Author Correction: Self-assembled poly-catenanes from supramolecular toroidal building blocks.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Self-assembled poly-catenanes from supramolecular toroidal building blocks.

Mechanical interlocking of molecules (catenation) is a nontrivial challenge in modern synthetic chemistry and materials science1,2. One strategy to achieve catenation is the design of pre-annular molecules that are capable of both efficient cyclization and of pre-organizing another precursor to engage in subsequent interlocking3-9. This task is particularly difficult when the annular target is composed of a large ensemble of molecules, that is, when it is a supramolecular assembly. However, the construction of such unprecedented assemblies would enable the visualization of nontrivial nanotopologies through microscopy techniques, which would not only satisfy academic curiosity but also pave the way to the development of materials with nanotopology-derived properties. Here we report the synthesis of such a nanotopology using fibrous supramolecular assemblies with intrinsic curvature. Using a solvent-mixing strategy, we kinetically organized a molecule that can elongate into toroids with a radius of about 13 nanometres. Atomic force microscopy on the resulting nanoscale toroids revealed a high percentage of catenation, which is sufficient to yield 'nanolympiadane'10, a nanoscale catenane composed of five interlocked toroids. Spectroscopic and theoretical studies suggested that this unusually high degree of catenation stems from the secondary nucleation of the precursor molecules around the toroids. By modifying the self-assembly protocol to promote ring closure and secondary nucleation, a maximum catenation number of 22 was confirmed by atomic force microscopy.

Detecting dynamic domains and local fluctuations in complex molecular systems via timelapse neighbors shuffling.

It is known that the behavior of many complex systems is controlled by local dynamic rearrangements or fluctuations occurring within them. Complex molecular systems, composed of many molecules interacting with each other in a Brownian storm, make no exception. Despite the rise of machine learning and of sophisticated structural descriptors, detecting local fluctuations and collective transitions in complex dynamic ensembles remains often difficult. Here, we show a machine learning framework based on a descriptor which we name Local Environments and Neighbors Shuffling (LENS), that allows identifying dynamic domains and detecting local fluctuations in a variety of systems in an abstract and efficient way. By tracking how much the microscopic surrounding of each molecular unit changes over time in terms of neighbor individuals, LENS allows characterizing the global (macroscopic) dynamics of molecular systems in phase transition, phases-coexistence, as well as intrinsically characterized by local fluctuations (e.g., defects). Statistical analysis of the LENS time series data extracted from molecular dynamics trajectories of, for example, liquid-like, solid-like, or dynamically diverse complex molecular systems allows tracking in an efficient way the presence of different dynamic domains and of local fluctuations emerging within them. The approach is found robust, versatile, and applicable independently of the features of the system and simply provided that a trajectory containing information on the relative motion of the interacting units is available. We envisage that "such a LENS" will constitute a precious basis for exploring the dynamic complexity of a variety of systems and, given its abstract definition, not necessarily of molecular ones.

Stereocontrolled Self-Assembly of a Helicate-Bridged CuI12L4 Cage That Emits Circularly Polarized Light.

Control over the stereochemistry of metal-organic cages can give rise to useful functions that are entwined with chirality, such as stereoselective guest binding and chiroptical applications. Here, we report a chiral CuI12L4 pseudo-octahedral cage that self-assembled from condensation of triaminotriptycene, aminoquinaldine, and diformylpyridine subcomponents around CuI templates. The corners of this cage consist of six head-to-tail dicopper(I) helicates whose helical chirality can be controlled by the addition of enantiopure 1,1'-bi-2-naphthol (BINOL) during the assembly process. Chiroptical and nuclear magnetic resonance (NMR) studies elucidated the process and mechanism of stereochemical information transfer from BINOL to the cage during the assembly process. Initially formed CuI(BINOL)2 thus underwent stereoselective ligand exchange during the formation of the chiral helicate corners of the cage, which determined the overall cage stereochemistry. The resulting dicopper(I) helicate corners of the cage were also shown to generate circularly polarized luminescence.

Proton Affinity and Conformational Integrity of a 24-Atom Triazine Macrocycle across Physiologically Relevant pH.

For 24-atom triazine macrocycles, protonation of the heterocycle leads to a rigid, folded structure presenting a network of hydrogen bonds. These molecules derive from dynamic covalent chemistry wherein triazine monomers bearing a protected hydrazine group and acetal tethered by the amino acid dimerize quantitatively in an acidic solution. Here, lysine is used, and the product is a tetracation. The primary amines of the lysine side chains do not interfere with quantitative yields of the desired bis(hydrazone) at concentrations of 5-125 mg/mL. Mathematical modeling of data derived from titration experiments of the macrocycle reveals that the pKa values of the protonated triazines are 5.6 and 6.7. Changes in chemical shifts of resonances in the 1H NMR spectra corroborate these values and further support assignment of the protonation sites. The pKa values of the lysine side chains are consistent with expectation. Upon deprotonation, the macrocycle enjoys greater conformational freedom as evident from the broadening of resonances in the 1H and 13C NMR spectra indicative of dynamic motion on the NMR time scale and the appearance of additional conformations at room temperature. While well-tempered metadynamics suggests only a modest difference in accessible conformational footprints of the protonated and deprotonated macrocycles, the shift in conformation(s) supports the stabilizing role that the protons adopt in the hydrogen-bonded network.

Emergence of Photomodulated Protometabolism by Short Peptide-Based Assemblies.

In the early Earth, rudimentary enzymes must have utilized the available light energy source to modulate protometabolic processes. Herein, we report the light-responsive C-C bond manipulation via short peptide-based assemblies bound to the photosensitive molecular cofactor (azo-based photoswitch) where the energy of the light source regulated the binding sites which subsequently modulated the retro-aldolase activity. In the presence of a continual source of high-energy photons, temporal realization of a catalytically more proficient state could be achieved under nonequilibrium conditions. Further, the hydrophobic surface of peptide assemblies facilitated the binding of an orthogonal molecular catalyst that showed augmented activity (promiscuous hydrolytic activity) upon binding. This latent activity was utilized for the in situ generation of light-sensitive cofactor that subsequently modulated the retro-aldolase activity, thus creating a reaction network.

Subtle Stereochemical Effects Influence Binding and Purification Abilities of an FeII4L4 Cage.

A tetrahedral FeII4L4 cage assembled from the coordination of triangular chiral, face-capping ligands to iron(II). This cage exists as two diastereomers in solution, which differ in the stereochemistry of their metal vertices, but share the same point chirality of the ligand. The equilibrium between these cage diastereomers was subtly perturbed by guest binding. This perturbation from equilibrium correlated with the size and shape fit of the guest within the host; insight as to the interplay between stereochemistry and fit was provided by atomistic well-tempered metadynamics simulations. The understanding thus gained as to the stereochemical impact on guest binding enabled the design of a straightforward process for the resolution of the enantiomers of a racemic guest.

A Model for the Rapid Assessment of Solution Structures for 24-Atom Macrocycles: The Impact of ß-Branched Amino Acids on Conformation.

Experiment and computation are used to develop a model to rapidly predict solution structures of macrocycles sharing the same Murcko framework. These 24-atom triazine macrocycles result from the quantitative dimerization of identical monomers presenting a hydrazine group and an acetal tethered to an amino acid linker. Monomers comprising glycine and the ß-branched amino acids threonine, valine, and isoleucine yield macrocycles G-G, T-T, V-V, and I-I, respectively. Elements common to all members of the framework include the efficiency of macrocyclization (quantitative), the solution- and solid-state structures (folded), the site of protonation (opposite the auxiliary dimethylamine group), the geometry of the hydrazone (E), the C2 symmetry of the subunits (conserved), and the rotamer state adopted. In aggregate, the data reveal metrics predictive of the three-dimensional solution structure that derive from the fingerprint region of the 1D 1H spectrum and a network of rOes from a single resonance. The metrics also afford delineation of more nuanced structural features that allow subpopulations to be identified among the members of the framework. Well-tempered metadynamics provides free energy surfaces and population distributions of these macrocycles. The areas of the free energy surface decrease with increasing steric bulk (G-G > V-V ∼ T-T > I-I). In addition, the surfaces are increasingly isoenergetic with decreasing steric bulk (G-G > V-V ∼ T-T > I-I).

Automatic Optimization of Lipid Models in the Martini Force Field Using SwarmCG.

After two decades of continued development of the Martini coarse-grained force field (CG FF), further refinment of the already rather accurate Martini lipid models has become a demanding task that could benefit from integrative data-driven methods. Automatic approaches are increasingly used in the development of accurate molecular models, but they typically make use of specifically designed interaction potentials that transfer poorly to molecular systems or conditions different than those used for model calibration. As a proof of concept, here, we employ SwarmCG, an automatic multiobjective optimization approach facilitating the development of lipid force fields, to refine specifically the bonded interaction parameters in building blocks of lipid models within the framework of the general Martini CG FF. As targets of the optimization procedure, we employ both experimental observables (top-down references: area per lipid and bilayer thickness) and all-atom molecular dynamics simulations (bottom-up reference), which respectively inform on the supra-molecular structure of the lipid bilayer systems and on their submolecular dynamics. In our training sets, we simulate at different temperatures in the liquid and gel phases up to 11 homogeneous lamellar bilayers composed of phosphatidylcholine lipids spanning various tail lengths and degrees of (un)saturation. We explore different CG representations of the molecules and evaluate improvements a posteriori using additional simulation temperatures and a portion of the phase diagram of a DOPC/DPPC mixture. Successfully optimizing up to ∼80 model parameters within still limited computational budgets, we show that this protocol allows the obtainment of improved transferable Martini lipid models. In particular, the results of this study demonstrate how a fine-tuning of the representation and parameters of the models may improve their accuracy and how automatic approaches, such as SwarmCG, may be very useful to this end.

TimeSOAP: Tracking high-dimensional fluctuations in complex molecular systems via time variations of SOAP spectra.

Many molecular systems and physical phenomena are controlled by local fluctuations and microscopic dynamical rearrangements of the constitutive interacting units that are often difficult to detect. This is the case, for example, of phase transitions, phase equilibria, nucleation events, and defect propagation, to mention a few. A detailed comprehension of local atomic environments and of their dynamic rearrangements is essential to understand such phenomena and also to draw structure-property relationships useful to unveil how to control complex molecular systems. Considerable progress in the development of advanced structural descriptors [e.g., Smooth Overlap of Atomic Position (SOAP), etc.] has certainly enhanced the representation of atomic-scale simulations data. However, despite such efforts, local dynamic environment rearrangements still remain difficult to elucidate. Here, exploiting the structurally rich description of atomic environments of SOAP and building on the concept of time-dependent local variations, we developed a SOAP-based descriptor, TimeSOAP (τSOAP), which essentially tracks time variations in local SOAP environments surrounding each molecule (i.e., each SOAP center) along ensemble trajectories. We demonstrate how analysis of the time-series τSOAP data and of their time derivatives allows us to detect dynamic domains and track instantaneous changes of local atomic arrangements (i.e., local fluctuations) in a variety of molecular systems. The approach is simple and general, and we expect that it will help shed light on a variety of complex dynamical phenomena.

Innate dynamics and identity crisis of a metal surface unveiled by machine learning of atomic environments.

Metals are traditionally considered hard matter. However, it is well known that their atomic lattices may become dynamic and undergo reconfigurations even well below the melting temperature. The innate atomic dynamics of metals is directly related to their bulk and surface properties. Understanding their complex structural dynamics is, thus, important for many applications but is not easy. Here, we report deep-potential molecular dynamics simulations allowing to resolve at an atomic resolution the complex dynamics of various types of copper (Cu) surfaces, used as an example, near the Hüttig (∼1/3 of melting) temperature. The development of deep neural network potential trained on density functional theory calculations provides a dynamically accurate force field that we use to simulate large atomistic models of different Cu surface types. A combination of high-dimensional structural descriptors and unsupervized machine learning allows identifying and tracking all the atomic environments (AEs) emerging in the surfaces at finite temperatures. We can directly observe how AEs that are non-native in a specific (ideal) surface, but that are, instead, typical of other surface types, continuously emerge/disappear in that surface in relevant regimes in dynamic equilibrium with the native ones. Our analyses allow estimating the lifetime of all the AEs populating these Cu surfaces and to reconstruct their dynamic interconversions networks. This reveals the elusive identity of these metal surfaces, which preserve their identity only in part and in part transform into something else under relevant conditions. This also proposes a concept of "statistical identity" for metal surfaces, which is key to understanding their behaviors and properties.

Lessons Learned from Multiobjective Automatic Optimizations of Classical Three-Site Rigid Water Models Using Microscopic and Macroscopic Target Experimental Observables.

The development of accurate water models is of primary importance for molecular simulations. Despite their intrinsic approximations, three-site rigid water models are still ubiquitously used to simulate a variety of molecular systems. Automatic optimization approaches have been recently used to iteratively refine three-site water models to fit macroscopic (average) thermodynamic properties, providing state-of-the-art three-site models that still present some deviations from the liquid water properties. Here, we show the results obtained by automatically optimizing three-site rigid water models to fit a combination of microscopic and macroscopic experimental observables. We use Swarm-CG, a multiobjective particle-swarm-optimization algorithm, for training the models to reproduce the experimental radial distribution functions of liquid water at various temperatures (rich in microscopic-level information on, e.g., the local orientation and interactions of the water molecules). We systematically analyze the agreement of these models with experimental observables and the effect of adding macroscopic information to the training set. Our results demonstrate how adding microscopic-rich information in the training of water models allows one to achieve state-of-the-art accuracy in an efficient way. Limitations in the approach and in the approximated description of water in these three-site models are also discussed, providing a demonstrative case useful for the optimization of approximated molecular models, in general.

Synthesis of C60 /[10]CPP-Catenanes by Regioselective, Nanocapsule-Templated Bingel Bis-Addition.

The addition of two unsymmetric malonate esters to the Buckminster fullerene C60 can lead to 22 spectroscopically distinguishable isomeric products and therefore represents a formidable synthesis challenge. In this work, we achieve 87 % selectivity for the formation of a single (in,out-trans-3) isomer by combining three approaches: (i) we use a starting material, in which the two malonates are covalently connected (tether approach); (ii) we form the strong supramolecular complex of C60 with the shape-persistent [10]CPP macrocycle (template approach) and (iii) we embed this complex further within a self-assembled nanocapsule (shadow mask approach). Variation of the spacer chain shed light on the limitations of the approach and the ring dynamics in the unusual [2]catenanes were studied in silico with atomistic resolution. This work significantly widens the scope of mechanically interlocked architectures comprising cycloparaphenylenes (CPP).

Density-tunable pathway complexity in a minimalistic self-assembly model.

An open challenge in self-assembly is learning how to design systems that can be conditionally guided towards different target structures depending on externally-controlled conditions. Using a theoretical and numerical approach, here we discuss a minimalistic self-assembly model that can be steered towards different types of ordered constructs at the equilibrium by solely tuning a facile selection parameter, namely the density of building blocks. Metadynamics and Langevin dynamics simulations allow us to explore the behavior of the system in and out of equilibrium conditions. We show that the density-driven tunability is encoded in the pathway complexity of the system, and specifically in the competition between two different main self-assembly routes. A comprehensive set of simulations provides insight into key factors allowing to make one self-assembling pathway prevailing on the other (or vice versa), determining the selection of the final self-assembled products. We formulate and validate a practical criterion for checking whether a specific molecular design is predisposed for such density-driven tunability of the products, thus offering a new, broader perspective to realize and harness this facile extrinsic control of conditional self-assembly.

Ephemeral ice-like local environments in classical rigid models of liquid water.

Despite great efforts over the past 50 years, the simulation of water still presents significant challenges and open questions. At room temperature and pressure, the collective molecular interactions and dynamics of water molecules may form local structural arrangements that are non-trivial to classify. Here, we employ a data-driven approach built on Smooth Overlap of Atomic Position (SOAP) that allows us to compare and classify how widely used classical models represent liquid water. Macroscopically, the obtained results are rationalized based on water thermodynamic observables. Microscopically, we directly observe how transient ice-like ordered environments may dynamically/statistically form in liquid water, even above freezing temperature, by comparing the SOAP spectra for different ice structures with those of the simulated liquid systems. This confirms recent ab initio-based calculations but also reveals how the emergence of ephemeral local ice-like environments in liquid water at room conditions can be captured by classical water models.

Automatic multi-objective optimization of coarse-grained lipid force fields using SwarmCG.

The development of coarse-grained (CG) molecular models typically requires a time-consuming iterative tuning of parameters in order to have the approximated CG models behave correctly and consistently with, e.g., available higher-resolution simulation data and/or experimental observables. Automatic data-driven approaches are increasingly used to develop accurate models for molecular dynamics simulations. However, the parameters obtained via such automatic methods often make use of specifically designed interaction potentials and are typically poorly transferable to molecular systems or conditions other than those used for training them. Using a multi-objective approach in combination with an automatic optimization engine (SwarmCG), here, we show that it is possible to optimize CG models that are also transferable, obtaining optimized CG force fields (FFs). As a proof of concept, here, we use lipids for which we can avail reference experimental data (area per lipid and bilayer thickness) and reliable atomistic simulations to guide the optimization. Once the resolution of the CG models (mapping) is set as an input, SwarmCG optimizes the parameters of the CG lipid models iteratively and simultaneously against higher-resolution simulations (bottom-up) and experimental data (top-down references). Including different types of lipid bilayers in the training set in a parallel optimization guarantees the transferability of the optimized lipid FF parameters. We demonstrate that SwarmCG can reach satisfactory agreement with experimental data for different resolution CG FFs. We also obtain stimulating insights into the precision-resolution balance of the FFs. The approach is general and can be effectively used to develop new FFs and to improve the existing ones.

Discordant Supramolecular Fibres Reversibly Depolymerised by Temperature and Light.

Synthetic stimuli responsive supramolecular polymers attract increasing interest for their ability to mimic the unique properties of natural assemblies. Here we focus on the well-studied benzene-1,3,5-tricarboxamide (BTA) motif, and substitute it with two (S)-3,7-dimethyloctyl groups and an azobenzene photoswitch. We demonstrate the UV (λ=365 nm) induced depolymerisation of the helical hydrogen-bonded polymers in methylcyclohexane (MCH) through circular dichroism and UV-vis spectroscopy in dilute solution (15 µm), and NMR and iPAINT super-resolution microscopy in concentrated solution (300 µm). The superstructure can be regenerated after thermal depolymerization, whilst repeated depolymerisation can be reversed without degradation by irradiating at λ=455 nm. Molecular dynamics simulations show that the most energetically favourable configuration for these polymers in MCH is a left-handed helical network of hydrogen-bonds between the BTA cores surrounded by two right-handed helices of azobenzenes. The responsiveness to two orthogonal triggers across a broad concentration range holds promise for use in, for example, photo-responsive gelation.

Non-uniform Photoinduced Unfolding of Supramolecular Polymers Leading to Topological Block Nanofibers.

Synthesis of one-dimensional nanofibers with distinct topological (higher-order structural) domains in the same main chain is one of the challenging topics in modern supramolecular polymer chemistry. Non-uniform structural transformation of supramolecular polymer chains by external stimuli may enable preparation of such nanofibers. To demonstrate feasibility of this post-polymerization strategy, we prepared a photoresponsive helically folded supramolecular polymers from a barbiturate monomer containing an azobenzene-embedded rigid π-conjugated scaffold. In contrast to previous helically folded supramolecular polymers composed of a more flexible azobenzene monomer, UV-light induced unfolding of the newly prepared helically folded supramolecular polymers occurred nonuniformly, affording topological block copolymers consisting of folded and unfolded domains. The formation of such blocky copolymers indicates that the photoinduced unfolding of the helically folded structures initiates from relatively flexible parts such as termini or defects. Spontaneous refolding of the unfolded domains was observed after visible-light irradiation followed by aging to restore fully folded structures.

Solvent-Driven Supramolecular Wrapping of Self-Assembled Structures.

Self-assembly relies on the ability of smaller and discrete entities to spontaneously arrange into more organized systems by means of the structure-encoded information. Herein, we show that the design of the media can play a role even more important than the chemical design. The media not only determines the self-assembly pathway at a single-component level, but in a very narrow solvent composition, a supramolecular homo-aggregate can be non-covalently wrapped by a second component that possesses a different crystal lattice. Such a process has been followed in real time by confocal microscopy thanks to the different emission colors of the aggregates formed by two isolated PtII complexes. This coating is reversible and controlled by the media composition. Single-crystal X-ray diffraction and molecular simulations based on coarse-grained (CG) models allowed the understanding of the properties displayed by the different aggregates. Such findings could result in a new method to construct hierarchical supramolecular structures.