Effects of knot tightness at the molecular level Liang Zhanga,b, Jean-François Lemonnierb, Angela Acocellac, Matteo Calvaresic, Francesco Zerbettoc,1, and David A. Leigha,b,1 aSchool of Chemistry and Molecular Engineering, East China Normal University, 200062 Shanghai, China; bSchool of Chemistry, University of Manchester, M13 9PL Manchester, United Kingdom; and cDipartimento di Chimica “G. Ciamician”, Università di Bologna, 40126 Bologna, Italy Edited by Michael L. Klein, Institute of Computational Molecular Science, Temple University, Philadelphia, PA 19122, and approved December 18, 2018 (received for review September 8, 2018) Three 819 knots in closed-loop strands of different lengths (∼20, by analogy to that previously used to prepare 1 (29). Treatment of 23, and 26 nm) were used to experimentally assess the conse- the ligands with equimolar amounts of FeCl2, followed by ring- quences of knot tightness at the molecular level. Through the closing metathesis (30), gave the corresponding 819 knot com- 1 use of H NMR, diffusion-ordered spectroscopy (DOSY), circular plexes [Fe4Knot](PF6)8 (Knot = 1–3; Fig. 1) which were isolated dichroism (CD), collision-induced dissociation mass spectrometry and characterized by electrospray ionization mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different- and 1H NMR spectroscopy (SI Appendix, Figs. S1–S8). The 1H sized knots, we find that the structure, dynamics, and reactivity of NMR spectra of the three knotted complexes are essentially su- the molecular chains are dramatically affected by the tightness of perimposable (SI Appendix, Figs. S14 and S15), other than the the knotting. The tautness of entanglement causes differences in alkyl region due to the differences in chain length, indicating that conformation, enhances the expression of topological chirality, metal coordination of the knotted ligands holds the three com- weakens covalent bonds, inhibits decomplexation events, and plexes in similar conformations. Subjecting the metallated knots to changes absorption properties. Understanding the effects of tight- a 1:1 MeCN/NaOHaq (1 M) solution at 80 °C, followed by size- ening nanoscale knots may usefully inform the design of knotted exclusion chromatography, afforded the corresponding demetal- and entangled molecular materials. lated knots 1–3 with different degrees of tightness (Fig. 1 and SI Appendix, Figs. S9–S12). The BCRs (11) of 1–3 are 24, 27, and 30, molecular knots | supramolecular chemistry | chemical topology respectively. The diffusion coefficients (D)valuesofthethree knots were measured by diffusion-ordered spectroscopy experi- CHEMISTRY nots are found in some proteins (1), linear and circular DNA ments; the relative effective hydrated radius of the knots increases K(2), and polymers of sufficient length and flexibility (3). The by 8% from 1 to 2 and 16% from 2 to 3 in line with the 12.5% and strand entanglements affect molecular size (4), stability (5), and 25% increase in the length of the flexible regions, respectively (SI various mechanical properties (6–8), although much of the un- Appendix, Figs. S19–S21). The optimized reaction times used in 1 derstanding as to how and why remains unclear. To date the the demetallation process were 15 min for [Fe4 ](PF6)8 (resulting 1 2 2 influence of various structural traits, such as the number of knot in a 35% yield of ), 10 min for [Fe4 ](PF6)8 (43% yield of ), and 3 3 crossings (9), writhe (10), backbone crossing ratio (BCR) (11), less than 5 min for [Fe4 ](PF6)8 (65% yield of ). The differences and the global radius of curvature (12), on properties has mainly in reactivity (yield and reaction time) can be rationalized by loos- been studied by simulations (13–16) rather than experiment (17, ening of the knot giving the strand significantly greater flexibility, 18). Knot tightness (19–21) is a particularly easy-to-appreciate particularly after displacement of the first iron cation. This makes it characteristic, familiar from our everyday experience in the easier for hydroxyl ions to access the remaining iron centers (31), macroscopic world, that may also have significant effects at the decreasing the amount of the poorly soluble iron bipyridine hy- molecular level (4, 22–27). Long polymers are predicted to have droxide by-products (32) that reduce the yield of metal-free knot. knotted regions that are both frequent and tight (25). The tight- ness of knotting is implicated in variations in the thermostability Significance of entangled proteins (26) and is thought to have consequences for tensile strength (27). However, it is difficult to assess intrinsic Knots and entanglements occur in proteins, DNA, and synthetic effects of knotting by comparing structures with rather different polymers and are being used to form the basis of interwoven chemical compositions. Monodispersed synthetic molecular knots nanomaterials. Understanding how the tautness of molecular are ideal models through which to evaluate the influence of knot entanglements affects properties is crucial for the future de- tightening on physical and chemical properties (17, 18). Here we sign of knotted, woven, and entangled molecules and mate- report experimentally determined property differences in a set of rials. However, while there are many theoretical studies on three knotted molecules that differ only in the length of flexible such systems there are very few experimental studies. Here we regions (alkyl chains) that separate more rigid sections (com- investigate the influence of knot tightness in a range of posed of aromatic rings) of the strand. Using a braiding strategy physical and chemical properties for three knots tied in 20-, 23-, previously used to assemble (28) an extremely tightly knotted and 26-nm closed-loop strands. We find that the tightness of 1 192-atom loop 819 knot ( ) (29), the alkene-terminated chains the molecular knots significantly affects reactivity, conforma- used to close the knotted structure were extended without tion, and the expression of chirality. otherwise altering the outcome of the knot synthesis (Fig. 1). This resulted in a set of three 819 molecular knots that differ Author contributions: L.Z., F.Z., and D.A.L. designed research; L.Z., J.-F.L., A.A., M.C., and only in the length of the alkyl chains in the loop (1 is 192 atoms F.Z. performed research; A.A., M.C., and F.Z. analyzed data; and L.Z., J.-F.L., A.A., M.C., long, 2 is 216 atoms long, and 3 is 240 atoms long, a 25% vari- F.Z., and D.A.L. wrote the paper. ation in strand length involving only the flexible regions). We The authors declare no conflict of interest. 1 probed the properties of the different-sized knots by HNMR This article is a PNAS Direct Submission. spectrometry, mass spectrometry, UV spectroscopy, and circu- Published under the PNAS license. lar dichroism, and used computational studies to help explain 1To whom correspondence may be addressed. Email: [email protected] or the role the increasing tightness of knotting plays in altering [email protected]. physical and chemical behavior. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Ligand strands L1–L3 bearing Tris(2,2′-bipyridine) motifs with 1073/pnas.1815570116/-/DCSupplemental. different lengths of alkene-terminated alkyl chains were prepared www.pnas.org/cgi/doi/10.1073/pnas.1815570116 PNAS Latest Articles | 1of6 Downloaded by guest on October 1, 2021 Fig. 1. Synthesis of [Fe4Knot](PF6)8 (Knot = 1–3) and their subsequent demetallation to 819 knots 1–3. The yields of the demetallated 819 knots did not increase with The resonances of the aromatic protons in the looser knots, 2 longer reaction times. and 3, shift to low field, their chemical shifts moving closer to In contrast to the similar chemical environments observed for those of the corresponding building blocks (L2 and L3). The 1 1–3 the protons of the metallated knots, the H NMR spectra of shielding of Hd,He,Hf, and Hk, in particular, are intermediate differ markedly from each other in several regions (Fig. 2). between that of the corresponding protons in 1 and 3. Con- 1 Methylene (CH2)groupsHd and He in the tightest knot, , appear comitantly, the resonances of most of the alkyl protons (e.g., Hn) as multiplets because the constricted chiral environment accentu- move upfield. Both effects are consistent with a loss of π–π in- ates their diastereotopicity. With the loosening of the knot from 1 teractions in the tightly knotted structures and the rise of CH–π to 2,thesignalsofHd and He broaden, becoming a single broad interactions between the alkyl protons and aromatic motifs in the signal (at 600 MHz in CDCl3)in3 in line with the protons occu- looser knots (Fig. 2B and SI Appendix, Fig. S22 and Table S1). It pying less-constricted, less well-defined, environments (Fig. 2C). suggests that the conformation of the tightest knot, 1, is stabilized Variable-temperature 1H NMR spectra of 1–3 show little change by π–π stacking with the aromatic groups involved in the entangled over a large temperature range (238–318 K), indicating that the region of the structure with the alkyl chains to the outside. In variances in the 1H NMR spectra of the three knots are primarily 2 and 3, the longer alkyl chains slip into the knotted region due to the differences in tightness affecting conformation and not while the aromatic groups move to the periphery, thus gener- general dynamic phenomena (SI Appendix, Figs. S16–S18). ating fewer π–π interactions but more CH–π interactions. These 2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1815570116 Zhang et al. Downloaded by guest on October 1, 2021 1 Fig. 2. Partial H NMR spectra (600 MHz, CDCl3, 298 K) of 819 knots 1, 2, and 3;(A) region 0.25–10.0 ppm.