Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains of sufficient length and flexibility randomly form tangled mixtures containing open knots of different sizes, shapes and complexity. However, discrete molecular knots of precise topology can also be obtained by controlling the number, sequence and stereochemistry of strand crossings: orderly molecular entanglements. During the last decade, substantial progress in the nascent field of molecular nanotopology has been made, with general synthetic strategies and new knotting motifs introduced, along with insights into the properties and functions of ordered tangle sequences. Conformational restrictions imparted by knotting can induce allostery, strong and selective anion binding, catalytic activity, lead to effective chiral expression across length scales, binding modes in conformations efficacious for drug delivery, and facilitate mechanical function at the molecular level. As complex molecular topologies become increasingly synthetically accessible they have the potential to play a significant role in molecular and materials design strategies. We highlight particular examples of molecular knots to illustrate why these are a few of our favourite things. We review recent progress in molecular knotting, the chemistry of orderly molecular entanglements. As complex nanotopologies become increasingly accessible they may play significant roles in molecular design. Even today knots provide solutions to technical challenges, from modern surgical sutures14–16 hydrophobic assembly,13,17–19 lanthanide ion template synthesis,20 and the folding and entanglement of single strands by metal ions in a manner reminiscent of biological chaperones.21 Long dreamt of22 extended arrays of well-defined tangles have finally become realistic targets for chemical synthesis through molecular weaving23–26 and Vernier template synthesis.27Whilst these issues remain significant, in the last decade strategies have been developed that increasingly allow them to be overcome. Molecular knots have been synthesised with evermore complex topologies . Metalla28 or fuelling. The dynamic properties and features of molecular entanglements may ultimately prove similarly significant.With such advances molecular knotting is ready to answer questions regarding nanoscale topology relevant to chemistry, biology and physics. Entangling molecular strands with robust backbones has two important consequences: (i) strand crossing regions cannot pass through each other, blocking pathways to particular conformations and altering molecular dynamics; (ii) the structure becomes non-trivial in topological terms (each crossing can be over or under with respect to others), imparting additional stereochemical complexity. Other mechanically restricted molecules, such as catenanes and rotaxanes can undergo well-defined rearrangements of their components in response to stimuli9 We focus on synthetic strategies and insights that have recently been disclosed regarding the functions and characteristics of knotted molecular structures. A limited number of catenanes (links) are also included in the review, shown only to highlight similarities and/or differences to molecular knots synthesised by related methods, or when the links occur as side products of knot synthesis.This review outlines the state-of-the-art in the synthesis and what is known of the properties of orderly molecular entanglements.2.2.1.29 the Sauvage group entwined two ligand strands (1) in a linear helicate CuI212 such that the strands cross each other three times with over-under-over relative stereochemistry  resulting from different regiochemical strand connections.12Extrapolating from the seminal metal template synthesis of catenanes,hemistry .12 Macro9 (ii) The template can often be removed after covalent capture of the closed loop, which prevents the resulting wholly organic knot from untying. (iii) Metal helicates have an additional useful property, as every metal centre within the same helicate has the same stereochemistry, imparting a defined crossing sequence if the strands ends are connected in the right way.The use of metal templates to organise ligand strand crossings, followed by covalent capture of the entangled structure, is an attractive principle for several reasons: (i) coordination to metal templates is often dynamic, which enables ‘error checking’ during the assembly to generate the required entanglements under thermodynamic or pseudo-thermodynamic control.303 as a trefoil knot, a compound that had originally been reported31 to be a hydrogen bond assembled [2]catenane. Feigel discovered another hydrogen bond assembled trefoil knot 4, derived from steroidal peptide building blocks.32 Dynamic disulfide exchange of hydrophobic components was found by Sanders to unexpectedly form a trefoil knot135 and figure-eight (41) knot176.  These early largely unexpected examples of molecular knots gave some indications into how the synthesis of topologically complex structures might be tackled. However, the evolution of more rational syntheses of molecular knots has been greatly aided by advances in synthetic methodology, instrumentation, characterisation methods, and the consideration of tangle theory in molecular design.A number of the early knot-forming reactions were unanticipated discoveries . From an2.2.The process of knotting a strand has different requirements at different length scales. When tying a shoelace, we rely on friction and inertia to hold the strand in the entangled conformation. But such effects are not significant at the nanoscale and so the construction of molecular knots must rely on inter/intramolecular forces to direct entanglement. It follows that most synthetic molecular knots are either formed as a thermodynamically stable product or are derived from the covalent capture of a similarly stabilised complex.etc.) or by targeting particular symmetric representations of a knot  and rotaxanes .28 Mathematicians treat knots as 1D strands with no restrictions on how the strand can be twisted or turned, but for molecules it is important to bear in mind both mathematics and the physical laws of chemistry  when considering the properties and features of entanglements.35Mathematically a knot is a closed loop with a topology that cannot be changed by continuous deformation. A molecular knot is hence a self-entangled macrocycle where non-nugatory36 A tangle is a portion of a knot containing two 1D parts of the strand (‘strings’) within an imaginary circle that the strands cross four times. Connections between strings occur outside circles, whilst crossings occur inside. Some simple tangles and their chemical equivalents are shown in There are an infinite number of possible knots and links, so a theory that describes their structural relationship in terms of smaller fragments is helpful. Such a system, tangle theory, was introduced by Conway in the 1970s.e.g. 4, 6, 9), coordination geometry  and angle of divergence (‘turn angle’) within crossing points.22 This provided a collection of motifs that can be used as synthons for complex topologies. As template strategies for orderly entanglements have evolved, the focus has shifted from tuning individual crossing points towards controlling their connectivity. Polytopic ligands containing different binding sites and multiple functionalities, and thus sequence information, have been used to generate increasingly complex topologies. Joining tangles (i.e. crossing points) gives a rationally designed tangle sequence  Map crossings in terms of tangles.(2) Establish absolute stereochemistry of each tangle.(3) Establish relative stereochemistry in the tangle sequence.i.e. ligand connectivity.(4) Define sequence information, i.e. geometrical information regarding strand proximity.(5) Define tangle closures, 12 the racemic linear helicate generated by complex formation between two CuI ions and two molecules of bidentate ligand 1 maps out the [±3] tangle (i.e. a racemic mixture of helicates). A numerator closure  and a conformation that favours the necessary numerator or denominator closures. With extended ligands, the linear helicate strategy proved amenable for the synthesis of a Solomon 421 link from a complex mapping the [±4] tangle  ligands and metal ions into pentameric and hexameric circular helicates was serendipitously discovered by the Lehn group in the 1980s.40 Circular helicates, and related ligand systems, are effective scaffolds for the generation of higher-order knots and links, as each overlap of the ligands produces a crossing point (a [±1] tangle). The well-defined structures of these complexes can be organised such that particular regiochemical closures are favoured over others, by designing strands whose conformations either bring the end groups into close proximity for the required connection or simply preclude other connections. This corresponds mathematically to the stepwise connection of a  or  tangle sequence, rather than the numerator closure of the corresponding [n] tangle  links41 under thermodynamic control and subsequently applied to molecular Borromean rings42 (632 link). The first molecular pentafoil (51) knot was prepared by this strategy in 2012  bridge of the bisamine proved crucial for knot formation as it favours a gauche conformation stereoelectronically, facilitating the turn required in the connecting loop. In contrast, alkyl chain bis-amines gave polymeric mixtures and no evidence of knots. The X-ray crystal structure of FeII59 indicates that if the glycol oxygen atoms of the chain were replaced with CH2 groups then 1,3-diaxial clashes of the C–H groups would also disfavour cyclization of the loop.The generation of a pentafoil knot requires five sets of building block connections from a pentameric circular helicate . Bis-ald40 The corresponding Solomon link FeII411 was obtained in 75% yield with bis-amine 8 .48Reflecting the selective formation of tetra- and pentameric helicates from ligands 10 and 7, respectively, combining both dialdehydes with hexylamine 12 and FeClelicates .46 Mixin2.3.2.Whilst imine condensation is an effective means of connecting building blocks organised on scaffolds through metal coordination, the lability of imine bonds means the strands can (reversibly) reopen upon demetallation. This results in the demetallated knot unravelling unless it is thermodynamically stable without metal ion coordination. It can be difficult to ‘trap out’ knots from coordinated complexes by reducing imine groups to kinetically robust amines. This is likely because each imine reduction successively weakens the metal complex and so it disassembles, and the strand unravels, before the entire knot can be covalently captured through amine linkages.51Other strand-connecting reactions featuring less dynamic chemical bonds have been used to join building blocks organised on metal-coordinated scaffolds. Olefin metathesis has proved amongst the most useful in this respect, as the alkene connections are only dynamic (useful for error correction of building block connections) in the presence of a catalyst.via a trimeric circular helicate by olefin metathesis was achieved through a modification of a complex reported by Brooker et al.,52 assembled from ZnII(BF4)2, pyrazine-2,5-dicarbaldehyde 13 and pyridine 14 -16 or (S)-16 directs the stereoselective formation of either Λ-ZnII3173 or Δ-ZnII3173 giving, after olefin metathesis, the respective knots Λ-ZnII318 and Δ-ZnII318 (54 Using a 1 : 1 mixture of (R)-16 and (S)-16 gave a self-sorted mixture of Λ-ZnII3173 and Δ-ZnII3173, with no diastereomeric scrambling observed.The synthesis of a trefoil knot idine 14 .53 Closu-ZnII318 .54 Using21, a [2]catenane composed of two triply-entwined macrocycles) were obtained  or alkyl chains, no knot was obtained. Unlike imine-metal-coordinated knots and links, demetallation of FeII520 proceeded smoothly to generate 20, a wholly organic molecular pentafoil knot.Using a similar approach but from pentameric and hexameric circular helicates, respectively, a molecular pentafoil knot and a molecular Star of David link 2 salts, suggesting that labile ZnII ions pre-organize the relative positions of the bipyridyl binding sites. Stepwise exchange of the ZnII ions for other metal ions can then proceed without generating ‘mistakes’ in the coordination mode of the knotted strand, which would be slow to correct with less labile metal ions. The affinities of the metallated knots towards chloride anions was measured with isothermal titration calorimetry, with FeII520, CoII520 and NiII520 having similar binding affinities (K ∼ 107 M−1) whilst ZnII520 (K ∼ 106 M−1) and CuII520 (K ∼ 104 M−1) exhibit lower affinities for chloride ion. The differences likely reflect the effect of the different metal ion coordination geometries on the knot conformation, and therefore the size, shape and electronics of the central chloride binding cavity.The robustness of metal-free pentafoil knot 20 allowed its coordination chemistry to be investigated.58 Connecting the ligands of hexameric circular helicate FeII6226 by olefin metathesis gave racemic (+31#+31#+31 and −31#−31#−31) composite knot FeII623 (i.e. a knot consisting of three trefoil entanglements of the same handedness joined together). However, each ligand terminus in FeII6226 is equidistant to two inequivalent ligands. This meant that another topology, 937 link FeII624, was also formed in equal amounts to the knot. Knot FeII623 was separated from the link isomer by crystallisation. Analysis by X-ray crystallography confirmed that the 324-atom loop of FeII623 crosses itself nine times with the same handedness at all six metal centres.By designing the ligand strands so that they were organised to make different regiochemical connections, a hexameric circular helicate gave access to a composite knot  containing nine alternating crossings .58 Conne2.3.3.2 in 60% yield to form a circular tetrameric helicate where each metal coordinates to three separate ligand strands 6-31 was prepared diastereoselectively via enantiopure dianiline -30  to synthesize a range of intricate higher-order catenanes from molecular cage structures.iline 28 .60 The mS,2S)-30 .61 and a universal 3-ravel from Lindoy.62 These structures are metalla-architectures, with metal–ligand bonds as an intrinsic part of the topology, rather than molecular knots with a continuous backbone of covalent bonds (see Section 2.10). The Fujita group has reported a series of entangled cage architectures, including a double-walled cage capable of guest-adaptive molecular recognition,63 and a series of interconvertible entangled cages driven by weak secondary π-acetylene interactions.64 These architectures display unusual co-crystallisation behaviour65 and show potential for enantioselective catalytic and host–guest applications.66Other early examples of entangled architectures derived from cages include a ‘double trefoil knot’ from the Clever group2.4.III complexes incorporating a 3 : 1 ligand : metal ratio has been extensively investigated by the Gunnlaugsson67 and Piguet68 groups, and others, over the past two decades. The Leigh group have developed these lanthanide template systems for the formation of knots. The initial approach was based on helicate LuIII323, assembled by combining diamagnetic LuIII with three equivalents of a 2,6-pyridinedicarboxamide (pdc) ligand 32 , a trefoil knot of single handedness Λ-LuIII35 was formed -ZnII3173, chiral self-sorting of individual enantiometic building blocks did not occur. However, in later work27 featuring several chiral pdc units connected within the same strand, self-sorting does occur because of the strain and steric clashes involved in wrapping a multidentate strand around a single metal ion in order to coordinate to several sites at once.A class of Lnigand 32 .20 The u2.571 Tying a knot in a preformed strand simplifies covalent capture of the entanglement: only two reactive ends need to be positioned, incorrect intramolecular connections cannot occur, and only intermolecular reactions (oligomerisation) need to be avoided. However, encoding sufficient structural information to control the number, stereochemistry and sequence of crossings, while also restricting the conformations the strand can adopt, is much more demanding with a single component. With a look to the future, programming entanglements into sequence-specific polymers formed by solid phase synthesis may prove helpful for single strand folding-and-entangling approaches.Knotting in polymer chains and proteins occurs by the folding and entanglement of a single strand about itself. This is more reminiscent of how knots are tied in the macroscopic world than the multicomponent self-assembly strategies discussed in this Review so far .72  to give CuI236. Unfortunately, CuI236 exists as a dynamic mixture of two conformers, featuring either a numerator or denominator closure. Nevertheless, dimerisation of the impure overhand knot by Glaser coupling gave a mixture of granny and square composite knots (as well as trefoil knot and unknot macrocycle side products), derived from the connection of tangles of the same and opposite handedness, respectively.An overhand ‘open trefoil’ knot was accessed by Sauvage72 , by perf73 Trefoil knots were prepared in up to 14% yield from a preformed decaamide thread, containing the required six bisphenol Z moieties, and various pyridine dicarboxylic acid dichlorides. In these cases, the overhand knot conformation was not directly observed and yields of trefoil knot were modest, presumably due to the presence of different conformers of the open strand.Vögtle's serendipitous discovery of hydrogen bonded trefoil knot synthesis  also pro74 with the strategy experimentally realized by Hunter and co-workers in 200175  building blocks and the catalytic properties of the metal ions to promote covalent capture of an interlocked or entwined product. Unlike many ‘passive template’ syntheses, active template synthesis occurs under kinetic control. Active metal template synthesis has been used to accelerate covalent bond formation through a transiently formed loop to generate a trefoil knot  reaction through the resulting cavity to close trefoil knot 41 in 24% yield. Entangled molecular strands formed under kinetic control more closely mimic aspects of the stochastic knotting of synthetic polymer strands and biopolymers.79Active template synthesisoil knot .78 Stran20 A folding approach was developed by covalently connecting three homochiral 2,6-pyridinedicarboxamide ligands to form strand 42  has emerged as an effective route to molecular knotting.trand 42 .80 In th81 By introducing different functional groups at the termini of an overhand knot, the stepwise dimerization of lanthanide overhand knots provides composite knots in a stereoselective manner  of the same handedness gives either enantiomer of granny knot /-LuIII246. Alternatively, combining overhand knots of opposite handedness gives a pseudo-meso square knot -LuIII246.An advantage of the folding approach over multicomponent self-assembly is the ability to programme functionality into the knotted strand at specific positions, much like engineering protein secondary structure into peptide sequences.e manner .82 ConneIII246 and -LuIII246 give pronounced Cotton effects, whilst square knot -LuIII246 displays almost no chiral response -Luresponse . The ver2 three-twist knot  interspersed with two 1,10-diphenyl phenanthroline sites (to bind to CuI). To access knot (+52)-48, CuI was first added to generate the first two crossing points by forming ‘clasp’ complex (Λ/Δ)-CuI47. Next, LuIII was added to produce CuILuIII47, generating three further crossing points. As the 2,6-pyridinedicarboxamide units bind to LuIII with a specific helical handedness, the stereochemistry of the CuI clasp is dictated by the mechanical constraints on the ligand strand: the point chirality that enforces the helical chirality of the [+3] tangle also ultimately directs the handedness of the [−2] tangle. The resulting open knot CuILuIII-47 was closed by olefin metathesis, giving (+52)-48 after demetallation.Recently, the folding-and-entwining approach was used to generate a low symmetry higher-order prime knot, the 5ist knot .21 This 1)-48 was obtained when only LuIII coordination was used with 47, whilst unknot (01)-48 resulted if no metal ions were added prior to macrocyclisation. The strand folding showed pathway dependence (i.e. is under kinetic not thermodynamic control): if instead the LuIII is added first to 47, the open 52 knot does not form upon addition of CuI. Being able to tie different knots in a molecular strand should aid understanding of the fundamental influence of different knot topologies on chemical and physical properties.The folding-and-entwining strategy allows different knots to be tied in the same molecular strand. Topoisomeric trefoil knot  groups with nine-coordinate lanthanide ions: if, instead of a tritopic ligand such as 42,80 ditopic ligand R4-49 is introduced to LuIII, a 3 : 2 ligand/metal complex -LuIII2493 forms, which can be covalently captured by olefin metathesis to form the six-crossing granny knot -LuIII250 -LuIII452 featuring 12 crossings—the most topologically complex synthetic molecular knot realised to date -LuIII452 is an isomer of triskelion knot -LuIII452, and has six alternating and six non-alternating crossings  from relatively simple building blocks.2.7.86 Almost all of the molecular grids reported to date are racks, i.e. consist of stacked layers of ligand strands that are not woven through the plane described by the metal ions. Connecting the ends of adjacent ligands in such grids would only produce unknot macrocycles of various sizes. Interwoven grids, where each ligand strand passes back-and-forth and over-and-under other strands through the plane of metal ions, have the potential to generate strand entanglements. The use of grids as precursors for knots and more extended molecular weaves was first postulated three decades ago by Busch: “The ultimate aspiration of chemists working on interlocked structures might be to weave molecules as if they were macroscopic threads”.22Molecular grids consist of polytopic ligands coordinated to two-dimensional arrays of metal ions. Interest in this class of assembly includes the electronic and magnetic properties of well-defined spatially separated and organised metal ions within a molecular framework.d]thiazole (TTZ) moiety.87 The TTZ moiety is flanked by pyridylbenzimidazole units to induce a zig-zag shape in ligand coordination and favour the formation of interwoven grids. Treatment of ligand 53 with MII(BF4)2  quantitatively formed 2 × 2 interwoven grids MII4534.14 Solomon link ZnII454 was obtained in 72% yield 2 gave 2 × 2 interwoven grid FeII4554, for which the ligands are forced into a conformation such that adjacent olefin chains are directed to opposite faces of the grid. Suprafacial connections (23 link FeII456 (a twisted [2]catenane) and the isomeric composite granny (+31#+31/−31#−31) knot FeII457.15 The isomers were separable using gel permeation chromatography. The X-ray crystal structure of demetallated link 56  knot, an iconic knot and symbol common to many cultures and religions 2 or Fe(BF4)2. The BF4− anions proved to be crucial for grid assembly, without them it does not form. The X-ray crystal structure of FeII9586(BF4)18 shows BF4− anions bound within each of the four square cavities of the complex, stabilising the assembly through B–F⋯π and electrostatic interactions. Joining the ligand termini within the grid by olefin metathesis followed by demetallation with Na4EDTA afforded molecular 74 knot 59. A Solomon link and unknot macrocycle are also formed as side-products from other patterns of strand closure on the grid.16The strand connectivities set up by their positioning within interwoven grids is different to that possible with circular or linear helicates, enabling different topologies to be accessed through the use of more than two weft and two warp ligands.eligions .16 The 32.8.88 Schill, one of the pioneers of this approach, was unsuccessful in efforts to synthesize a molecular trefoil knot using a covalent template based on quinone.89 The failure was partly due to the lengthy and rather convoluted synthesis necessary because of the synthetic methods available at the time, but removing the template attached to the putative knotted strand through several chemically robust covalent bonds was also problematic.89 Despite a number of other attempts over the subsequent five decades,90 the first report of a trefoil knot synthesized through a covalent template strategy was disclosed by Itami and co-workers in 2019.91 They used this approach in a synthesis of two cycloparaphenylene [2]catenanes and a trefoil knot 62 . The topology of the entangled product is dictated by the choice of counter-anion and dihydrazide bridging unit, and could be biased to generate either Hopf link 67, Solomon link 68 or trefoil knot 69 in 70–90% yield. The aldehyde and hydrazide building blocks entangle to minimise the amount of organic molecular surface exposed to water. The conformation of 68 was found to be sensitive to the amount of water present, with even small amounts of moisture inducing a large conformational switch.19Although several notable early knot syntheses utilised solvophobic effects (see Section 2.1), the lack of control over product formation limited its application as a design strategy. However, recently Cougnon has used the hydrophobic effect to access a number of interlocked structures .18 Assem2.10.The syntheses discussed in Sections 2.3–2.7 mostly rely on metal ions as scaffolds around which organic ligands are entangled. Metalla-knots are metal complexes where the metal ions form part of the knotted strand itself and so cannot act as removable templates.92 This is in contrast to metal template molecular knots, which generally use either 1st row transition metals or lanthanides. Certain coordination geometries, such as linear or square planar, are more readily accessed with heavy transition metals. The majority of the ligands used in metalla-knots feature pyridyl-type end groups in metal coordination.A variety of metals have been employed in metalla-knots, including some from the 2nd and 3rd rows of the periodic table.I and quinoline units linked by glycol chains to generate complexes with either a trefoil or figure-eight topology.93 Secondary interactions between the metal ions and the glycol linkers were apparent in the X-ray crystal structures of the metalla-knots. Jin has since described a wide variety of metalla-knots based on organometallic dimers and dipyridyl ligands.94 In some cases the dynamic coordination behaviour characteristic of metalla-structures has been exploited to produce stimuli responsive interconversion of different species.95The earliest example of a metalla-knot was reported by Hosseini in 2008 and featured linear coordination between AgIII or IrIII half-sandwich complexes and bis-pyridyl linkers—has led to metalla-knots and links of remarkable stability.96 The majority of metalla-knots reported by Jin are trefoil knots,94 but also include figure-eight knots,97 an unsymmetrical trefoil knot that interconverts with a Solomon link,95 and a ‘double’ trefoil knot bridged by alkali metal ions.98 Particularly noteworthy is the K+ mediated interconversion of the double 31 knot KRh12Cp*12706716 and 41 knot Rh8Cp*8704714 2OTf272 in the synthesis of an 818 metalla-knot (100 Combining the dimer with an equimolar ratio of dipyridyl ligand 73 gave [8+8] assembly Ru16(p-cymene)16728738 in 74% yield. Recently, the Chi group also reported a 631 link, accessed by combining the same RuII dimer with a bipyridyl linker with a slightly larger bend angle.101 This sensitivity to ligand geometry highlights some of the advantages and limitations of metalla-knots: small changes can afford a diverse range of topologies, but structural designs are therefore difficult to confidently predict in advance.In 2018 Chi and co-workers employed Rulla-knot .100 CombI ions to pyridyl-capped polypeptide ligands.102–104 Examples include a series of topoisomeric [4]catenanes102 and the divergent synthesis of 71 and 821 metalla-knots  differentiates woven materials from the random strand knots and tangles that occur generally with polymers of sufficient length and flexibility.108 In contrast to macroscopic weaving, in which pre-formed threads are passed over and under each other to build up the material,109 molecularly woven fabrics can be prepared from pre-formed tangles or reticular chemistry. Rather than connecting crossings intramolecularly to form a molecular knot or link, intermolecular connections can form extended woven networks.Molecularly woven materials share many of the same design principles and structural considerations as molecular knots.24 Bisphenanthroline Cu(i) complex CuI75 positions the four aldehyde groups in a tetrahedral geometry. Subsequent condensation of CuI75 with diamine 76 forms 3D interwoven COF CuIn77. Demetallation with KCN yielded COF 77 with only 3–8% of the CuI ions that hold the strands in fixed registry remaining. The result was a material with a tenfold increase in elasticity.In 2016 Yaghi and coworkers reported a material molecularly woven in three-dimensions through reticular chemistry .24 Bisph25 Mayor has used a surface-mounted MOF template approach to synthesise a single layer 2D woven polymer network. However, the structure did not prove sufficiently robust to survive removal of the template.26A 2D supramolecular triaxial Kagome weave has been reported by the Wennemers group, featuring woven strands with intermolecular π–π interactions between perylene monoamide groups. Although the non-covalent connectivity may enable the strands to pass through each other in this material, the relative robustness and uniform pore structure augurs well for separation and storage-type properties.23 Ligand 78, derived from 58 used to form a 74 knot (see Section 2.7),16 is appended with thiol end groups. Following formation of interwoven 3 × 3 grid FeII9786, crosslinking by disulfide formation was carried out in air to form a layered molecularly woven material FeIIn79. Demetalation with KCN afforded a metal-free organic woven polymer 79 in nanosheet layers of uniform 4 nm thickness which possessed long-range order. Notable property differences were found between the woven 2D polymer sheets and non-woven 1D strands of the same polymer, including thermal stability, stiffness and ion permeability. The ability to weave polymer chains in two-dimensions—forming molecularly woven fabrics—marks the intersection of three major research fields: polymer science, two-dimensional materials and molecular nanotopology.106The 2D molecular weaving of polymer strands has been achieved by tessellation of a preformed 3 × 3 grid .23 Ligan3.3.1.110,111 In such a case the reduction in strength varies with the knot topology.112 Similar effects have been observed when stretching knotted macromolecules, such as actin filaments and DNA.113 Simulations on a polyethylene chain indicate that the tighter the knot (i.e. the shorter the average distance per crossing) the more severe the strain imposed at the knot apex becomes.114,115 The weakening of the molecular strand is caused by distortion and weakening of the covalent bonds at or close to the knot apex.Entangling strands at any length scale can have a significant effect on properties. For example, knotting a rope reduces its tensile strength, because an applied stretching force becomes unevenly distributed across the fibres at the entry to the knotted section.‡1) knot. Whilst the reduced representation of this knot cannot be depicted in an achiral form, the knotted strand can, in principle , be rearranged into either mirror image of the representation. Accordingly, the 41 knot is topologically achiral.An exception is amphichiral knots, such as the figure-eight  and ubiquitin hydrolase (52) contain knots that are highly conserved across the protein families.71 There is also evidence that knotted conformations can bring hydrophobic and hydrophilic parts of proteins closer together, a useful feature for enzyme active sites.117 It may not be coincidence that >80% of the known knotted proteins are enzymes. Another prevalent hypothesis is that knots increase the kinetic stability of proteins because the entangled region suppresses degradation by preventing entry of the protein into the proteasome.119 However, there is still ongoing debate whether knotting in proteins has been selected by evolutionary pressure, or if their occurrence remains relatively unimportant for function.Approximately 1% of proteins in the Protein Data Bank are knotted,120 Knotted and supercoiled DNA strands are unable to undergo transcription, replication or recombination, and therefore nature uses topoisomerase enzymes to mediate knotting and supercoiling.121 Failure to remove knots leads to cellular death.9 Spontaneous knotting has been implicated as a potential problem in DNA nanopore sequencing, as such pores may be unable to allow passage of knotted DNA strands.123In contrast to proteins, DNA undergoes stochastic knotting under biotic conditions.3.2.124 Hence, the tightness of a molecular knot is a useful metric for understanding some of the potential effects on properties. The backbone crossing ratio (BCR) is a measure of how tight a molecular knot is tied based purely on chain length, rather than chemical functionality.125 It is calculated by dividing the number of atoms in the shortest path along the backbone of the knotted strand by the total number of crossings (i.e. atoms per crossing). The BCR lies between 27–33 for most molecular knots synthesized to date  or required rigid linkers . The theoretical minimum BCR possible for a polyethylene chain knot is proposed to be 15, whilst the lowest value achieved to date is 24, for 819 knot 26.59 This knot was used as the basis of a study into the effects of strand tightness.126 Analogous knots with a BCR of 27 (80) and 30 (81) were formed by increasing the length of the flexible alkyl chain linker  for the hydrazone protons. This was attributed to the higher packing density resulting in a significant reduction in solvent-accessible surface area and the favouring of π–π interactions. From this study, and that of Similar conclusions were drawn by Kumpulainen and Cougnon in a study of links 67, 68 and trefoil knot 69, along with an unknot macrocycle.129 They used this to screen complex topological mixtures and to distinguish different species based on their size, shape and packing. The authors defined a so-called ‘floppiness factor’, by dividing the arrival time of the parent molecule by that of the least entangled fragment, corrected for mass and charge  conditions in travelling wave ion mobility mass spectrometers (TWIMS) varies predictably with topology and tightness.d charge . If the 3.3.35 Knot migration along polymer strands is dominated by reptation, the ‘snake-like’ motion of a chain in an entangled environment.131 A striking example of reptation occurs with the all-benzene trefoil knot 62.91 Simulations of the NMR spectra indicated that the static knot should exhibit 15 unique proton environments, but due to the rapid dynamic motion the 1H NMR spectrum of the knot consists of a single coalesced peak at 7.1 ppm, even at −95 °C. The dynamics of 62 were simulated by density-functional tight-binding with molecular dynamics methods -48 contains orthogonal coordination sites for both LuIII and CuI (21 Coordination to a LuIII ion occurs through the three pyridinedicarboxamide groups to give (−31)-LuIII48, which adopts a pseudo-C3 symmetric conformation with a writhe of 3 (1)-LuIII48 with CuI salts displaces the LuIII ion to afford (−31)-CuI48.21 In this complex the knot coordinates to the CuI through the two phenanthroline groups forcing the ligand strand to adopt a less symmetrical conformation with a writhe of 4  in D2O.135 In this case a 2 : 1 anion : knot binding stoichiometry was always observed, along with positive cooperativity in most cases (K2/K1 up to 22). This suggests that the first anion preorganizes the host cavity by restricting the entangled ligand to a specific conformation.A comparison of halide binding within the central cavity of a series of knots and links assembled from circular helicates has been determined for pentafoil knot FeK ≈ 104 M−1) towards halides in water.18 Two anions accept six preorganized intra-cavity N–H hydrogen bonds from the hydrazones. Stimuli-responsive guest capture and release can be affected by changing the pH as deprotonation of hydrazone units under basic conditions causes loss of Br− from the cavity of 69.Cougnon's hydrazone trefoil knot 69 and Solomon link 68 display affinity threading through a macrocyclic cavity .136 Axle4.3.137 The handedness of liquid crystalline matrices was controlled by tying a knot in a homochiral molecular strand dopant 84  into an overhand knot can influence the structure seven orders of magnitude  longer than itself.opant 84 . When doopant 84 . However4.4.II520 was exploited to initiate and regulate catalysis  of pentafoil knot Znatalysis . Treatmetivation .55 The tII520 can also accelerate chemical reactions itself: ZnII520 abstracts Br− from Ph2CHBr to give the corresponding carbocation, which then undergoes rapid hydrolysis to form 87  were used with 8-hydroxypyrene-1,3,6-trisulfonate (HPTS) assays to determine ion channel formation and ion selectivity. Pentafoil knot FeII520 showed only weak channel forming activity with Br− anions, presumably due to the small cavity size  hydrolyse in the hypoxic acidic environment found within cancer cells, causing metal ion release and subsequent cell death. All the knots tested showed potency against six cancer lines in vitro and in vivo in zebrafish embryos.Controlled metal ion release on fragmentation of an entangled strand has been used by Trabolsi to selectively target cancerous tissue .140 The via active transport rather than passive diffusion. Strand entanglement does not appear to play a role other than as a delivery vector in this system. However, in the future it may be that the chirality or charged surfaces of metal–organic knots could be used to target specific protein pockets and surfaces.Mechanistic studies suggested that the high activity of the knots was due to their nanoscale size, allowing them to be taken up into cells 5.II59  was synthesized in 1989, it took until 2012 to realise the second (pentafoil). However, since then a further seven prime molecular and metalla-knot topologies have succumbed to chemical synthesis along with the stereoselective synthesis of granny and square knots and three other composite knot topologies. New strategies such as folding-and-entwining, grids and Vernier template synthesis have allowed rapid synthesis of complex entanglements with up to 12 crossings. Advances in the understanding of metal–ligand coordination, characterisation techniques and instrumentation underpin these accelerated advances.141 Already it is evident that the restriction in conformation imposed by entanglement can be useful in catalysis and anion binding, and molecular weaving is a new frontier for materials fabrication, but what other uses are there? Among the many open questions in molecular nanotopology, we believe that the following are some of the most interesting and challenging:With molecular knots and links becoming accessible and the anchoring of synthetic strategies now rooted in mathematical knot theory, answers to the question ‘how?’ are becoming clearer and it is time for chemists to begin to answer ‘why?’(1) A particular knot for each function. In the macroscopic world, different types of knots have different characteristics that make them more or less suited for a given task: ‘bend knots’ provide the strongest binding between two lengths of rope; ‘hitches’ are best for tying rope around an object; and ‘loop knots’ or ‘nooses’ allow degrees of movement between the components they connect. Identifying which types of molecular knot topologies are best suited for specific functions could be important for the utility of orderly entanglements at the molecular level.e.g. through multicomponent self-assembly). With the advent of folding-and-entwining strategies, higher-order unsymmetrical knots, such as the Stevedore (61) twist knot, should be within reach through rational design.(2) Unsymmetrical knots. The synthesis of most of the knots made to date has been facilitated by exploiting their symmetry ((3) Exploring the size and tightness limits of knots. Tightness and number of crossings are two primary parameters that determine the properties of a knotted strand. Quantitative understanding of how these properties change strand behaviour are still lacking.(4) Kinetically trapping dynamic knots. Imine-based knots and metalla-knots (Sections 2.3.1 and 2.10) have dynamic backbones that allow the strand to pass through itself which is not consistent with the fundamental constraints of topology. Developing covalent capture methods for the tangled ligands of such coordination complexes could give access to kinetically stable strands, turning metal-coordination into template synthesis.(5) Orderly entangled materials. Random entanglements are present in virtually all polymer mixtures and play a major role in their materials properties. The time is ripe to systematically introduce synthetic knots and ordered strand entanglements into materials (Section 2.11) to explore the effect that regular topological restrictions have on properties.(6) Knots under force. Little is known about what happens when molecular level knots are subject to an applied force. Does knotting weaken the strand at the apex of the entanglement as for macroscopic knots? And if so, can the induced strain be exploited, for example in bond-breaking for synthesis?Given the substantial progress in the synthesis of molecular knots over the last few years, open questions such as these, and many others, can start to be tackled experimentally. So, like a needle pulling thread, we confidently predict that the exploration of orderly molecular entanglements has a long, long way to run.There are no conflicts to declare.


Quantitative three-dimensional molecular ultrasound is a promising technology for longitudinal imaging applications such as therapy monitoring; the risk profile is favorable compared to positron emission tomography and computed tomography. However, clinical translation of quantitative methods for this technology are limited in that they assume that tumor tissues are homogeneous, and often depend on contrast-destruction events that can produce unintended bioeffects. Here, we develop quantitative features (henceforth image features) that capture tumor spatial information, and that are extracted without contrast destruction. We compare these techniques with the contrast-destruction derived differential targeted enhancement parameter (dTE) in predicting response to therapy. We found thirty-three reproducible image features that predict response to antiangiogenic therapy, without the need for a contrast agent disruption pulse. Multiparametric analysis shows that several of these image features can differentiate treated versus control animals with comparable performance to post-destruction measurements, suggesting that these can potentially replace parameters such as the dTE. The highest performing pre-destruction image features showed strong linear correlations with conventional dTE parameters with less overall variance. Thus, our study suggests that image features obtained during the wash in of the molecular agent, pre-destruction, may replace conventional post-destruction image features or the dTE parameter. First, assessment of response (measurable change) does not occur until 90 days after therapy initiation which is a long time for patients to endure toxic side effects especially if the treatment is not effective. Second, size change may not reflect response in cytostatic oncologic therapies.Functional assessment of tumor response to cancer therapy is needed for individualized therapy. The Response Evaluation Criteria in Solid Tumors16 by identifying clinical response to cytostatic anti-angiogenic therapies earlier than anatomic imaging. Three-dimensional molecular contrast-enhanced ultrasonography (3D-mCEUS) has shown promising efficacy and safety in preclinical animal31 and pilot human32 data. Treatment response may be predicted as early as 24 h after treatment initiation based on conventional quantitative parameters33. However, the main parameter commonly employed in most of these studies relies on the differential targeted enhancement (dTE), where 5 + minutes of cine image acquisition and ultrasonic destruction of microbubble contrast is used to infer the bound fraction of targeted microbubbles34. These destruction pulses have been shown to generate unintended bioeffects in animal models36 limiting translation to clinical study. Further, prior work developing quantitative methods for therapy monitoring, such as the dTE, produce parameters averaged over the tumor region of interest (ROI), which may be overlooking valuable spatial information toward predicting therapy response. Many studies utilizing analysis of the image features of tumor tissues45 offer support of exploration for more granular parameters of heterogeneities inherent to tumor tissues.Quantitative functional imaging has been shown to help address these issues in multiple imaging modalities46, which, in turn, may provide improved discrimination of therapy effects. Raw 4D cine-image data were preprocessed into static 3D intensity maps using intensity projection methods. Spatial maps of the dTE and standard deviation of pre- and post-destruction signal intensities were obtained through a sliding window method16. Image feature data were then stratified by the size of raw imaging dataset used and the need for a destruction pulse to generate eleven intensity maps. With this approach, we compare the treatment effect discrimination of image features extracted from image data with and without contrast destruction. Our results demonstrate a small set of image features extracted from intensity maps from 10 cine frames prior to contrast destruction that perform as well or better in classifying treated and control animals. Thus, those image features could be used to quantify molecular ultrasound signals without the need for potentially invasive destruction events while imaging.As such, using conventional statistical methods and multiparametric analysis, we assess the feasibility of replacing the dTE parameter with image features extracted from data without contrast destruction. These image features include second-order statistical properties of signal intensity distribution and are expected to better capture tissue heterogeneities of tumorsIntensity maps derived from the four-dimensional (i.e. 3D volumes + time cine) imaging data represent a voxel-by-voxel transformation of assigned intensity values across the 3D volume of interest (VOI). Sampled properties of intensity dynamics for each voxel are taken throughout a predefined period of image acquisition Fig. b. We genWe carried out statistical analysis of 91 image features extracted from each of 11 intensity maps assessing for repeatability of measured image feature values with intraclass correlation coefficient  and the detection of a significant, and durable change from baseline in response to treatment with Wilcoxon Signed-Rank test ,  map contained the most selected image features with 28 showing reproducible data values and significant change from baseline on scan days 1, 3, and 10 compared to dTE image features where 13 met this strictest criterion. Four remaining intensity maps  contained image features with sufficient repeatability and significant baseline changes  as previously described.These image features were then stratified into 3 groups based on the burden incurred by the size of raw datasets for preprocessing, the length of time for image acquisition, and the use of a destructive ultrasound pulse: lowest clinical burden  representing 10 frames of raw cine data without contrast destruction, moderate clinical burden (former group plus full LIP) representing all cine frames prior to contrast destruction, and highest clinical burden (former group plus dTE) representing all cine frames before and after contrast destruction  comparing the significant and repeatable image features of each intensity map against the dTE mean intensity as well as the 13 dTE image features chosen at statistical feature selection. Only features from the AIP intensity map were found to have linear correlations with dTE image features. Two AIP image features met threshold with linear correlation to the dTE mean intensity  feature pairs within each set were eliminated. Assessment of classification performance predicting treated versus control animals was carried out with four supervised learning algorithms paired with recursive feature elimination (RFE) as appropriate: logistic regression (LR) with and without hyperparameters, linear determinant analysis (LDA), and an ensemble bagging classifier (BC). Generalizability was optimized using fivefold cross-validation (CV) for hyperparameter tuning, and tenfold CV for RFE. In total, four image feature sets were tested: AIP-only features, low burden group, moderate burden group, and high burden group for a total of 16 simple supervised learning models. Overall, performance on unseen data surpassed training data performance with excellent performance on unseen testing data Fig. a. NotablImage features commonly selected at RFE for optimizing performance of LR and LDA models were assembled to produce a dimensionally reduced, less complex feature set comprised of 10 image features . These were then passed through the same training/testing pipeline described previously, with similar predictive performance Fig. b. The reThe dimensionally reduced RFE feature set included 9 image features exclusively from low burden group intensity maps (AIP and LIP), which represent data from the last 10 frames of cine image data and do not require destruction pulse. One of the image features composing this set was found to correlate strongly with the conventional dTE parameter , the predominant endothelial receptor was found to be VEGFR250. However, there are currently no clinical tools to assess VEGFR2 expression to understand the significance of these findings and ultimately to support patient management, including therapy monitoring.The role of VEGFR2 is known to be critically important in mediating angiogenesis in tumors56. This is because it can be used to exclusively image molecular targets on endothelial cells, ideal for characterizing angiogenesis markers such as VEGFR2. An exact understanding of how these derived quantitative parameters relate to the biologic phenomena of treatment response, disease progression, etc. is still unknown. However, advancing non-invasive technologies such as those employed in this work to clinical study would allow for larger study designs to adequately capture the biologic variability seen in clinical cancers. Clinical translation of the traditional disruption approach (i.e. dTE) commonly used with mCEUS has been criticized57, and will likely be hampered by concerns of off-target bioeffects of contrast destruction on insonated tissues58. Additionally, prior work has focused on extracted intensity parameters averaged over an entire region or volume of interest. Such features are poorly suited to capture spatial heterogeneities characteristic of tumor tissues. The high variance measured in analysis of these parameters are likely in part reflective of variability introduced by inconsistencies in contrast administration, ultrasound probe handling, and differences in manufacturing of microbubble contrast59. To overcome these issues, we employed higher-order statistical texture features that provide quantitative parameters of relative differences of intensity values from smaller, sub-ROI neighborhoods of spatially related voxels61. By calculating texture feature values based on the relative intensity of spatially related voxels, we expect resultant parameters to be less susceptible to the extrinsic inconsistencies of imaging acquisition and contrast administration. Interestingly, we observed the range of values from texture features selected in our analysis to be decreased compared to averaged parameters previously reported from these tumors.Molecular contrast ultrasound as a tool to prospectively detect predictive, quantitative biomarkers of responsiveness of tumor tissue to anti-angiogenic therapy has received much interest in preclinical study and pilot human data with promising results and safety, respectively66. Application of radiomics analysis to molecular contrast ultrasound data is novel with this being the first study of its kind to the best of our knowledge. In addition, by alleviating the need for contrast destruction to generate predictive models, we see the imminent potential for translation of these methods to the clinical study of wild-type tumor biology. Beyond predicting binary response to anti-angiogenic therapy in clinical settings, the possibility of detecting in vivo the development of acquired resistance or worsening malignant phenotypes deserves exploration.Prior work studying similar image texture features in sonographic imaging of cancers have shown promising performance and image feature reproducibility in tumor type discrimination, prognostication, and monitoring of response to therapy68. Previous publication33 that utilized the dTE parameter in molecular imaging included comparison with a pre-clinical tumor model known to be non-responsive to bevacizumab therapy and found these tumors showed molecular intensity dynamics similar to untreated, responsive tumors. Whether the spatial patterns of molecular intensity textures in biologically non-responsive tumors would also be similar is presently unknown. Further, the variability of VEGF receptor expression expected in clinical cancers may be poorly represented in this pre-clinical murine model, limiting the generalizability of our results upon clinical translation. Second, our animal cohort was small for this proof-of-concept work testing the possibility of obviating the need for contrast destruction, and the potential of image features in molecular ultrasound. This small number of observations likely contributed to hyperparameter overfitting69, where model performance on unseen data is prioritized at the cost of performance on training data. Future work in this area would benefit from a larger cohort of subjects wherein a dedicated validation set and model calibration would be more feasible. Additionally, applying these methods in other discrete contexts of tumor biology and therapy is needed to determine the biologic underpinnings captured by image feature dynamics.Our study had several limitations. First, our experimental model was limited to a biologic context where the tumor model used is known to be responsive to bevacizumab therapyIn this study, we undertook an in-depth analysis of image features extracted from intensity maps of 3D mCEUS images with VEGFR2 microbubble contrast in a murine model of metastatic colorectal cancer. Utilizing data taken from 2 groups of mice—one treated with bevacizumab and one receiving sham infusions—we analyzed statistical properties of extracted image features to select for further analysis those which showed sensitivity to detecting early, durable changes in response to therapy, and those which were reproducible from a data values perspective. These statistically selected features were then stratified into multiparametric feature sets (burden groups) based on the computational requirements and/or necessity of a destruction pulse for producing each image feature’s respective intensity map. The performance of multiparametric feature sets’ predictive capacity classifying treated and control animals was then compared using several simple supervised learning algorithms for the prediction of response to anti-angiogenic therapy 24-h after initial treatment. Further analysis of image features for linear correlation between the conventional dTE molecular intensity parameter and statistically selected dTE image features was carried out to quantify complementarity of information encoded to image features extracted without use of contrast destruction.33 were obtained for our analysis. In brief, 16 female nude mice were injected with the human colon cancer cell line LS174T and after 10 days growth period, randomized to a treatment group (n = 8) receiving 10 mg/kg intravenous infusions of bevacizumab and a control group (n = 8) receiving sterile saline infusion on days 0, 3, and 7 after the growth period.All experiments involving animals were approved by the Stanford Institutional Administrative Panel on Laboratory Animal Care (APLAC) and were performed in accordance with the APLC guidelines and regulations. The present report was prepared in compliance with the ARRIVE guideline. Imaging data from prior published work3D mCEUS was performed using a clinical ultrasound scanner  with a clinical matrix array transducer . Reduction of near-field zone artifact of the transducer was achieved with a 3-cm custom standoff ultrasound gel placed to the skin of mice during image acquisition. Scans were performed in power modulation contrast imaging mode for all tumors with transducer fixed in a stable position with a clamp. All mice were anesthetized with 2% isoflurane in room air at 2 L/minute during imaging while positioned on a heated support to maintain stable body temperature for the duration of the experiment.VEGFR2+, 5 × 107 microbubbles/100 µL, BR55, Braco Suisse71) injected at a constant rate within 5 s using an infusion pump (Kent Scientific) through a 27G needle catheter  placed in a tail vein. Total scan time for each tumor each day was 5 min: 4 min to allow complete contrast-perfusion of the tumor volume followed by a sequence of 2 high-powered ultrasound pulses  applied for 2 s to destroy all bound and unbound microbubbles. The remaining minute allowed tumor volumes to fully replenish intravascular contrast and a second measurement of imaging signal was taken to quantify the bound fraction of molecular contrast from before and after destruction pulses. A further detailed account of image acquisition and contrast injection procedures can be found in Supplementary Methods.Contrast used was clinical-grade VEGFR2-targeted microbubbles  for all 3D mCEUS datasets that includes the entire tumor volume in sagittal, longitudinal, and coronal planes. From these raw imaging datasets, a sliding-window method was used to select all imaging data from prior to contrast destruction, only data from the last 10 frames prior to contrast destruction, or data from before and after contrast destruction. A Python pipeline was used to extract bolus-based parameters of molecular intensity used in conventional analysis on a voxel-by-voxel basis within the manually contoured VOI from the full set of raw imaging data, data from the final 10 frames, and those requiring a destruction pulse. These parameters include average intensity projection, maximum intensity projection, lowest intensity projection, standard deviation, post-destruction baseline, post-destruction standard deviation, and dTE. In total, 11 intensity maps were generated.41 for extraction and calculation of data values, generating a total of 1,001 image features from 91 image features for each of 11 intensity maps.Image feature extraction of statistical histogram and radiomics features was carried out using custom software developed in the Python coding language relying on PyRadiomics72 and Pingouin73 on image feature data normalized as fold change from baseline. Intraclass correlation coefficient  was calculated using a 2-way mixed model74 for the 1001 features using a separate database of serial 3D mCEUS cines obtained from LS174T tumors (n = 18) to determine features with reproducible values. Features that scored above threshold for ICC were kept if also meeting statistical significance by Wilcoxon signed-rank test.Statistical analysis was performed for feature selection using Python libraries SciPyWilcoxon Signed-Rank test was employed to detect significant (p < 0.05) change from baseline in treated animals. Three p-values were generated for each feature representing changes from baseline on scan days 1, 3, and 10. As such, each intensity map’s reproducible features were considered significant based on 3 criteria: all subsequent scan days from baseline are significantly different from baseline, scan days 1 and day 3 or 10 are significantly different from baseline, and any 2 scan days are significantly different from baseline.33 was tested against statistically selected intensity map image features for the detection of strong linear correlation.Measurement of strong correlation between intensity map image features and dTE features was explored with Spearman correlation (ρ > / = 0.8) comparing the raw data of treated and control animals’ intensity map image features with image feature data from the dTE map in treated and control animals, respectively. The mean intensity feature of dTE images, shown in prior work to carry predictive potential for detecting response to antiangiogenic therapyFurther correlation analysis was carried out similarly comparing statistically selected image feature data of each intensity map against the statistically selected features of the dTE map in treated and control animals, respectively using raw data to quantify the redundant encoding of information in image feature data.75 implementations of 4 supervised-learning classification implementations of logistic regression with and without hyperparameter tuning, linear determinant analysis, and ensemble bagging classifier. Model training was carried out with data from scan days 0, 3, and 10 with model testing performed on data from scan day 1. Hyperparameter tuning was carried out systematically for each algorithm with fivefold cross-validation before calculating ROC-AUC scores. In the cases of LR with hyperparameters and LDA models, RFE was utilized with tenfold cross-validation.Features selected through statistical analysis with Wilcoxon signed-rank test and ICC were stratified into groups representative of the total fraction of TIC necessary to include in calculating intensity maps and the necessity of a destruction pulse phase. The AIP intensity map presented a relatively large set of features (28 image features) and so was made a separate group apart from its image features inclusion in burden group feature sets. As such, four groups were considered: AIP-only features, low burden , moderate burden (prior maps plus full LIP), and highest burden (prior maps plus dTE). Burden group feature sets then underwent further feature selection with correlation feature elimination again using Spearman correlation with a high threshold (rho ≥ 0.80) and manual inspection of best-fit scatter-line plots to confirm a linear relationship, eliminating one feature from each high-correlation pair to reduce redundancy of information. Each group’s feature set was then preprocessed as fold-change from baseline value (scan day 0) and scaled to range from 0 to 1. Model tuning and testing was carried out in Sci-kitImage features selected at RFE for each feature set were collected to assess for commonly selected features. Any feature found selected in at least 3 times at RFE were included into a new, dimensionally-reduced feature set and again tested in multiparametric analysis as previously described.Supplementary Information.


Salmonella (NTS) is a major cause of bacterial enterocolitis globally but also causes invasive bloodstream infections. Antimicrobial resistance (AMR) hampers the treatment of these infections and understanding how AMR spreads between NTS may help in developing effective strategies. We investigated NTS isolates associated with invasive disease, diarrhoeal disease and asymptomatic carriage in animals and humans from Vietnam. Isolates included multiple serovars and both common and rare phenotypic AMR profiles; long- and short-read sequencing was used to investigate the genetic mechanisms and genomic backgrounds associated with phenotypic AMR profiles. We demonstrate concordance between most AMR genotypes and phenotypes but identified large genotypic diversity in clinically relevant phenotypes and the high mobility potential of AMR genes (ARGs) in this setting. We found that 84 % of ARGs identified were located on plasmids, most commonly those containing IncHI1A_1 and IncHI1B(R27)_1_R27 replicons (33%), and those containing IncHI2_1 and IncHI2A_1 replicons (31%). The vast majority (95%) of ARGS were found within 10 kbp of IS6/IS26 elements, which provide plasmids with a mechanism to exchange ARGs between plasmids and other parts of the genome. Whole genome sequencing with targeted long-read sequencing applied in a One Health context identified a comparatively limited number of insertion sequences and plasmid replicons associated with AMR. Therefore, in the context of NTS from Vietnam and likely for other settings as well, the mechanisms by which ARGs move contribute to a more successful AMR profile than the specific ARGs, facilitating the adaptation of bacteria to different environments or selection pressures.Non-typhoidal  The accession numbers and metadata of each isolate are described in Table S1 (available in the online version of this article).The sequence data generated during the current study are available in the European Nucleotide Archive  is a major cause of diarrhoea worldwide and can cause invasive infections. Antimicrobial resistance (AMR) hampers the treatment of these infections and understanding how it spreads may help in developing effective strategies to combat it. This study describes NTS isolates from Vietnam using whole genome sequencing and phenotypic testing to determine what contributes to a successful AMR profile. We found concordance between most AMR genotypes and phenotypes but isolates from the same AMR phenotypes often had different AMR genes. Most AMR genes were found on a small number of plasmid types and in the vicinity of insertion sequences that allow AMR genes to be exchanged between plasmids and other parts of the genome. Our study demonstrates that for NTS from Vietnam, a successful AMR profile is defined by the mechanisms available for AMR genes to move rather than the specific AMR genes the bacteria contain.Non-typhoidal Salmonella (NTS) comprise the >2500 Salmonella enterica subspecies enterica serovars that are not associated with enteric fever , 12:b:- (n=2) in which no ARGs were identified, but this may be due to a small number of isolates investigated belonging to these serovars. Overall, 84 % of identified ARGs were encoded on plasmid replicon-containing contigs, compared to 1 % of virulence and 7 % of metal-tolerance genes. The majority of ARGs were located on contigs containing IncHI1A_1/IncHI1B(R27)_1_R27 (33%) and IncHI2_1/IncHI2A_1 (31%) replicon types. Plasmid contig groupings were complicated by those encoding multiple replicons, e.g., all contigs with the IncFIA(HI1)_1_HI1 replicon also had the IncHI1A_1/IncHI1B(R27)_1_R27 replicon, but not vice versa.ARGs have been found co-located with metal-tolerance genes and therefore exposure to heavy metals can co-select for AMR . ARGs haPan-genome analysis revealed that no ARGs were incorporated in the core genome (defined as presence in >95 % of isolates), compared to 65 % of virulence and 60 % of metal-tolerance genes. The metal-tolerance genes encoded resistance to 47 metals and antibacterial biocides; the NTS isolates investigated contained one or more core resistance genes associated with 36 of these compounds.n=1982) were found throughout the plasmid (n=678) and chromosomal (n=1304) sequences of the Salmonella genomes. In total, 98 % of ARGs were located within 10 kb of insertion sequences, compared to 7 % of virulence and 5 % of metal-tolerance genes. However, this insertion sequence analysis was complicated by some genes being in the vicinity of multiple insertion sequence types. Regardless of the genomic distance used as a cut-off (Appendix C) we confirmed that a larger proportion of ARGs were found in proximity to insertion sequences compared to virulence or metal-tolerance genes. IS6/IS26 comprised 21 % of all identified insertion sequences, but 95 % of ARGs were within 10 kb of this insertion sequence. Six ARG types were identified that were never associated with IS6/IS26, and five plasmid replicons were identified that were never found on the same contigs as IS6/IS26-associated ARGs. However, few copies of these ARGs (1-3) and plasmid replicons (1-5) were identified amongst the 68 NTS isolates investigated, preventing comparisons between specific ARGs, location and dissociation with IS6/IS26.Insertion sequences (P=0.04). However, two circular plasmids were identified that almost entirely (>99 %) consisted of PHASTER-predicted phage genome and both contained the pO111 plasmid replicon, making them phage-like plasmids. BLASTn found 79–80 % coverage between these plasmids and a phage P1 representative (NC_005856.1) , 12:i:- has acquired resistance to metals on en added . In addi [et al.  found vaAn aim of this study was to determine the contributing factors to a successful AMR profile, where success is defined as presence in multiple serovars, host species and disease presentations. Initially, successful AMR profiles were defined by phenotypic testing, with rare phenotypic AMR profiles defined as those found in three or fewer isolates from the OUCRU Vietnam collection and common (successful) AMR profiles in more than ten isolates of at least three different serovars and with resistance to at least three of the considered drugs. This study demonstrates that while some AMR profiles are common based on phenotype data, diverse underlying genetic mechanisms contribute to the phenotype. Therefore, at the resolution of genotype there are few common AMR profiles. In addition, long-read sequencing revealed the genomic context of the ARGs, showing that most ARGs were found on plasmids in association with IS6/IS26. This facilitates the movement of ARGs between plasmids and results in a large diversity of ARG profiles within plasmids. Therefore, in the context of NTS from Vietnam and likely for other settings as well, the mechanisms by which ARGs move between NTS contribute more to a successful AMR profile than the specific ARGs, allowing NTS to gain and lose ARGs in response to environments with different antimicrobial agents or other selection pressures.Klebsiella pneumoniae to identify the plasmids with which carbapenemase genes are associated [Pseudomonas aeruginosa to multiple species of Citrobacter via a plasmid [Campylobacter jejuni ST6964 in New Zealand, where a tetracycline resistance gene moved from a plasmid into the chromosome [Salmonella, here we have demonstrated the importance of plasmids and insertion sequences, but the mobile genetic elements responsible were not the same in the different bacterial species. Therefore, long-read sequencing of different bacteria from around the world and in many different ecological compartments is required to investigate the predominant mobile genetic elements responsible for AMR transmission.Long-read sequencing has facilitated ascertainment of the genomic location of ARGs, and therefore the evolutionary pathways of resistant organisms and likely routes of ARG movement. For example, it has been used on carbapenem-resistant sociated , and the plasmid . Long-reromosome . As withWe have demonstrated the large genotypic diversity underlying clinically relevant phenotypes. The greater resolution offered by identification of specific mechanisms of AMR and the genomic context in which they are found provides insight into the evolution and sources of AMR by identifying the most common vehicles of AMR within their population using an approach which can and has been applied in other settings . Here, tClick here for additional data file.


Mkx−/− mice compared to their wild type littermates to decipher Mkx regulome. We therefore sought to reproduce TSPCs transition to myofibroblasts in-vitro by over-expressing MyoD and followed by phenotypic and experimental cells’ characterization using microscopy, qRT-PCR, flow cytometry sorting, presto-blue cell viability assay and immunofluorescence. Two different in vivo models were used to assess the effect of the MyoD-expressing myofibroblasts: transplantation in the dorsal area of immunodeficient mice and in an adult Achilles tendon injury model. To prevent angiofibrosis, we tested the molecule Xav939 and proceeded with histological stainings, q-RT PCR transcriptional quantification of angifibrotic markers, mechanical tests, and immunofluorescence. Tendinopathy samples showed fibrovascular healing with decreased tenolineage phenotype. Transcriptomic analysis of Mkx−/− tendons revealed myofibroblast-associated biological processes. Over-expression of MyoD in WT tendon stem progenitor cells (TSPCs) gave rise to myofibroblasts reprogramming in-vitro and fibrovascular scarring in-vivo. MKX directly binds to MyoD promoter and underlies global regulative processes related to angiogenesis and Wnt signaling pathway. Blocking Wnt signaling with the small molecule Xav393 resulted in higher histological and biomechanical properties. Taken together, our data provide the first in vivo and in-vitro evidence of tendon stem progenitor cells to myofibroblasts transition and show improved tendon healing via angiofibrosis modulation, thus opening potential therapeutic avenues to treat tendinopathy patients.Adult tendons heal via fibrovascular scarring with inferior biomechanical properties. Mohawk (Mkx) emerged as a pivotal actor in tenolineage commitment. However, its precise function in tendinopathy remains poorly understood. This study investigates the cellular and molecular mechanisms underlying Mkx’ role in fibrovascular healing. Human samples were collected to test fibrovascular markers. We then performed RNAseq on  Tendinopathies are commonly encountered in clinical practice and are associated with neo-fibrovascular tissue formation3. Adult tendons never regain their original biomechanical properties due to their poor regenerative potential and the current treatment strategies do not procure complete recovery given the lack of understanding of tendon physiopathology4.Tendons connect muscles to bones, ensuring force transmission and therefore joint movement. Repetitive loading and overuse make tendons prone to degeneration following injuries5. These cells have a phenotype combining both fibroblast and smooth muscle cells' characteristics7. In tendons, the cells underlying fibrovascular scarring are not fully defined.The persistence of myofibroblasts is a hallmark of fibrovascular scar healing in a wide range of organs and tissues9. Studies with Mkx−/− mice show that these mice exhibit reduced tendon formation throughout the body, suggesting the role of Mkx is extended during adult tendon homeostasis10. Moreover, in-vitro studies showed that Mkx over-expression promotes the expression of teno-related genes and safeguards tenogenic identity by preventing the expression of other cell lineages13. Mkx is substantially down regulated in human tendinopathy and the in-vivo transplantation of mesenchymal stem cell sheets expressing Mkx promoted tendon repair in a mouse model of Achilles‐tendon defect9. At present, no study has explored Mkx effectors during tendinopathy and the signaling cues leading to its down regulation remain to be determined. Given that tenocytes are specialized fibroblasts deriving from TSPCs/MSCs and that Mkx has a central role in maintaining tendon identity and conferring protection from aberrant cellular differentiation, we hypothesized that TSPCs may differentiate into myofibroblasts and that Mkx may have a negative control over this transition.Mkx, a key transcription factor (TF) of tenogenesis, participates decisively during development in tendon differentiation and morphogenesis by regulating type I collagen production in tendon cellsDetailed experimental procedures are available in the supplemental information section online.Human tendon biopsies were collected from 5 different patients undergoing proximal biceps tendon tenotomy in the Second Affiliated Hospital, School of Medicine, Zhejiang University. Surrounding, non-lesioned tissues were used as controls.Mkx−/− and wild type (WT) mice tail tendons. Husbandry, handling, and sacrifice of the mice prior to TSPCs isolation were carried out according to the guidelines of Zhejiang university animal center regulations. Mice were euthanized by intraperitoneal injection of a lethal dose of sodium pentobarbital (120 mg/kg). Cells at passages 1–5 are used for experiments.Mouse TSPCs were isolated from 2 weeks old 14 to filter the differentially expressed genes under the following criteria: (1) Fold Change > 1.5 or < 0.667; (2) FDR < 0.05.Total RNA of tail tendons was extracted (n = 3) using TRIzol reagent  and cDNA library was prepared using the Ion Total RNA-Seq Kit v2. RNA sequencing was performed on Ion Proton system. Clean reads were obtained from the raw reads by removing the adaptor sequences, reads with > 5% ambiguous bases (noted as N) and low-quality reads containing more than 20 percent of bases with qualities of < 13. The clean reads were then aligned to mouse genome (mm9) using the MapSplice program (v2.1.6). We applied EBseq algorithmMyoD expressing vectors  or with empty vectors  using lipofectamine 2000 reagent  according to the manufacturer’s recommendations. Cells were cultured in L/G DMEM medium that was changed every 2 days.Neonatal TSPCs were transfected at 60–70% confluence with MyoD-expressing myofibroblasts effect in-vivo, we transplanted 106 cells mixed with Gelatin methacryloyl; GelMA15, a biomaterial capable of fast photopolymerization under UV irradiation using an improved method16, into immunodeficient mice . Longitudinal skin incisions of about 2 cm in length were made on the dorsal surface. Cells/biomaterial mix were loaded dropwise into the subcutaneous pockets we made in the muscle adjacent to the incision . Incisions were closed with surgical sutures. The same procedure has been applied to the control group . Samples were collected 2 weeks after transplantation.To test MyoD vector (or empty vector for the control group) and stained both the myofibroblast and the control groups with Dil staining . Each group of mice  was subjected to Achilles tendon hemisection and cells were transplanted as described above. Tendons were collected 28 days after injury.To further explore whether myofibroblasts contribute to fibrosis and neo-angiogenesis in vivo, we transfected TSPCs isolated from WT mice with +/-Achilles tendons from 8 months old mice were treated with Xav939  to inhibit Wnt/β-Catenin pathway. A slow-release biomaterial technology was used as a biological glue. Xav939/GelMa mix was loaded dropwise into the injury site concomitantly to UV irradiation prior to suturing. Control group received GelMa alone. Samples were collected at two time points: at day 28 or day 52 after surgery.To modulate angiogenesis in-vivo during mice adult fibrovascular scar healing, injured MkxMkx+/− mice  were clamped from the calcaneus bone and myotendinous junction. Tissues were preloaded to 1 N for 5 loops followed by a speed of stretch of 10 mm/min using the single column electromechanical testing system Instron 5944. The maximum force, stiffness and yield elongation were measured. N = 7 independent samples were tested per group.Achilles’ tendons isolated from Data are presented as mean values ± SEM. Statistical analyses of quantitative experimental data are performed using the unpaired Student t-test. p-value < 0.05 was considered statistically significant. All the experiments have been independently reproduced at least 3 times.GraphPad Prism 6 software (GraphPad Software) was used to analyze quantitative data.This file contains supplementary information on methods, sypplementary figures  and S2, Animal experimentation procedures comply to the rules of Zhejiang University Institutional Animal Care and Use Committee and have been approved by the Ethics Committee of the School of Medical sciences of Zhejiang University (reference number: 12053). This study complies with ARRIVE guidelines. Human tendon biopsies collection was approved by ethics committee of the Second Affiliated Hospital, School of Medicine, Zhejiang University . The study conforms to the principles of the Declaration of Helsinki and participants gave informed consent.18. We therefore sought to investigate key fibrovascular markers in human tendinopathy. On the one hand, we screened publicly available data on human chronic tendinopathy19 from gene expression omnibus (GEO) datasets. The fibrotic markers ACTA2, COL3A1 and PDGFRB, in addition to the angiogenic marker Angptl2 were found to be up-regulated , and “Wnt signaling pathway”  were among the most enriched pathways. Some of the Mkx−/− resident cells  to compare with control TSPCs. Two weeks after transplantation, highly organized tendon-like structures were visualized in the control TSPCs’ transplanted group Fig. D and minMyoD and stained them with Dil 2 weeks after transfection to track their localization in-vivo. We then injured adult mice Achilles tendons and transplanted Dil stained cells at the injury site using the same carrier (GelMA). Myod-expressing myofibroblasts not only promoted fibrovascular scar formation but also participated to neo-vascularization as showed by Dil staining in the cells bordering structures resembling the vessels  , with the transactivation domain of MyoD efficiently reprogrammed mouse embryonic fibroblasts to smooth muscle-like cells29. MyoD mRNA has been found to be up-regulated in the trunk somites of Mkx Zebrafish morphants and the use of an immortalized mouse myoblast cell line (C2C12) showed that Mkx negatively regulates myoD expression20. MyoD temporal expression in relation to Mkx during tendon healing remains unexplored and deserves future investigations.When 30, and MyoD is no exception32. We are aware that the temporality of MyoD expression in relation to Mkx deserves to be studied, but we deem this beyond the scope of our work and we chose to use MyoD as a tool26 for myofibroblast transition.As muscle related terms were enriched in the RNAseq data of the KO mice, we checked MyoD expression in the Mkx−/− mice, but we could not reach unequivocal conclusions as the qRT-PCR and the western blot results were not consistent . This is likely linked to the highly dynamic nature of transcription factors in general35. This is supported by several studies demonstrating angiogenesis blocking as an efficient strategy to prevent fibrosis36.In addition to an increased vascularity around the fibrotic area in the injury/regeneration models, our results also showed angiogenesis as one of the most enriched biological processes according to RNA sequencing of the KO mice and MKX CHIP sequencing data analysis. Neovascularization has long been reported as an underlying condition in lung fibrosis. In kidney or adipose tissue, it is implicated in different pathological contexts, and is thought to participate to fibroproliferation37. Surgery remains the last treatment option, after exhausting all other conservative means of care38 and concerns late tendon disrepair and degenerative tendinopathy. Both late disrepair and degenerative stages present fibrovascular characteristics37.The “continuum model” proposed by Cook and Purdam in 2009 is one of the current dominant theories of tendinopathy. According to this model, tendinopathy ranges in 3 categories: from reactive tendinopathy, tendon disrepair to degenerative tendinopathy40, the participation of endothelial cells to the myofibroblast pool has on the other hand been a matter of debate. Surprisingly, when we transplanted MyoD-expressing myofibroblasts in-vivo, Dil staining was observable at the level of few cells constituting blood vessels, suggesting an opposite phenomenon: a myofibroblast to endothelial transition. Lemoinne et al.41 reported a similar phenomenon in the liver where portal myofibroblasts participate to hepatic vascular remodeling by releasing VEGFA microparticles and integrating the newly formed vessels as mural cells. Our prima facie finding in tendon necessitates further robust in-vivo evidence and a complete study per se.If the participation of resident cells  to the myofibroblast population in fibrotic diseases has been established44. In the study of human tendinopathy by Jelinsky et al.19, several genes involved in Wnt signaling were among the most enriched transcripts. β-catenin, a master molecule of the canonical Wnt/β-catenin signaling, is also up-regulated during human tendinopathy . In another study, in addition to β-catenin up-regulation, Wnt/β-catenin signaling activation was correlated to Scx, Mkx, and Tnmd suppression during adult rat Achilles tendon injury45.Injured Achilles tendon treatment for angiogenesis modulation with a selective Wnt/β-Catenin inhibitor, the small molecule Xav939, resulted in a phenomenally improved regeneration. The canonical Wnt/β-catenin pathway is involved in a range of processes related to angiogenesis, vascular remodeling and fibrosisMkx essentiality to preserving tendon integrity and impeding from fibrosis and neo-vascularization during wound healing. MyoD over-expression provokes TSPC to myofibroblast transition. And lastly, Xav939, a potent Wnt/β-Catenin pathway inhibitor to modulate angiogenesis leads to a markedly improved healing, providing a rationale for the use of Wnt/β-Catenin modulators for the treatment of tendinopathy.Our findings demonstrate Supplementary Information.