Biochemical topology: applications to DNA recombination and replication

Upsurge of Spontaneous Knotting in Polar Diblock Active Polymers

Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting increases by orders of magnitude in diblock polymers having a fraction p of self-propelled monomers. Remarkably, this enhancement is not monotonic in p with an optimal value independent of the monomer's activity. By monitoring the knot's size and position we elucidate the mechanisms of its formation, diffusion, and untying and ascribe the nonmonotonic behavior to the competition between the rate of knot formation and the knot's lifetime. These findings suggest a nonequilibrium mechanism to generate entangled filaments at the nano- and microscales.

Could Olympic Gels of Polystyrene be Produced by ARGET ATRP From Bifunctional Initiators?

The kinetics of gelation in the Activators Regenerated by Electron Transfer Atom Transfer Radical Polymerization (ARGET ATRP) of styrene, using a bifunctional initiator and no crosslinking agents are investigated. By applying the method of moments, we develop a system of differential equations that accounts for the formation of polymer rings. The kinetic rate constants of this model are optimized on the experimentally determined kinetics, varying the reaction temperature and ethanol fraction. Subsequently, we explore how variations in the amounts of catalyst, initiator, and reducing agents affect the simulated equilibria of ARGET ATRP, the emergence of gelation, and the swelling properties of the resulting networks. These findings suggest that favoring ring formation enhances the gelation phenomenon, supporting the hypothesis that the networks formed under the reported reaction conditions are olympic gels.

Molecular dynamics studies of knotted polymers

Molecular dynamics calculations have been used to explore the influence of knots on the strength of a polymer strand. In particular, the mechanism of breaking 31, 41, 51, and 52 prime knots has been studied using two very different models to represent the polymer: (1) the generic coarse-grained (CG) bead model of polymer physics and (2) a state-of-the-art machine learned atomistic neural network (NN) potential for polyethylene derived from electronic structure calculations. While there is a broad overall agreement between the results on the influence of the pulling rate on chain rupture based on the CG and atomistic NN models, for the simple 31 and 41 knots, significant differences are found for the more complex 51 and 52 knots. Notably, in the latter case, the NN model more frequently predicts that these knots can break not only at the crossings at the entrance/exit but also at one of the central crossing points. The relative smoothness of the CG potential energy surface also leads to stabilization of tighter knots compared to the more realistic NN model.

Motor domain of condensin and step formation in extruding loop of DNA

During the asymmetric loop extrusion of DNA by a condensin complex, one domain of the complex stably anchors to the DNA molecule, and another domain reels in the DNA strand into a loop. The DNA strand in the loop is fully relaxed, or there is no tension in the loop. Just outside of the loop, there is a tension that resists the extrusion of DNA. To maintain the extrusion of the DNA loop, the condensin complex must have a domain capable of generating a force to overcome the tension outside of the loop. This study proposes that the groove-shaped HEAT repeat domain Ycg1 plays the role of a molecular motor. A DNA molecule may bind to the groove electrostatically, and the weak binding force facilitates the random thermal motion of DNA molecules. A mechanical model that random collisions between DNA and the nonparallel inner surfaces of the groove may generate a directional force which is required for the loop extrusion to sustain. The hinge domain binds to the DNA molecule and acts as an anchor during asymmetric DNA loop extrusion. When the effects of ATP hydrolysis and the viscous drag of the fluid environment are considered, the motor-anchor model for the condensin complex and the mechanical model might explain the asymmetric loop extrusion, the formation of steps, the step size distribution in the loop extrusion, the tension-dependent extrusion speed, the interaction between coexisting loops on the DNA strand, and untying the knots during extrusion. This model can also explain the observed formation of the Z-loop.

The chromosome folding problem and how cells solve it

Every cell must solve the problem of how to fold its genome. We describe how the folded state of chromosomes is the result of the combined activity of multiple conserved mechanisms. Homotypic affinity-driven interactions lead to spatial partitioning of active and inactive loci. Molecular motors fold chromosomes through loop extrusion. Topological features such as supercoiling and entanglements contribute to chromosome folding and its dynamics, and tethering loci to sub-nuclear structures adds additional constraints. Dramatically diverse chromosome conformations observed throughout the cell cycle and across the tree of life can be explained through differential regulation and implementation of these basic mechanisms. We propose that the first functions of chromosome folding are to mediate genome replication, compaction, and segregation and that mechanisms of folding have subsequently been co-opted for other roles, including long-range gene regulation, in different conditions, cell types, and species.

Folding a Molecular Strand into a Trefoil Knot of Single Handedness with Co(II)/Co(III) Chaperones

We report the synthesis of a right-handed (Δ-stereochemistry of strand crossings) trefoil knot from a single molecular strand containing three pyrazine-2,5-dicarboxamide units adjacent to point-chiral centers and six pyridine moieties. The oligomeric ligand strand folds into an overhand (open-trefoil) knot through the assistance of coordinatively dynamic Co(II) "chaperones" that drive the formation of a three-metal-ion circular helicate. The entangled structure is kinetically locked by oxidation to Co(III) and covalently captured by ring-closing olefin metathesis to generate a trefoil knot of single topological handedness. The stereochemistry of the strand crossings in the metal-coordinated overhand knot is governed by the stereochemistry of the point-chiral carbon centers in the ligand strand. The overhand and trefoil knots were characterized by NMR spectroscopy, mass spectrometry, and X-ray crystallography. Removal of the metal ions from the knot, followed by hydrogenation of the alkene, yielded the wholly organic trefoil knot. The metal-free knot and parent ligand were investigated by circular dichroism (CD) spectroscopy. The CD spectra indicate that the topological stereochemistry of the knot has a greater effect on the asymmetry of the chromophore environment than do the point-chiral centers of the strand.

Molecular entanglement can strongly increase basicity

Brønsted basicity is a fundamental chemical property featured by several kinds of inorganic and organic compounds. In this Review, we treat a particularly high basicity resulting from the mechanical entanglement involving two or more molecular subunits in catenanes and rotaxanes. Such entanglement allows a number of basic sites to be in close proximity with each other, highly increasing the proton affinity in comparison with the corresponding, non-entangled counterparts up to obtain superbases, properly defined as mechanically interlocked superbases. In the following pages, the development of this kind of superbases will be described with a historical perusal, starting from the initial, serendipitous findings up to the most recent reports where the strong basic property of entangled molecular units is the object of a rational design.

Distinguishing Protein Chemical Topologies Using Supercharging Ion Mobility Spectrometry-Mass Spectrometry

A technique combining ion mobility spectrometry-mass spectrometry (IMS-MS) and supercharging electrospray ionization (ESI) has been demonstrated to differentiate protein chemical topology effectively. Incorporating as many charges as possible into proteins via supercharging ESI allows the protein chains to be largely unfolded and stretched, revealing their hidden chemical topology. Different chemical topologies result in differing geometrical sizes of the unfolded proteins due to constraints in torsional rotations in cyclic domains. By introducing new topological indices, such as the chain-length-normalized collision cross-section (CCS) and the maximum charge state (zM ) in the extensively unfolded state, we were able to successfully differentiate various protein chemical topologies, including linear chains, ring-containing topologies (lasso, tadpole, multicyclics, etc.), and mechanically interlocked rings, like catenanes.

Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions

Topological features embedded in ancient braiding and knotting arts endow significant impacts on our daily life and even cutting-edge science. Recently, fast growing efforts are invested to the braiding topology of complex Bloch bands in non-Hermitian systems. This new classification of band topology goes far beyond those established in Hermitian counterparts. Here, we present the first acoustic realization of the topological non-Hermitian Bloch braids, based on a two-band model easily accessible for realizing any desired knot structure. The non-Hermitian bands are synthesized by a simple binary cavity-tube system, where the long-range, complex-valued, and momentum-resolved couplings are accomplished by a well-controlled unidirectional coupler. In addition to directly visualizing various two-band braiding patterns, we unambiguously observe the highly elusive topological phase transitions between them. Not only do our results provide a direct demonstration for the non-Hermitian band topology, but also the experimental techniques open new avenues for designing unconventional acoustic metamaterials.

Shape-Dependent Complementary Ditopic Terpyridine Pair with Two Levels of Self-Recognition for Coordination-Driven Self-Assembly

Molecular recognition in biological systems plays a vital role in the precise construction of biomacromolecules and the corresponding biological activities. Such recognition mainly relies on the highly specific binding of complementary molecular pairs with complementary sizes, shapes, and intermolecular forces. It still remains challenging to develop artificial complementary motif pairs for coordination-driven self-assembly. Herein, a series of shape-dependent complementary motif pairs, based on ditopic 2,2':6',2″-terpyridine (TPY) backbone, are designed and synthesized. The fidelity degrees of self-assemblies from these motifs are carefully evaluated by multi-dimensional mass spectrometry, nuclear magnetic resonance spectroscopy, and molecular modeling. In addition, two levels of self-recognition in both homoleptic and heteroleptic assembly are discovered in the assembled system. Through finely tuning the shape and size of the ligands, a complementary pair is developed with error-free narcissistically self-sorting at two levels of self-recognition, and the intrinsic principle is carefully investigated.

Adherent Moving of Polymers in Spherical Confined Binary Semiflexible Ring Polymer Mixtures

Based on the coarse-grained model, we used molecular dynamics methods to calculate and simulate a semiflexible long ring–semiflexible short ring blended polymer system confined in a hard sphere. We systematically studied the distribution and motion characteristics of the long ring chain. The results show that when the short ring is short enough (Lshort < 20), the long ring (Llong = 50) is separated from the blend system and then distributed against the inner wall. As the length of the short ring increases (Lshort ≥ 20), the long ring can no longer be separated from the blending system. Moreover, we found that the long ring demonstrates a random direction of adherent walking behavior on the inner surface of the hard sphere. The velocity of the long ring decreases with the increase in the short ring length Lshort. Specifically for Lshort ≥ 20, the system does not undergo phase separation and the speed of the long ring decreases sharply along with the long ring distributed inside the confined bulk. This is related to the inner wall layer moving faster than the inside bulk of the restricted system. Our simulation results can help us to understand the distribution of macromolecules in biological systems in confined systems, including the restricted chromosome partitioning distribution and packing structure of circular DNA molecules.

Topological gelation of reconnecting polymers

Shuffling of genetic material via reconnection of proximal DNA segments is seen in meiosis and some cancers. In contrast with textbook pictures, reconnections are performed within an entangled environment and can result in knotting or linking, detrimental for cells. By performing Brownian dynamics simulations of reconnecting polymers under confinement, modeling the genome in vivo, we find a topological transition between a gas or liquid of unlinked rings and a gel-like structure with a large number of polydisperse linked rings. This transition can be triggered by increasing polymer stiffness or confinement. Our results suggest ways to design future topological materials, such as DNA-based gels involving recombinase proteins.

DNA recombination is a ubiquitous process that ensures genetic diversity. Contrary to textbook pictures, DNA recombination, as well as generic DNA translocations, occurs in a confined and highly entangled environment. Inspired by this observation, here, we investigate a solution of semiflexible polymer rings undergoing generic cutting and reconnection operations under spherical confinement. Our setup may be realized using engineered DNA in the presence of recombinase proteins or by considering micelle-like components able to form living (or reversibly breakable) polymer rings. We find that in such systems, there is a topological gelation transition, which can be triggered by increasing either the stiffness or the concentration of the rings. Flexible or dilute polymers break into an ensemble of short, unlinked, and segregated rings, whereas sufficiently stiff or dense polymers self-assemble into a network of long, linked, and mixed loops, many of which are knotted. We predict that the two phases should behave qualitatively differently in elution experiments monitoring the escape dynamics from a permeabilized container. Besides shedding some light on the biophysics and topology of genomes undergoing DNA reconnection in vivo, our findings could be leveraged in vitro to design polymeric complex fluids—e.g., DNA-based complex fluids or living polymer networks—with desired topologies.

Knotting matters: orderly molecular entanglements

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.

Characteristics and possible mechanisms of formation of microinversions distinguishing human and chimpanzee genomes

Genomic inversions come in various sizes. While long inversions are relatively easy to identify by aligning high-quality genome sequences, unambiguous identification of microinversions is more problematic. Here, using a set of extra stringent criteria to distinguish microinversions from other mutational events, we describe microinversions that occurred after the divergence of humans and chimpanzees. In total, we found 59 definite microinversions that range from 17 to 33 nucleotides in length. In majority of them, human genome sequences matched exactly the reverse-complemented chimpanzee genome sequences, implying that the inverted DNA segment was copied precisely. All these microinversions were flanked by perfect or nearly perfect inverted repeats pointing to their key role in their formation. Template switching at inverted repeats during DNA replication was previously discussed as a possible mechanism for the microinversion formation. However, many of definite microinversions found by us cannot be easily explained via template switching owing to the combination of the short length and imperfect nature of their flanking inverted repeats. We propose a novel, alternative mechanism that involves repair of a double-stranded break within the inverting segment via microhomology-mediated break-induced replication, which can consistently explain all definite microinversion events.

DNA Knot Malleability in Single-Digit Nanopores

Knots in long DNA molecules are prevalent in biological systems and serve as a model system for investigating static and dynamic properties of biopolymers. We explore the dynamics of knots in double-stranded DNA in a new regime of nanometer-scale confinement, large forces, and short time scales, using solid-state nanopores. We show that DNA knots undergo isomorphic translocation through a nanopore, retaining their equilibrium morphology by swiftly compressing in a lateral direction to fit the constriction. We observe no evidence of knot tightening or jamming, even for single-digit nanopores. We explain the observations as the malleability of DNA, characterized by sharp buckling of the DNA in nanopores, driven by the transient disruption of base pairing. Our molecular dynamics simulations support the model. These results are relevant not only for the understanding of DNA packing and manipulation in living cells but also for the polymer physics of DNA and the development of nanopore-based sequencing technologies.

819 molecular knot: a theoretical analysis of the electronic structure using an ONIOM approach

The present work analyzes the electronic and molecular properties of the 8₁₉ ([Fe(II)₄]Cℓ) and metal-free knot ligand complexes obtained from X-ray crystal structure of molecular 8₁₉ knot complex [Fe(II)₄(PF₆)₇]Cℓ. The studies were theoretically investigated by means of DFT, TD-DFT, and ONIOM approaches. Basis sets functions from all-electron calculations for bromine, iodine, and iron atoms were adapted to be used along with relativistic effective core potential, while H, C, N, O, and Cℓ atoms were described by Pople basis sets. The diffusion effect of halogen into the 8₁₉ cavity, UV-Vis, and Electronic Circular Dichroism spectra were also analyzed. All calculations were performed using solvent effect through the SCRF/SMD model and dispersion effects by Grimme methodology. The value of mean separation distance between Cℓ and iron atom (7.218 Å) is in good agreement with X-ray experimental result (7.258 Å). Circular dichroism spectrum of metal-free 8₁₉ knot ligand was calculated and the maximum absorption in 262 nm, Δ𝜖 obtained was 67 L mol^- 1 cm^- 1. These results are qualitatively similar to those obtained experimentally, 295 nm and 80 L mol^- 1 cm^- 1, respectively. In this study, we report the electronic and molecular properties of the 8₁₉ ([Fe(II)₄]Cl and metal-free knot ligand complexes and compare with the results obtained from X-ray crystallographic data of 8₁₉ knot complex [Fe(II)₄(PF₆)₇]Cl. The 8₁₉ knot were investigated by means of DFT, TD-DFT, and ONIOM approaches. Basis sets functions from all-electron for Br, I, and Fe atoms were adapted to be used along with relativistic effective core potential, while H, C, N, O, and Cl atoms were described by Pople basis sets. The objective was to understand the stability of the 8₁₉ knot as a function of the substitution of the central halogen atom (Cl), and the signal in the circular dichroism spectra. From the equilibrium geometries, we have obtained good results for values of the bond distance, bond angle, and dihedral angle along the molecular structure when these variables are compared with the results obtained from X-ray data. The diffusion effect of halogen into the 8₁₉ cavity, UV-Vis, and Electronic Circular Dichroism spectra was also analyzed. Circular dichroism spectrum of metal-free 8₁₉ knot ligand was calculated, and the maximum absorption is in good agreement with the experimental value. The ONIOM methodology combined with the relativistic effective core potential and the atomic basis sets provide good results for systems with a complex topology, such as knots.

Self-assembly and guest-induced disassembly of triply interlocked [2]catenanes

Two triply interlocked [2]catenanes and one simple metallacage were constructed by tuning the widths of the organometallic dinuclear building blocks, and the interlocked architectures were disassembled by large aromatic molecules.

Effects of turn-structure on folding and entanglement in artificial molecular overhand knots

The length and constitution of spacers linking three 2,6-pyridinedicarboxamide units in a molecular strand influence the tightness of the resulting overhand (open-trefoil) knot that the strand folds into in the presence of lanthanide(iii) ions. The use of β-hairpin forming motifs as linkers enables a metal-coordinated pseudopeptide with a knotted tertiary structure to be generated. The resulting pseudopeptide knot has one of the highest backbone-to-crossing ratios (BCR)—a measure of knot tightness (a high value corresponding to looseness)—for a synthetic molecular knot to date. Preorganization in the crossing-free turn section of the knot affects aromatic stacking interactions close to the crossing region. The metal-coordinated pseudopeptide knot is compared to overhand knots with other linkers of varying tightness and turn preorganization, and the entangled architectures characterized by NMR spectroscopy, ESI-MS, CD spectroscopy and, in one case, X-ray crystallography. The results show how it is possible to program specific conformational properties into different key regions of synthetic molecular knots, opening the way to systems where knotting can be systematically incorporated into peptide-like chains through design.

Spacers linking 2,6-pyridinedicarboxamide units influence the tightness of the corresponding lanthanide-coordinated overhand knot. β-Hairpin forming motifs generate a metal-coordinated pseudopeptide with a knotted tertiary structure.

Lasso Proteins: Modular Design, Cellular Synthesis, and Topological Transformation

Entangled proteins have attracted significant research interest. Herein, we report the first rationally designed lasso proteins, or protein [1]rotaxanes, by using a p53dim-entwined dimer for intramolecular entanglement and a SpyTag-SpyCatcher reaction for side-chain ring closure. The lasso structures were confirmed by proteolytic digestion, mutation, NMR spectrometry, and controlled ligation. Their dynamic properties were probed by experiments such as end-capping, proteolytic digestion, and heating/cooling. As a versatile topological intermediate, a lasso protein could be converted to a rotaxane, a heterocatenane, and a "slide-ring" network. Being entirely genetically encoded, this robust and modular lasso-protein motif is a valuable addition to the topological protein repertoire and a promising candidate for protein-based biomaterials.

Polymer Knot in Solution near the θ Point

We study knot effects on polymer dynamics in aqueous solution by dissipative particle dynamics. A methodology to identify the θ point is developed by combining simulation data and analytical methods. Polymer internal motions are investigated systematically by gradually changing solvent quality from a good to poor case. In a good solvent, the knot length grows with fluctuations (breathing stage) and then moves to chain ends (moving stage) to release. Nearby the θ point from the good solvent side, the breathing effect becomes stronger with a weak moving effect. As a result, it is easy for the knot to release because of strong fluctuations in chain conformation. In a poor solvent, both breathing and moving effects are weak. A knot is confined in the chain and suppresses polymer condensation because of the excluded volume effect. Our results are useful for the interpretation of relevant experiments and industrial applications of polymer knots.

Effects of topological constraints on linked ring polymers in solvents of varying quality

We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.

Complex DNA knots detected with a nanopore sensor

Equilibrium knots are common in biological polymers-their prevalence, size distribution, structure, and dynamics have been extensively studied, with implications to fundamental biological processes and DNA sequencing technologies. Nanopore microscopy is a high-throughput single-molecule technique capable of detecting the shape of biopolymers, including DNA knots. Here we demonstrate nanopore sensors that map the equilibrium structure of DNA knots, without spurious knot tightening and sliding. We show the occurrence of both tight and loose knots, reconciling previous contradictory results from different experimental techniques. We evidence the occurrence of two quantitatively different modes of knot translocation through the nanopores, involving very different tension forces. With large statistics, we explore the complex knots and, for the first time, reveal the existence of rare composite knots. We use parametrized complexity, in concert with simulations, to test the theoretical assumptions of the models, further asserting the relevance of nanopores in future investigation of knots.

Self-Sorting Assembly of Molecular Trefoil Knots of Single Handedness

We report on the stereoselective synthesis of trefoil knots of single topological handedness in up to 90% yield (over two steps) through the formation of trimeric circular helicates from ligand strands containing either imine or, unexpectedly, amide chelating units and metal ion templates of the appropriate coordination character (zinc(II) for imines; cobalt(III) for amides). The coordination stereochemistry of the octahedral metal complexes is determined by asymmetric carbon centers in the strands, ultimately translating into trefoil knots that are a single enantiomer, both physically and in terms of their fundamental topology. Both the imine-zinc and amide-cobalt systems display self-sorting behavior, with racemic ligands forming knots that individually contain only building blocks of the same chirality. The knots and the corresponding trimeric circular helicate intermediates (Zn(II)₃ complex for the imine ligands; Co(III)₃ complex for the amide ligands) were characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and X-ray crystallography. The latter confirms the trefoil knots as 84-membered macrocycles, with each of the metal ions sited at a crossing point for three regions of the strand. The stereochemistry of the octahedral coordination centers imparts alternating crossings of the same handedness within each circular helicate. The expression of chirality of the knotted molecules was probed by circular dichroism: The topological handedness of the demetalated knots was found to have a greater effect on the CD response than the Euclidean chirality of an individual chiral center.

Two convergent pathways of DNA knotting in replicating DNA molecules as revealed by θ-curve analysis

During DNA replication in living cells some DNA knots are inadvertently produced by DNA topoisomerases facilitating progression of replication forks. The types of DNA knots formed are conditioned by the 3D organization of replicating DNA molecules. Therefore, by characterizing formed DNA knots it is possible to infer the 3D arrangement of replicating DNA molecules. This topological inference method is highly developed for knotted DNA circles. However, partially replicated DNA molecules have the form of θ-curves. In this article, we use mathematical formalism of θ-curves to characterize the full possibilities of how knotting can occur during replication of DNA molecules in vivo. To do this, we reanalyze earlier experimental studies of knotted, partially replicated DNA molecules and the previously proposed pathway of their formation. We propose a general model of knotting in replication intermediates, and demonstrate that there is an additional, equally important, parallel knotting pathway that also explains how DNA topoisomerases can produce experimentally observed knotted θ-curves. Interestingly, both pathways require intertwining of freshly replicated sister duplexes (precatenanes).

Design of and Stability Studies on Trefoil Knots Featuring RhCp* Building Blocks

Four flexible ligands with different lengths, degrees of flexibility, and steric bulk were synthesized and used to prepare metal-directed assemblies. Interestingly, minor differences among the ligands led to products with dramatically different topologies: a binuclear D-shaped macrocycle, tetranuclear rectangles, and hexanuclear trefoil knots. The interconversion of the trefoil-shaped complexes was also investigated. This contribution introduces a rare ligand-controlled trefoil-rectangle shape transformation in solution.

Observations of metastable states of the free swelling knots and directional motion of tensioned knots in vibrated bead chains

The free swelling of knots and the directional motion of knots under tension were studied in vertically vibrated bead chains. A metastable state of swelling was observed in the strongly vibrated two-end-free bead chains, as predicted by Grosberg and Rabin (Phys. Rev. Lett. 99, 217801 (2007)). Knots in the two-end-fixed chains were found to move directionally. The direction of motion could be changed by flipping the knot over. The velocity of motion depended on the tension in the bead chain. The effects of tension on the motion of knots were studied in one-end-fixed chains. The directional reptation might have been influenced by the random motion of the leading arc of the knot. The knots might move in a forced-reptation manner under the interaction with a simulated translocase.

Coordination Chemistry of a Molecular Pentafoil Knot

The binding of Zn(II) cations to a pentafoil (5₁) knotted ligand allows the synthesis of otherwise inaccessible metalated molecular pentafoil knots via transmetalation, affording the corresponding “first-sphere” coordination Co(II), Ni(II), and Cu(II) pentanuclear knots in good yields (≥85%). Each of the knot complexes was characterized by mass spectrometry, the diamagnetic (zinc) knot complex was characterized by ¹H and ¹³C NMR spectroscopy, and the zinc, cobalt, and nickel pentafoil knots afforded single crystals whose structures were determined by X-ray crystallography. Lehn-type circular helicates generally only form with tris-bipy ligand strands and Fe(II) (and, in some cases, Ni(II) and Zn(II)) salts, so such architectures become accessible for other metal cations only through the use of knotted ligands. The different metalated knots all exhibit “second-sphere” coordination of a single chloride ion within the central cavity of the knot through CH···Cl^– hydrogen bonding and electrostatic interactions. The chloride binding affinities were determined in MeCN by isothermal titration calorimetry, and the strength of binding was shown to vary over 3 orders of magnitude for the different metal-ion–knotted-ligand second-sphere coordination complexes.

Effects of knot tightness at the molecular level

Three 819 knots in closed-loop strands of different lengths (∼20, 23, and 26 nm) were used to experimentally assess the consequences of knot tightness at the molecular level. Through the use of 1H NMR, diffusion-ordered spectroscopy (DOSY), circular dichroism (CD), collision-induced dissociation mass spectrometry (CID-MS) and molecular dynamics (MD) simulations on the different-sized knots, we find that the structure, dynamics, and reactivity of the molecular chains are dramatically affected by the tightness of the knotting. The tautness of entanglement causes differences in conformation, enhances the expression of topological chirality, weakens covalent bonds, inhibits decomplexation events, and changes absorption properties. Understanding the effects of tightening nanoscale knots may usefully inform the design of knotted and entangled molecular materials.

Selective and quantitative synthesis of a linear [3]catenane by two component coordination-driven self-assembly

Coordination-driven self-assembly and synergistic non-covalent intercycler interactions (π–π, CH–π and CH–N) for the selective formation of a linear [3]catenane.

A Six-Crossing Doubly Interlocked [2]Catenane with Twisted Rings, and a Molecular Granny Knot

A molecular 6 2 3 link (a six crossing, doubly interlocked, [2]catenane with twisted rings) and a 31 #31 granny knot (a composite knot made up of two trefoil tangles of the same handedness) were constructed by ring-closing olefin metathesis of an iron(II)-coordinated 2×2 interwoven grid. The connections were directed by pendant phenyl groups to be between proximal ligand ends on the same faces of the grid. The 6 2 3 link was separated from the topoisomeric granny knot by recycling size-exclusion chromatography. The identity of each topoisomer was determined by tandem mass spectrometry and the structure of the 6 2 3 link confirmed by X-ray crystallography, which revealed two 82-membered macrocycles, each in figure-of-eight conformations, linked through both pairs of loops.

Coordination-Driven Self-Assembly of a Molecular Knot Comprising Sixteen Crossings

Molecular knots have become highly attractive to chemists because of their prospective properties in mimicking biomolecules and machines. Only a few examples of molecular knots from the billions tabulated by mathematicians have been realized and molecular knots with more than eight crossings have not been reported to date. We report here the coordination-driven [8+8] self-assembly of a higher-generation molecular knot comprising as many as sixteen crossings. Its solid-state X-ray crystal structure and multinuclear 2D NMR findings confirmed its architecture and topology. The formation of this molecular knot appears to depend on the functionalities and geometries of donor and acceptor in terms of generating appropriate angles and strong π-π interactions supported by hydrophobic effects. This study shows coordination-driven self-assembly offers a powerful potential means of synthesizing more and more complicated molecular knots and of understanding differences between the properties of knotted and unknotted structures.

Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers

The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.

Ambient chemical fixation of CO2 using a highly efficient heterometallic helicate catalyst system

Two novel heptanuclear 3d–4f helicates have been synthesized and characterized.

Topology-Sensitive Microfluidic Filter for Polymers of Varying Stiffness

The separation of polymers based on their size, rigidity, and topology is an essential but also highly challenging task for nanoscience and engineering. Using hybrid molecular dynamics simulations that correctly take into account hydrodynamics, we have designed microfluidic channels for separating linear from ring polymers in dilute solutions. We establish that the transport velocity of the polymers is independent of their topology and rigidity when the channel walls are smooth and repulsive. However, when the walls are decorated with attractive spots arranged on lines parallel to the flow, ring polymers exhibit an order of magnitude higher transport velocity compared to linear chains. The spots induce a homeotropic-like reorientation of ring polymers close to walls leading to a tank treading motion along them, whereas linear chains are immobilized upon adsorption. This mechanism becomes more enhanced with increasing polymer rigidity. The presented technique holds thus promise for reliably separating nanoparticles based on their topology.

Steady-State and Transient Behavior of Knotted Chains in Extensional Fields

Recently, there has been a push to understand how molecular topology alters the nonequilibrium dynamics of polymer systems. In this paper, we probe how knotted polymers evolve in planar extensional fields using Brownian dynamics simulations and single-molecule experiments. In the first part of the study, we quantify the extension versus strain-rate curves of polymers and find that knots shift these curves to larger strain-rates. These trends can be quantitatively explained by Rouse-like scaling theories. In the second half of the study, we examine the consequences of knot untying on the time-dependent conformations of polymers in these external fields. We find that knot untying creates significant, transient changes in chain extension. If the topology is complex, the chain undergoes a wide range of time-dependent conformations since knot untying proceeds through many different stages. We provide examples of such untying trajectories over time.