Like their macroscopic counterparts, such as fishing nets and woven fabrics1, molecular knots2 are ubiquitous in the microscopic world. For example, flexible polymer chains3,4 are known to form entanglements. Knots can also be observed in assorted biological systems such as DNA and proteins5,6,7. In some cases, these topologically complicated architectures are related to their biological activity5. In order to unravel the formation mechanism of these knots, as well as building a connection between functions and topology, synthesizing artificial knots in water, the medium for life, needs to be exploited. One commonly used strategy to construct such structures relies on the templation of transition metal cations, whose specific coordination geometries help to pre-organize the building blocks into the corresponding intermediates with crossing points. A variety of molecules with complex topology have been synthesized efficiently following this pathway, including trefoil knots8,9,10,11,12,13, pentafoil knots14,15,16, Borromean rings17,18, Solomon links19,20,21, Star of David catenanes22,23,24 as well as eight-crossing molecular knots25, In comparison, the number of topologically nontrivial molecules synthesized without the involvement of transition metal templates is much smaller26,27,28,29,30,31,32. Feigel et al.26 employed amino acid precursors in synthesizing a trefoil knot, whose formation is driven by hydrogen bonding between the amide building blocks. The Itami group27,28 synthesized an all-benzene trefoil knot beautifully by using a removable silicon template to drive the formation of intertwined intermediates. Even though these methods represent milestones in the synthesis of topologically non-trivial molecules, their (further study) practical use is limited owing to the tedious multistep procedures and low yields. On the other hand, instead of employing external templates, the hydrophobic effect31,32,33,34 can be used as the main driving force to fold the corresponding building blocks into the desired topologically nontrivial structures. When coupled with dynamic covalent bond formation, this approach enables the targeted trefoil knots to be obtained efficiently in one-pot reactions as the most thermodynamically favored products. This method has been demonstrated successfully by Sanders34, who took advantage of the dynamic nature35,36,37,38,39 of disulfide bond40, as well as Cougnon32, who employed hydrazone41 formation reaction, for the synthesis of trefoil knots in water.

The dynamic covalent chemistry associated with imine formation42,43,44,45, which involves aldehyde and amine precursors, is highly accessible synthetically and environmentally friendly. The labile nature of imine in the presence of water implies that it is not amenable to use in aqueous media. In the literature, it is reported that imine condensation was employed in the self-assembly of various micelles46,47,48, dynamers49, and supramolecular polymers50,51. In these cases, these polymeric structures act as the shelters for the imine bonds, protecting the latter from hydrolysis. The examples of using imine condensation in the self-assembly of small molecules with well-defined structures are much rarer. It has been shown52,53,54,55 that a self-assembled molecule, whose building blocks are connected via multiple imine bonds, can be robust enough to stay stable even in pure water. By exploiting this so-called multivalency-enhanced stability of imine and hydrophobic effect altogether, we envision that the self-assembly of topologically complex molecules in water can be achieved.

Here, we show that a trefoil knot is obtained as the predominant product by condensing three equivalents of a tetraformyl precursor and six equivalents of a chiral bisamine in water. The formation of the trefoil knot is highly enantioselective. That is, the bisamines with RR and SS stereocenters exclusively produce the left-handed (M) and right-handed (P) trefoil knots, respectively. When a racemic mixture of the bisamine linker is used in the reaction, narcissistic self-sorting occurs, yielding a pair of enantiomeric trefoil knots, each of which contains six linker units with the same stereochemical configuration. When a similar reaction is performed in an organic media (Me2SO or MeCN) instead of water, the resulting product changes to a topologically trivial macrocycle assembled from two equivalents of the tetraformyl precursor and four equivalents of the chiral bisamine. This result indicates unambiguously that hydrophobic effect is the major driving force in the formation of these trefoil knots.


Self-assembly of the trefoil knot

A dicationic tetraaldehyde precursor 12+·2Br and (1S,2S)-(+)-1,2-diaminocyclohexane ((SS)-CHDA) were combined (Fig. 1A) in a 1:2 ratio in H2O (1 mL). Here, H2O was employed instead of D2O, in order to avoid deuteration. After the mixture was heated at 80 °C for 12 h, the solution was cooled down to room temperature. CD3SOCD3 (0.33 mL) was then added to the aqueous solution in order to perform 1H NMR spectroscopic experiments. Both 1H NMR spectrum (Fig. 2C) and ESI-HRMS (Supplementary Fig. S14) were recorded. ESI-HRMS reveals that a product, namely S-26+, containing three equivalents of 12+ and six equivalents of (SS)-CHDA, was obtained as the major product. Two predominant peaks corresponding to [2 – H]5+ and [2 + Br]5+ were observed in the mass spectrum (Supplementary Fig. S14). The 1H NMR spectrum shows a set of sharp resonances (Fig. 2C), indicating that the structure of S-26+ is highly symmetrical. The assignments were confirmed by two-dimensional NMR spectroscopy (Supplementary Figs. S6S13). The resonance corresponding to the proton f in the biphenyl protons undergoes a significant upfield shift of around –2.4 ppm compared to the corresponding resonance in the precursor 12+ (Fig. 2B). This result indicates that the biphenyl unit is buried deeply within the framework of S-26+ and therefore experiences a shielded magnetic environment. Only one resonance was observed corresponding to each proton in the biphenyl units including either g or f, indicating that the biphenyl units in the framework of S-26+ undergo fast circumvolution around the –biphenyl– axis on the 1H NMR timescale. No other products in substantial amounts were observed in the 1H NMR spectrum. The 2D DOSY spectrum (Fig. 2D) demonstrates that all resonances of S-26+ have the same diffusion coefficient. By using the Stokes–Einstein equation, the hydrodynamic diameter of S-26+ was calculated to be ~2.6 nm. In the framework of S-26+, the protons e/e’ become diastereotopic in the 1H NMR spectrum, revealing the chirality of the knot. In addition, the resonances corresponding to protons including either c/c’ or h/h’ also split into two peaks. This observation results from the fact that the two imine bonds grafted on a phenyl unit adopt two different orientations.

Fig. 1: Structural formulae of a pair of enantiomeric trefoil knots R-26+·6Br, S-26+·6Br and the corresponding precursors including 12+·2Br and CHDA.
figure 1

A R-26+·6Br and S-26+·6Br were self-assembled as the predominant products, by condensing the tetraformyl precursor 12+·2Br and a chiral bisamine namely either (RR)-CHDA or (SS)-CHDA in aqueous media. DFT calculation indicated that the most thermodynamically favored products of R-26+ and S-26+ adopt intrinsic left-handed (M) and right-handed (P) configurations, respectively. B Each 1,3-bisiminophenyl unit in the 12+ residues of the trefoil knot M-R-26+ and P-S-26+ could adopt four possible conformations including endo-endo, endo-exo, exo-endo and exo-exo, defined by the positions of each imino units relative to the central proton. NOESY spectrum (Fig. 2E) indicated that among these four conformations, only endo-exo and exo-endo were observed in the trefoil knots R-26+ and S-26+. Also, because the corresponding 1H NMR spectrum of either M-R-26+ or P-S-26+ only show a set of resonances, it is reasonable to propose that within the framework of each trefoil knot either M-R-26+ or P-S-26+, all of the six 1,3-bisiminophenyl units adopt the same conformation. DFT calculation indicated that the most thermodynamically favored conformations of M-R-26+ and P-S-26+ are (endo-exo)6 and (exo-endo)6, which are denoted as A and , respectively.

Fig. 2: 1H NMR spectroscopic characterization of S-26+·6Br.
figure 2

A Structural formulae of S-26+·6Br. The partial 1H NMR spectra (600 MHz, 298 K) of B the precursor 12+·2Br recorded in CD3SOCD3 and C S-26+·6Br recorded in H2O/CD3SOCD3 (v/v, 3:1). The sample used in C was obtained by heating a solution of 12+·2Br (3 mM) and (SS)-CHDA (6 mM) in H2O (1 mL) at 80 °C for 12 h, followed by adding CD3SOCD3 (0.33 mL) into the solution. D 2D DOSY spectrum (298 K, D2O/CD3SOCD3 (v/v, 3:1)) of S-26+·6Br, which was prepared in the same procedure as that used in C, using D2O instead of H2O. The protons “e” and “a” underwent deuteration and the corresponding resonances disappeared. E The partial 2D NOESY spectrum (298 K, D2O/CD3SOCD3 (v/v, 1:1)) of S-26+·6Br. NOE signals were clearly observed between the biphenyl protons (f and g) and those in either the pyridinium or the phthalaldehyde residues (including c, c’, b and h’), which are encircled with red rectangles. NOE signals were also observed between the protons c’ and h’, as well as h and d, indicating the two imine units orientate in exo and endo manners respectively with respect to the central proton d.

Two-dimensional NMR spectroscopic characterization

In order to shed more light on the structure of S-26+, its NOESY spectrum (Fig. 2E) was recorded. NOE signals were observed between the biphenyl protons (namely g and f), and the pyridinium or the phthalaldehyde protons including c, c’, b, and h’. The latter group of protons are believed to be relatively remote from the central biphenyl units. The appearance of NOE signal thus confirms that within the framework of S-26+, the building blocks form an intertwined architecture and have close contacts. NOE signals were also observed between the protons c’ and h’, as well as h and d. These observations indicate that the two imine units in each phthalaldehyde residue have two different orientations relative to the central proton d—namely endo and exo. See the molecular formula in Fig. 2E. Given that the 1H NMR spectrum of S-26+ exhibits only one set of resonances, we propose that the six bisimino residues in the framework of S-26+ have the same conformation, either (endo-exo)6 or (exo-endo)6, which is denoted as A or (Fig. 1B), respectively.

Self-assembly in organic media

It is noteworthy that water is indispensable in the self-assembly of S-26+, indicating that hydrophobic effect is the major driving force of the knot formation. Condensing 12+·2Br and (SS)-CHDA in D2O produces the same product—namely S-26+—as that occurs in the water-organic mixture namely H2O/CD3SOCD3 (v/v, 3:1). The only difference is that, in D2O, the relatively more acidic protons a and e/e’ undergo deuteration, which leads to disappearance of the corresponding resonances in the 1H NMR spectrum (Supplementary Fig. S24a). When the solvent was switched to purely organic media, the self-assembly yielded a different product. That is, when a 1:2 mixture of 12+·2Br (2 mM) and (SS)-CHDA (4 mM) were combined in CD3SOCD3, a macrocycle S-34+·4Br was obtained as the major product containing two tetraformyl and four bisamino precursors, as indicated by the corresponding 1H NMR spectrum (Fig. 3) and ESI-HRMS (Supplementary Fig. S22). When 12+·2PF6 was used for the self-assembly in CD3CN, a macrocycle S-34+·4PF6 was obtained. In contrast with the trefoil knot S-26+ that was self-assembled as the only observable product in water, the formation of S-34+ was accompanied with a library of larger oligomeric or polymeric byproducts, which were observed as the minor products in the corresponding 1H NMR spectra recorded in both CD3SOCD3 and CD3CN. Performing counterion exchange to S-34+·4PF6 yielded S-34+·4Br in a 47% yield. See details in the SI. Once dissolved in an aqueous phase, 1H NMR spectroscopic studies (Supplementary Fig. S31) indicated that the macrocycle S-34+ underwent transformation gradually into S-26+, driven by hydrophobic effect. At room temperature, it took a few months to finish the transformation, while at 80 °C, the structural change was nearly complete within no longer than 12 h. We recorded the NOESY spectrum (Supplementary Fig. S21) of S-34+·4Br, which was in sharp contrast to that of S-26+·6Br. Firstly, no NOE signals were observed between the protons in the biphenyl units and those protons in either the pyridinium or phthalaldehyde residues. This observation is consistent with our hypothesis that, unlike the structure of S-26+, S-34+ does not have an intertwined architecture. Secondly, a NOE signal was observed between two imine protons h and h’, which was not observed in the case of the trefoil knot. This observation indicates that both of the two imine bonds in a phthalaldehyde residue of S-34+ orientate in an exo-exo manner (Fig. 1B), so that a proton h is relatively close to a proton h’ in an adjacent phthalaldehyde residue. See the red two-headed arrow in Fig. 3.

Fig. 3: Partial 1H NMR spectra (600 MHz, 298 K, CD3SOCD3) of S-34+·4Br.
figure 3

S-34+·4Br was obtained by heating a 1:2 mixture of 12+·2Br (2 mM) and (SS)-CHDA (4 mM) at 80 °C for 12 h in CD3SOCD3.

Chirality of the trefoil knot

The enantiomer of S-26+·6Br, namely R-26+·6Br, was also self-assembled successfully by condensing a 1:2 mixture of 12+·2Br and (RR)-CHDA, which is the enantiomer of (SS)-CHDA, in either D2O or H2O. When a racemic mixture of bisamino precursors was used in self-assembly, narcissistic self-sorting occurred. That is, a 1:1:1 mixture of 12+·2Br, (RR)-CHDA, and (SS)-CHDA in an aqueous media produced a racemic mixture of S-26+·6Br and R-26+·6Br, whose 1H NMR spectrum is identical to each of the individual chiral trefoil knots namely either S-26+·6Br or R-26+·6Br. Such narcissistic self-sorting behavior was also observed by other scientists such as Sanders34. Replacing CHDA with a more flexible diamino linker, namely ethylenediamine, led to the failure of trefoil knot formation. This experiment indicated that restricted gauche conformation of the two amino units in CHDA is of importance in suppressing the entropy loss in knot formation. The importance of gauche effect in determining the distribution of self-assembly products was also reported by other scientists such as Cougnon55. The circular dichroism (CD) spectra of S-26+·6Br, R-26+·6Br, as well as the racemic mixture were recorded (Fig. 4). S-26+·6Br (red trace) and R-26+·6Br (black trace) have mirror-like CD signals, while the racemic mixture (blue trace) of S-26+·6Br and R-26+·6Br is CD-silent. It is noteworthy that the approach of using a building block with stereo chiral centers to dictate the handedness of a topological complex molecule was also reported by other scientist25,34, including Sauvage56.

Fig. 4: CD spectra of the product (0.04 mM) S-26+·6Br (red trace), R-26+·6Br (black trace), and their racemic mixture (blue trace) recorded in water.
figure 4

The racemic cage mixture was self-assembled by condensing a racemic CHDA and the tetraaldehyde 12+·2Br in water. Insert: the CD spectra of S-26+·6Br based on experiment (red trace), and theoretical calculated structure (yellow trace) which was obtained based on the optimized structure of the knot P--S-26+ shown in Fig. 5. P--S-26+ was considered as the most thermodynamically favored isomer among the four possible conformational diastereomers.

Theoretical calculations

Several trails to obtain diffraction grade single crystals of S-26+·6Br and R-26+·6Br as well as the macrocycle S-34+·4PF6 have so far proved unsuccessful. Hence, density functional theory (DFT) calculation (see details in the SI) was used to shed more light on the architectures of these trefoil knots. Theoretically, the trefoil knot 26+ might have a number of diastereoisomers due to three asymmetrical factors. Firstly, the CHDA linkers could be either (SS) or (RR), depending on the bisamino precursor used in self-assembly. Secondly, the framework of a trefoil knot could be intrinsically right-handed (P) or left-handed (M), depending on the intertwining direction of the building blocks. Thirdly, as mentioned before, NOE signals indicated that each of the six phthalaldehyde residues in the trefoil knot should have the same conformation, namely either (endo-exo)6 or (exo-endo)6, which is denoted as A or (Fig. 1B), respectively. The implication is that, the trefoil S-26+ is supposed to have four diastereoisomers, including P--S-26+, M--S-26+, M-A-S-26+, and P-A-S-26+, whose enantiomers are M-A-R-26+, P-A-R-26+, P--R-26+, and M--R-26+, respectively. DFT calculations (Fig. 5) indicated that the relative free energy is 0, 17.6, 25.6, and 39.4 kcal/mol in the case of P--S-26+/M-A-R-26+, M--S-26+/P-A-R-26+, M-A-S-26+/P--R-26+, and P-A-S-26+/M--R-26+, respectively, given that enantiomers should be thermodynamically equal in achiral solvent. The implication is that P--S-26+/M-A-R-26+ with the lowest stabilization energy are the most favored products among the four diastereoisomers. Based on theoretically optimized structures of all four diastereoisomers namely P--S-26+, P--R-26+, P-A-R-26+, and P-A-S-26+, we were able to calculate their electronic CD spectra (Supplementary Fig. S33d). However, only the spectrum of P--S-26+ (Fig. 4, insert, yellow trace) matched well with the experimental one (Fig. 4, red trace), supporting our hypothesis that among the four isomers, P--S-26+ is self-assembled selectively as the most thermodynamically favored product. The diameter of the optimized structure of P--S-26+ is measured to be about 26.4 Å, which is consistent with the experimental value (i.e., 26 Å) from DOSY experiment.

Fig. 5: Optimized structures of different possible conformational diastereomers of S-26+ (top) and R-26+ (bottom) with the relative free energies.
figure 5

The calculation was performed by using DFT calculations at the level of BP86-D3 functional and 6-311G(d) basis set. The result indicates that P--S-26+ and its enantiomer namely M-A-S-26+ are the most favored products among the diastereomers of R-26+ and S-26+.


By taking advantage of the marriage of hydrophobic driving force and the dynamic behavior of imine formation, a pair of enantiomers of purely covalent chiral trefoil knots was self-assembled as the predominant product in a one-pot manner in aqueous media. Thanks to multivalency, the trefoil knot containing 12 imine bonds is robust enough in both water and water-organic mixture (a 3:1 mixture of water and CD3SOCD3). In organic media including either CD3SOCD3 or CD3CN, self-assembly went to another pathway—namely that a topologically trivial macrocyclic compound was self-assembled. This result indicated unambiguously that hydrophobic effect is the major driving force of the formation of trefoil knot. The intrinsic handedness of the trefoil knot is dictated precisely by the stereo chirality of the bisamino precursors, namely that the biamines with SS or RR stereo-centers led to exclusively the formation of trefoil knots with P or M handedness, respectively. The success in self-assembly of trefoil knot with controllable handedness improved our fundamental understanding on how nature uses small chiral building blocks to create topologically complex architectures with amplified chirality. This work further supports that imine-based dynamic covalent chemistry can be performed in the presence of water, which would encourage chemists to self-assemble another topologically complex molecule in aqueous media. The water compatibility of this trefoil knot also encourages chemists to explore its potential functions in biological media.


Self-assembly of S-26+·6Br

A 1:2 mixture of 12+·2Br (1.5 mg, 0.002 mmol) and (1S,2S)-(+)-1,2-diaminocyclohexane (0.46 mg, 0.004 mmol) was dissolved in D2O (0.6 mL). The corresponding reaction mixture was heated at 80 °C for 12 h. S-26+ was self-assembled as the only observable product in the corresponding 1H NMR spectrum, without further manipulation. The attempts to isolate the trefoil knot S-26+ from its aqueous solution via counterion exchange proved unsuccessful, probably because imine bonds underwent degradation during these processes. We also tried to fix the architecture of the trefoil knot by means of imine reduction. Such trials were not successful either, because under such conditions, the cationic pyridinium building blocks became labile.

Synthesis of S-34+·4Br

A 1:2 mixture of 12+·2PF6 (30 mg, 0.034 mmol) and (1S,2S)-(+)-1,2-diaminocyclohexane (7.8 mg, 0.068 mmol) was dissolved in CH3CN (18 mL). The corresponding reaction mixture was heated at 70 °C for 12 h. After cooling down the reaction solution to room temperature, tetrabutylammonium bromide (TBA+·Br) (100 mg) was then added to the solution, after which a white solid was collected by filtration and washed with CH2Cl2 three times, yielding S-34+·4Br (30 mg, 47%) as a white solid. It is noteworthy that raising the concentrations of the precursors namely 12+·2PF6 and (1S,2S)-(+)-1,2-diaminocyclohexane would lead to the formation of oligomeric and polymeric byproducts.

Structural characterization of S-26+·6Br and S-34+·4Br

Nuclear magnetic resonance (NMR) spectra were recorded at ambient temperature using Agilent DD2 600 spectrometers, with working frequencies of 600 and 150 for 1H and 13C respectively. Chemical shifts are reported in ppm relative to the residual internal non-deuterated solvent signals (for proton NMR, D2O: δ = 4.70 ppm, CD3SOCD3: δ = 2.50 ppm). High-resolution mass spectra were recorded on a Fourier transform ion cyclotron resonance mass spectrometry. CD spectra were recorded on a Circular Dichroism Spectrometer (Chirascan V100, Applied Photophysics Ltd).

Theoretical calculations

The trefoil knots were optimized by using the DFT at the BP86-D3/6-311G(d) level with the Gaussian 16 package57. The solvent effect of water was included with the polarizable continuum model using solvent-accessible surface. The UV–Vis and electronic CD spectra for the optimized geometries were predicted by the time-dependent DFT at the wB97XD/6-311G(d) level with 500 states by the Gaussian 16 package57. The solvent effect was also considered. Both the UV–Vis and CD spectra were broadened using Gaussian functions by Multiwfn58. The full width at half maximum was set as 0.8 eV.