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Stereoselective synthesis of a composite knot with nine crossings


The simultaneous synthesis of a molecular nine-crossing composite knot that contains three trefoil tangles of the same handedness and a \(9_7^3\) link (a type of cyclic [3]catenane topologically constrained to always have at least three twists within the links) is reported. Both compounds contain high degrees of topological writhe (w= 9), a structural feature of supercoiled DNA. The entwined products are generated from the cyclization of a hexameric Fe(ii) circular helicate by ring-closing olefin metathesis, with the mixture of topological isomers formed as a result of different ligand connectivity patterns. The metal-coordinated composite knot was isolated by crystallization, the topology unambiguously proven by tandem mass spectrometry, with X-ray crystallography confirming that the 324-atom loop crosses itself nine times with matching handedness (all Δ or all Λ) at every metal centre within each molecule. Controlling the connectivity of the ligand end groups on circular metal helicate scaffolds provides an effective synthetic strategy for the stereoselective synthesis of composite knots and other complex molecular topologies.


Molecular knots1,2,3,4,5 are found in DNA6,7,8 and proteins3 and they also form spontaneously in polymer chains of sufficient length and flexibility9. Such entanglements affect molecular size and shape10, strength and stability3,11, resistance to mechanical stretching12,13 and behaviour under spatial confinement14, although much of the understanding as to how and why remains unclear. Composite knots consist of several ring-opened prime knots joined together and then ring closed, analogous to composite numbers being the product of smaller prime factors15. Simulations indicate that composite knots are among the most common knot types in globular polymers16 and long DNA chains17. Although synthetic routes to several small-molecule prime knots have been developed18,19,20,21,22,23,24,25,26, or discovered serendipitously27,28,29,30,31, the synthesis of discrete composite knots is complicated by different knots being produced depending on whether the prime knots being combined are of the same or opposing handedness1,4. The only attempt at small-molecule composite knot synthesis reported to date proceeded without stereochemical control, and the final step (dimerization of a linear Cu(i) helicate) generated an inseparable mixture of granny—itself a mixture of (R,R) and (S,S) knots—and square (R,S) knot topoisomers in just 2.5% yield32.

Circular metal helicates can be used to position ligand strands so as to simultaneously create the multiple crossings necessary for various knots and links4,22,24,25,26,33,34,35. The stereochemistry at all the metal ions within a circular helicate is the same, all Δ or all Λ, which means that using such scaffolds to assemble composite knots overcomes the stereochemical issues of connecting prime knots of assorted handedness. The number of repeat units of the helicate (trimer, tetramer, pentamer, hexamer and so on) affects the topology of the product4, but also switching which ligand building block is connected to which can change both the number of crossings and the ways that the strands traverse each other (for example, alternating over–under or non-alternating crossings). A Star of David [2]catenane (two rings triply entwined to form six crossings) was previously prepared35 by joining the ends of ligands bound to the same metal ions in a hexameric circular helicate36. A ligand design that favoured the connection of strands coordinated to neighbouring metal ions on the same face of a hexameric circular helicate should stereoselectively generate a nine-crossing composite +31#+31#+31 knot (Fig. 1 and its legend give an explanation of knot nomenclature4). However, as each strand end is equidistant to those of the two closest ligands on the same face of the circular helicate, another product with a different topology will also form—when the strand ends on the two faces of the circular helicate join in the same direction a composite knot is produced; when the strand ends join in opposite directions on the two faces a \(9_7^3\) link, which is a cyclic [3]catenane with twisted rings, is generated (Fig. 1).

Fig. 1: Topologies that result from joining ligand strands with the terminal binding sites coordinated to neighbouring metal ions in a hexameric circular helicate.

Only the Δ6 circular helicate is shown, which results in products with +9 topological writhe. The corresponding topologies with w= –9 are formed from the enantiomeric helicate (Λ6 Fe(ii) centres). In the composite knot nomenclature (+31#+31#+31), 31 indicates a trefoil tangle4 (31 is the Alexander–Briggs notation for a trefoil knot48 in which the 3 refers to the number of crossings), the + sign for all three tangles means they are all of the same handedness and the # symbol depicts connected tangles, with the first and last joined to form a closed loop (Supplementary Fig. 13). In the \(9_7^3\) link nomenclature, 9 refers to the number of crossings in the reduced representation (shown), 3 is the number of components and 7 indicates that it is the 7th link with nine crossings and three components listed in the Rolfsen link table (link L9a45 in the Thistlethwaite link table (Supplementary Fig. 16))49. Other complex topologies synthesized through M6L6 complexes include a cyclic [3]catenane34, Star of David catenane35, Borromean rings50 and extended Borromean networks51.

Results and discussion

Molecular modelling indicated that ligand strand 1, which features an angled extension to a tris(2,2′-bipyridine) ligand used to assemble a Star of David catenane35, has the conformational freedom only to be joined to others in the same helicate with the connectivity shown in Fig. 1. Ligand 1 was prepared in five steps from commercially available building blocks (Supplementary Section 3). Heating 1 at 130 °C in dimethylformamide with an equimolar amount of Fe(BF4)2·6H2O for 24 hours followed by precipitation with methanolic KPF6 resulted in a reddish-purple solid characteristic of low-spin Fe(ii) tris-bipyridine complexes (Fig. 2, steps (1) and (2)). The 1H NMR spectrum (CD3CN, 298 K (Fig. 3b)) of the product shows all the ligands to be in equivalent environments. Together with the diastereotopic splitting of protons Hd and He, this indicated the structure was a circular helicate, and the molecular mass determined by electrospray ionization–mass spectrometry (ESI–MS) (Supplementary Figs. 1 and 2) confirmed it to be the hexamer [Fe616](PF6)12.

Fig. 2: The 12 component (6 × ligand 1; 6 × Fe2+) assembly of the intermediate hexameric circular helicate [Fe616](PF6)12 and the synthesis of the +31#+31#+31 composite knot 2 and \({\mathbf{9}}_{\mathbf{7}}^{\mathbf{3}}\) link 3.

Reaction conditions: (1) 1 (1.0 equiv.), Fe(BF4)2·6H2O (1.0 equiv.), N,N-dimethylformamide, 130 °C, 24 h; (2) KPF6, MeOH, 90% yield (over two steps); (3) Hoveyda–Grubbs second-generation catalyst (17 mol% per ligand), MeNO2/1,2-dichloroethane 1:1, 60 °C, 24 h; (4) KPF6, MeOH, 92% yield (over two steps; >98% per internal olefin formed); (5) NaOH(aq) (1 M)/MeCN 1:1, 80 °C, 15 min, 35% yield.

Fig. 3: 1H NMR spectra (600 MHz, 298 K) of molecular knot 2, link 3, building block 1 and their coordination complexes.

a, Ligand strand 1 (solvent CDCl3). b, Hexameric circular helicate [Fe616](PF6)12 (solvent CD3CN). c, Mixture of composite knot complex [Fe62](PF6)12 and \(9_7^3\) link complex [Fe63](PF6)12 (solvent CD3CN). d, Composite knot complex [Fe62](PF6)12 (solvent CD3CN). e, Mixture of metal-free composite knot 2 and \(9_7^3\) link 3 (solvent CDCl3). The lettering corresponds to the proton labelling in Fig. 2.

Hexameric circular helicate [Fe616](PF6)12 was subjected to ring-closing metathesis of the 12 olefin end groups in nitromethane/1,2-dichloroethane (1:1) at 60 °C using the Hoveyda–Grubbs second-generation catalyst37. After 24 hours, the reaction was quenched and the products [Fe62](PF6)12 and [Fe63](PF6)12 precipitated with methanolic KPF6 (Fig. 2, steps 3 and 4). The 1H NMR spectrum of the products is broad (Fig. 3c), indicative of the generation of some paramagnetic high-spin Fe(ii) centres during the ring-closing step38, although the loss of the terminal alkene protons Hs is apparent (and confirmed by ESI–MS (Supplementary Figs. 3 and 4)).

Demetallation of the topoisomeric mixture of knot [Fe62](PF6)12 and cyclic [3]catenane [Fe63](PF6)12 was achieved by treatment of an acetonitrile solution with NaOH (1 M) at 80 °C for 15 minutes (Fig. 2, step 5), and the resulting metal-free organic molecules 2 and 3 were separated from minor by-products by size-exclusion chromatography. The molecular mass of the topoisomers was confirmed by ESI–MS of the mixture of 2 and 3 (Fig. 4a). The 1H NMR spectrum (CDCl3, 298 K (Fig. 3e)) of the mixture of 2 and 3 has a single set of sharp signals, which indicates that very similar environments are experienced by the protons, and a rapid reptation (the thermal motion of long, entangled, polymer chains39) of the strands occurs in both topoisomers. In diffusion-ordered NMR spectroscopy experiments, all the protons possessed the same diffusion coefficient, D, of 2.1(2) 10–10 m2 s–1 (Supplementary Fig. 12).

Fig. 4: ESI–MS and MS/MS experiments on molecular knot 2 and link 3.

a, The demetallated mixture of composite knot 2 and [3]catenane 3 with formic acid added to generate multiply-protonated ions. b, Tandem mass spectrometry of the [M + 4H]4+ peak (m/z = 1,454.50) from the demetallated mixture of composite knot 2 and [3]catenane 3, which demonstrates the formation of a macrocycle (m/z = 969.42 and m/z = 1,938.92) and [2]catenane (m/z = 1,293.17 and m/z = 1,938.92) from the fragmentation of [3]catenane 3 and the non-interlocked thread from the fragmentation of the knotted structure 2 (m/z = 1,434.25). c, The demetallated crystals of composite knot 2 with formic acid added to generate multiply protonated ions; the mass spectrum is similar to that arising from the mixture in a. d, In the tandem mass spectrometry of the [M + 4H]4+ peak (m/z = 1,454.50) from the demetallated composite knot 2 in c, only the non-interlocked thread from the fragmentation of knotted structure 2 was detected (m/z = 1,434.33). The charges of the ion(s) associated with each peak were determined from isotope spacing.

Evidence for the presence of both topoisomers in the demetallated product mixture was obtained by tandem mass spectrometry experiments (Fig. 4a,b). The [M + 4H]4+ ion at m/z 1,454.50 was activated by collision-induced dissociation, which resulted in multiply charged ions that originate from two different species. The signal at m/z 1,434.25 displays a small loss of mass from the intact ion consistent (Supplementary Scheme 3) with scission and subsequent unravelling of the single continuous strand of knot 2 (Fig. 4b and Supplementary Fig. 10). This m/z value cannot result from fragmentation of the cyclic [3]catenane as the cleavage of any macrocycle leads to dethreading and the resulting loss of mass. However, the other two peaks at m/z 969.42 and 1,293.17 correspond to one-third and two-thirds, respectively, of the original ion mass (Fig. 4b and Supplementary Fig. 10). Fragmentation of the \(9_7^3\) link (3) breaks one or two macrocycles, which causes dethreading to form a single ring or a [2]catenane that remains charged through protonation. This is related to the process commonly observed in electron ionization mass spectrometry in which fragmentation of a catenane characteristically gives a charged linear fragment with a mass that corresponds to one of the originally linked components40.

Attempts to separate 2 and 3 using size-exclusion chromatography, gel permeation chromatography and HPLC (both standard and chiral) were unsuccessful, presumably as a consequence of the similarity of the component environments within the topoisomers. However, [Fe62](PF6)12 could be separated from the mixture of the metal complexes of the knot and link by crystallization. Crystals of [Fe62](PF6)12 were isolated from slow diffusion of isopropanol vapour into a solution of [Fe62](PF6)12/[Fe63](PF6)12 in acetonitrile. The 1H NMR spectrum of the redissolved crystals (Fig. 3d and Supplementary Fig. 8) is much sharper than that of the 2/3 mixture (Fig. 3c) and shows no signs of high-spin Fe(ii) ions. The ESI–MS of the demetallated crystals gives a spectrum (Fig. 4c) similar to that of the 2/3 mixture (Fig. 4a). However, the tandem mass spectrum (Fig. 4d) shows fragmentation to a single m/z value, 1,434.33, that can only arise from knot 2, which demonstrates that only the composite knot is present in the isolated crystals of [Fe62](PF6)12.

Despite the collection of high-quality data up to a 1.8 Å resolution with synchrotron radiation, the X-ray diffraction data on single crystals of [Fe62](PF6)12 resembled those of proteins rather than conventional metal complexes41,42,43. A structure solution was obtained using a rigid body approach, in which parts of the molecule are geometrically restrained in a manner analogous to protein crystallography (see Supporting Information, Section 7). A similar approach has been used by Fujita et al.41,42 to overcome similar problems encountered with very large metallosupramolecular cages. The refined structure of [Fe62](PF6)12 shows the topology of the composite knot (Fig. 5). The knot has nine alternating crossings in a single strand 324 atoms long. The sites at which the ligands were joined by ring-closing metathesis are offset from each other across opposite sides of the hexagon defined by the Fe(ii) cations, which results in six large loops (Fig. 5b) that make up the three trefoil tangles. Two PF6 anions are located in the central cavity, stabilized by CHa…F interactions between the fluorine atoms and the 12 electron-poor aromatic CHa hydrogens. Within each circular helicate, every Fe(ii) centre has the same coordination stereochemistry (Δ or Λ) and each trefoil tangle has the same handedness, to form a +31#+31#+31 (or –31#–31#–31) composite knot of topological writhe (w) = 9 (Supplementary Fig. 13).

Fig. 5: A 1.8 Å resolution X-ray crystal structure of the +31#+31#+31 composite knot [Fe62](PF6)12, in which parts of the molecule are well resolved (for example, the metal ions and much of the circular helicate), whereas others (in particular the flexible linker chains) needed to be modelled to fit the electron density map in a manner analogous to protein crystallography.

a, Viewed perpendicular to the plane of the six Fe(ii) ions. b, Side view in the plane of the six Fe(ii) ions. C, light grey (turquoise in one repeat unit of the knot); N, blue; O, red; Fe, purple; P, orange; F, yellow. The Fe(ii) centres in each molecular knot have the same coordination stereochemistry (Δ or Λ). Both enantiomers are present in each unit cell; the all-Δ enantiomer is shown here and corresponds to a writhe value of +9. The X-ray data are at a resolution (1.8 Å) that does not allow bond lengths or angles to be determined, but provides further confirmation of the knot topology (Supplementary Fig. 14).

Writhe (w) is the total number of positive crossings minus the total number of negative crossings in a particular representation of a knot44. In the reduced representation of the \(9_7^3\) link (Figs. 1 and 2), none of the macrocycles can untwist from a figure-of-eight conformation to a circle without an extra twist being added to one of the other macrocycles. Circular DNA forms figure-of-eight structures under torsional stress7. Writhe also determines how supercoiled DNA unwinds7,8, and which knotted topologies are adopted by viral DNA45 that, in turn, influence the rate the virus can eject DNA from its capsid46. The study of writhe in small-molecule systems may shed light on the fundamental nature of such molecular processes and, in principle, also provide a mechanism for the transfer of conformational information across long distances other than through a continuous covalent framework47.


Large, monodispersed molecular rings are difficult to make. Composite knot 2 is a 324-membered ring, with the additional complexity of having nine alternating crossings. The synthetic design uses an octahedral metal–ion helicate formation to entwine six ligand strands, short linkers between the chelating sites to favour cyclic double helicates over linear triple helicates, the counterion of the metal salt to determine the size of the helicate formed22,35,36 and the length and constitution of the extended ligand to conformationally restrict the strand ends so that they can only react with groups at the termini of ligands bound to neighbouring metal ions. This level of design allows the stereoselective two-step synthesis of the composite knot in a 41% yield, with a similar amount of the corresponding isomeric link formed. The +31#+31#+31 composite knot is the size of a small protein (the chain length is the same as a 108-residue peptide). By way of comparison, other molecular knots have been synthesized with strand lengths of 76–102 atoms (trefoil)18,19,20,21,26,27,28,29,30, 112 atoms (figure-eight)31, 160–190 atoms (pentafoil)22,24 and 192 atoms (819 knot)25. Both composite knot 2 and the isomeric \(9_7^3\) link 3 have a topological writhe value (w) of 9, a structural characteristic yet to be explored with small-molecule systems. The figure-of-eight conformation that each macrocycle is forced to adopt in the reduced representation of the \(9_7^3\) link is analogous to the shape assumed by circular DNA under torsional stress7.

Data availability

Crystallographic data are deposited at the Cambridge Crystallographic Data Centre (CCDC) as CCDC 1565130. The other 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 ( with

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We thank the Engineering and Physical Sciences Research Council (EP/P027067/1) and the European Research Council (Advanced Grant no. 339019) for funding, the Diamond Light Source (UK) for synchrotron beam time on I19 (XR029), the University of Manchester for a President’s Doctoral Scholar Award (to L.Z.) and the Finnish Cultural Foundation for a postdoctoral grant (to P.J.). D.A.L. is a Royal Society Research Professor.

Author information

L.Z., A.J.S., A.L.N., J.-F.L. and P.J. carried out the synthesis and characterization studies. I.J.V.-Y. solved the crystal structure. D.A.L. directed the research. All the authors contributed to the analysis of the results and the writing of the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to David A. Leigh.

Supplementary information

Supplementary information

Experimental methods, synthetic procedures and the characterization details for all new compounds, including the X-ray experimental details

Crystallographic data

CIF for compound [Fe62](PF6)12; CCDC reference: 1565130

Supplementary Video

A video file of the rotating X-ray crystal structure of the composite knot

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