closing on an octahedral coordination template. Nat. Chem. 2, 218–222 (2010).

    CAS  PubMed  Google Scholar 

  33. 33.

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

    CAS  Google Scholar 

  34. 34.

    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).

    CAS  Google Scholar 

  35. 35.

    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).

    CAS  PubMed  Google Scholar 

  36. 36.

    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).

    CAS  PubMed  Google Scholar 

  37. 37.

    Marcos, V. et al. Allosteric initiation and regulation of catalysis with a molecular knot. Science 352, 1555–1559 (2016).

    CAS  PubMed  Google Scholar 

  38. 38.

    Zhang, L. et al. Effects of knot tightness at the molecular level. Proc. Natl Acad. Sci. USA 116, 2452–2457 (2019).

    CAS  PubMed  Google Scholar 

  39. 39.

    Leigh, D. A., Pirvu, L., Schaufelberger, F., Tetlow, D. J. & Zhang, L. Securing a supramolecular architecture by tying a stopper knot. Angew. Chem. Int. Ed. 57, 10484–10488 (2018).

    CAS  Google Scholar 

  40. 40.

    Ayme, J.-F. et al. Strong and selective anion binding within the central cavity of molecular knots and links. J. Am. Chem. Soc. 137, 9812–9815 (2015).

    CAS  PubMed  Google Scholar 

  41. 41.

    Benyettou, F. et al. Potent and selective in vitro and in vivo antiproliferative effects of metal-organic trefoil knots. Chem. Sci. 10, 5884–5892 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  42. 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).

    PubMed  PubMed Central  Google Scholar 

  43. 43.

    Kitchen, J. A. Lanthanide-based self-assemblies of 2,6-pyridyldicarboxamide ligands: recent advances and applications as next-generation luminescent and magnetic materials. Coord. Chem. Rev. 340, 232–246 (2017).

    CAS  Google Scholar 

  44. 44.

    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).

    CAS  PubMed  Google Scholar 

  45. 45.

    Zhang, G. et al. Lanthanide template synthesis of trefoil knots of single handedness. J. Am. Chem. Soc. 137, 10437–10442 (2015).

    CAS  PubMed  Google Scholar 

  46. 46.

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

    CAS  PubMed  PubMed Central  Google Scholar 

  47. 47.

    Pieraccini, S., Masiero, S., Ferrarini, A. & Spada, G. P. Chirality transfer across length-scales in nematic liquid crystals: fundamentals and applications. Chem. Soc. Rev. 40, 258–271 (2011).

    CAS  PubMed  Google Scholar 

  48. 48.

    Eelkema, R. & Feringa, B. L. Macroscopic expression of the chirality of amino alcohols by a double amplification mechanism in liquid crystalline media. J. Am. Chem. Soc. 127, 13480–13481 (2005).

    CAS  PubMed  Google Scholar 

  49. 49.

    Zahn, S., Proni, G., Spada, G. P. & Canary, J. W. Supramolecular detection of metal ion binding: ligand conformational control of cholesteric induction in nematic liquid crystalline phases. Chem. Eur. J. 7, 88–93 (2001).

    CAS  PubMed  Google Scholar 

  50. 50.

    Meudtner, R. M. & Hecht, S. Helicity inversion in responsive foldamers induced by achiral halide ion guests. Angew. Chem. Int. Ed. 47, 4926–4930 (2008).

    CAS  Google Scholar 

  51. 51.

    Ryabchun, A. & Bobrovsky, A. Cholesteric liquid crystal materials for tunable diffractive optics. Adv. Opt. Mater. 6, 1800335 (2018).

    Google Scholar 

  52. 52.

    Bisoyi, H. K., Bunning, T. J. & Li, Q. Stimuli-driven control of the helical axis of self-organized soft helical superstructures. Adv. Mater. 30, 1706512 (2018).

    Google Scholar 

  53. 53.

    Orlova, T. et al. Revolving supramolecular chiral structures powered by light in nanomotor-doped liquid crystals. Nat. Nanotechnol. 13, 304–308 (2018).

    CAS  PubMed  Google Scholar 

  54. 54.

    Mathews, M. et al. Light-driven reversible handedness inversion in self-organized helical superstructures. J. Am. Chem. Soc. 132, 18361–18366 (2010).

    CAS  PubMed  Google Scholar 

  55. 55.

    De Gennes, P. G. & Prost, J. The Physics of Liquid Crystals (Oxford Univ. Press, 1997).

  56. 56.

    Kasyanyuk, D., Slyusarenko, K., West, J., Vasnetsov, M. & Reznikov, Y. Formation of liquid-crystal cholesteric pitch in the centimeter range. Phys. Rev. E 89, 022503 (2014).

    Google Scholar 

  57. 57.

    Nemati, A. et al. Chirality amplification by desymmetrization of chiral ligand-capped nanoparticles to nanorods quantified in soft condensed matter. Nat. Commun. 9, 3908 (2018).

    PubMed  PubMed Central  Google Scholar 

  58. 58.

    Ishida, Y. et al. Tunable chiral reaction media based on two-component liquid crystals: regio-, diastereo-, and enantiocontrolled photodimerization of anthracenecarboxylic acids. J. Am. Chem. Soc. 132, 17435–17446 (2010).

    CAS  PubMed  Google Scholar 

  59. 59.

    Akagi, K. et al. Helical polyacetylene synthesized with a chiral nematic reaction field. Science 282, 1683–1686 (1998).

    CAS  PubMed  Google Scholar 

  60. 60.

    Thitamadee, S., Tuchihara, K. & Hashimoto, T. Microtubule basis for left-handed helical growth in Arabidopsis. Nature 417, 193–196 (2002).

    CAS  PubMed  Google Scholar 

  61. 61.

    Gerber, P. R. On the determination of the cholesteric screw sense by the Grandjean-Cano-method. Z. Naturforsch. 35, 619–622 (1980).

    Google Scholar 

  62. 62.

    Stalder, M. & Schadt, M. Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters. Opt. Lett. 21, 1948–1950 (1996).

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We thank the Engineering and Physical Sciences Research Council (EPSRC; EP/P027067/1), the Dutch Research Council (Projectruimte, 13PR3105), the European Research Council (ERC Consolidator Grant to N.K., 772564; ERC Advanced Grant to D.A.L., 786630) and the Marie Skłodowska-Curie Actions of the European Union (Individual Postdoctoral Fellowship to F.S., EC 746993) for funding, the University of Manchester Mass Spectrometry Service Centre for high-resolution mass spectrometry and the COST Action CA17139, EUTOPIA, for networking costs. D.A.L. is a Royal Society Research Professor.

Author information




F.S. and L.P. planned and carried out the synthetic work. F.L. and A.R. designed and performed the liquid crystal experiments. D.A.L. and N.K. directed the research. All authors contributed to the analysis of the results and the writing of the manuscript.

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Correspondence to Nathalie Katsonis or David A. Leigh.

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Extended data

Extended Data Fig. 1 Effect of strand and knot doping in different liquid crystalline hosts.

a, Molecular structures of ZLI-1083 and 5CB which form liquid crystalline phases. b, Table summarizing HTP values for strand 13 and knots Λ-Lu1Λ-Lu3 in ZLI-1083 and 5CB. c, Polarized optical micrograph images (Grandjean-Cano lines and θ-cell measurements) highlighting the chiral helical organization induced by strands 13 and corresponding knots in different liquid crystalline hosts. The dashed line shows the rubbing direction of the top substrate. The red arrow shows the rotation of disclination line. Scale bars corresponds to 200 μm. d, CD spectra on ligands 1 (d) and 2 (e) in different solvent mixtures (0.025 mM, 298 K), highlighting how the chiral expressions change with decreasing polarity. Normalized for absorbance.

Extended Data Fig. 2 Probing the effect of the knotted conformation with macrocyclic strands.

a, Treatment of macrocycle 5 with Lu(OTf)3 does not produce a trefoil knot due to topological restrictions, nor does this operation invert macroscopic chirality in liquid crystals. Conditions: Lu(OTf)3, MeCN, 80 °C, 24 h. b, CD spectra of the mixture obtained upon complexation of 5 with Lu(OTf)3 (purple trace, MeCN, 298 K) overlaid with reference knot spectrum belonging to Λ-Lu1 (green trace, MeCN, 298 K). Normalized for absorbance. c, d, Polarized optical image of θ-cell filled with ZLI-1083 nematic host doped with 0.1 wt% of 5 after complexation with Lu(OTf)3 (c) and after decomplexation with tetramethylammonium fluoride (d). Notice that handedness of the chiral nematic liquid crystal is not modified. Thickness of the θ-cell is 50 µm. Scale bars correspond to 200 μm.

Supplementary information

Supplementary Information

General experimental information, synthetic procedures, Supplementary Figs. 1–27, Schemes 1–10, Spectra 1–28 and Table 1.

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Katsonis, N., Lancia, F., Leigh, D.A. et al. Knotting a molecular strand can invert macroscopic effects of chirality. Nat. Chem. 12, 939–944 (2020).

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