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Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe " Onion Clustering ": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data., Competing Interests: Competing interests statement:The authors declare no competing interest.

Even at low temperatures, metal nanoparticles (NPs) possess atomic dynamics that are key for their properties but challenging to elucidate. Recent experimental advances allow obtaining atomic-resolution snapshots of the NPs in realistic regimes, but data acquisition limitations hinder the experimental reconstruction of the atomic dynamics present within them. Molecular simulations have the advantage that these allow directly tracking the motion of atoms over time. However, these typically start from ideal/perfect NP structures and, suffering from sampling limits, provide results that are often dependent on the initial/putative structure and remain purely indicative. Here, by combining state-of-the-art experimental and computational approaches, how it is possible to tackle the limitations of both approaches and resolve the atomistic dynamics present in metal NPs in realistic conditions is demonstrated. Annular dark-field scanning transmission electron microscopy enables the acquisition of ten high-resolution images of an Au NP at intervals of 0.6 s. These are used to reconstruct atomistic 3D models of the real NP used to run ten independent molecular dynamics simulations. Machine learning analyses of the simulation trajectories allow resolving the real-time atomic dynamics present within the NP. This provides a robust combined experimental/computational approach to characterize the structural dynamics of metal NPs in realistic conditions., (© 2024 The Authors. Advanced Science published by Wiley‐VCH GmbH.)

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 p K a values of the protonated triazines are 5.6 and 6.7. Changes in chemical shifts of resonances in the 1 H NMR spectra corroborate these values and further support assignment of the protonation sites. The p K a 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 1 H and 13 C 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.

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 Cu I 12 L 4 pseudo-octahedral cage that self-assembled from condensation of triaminotriptycene, aminoquinaldine, and diformylpyridine subcomponents around Cu I 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 Cu I (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.

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., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Supramolecular polymerisation of two-dimensional (2D) materials requires monomers with non-covalent binding motifs that can control the directionality of both dimensions of growth. A tug of war between these propagation forces can bias polymerisation in either direction, ultimately determining the structure and properties of the final 2D ensemble. Deconvolution of the assembly dynamics of 2D supramolecular systems has been widely overlooked, making monomer design largely empirical. It is thus key to define new design principles for suitable monomers that allow the control of the direction and the dynamics of two-dimensional self-assembled architectures. Here, we investigate the sequential assembly mechanism of new monolayer architectures of cyclic peptide nanotubes by computational simulations and synthesised peptide sequences with selected mutations. Rationally designed cyclic peptide scaffolds are shown to undergo hierarchical self-assembly and afford monolayers of supramolecular nanotubes. The particular geometry, the rigidity and the planar conformation of cyclic peptides of alternating chirality allow the orthogonal orientation of hydrophobic domains that define lateral supramolecular contacts, and ultimately direct the propagation of the monolayers of peptide nanotubes. A flexible 'tryptophan hinge' at the hydrophobic interface was found to allow lateral dynamic interactions between cyclic peptides and thus maintain the stability of the tubular monolayer structure. These results unfold the potential of cyclic peptide scaffolds for the rational design of supramolecular polymerisation processes and hierarchical self-assembly across the different dimensions of space., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The addition of two unsymmetric malonate esters to the Buckminster fullerene C 60 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 C 60 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)., (© 2023 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

Cages are macrocyclic structures with an intrinsic internal cavity that support applications in separations, sensing and catalysis. These materials can be synthesised via self-assembly of organic or metal-organic building blocks. Their bottom-up synthesis and the diversity in building block chemistry allows for fine-tuning of their shape and properties towards a target property. However, it is not straightforward to predict the outcome of self-assembly, and, thus, the structures that are practically accessible during synthesis. Indeed, such a prediction becomes more difficult as problems related to the flexibility of the building blocks or increased combinatorics lead to a higher level of complexity and increased computational costs. Molecular models, and their coarse-graining into simplified representations, may be very useful to this end. Here, we develop a minimalistic toy model of cage-like molecules to explore the stable space of different cage topologies based on a few fundamental geometric building block parameters. Our results capture, despite the simplifications of the model, known geometrical design rules in synthetic cage molecules and uncover the role of building block coordination number and flexibility on the stability of cage topologies. This leads to a large-scale and systematic exploration of design principles, generating data that we expect could be analysed through expandable approaches towards the rational design of self-assembled porous architectures., Competing Interests: There are no conflicts of interest to declare., (This journal is © The Royal Society of Chemistry.)

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.

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.

It is known that metal nanoparticles (NPs) may be dynamic and atoms may move within them even at fairly low temperatures. Characterizing such complex dynamics is key for understanding NPs' properties in realistic regimes, but detailed information on, e.g., the stability, survival, and interconversion rates of the atomic environments (AEs) populating them are non-trivial to attain. In this study, we decode the intricate atomic dynamics of metal NPs by using a machine learning approach analyzing high-dimensional data obtained from molecular dynamics simulations. Using different-shape gold NPs as a representative example, an AEs' dictionary allows us to label step-by-step the individual atoms in the NPs, identifying the native and non-native AEs and populating them along the MD simulations at various temperatures. By tracking the emergence, annihilation, lifetime, and dynamic interconversion of the AEs, our approach permits estimating a "statistical equivalent identity" for metal NPs, providing a comprehensive picture of the intrinsic atomic dynamics that shape their properties., (© 2023. The Author(s).)

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.

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., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Mechanically-interlocked molecules (MIMs) are at the basis of artificial molecular machines and are attracting increasing interest for various applications, from catalysis to drug delivery and nanoelectronics. MIMs are composed of mechanically-interconnected molecular sub-parts that can move with respect to each other, imparting these systems innately dynamical behaviors and interesting stimuli-responsive properties. The rational design of MIMs with desired functionalities requires studying their dynamics at sub-molecular resolution and on relevant timescales, which is challenging experimentally and computationally. Here, we combine molecular dynamics and metadynamics simulations to reconstruct the thermodynamics and kinetics of different types of MIMs at atomistic resolution under different conditions. As representative case studies, we use rotaxanes and molecular shuttles substantially differing in structure, architecture, and dynamical behavior. Our computational approach provides results in agreement with the available experimental evidence and a direct demonstration of the critical effect of the solvent on the dynamics of the MIMs. At the same time, our simulations unveil key factors controlling the dynamics of these systems, providing submolecular-level insights into the mechanisms and kinetics of shuttling. Reconstruction of the free-energy profiles from the simulations reveals details of the conformations of macrocycles on the binding site that are difficult to access via routine experiments and precious for understanding the MIMs' behavior, while their decomposition in enthalpic and entropic contributions unveils the mechanisms and key transitions ruling the intermolecular movements between metastable states within them. The computational framework presented herein is flexible and can be used, in principle, to study a variety of mechanically-interlocked systems., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

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.

The reshuffling mobility of molecular building blocks in self-assembled micelles is a key determinant of many their interesting properties, from emerging morphologies and surface compartmentalization, to dynamic reconfigurability and stimuli-responsiveness. However, the microscopic details of such complex structural dynamics are typically nontrivial to elucidate, especially in multicomponent assemblies. Here we show a machine-learning approach that allows us to reconstruct the structural and dynamic complexity of mono- and bicomponent surfactant micelles from high-dimensional data extracted from equilibrium molecular dynamics simulations. Unsupervised clustering of smooth overlap of atomic position (SOAP) data enables us to identify, in a set of multicomponent surfactant micelles, the dominant local molecular environments that emerge within them and to retrace their dynamics, in terms of exchange probabilities and transition pathways of the constituent building blocks. Tested on a variety of micelles differing in size and in the chemical nature of the constitutive self-assembling units, this approach effectively recognizes the molecular motifs populating them in an exquisitely agnostic and unsupervised way, and allows correlating them to their composition in terms of constitutive surfactant species.

A tetrahedral Fe II 4 L 4 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.

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 β-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 1 H 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 ).

The self-assembly of nanoparticles driven by small molecules or ions may produce colloidal superlattices with features and properties reminiscent of those of metals or semiconductors. However, to what extent the properties of such supramolecular crystals actually resemble those of atomic materials often remains unclear. Here, we present coarse-grained molecular simulations explicitly demonstrating how a behavior evocative of that of semiconductors may emerge in a colloidal superlattice. As a case study, we focus on gold nanoparticles bearing positively charged groups that self-assemble into FCC crystals via mediation by citrate counterions. In silico ohmic experiments show how the dynamically diverse behavior of the ions in different superlattice domains allows the opening of conductive ionic gates above certain levels of applied electric fields. The observed binary conductive/nonconductive behavior is reminiscent of that of conventional semiconductors, while, at a supramolecular level, crossing the "band gap" requires a sufficient electrostatic stimulus to break the intermolecular interactions and make ions diffuse throughout the superlattice's cavities.

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.

Nanocapsules that collapse in response to guanosine triphosphate (GTP) have the potential as drug carriers for efficiently curing diseases caused by cancer and RNA viruses because GTP is present at high levels in such diseased cells and tissues. However, known GTP-responsive carriers also respond to adenosine triphosphate (ATP), which is abundant in normal cells as well. Here, we report the elaborate reconstitution of microtubule into a nanocapsule that selectively responds to GTP. When the tubulin monomer from microtubule is incubated at 37 °C with a mixture of GTP (17 mol%) and nonhydrolysable GTP* (83 mol%), a tubulin nanosheet forms. Upon addition of photoreactive molecular glue to the resulting dispersion, the nanosheet is transformed into a nanocapsule. Cell death results when a doxorubicin-containing nanocapsule, after photochemically crosslinked for properly stabilizing its shell, is taken up into cancer cells that overexpress GTP., (© 2022. The Author(s).)

Spatial confinement is widely employed by nature to attain unique efficiency in controlling chemical reactions. Notable examples are enzymes, which selectively bind reactants and exquisitely regulate their conversion into products. In an attempt to mimic natural catalytic systems, supramolecular metal-organic cages capable of encapsulating guests in their cavity and of controlling/accelerating chemical reactions under confinement are attracting increasing interest. However, the complex nature of these systems, where reactants/products continuously exchange in-and-out of the host, makes it often difficult to elucidate the factors controlling the reactivity in dynamic regimes. As a case study, here we focus on a coordination cage that can encapsulate amide guests and enhance their hydrolysis by favoring their mechanical twisting towards reactive molecular configurations under confinement. We designed an advanced multiscale simulation approach that allows us to reconstruct the reactivity in such host-guest systems in dynamic regimes. In this way, we can characterize amide encapsulation/expulsion in/out of the cage cavity (thermodynamics and kinetics), coupling such host-guest dynamic equilibrium with characteristic hydrolysis reaction constants. All computed kinetic/thermodynamic data are then combined, obtaining a statistical estimation of reaction acceleration in the host-guest system that is found in optimal agreement with the available experimental trends. This shows how, to understand the key factors controlling accelerations/variations in the reaction under confinement, it is necessary to take into account all dynamic processes that occur as intimately entangled in such host-guest systems. This also provides us with a flexible computational framework, useful to build structure-dynamics-property relationships for a variety of reactive host-guest systems., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Inspired by therapeutic potential, the molecular engineering of macrocycles is garnering increased interest. Exercising control with design, however, is challenging due to the dynamic behavior that these molecules must demonstrate in order to be bioactive. Herein, the value of metadynamics simulations is demonstrated: the free-energy surfaces calculated reveal folded and flattened accessible conformations of a 24-atom macrocycle separated by barriers of ∼6 kT under experimentally relevant conditions. Simulations reveal that the dominant conformer is folded-an observation consistent with a solid-state structure determined by X-ray crystallography and a network of rOes established by 1 H NMR. Simulations suggest that the macrocycle exists as a rapidly interconverting pair of enantiomeric, folded structures. Experimentally, 1 H NMR shows a single species at room temperature. However, at lower temperature, the interconversion rate between these enantiomers becomes markedly slower, resulting in the decoalescence of enantiotopic methylene protons into diastereotopic, distinguishable resonances due to the persistence of conformational chirality. The emergence of conformational chirality provides critical experimental support for the simulations, revealing the dynamic nature of the scaffold-a trait deemed critical for oral bioactivity., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

Unlike molecular crystals, soft self-assembled fibers, micelles, vesicles, etc., exhibit a certain order in the arrangement of their constitutive monomers but also high structural dynamicity and variability. Defects and disordered local domains that continuously form-and-repair in their structures impart to such materials unique adaptive and dynamical properties, which make them, e.g., capable to communicate with each other. However, objective criteria to compare such complex dynamical features and to classify soft supramolecular materials are non-trivial to attain. Here we show a data-driven workflow allowing us to achieve this goal. Building on unsupervised clustering of Smooth Overlap of Atomic Position (SOAP) data obtained from equilibrium molecular dynamics simulations, we can compare a variety of soft supramolecular assemblies via a robust SOAP metric. This provides us with a data-driven "defectometer" to classify different types of supramolecular materials based on the structural dynamics of the ordered/disordered local molecular environments that statistically emerge within them., (© 2022. The Author(s).)

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.

Carbon nanotubes, and synthetic organic nanotubes more generally, have in recent decades been widely explored for application in electronic devices, energy storage, catalysis and biosensors. Despite noteworthy progress made in the synthesis of nanotubular architectures with well-defined lengths and diameters, purely covalently bonded organic nanotubes have remained somewhat challenging to prepare. Here we report the synthesis of covalently bonded porous organic nanotubes (CONTs) by Schiff base reaction between a tetratopic amine-functionalized triptycene and a linear dialdehyde. The spatial orientation of the functional groups promotes the growth of the framework in one dimension, and the strong covalent bonds between carbon, nitrogen and oxygen impart the resulting CONTs with high thermal and chemical stability. Upon ultrasonication, the CONTs form intertwined structures that go on to coil and form toroidal superstructures. Computational studies give some insight into the effect of the solvent in this assembly process., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Supramolecular polymers are composed of monomers that self-assemble non-covalently, generating distributions of monodimensional fibres in continuous communication with each other and with the surrounding solution. Fibres, exchanging molecular species, and external environment constitute a sole complex system, which intrinsic dynamics is hard to elucidate. Here we report coarse-grained molecular simulations that allow studying supramolecular polymers at the thermodynamic equilibrium, explicitly showing the complex nature of these systems, which are composed of exquisitely dynamic molecular entities. Detailed studies of molecular exchange provide insights into key factors controlling how assemblies communicate with each other, defining the equilibrium dynamics of the system. Using minimalistic and finer chemically relevant molecular models, we observe that a rich concerted complexity is intrinsic in such self-assembling systems. This offers a new dynamic and probabilistic (rather than structural) picture of supramolecular polymer systems, where the travelling molecular species continuously shape the assemblies that statistically emerge at the equilibrium., (© 2022. The Author(s).)

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.

Multi-component systems often display convoluted behavior, pathway complexity and coupled equilibria. In recent years, several ways to control complex systems by manipulating the subtle balances of interaction energies between the individual components have been explored and thereby shifting the equilibrium between different aggregate states. Here we show the enantioselective chain-capping and dilution-induced supramolecular polymerization with a Zn 2+ -porphyrin-based supramolecular system when going from long, highly cooperative supramolecular polymers to short, disordered aggregates by adding a monotopic Mn 3+ -porphyrin monomer. When mixing the zinc and manganese centered monomers, the Mn 3+ -porphyrins act as chain-cappers for Zn 2+ -porphyrin supramolecular polymers, effectively hindering growth of the copolymer and reducing the length. Upon dilution, the interaction between chain-capper and monomers weakens as the equilibria shift and long supramolecular polymers form again. This dynamic modulation of aggregate morphology and length is achieved through enantioselectivity in the aggregation pathways and concentration-sensitive equilibria. All-atom and coarse-grained molecular simulations provide further insights into the mixing of the species and their exchange dynamics. Our combined experimental and theoretical approach allows for precise control of molecular self-assembly and chiral discrimination in complex systems., (© 2022. The Author(s).)

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., (© 2021 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

Nature designs chemotactic supramolecular structures that can selectively bind specific groups present on surfaces, autonomously scan them moving along density gradients, and react once a critical concentration is encountered. Since such properties are key in many biological functions, these also offer inspirations for designing artificial systems capable of similar bioinspired autonomous behaviors. One approach is to use soft molecular units that self-assemble in an aqueous solution generating nanoparticles (NPs) that display specific chemical groups on their surface, enabling multivalent interactions with complementarily functionalized surfaces. However, a first challenge is to explore the behavior of these assemblies at sufficiently high-resolution to gain insights on the molecular factors controlling their behaviors. Here, by coupling coarse-grained molecular models and advanced simulation approaches, we show that it is possible to study the (autonomous or driven) motion of self-assembled NPs on a receptor-grafted surface at submolecular resolution. As an example, we focus on self-assembled NPs composed of facially amphiphilic oligomers. We observe how tuning the multivalent interactions between the NP and the surface allows to control of the NP binding, its diffusion along chemical surface gradients, and ultimately, the NP reactivity at determined surface group densities. In silico experiments provide physical-chemical insights on key molecular features in the self-assembling units which determine the dynamic behavior and fate of the NPs on the surface: from adhesion, to diffusion, and disassembly. This offers a privileged point of view into the chemotactic properties of supramolecular assemblies, improving our knowledge on how to design new types of materials with bioinspired autonomous behaviors.

Coulombic interactions can be used to assemble charged nanoparticles into higher-order structures, but the process requires oppositely charged partners that are similarly sized. The ability to mediate the assembly of such charged nanoparticles using structurally simple small molecules would greatly facilitate the fabrication of nanostructured materials and harnessing their applications in catalysis, sensing and photonics. Here we show that small molecules with as few as three electric charges can effectively induce attractive interactions between oppositely charged nanoparticles in water. These interactions can guide the assembly of charged nanoparticles into colloidal crystals of a quality previously only thought to result from their co-crystallization with oppositely charged nanoparticles of a similar size. Transient nanoparticle assemblies can be generated using positively charged nanoparticles and multiply charged anions that are enzymatically hydrolysed into mono- and/or dianions. Our findings demonstrate an approach for the facile fabrication, manipulation and further investigation of static and dynamic nanostructured materials in aqueous environments., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

Supramolecular fibers composed of monomers that self-assemble directionally via noncovalent interactions are ubiquitous in nature, and of great interest in chemistry. In these structures, the constitutive monomers continuously exchange in-and-out the assembly according to a well-defined supramolecular equilibrium. However, unraveling the exchange pathways and their molecular determinants constitutes a nontrivial challenge. Here, we combine coarse-grained modeling, enhanced sampling, and machine learning to investigate the key factors controlling the monomer exchange pathways in synthetic supramolecular polymers having an intrinsic dynamic behavior. We demonstrate how the competition of directional vs. nondirectional interactions between the monomers controls the creation/annihilation of defects in the supramolecular polymers, from where monomers exchange proceeds. This competition determines the exchange pathway, dictating whether a fiber statistically swaps monomers from the tips or from all along its length. Finally, thanks to their generality, our models allow the investigation of molecular approaches to control the exchange pathways in these dynamic assemblies.

Molecular dynamics simulations of all-atom and coarse-grained lipid bilayer models are increasingly used to obtain useful insights for understanding the structural dynamics of these assemblies. In this context, one crucial point concerns the comparison of the performance and accuracy of classical force fields (FFs), which sometimes remains elusive. To date, the assessments performed on different classical potentials are mostly based on the comparison with experimental observables, which typically regard average properties. However, local differences of the structure and dynamics, which are poorly captured by average measurements, can make a difference, but these are nontrivial to catch. Here, we propose an agnostic way to compare different FFs at different resolutions (atomistic, united-atom, and coarse-grained), by means of a high-dimensional similarity metrics built on the framework of Smooth Overlap of Atomic Position (SOAP). We compare and classify a set of 13 FFs, modeling 1-palmitoyl-2-oleoyl- sn -glycero-3-phosphocholine (POPC) bilayers. Our SOAP kernel-based metrics allows us to compare, discriminate, and correlate different FFs at different model resolutions in an unbiased, high-dimensional way. This also captures differences between FFs in modeling nonaverage events (originating from local transitions), for example, the liquid-to-gel phase transition in dipalmitoylphosphatidylcholine (DPPC) bilayers, for which our metrics allows us to identify nucleation centers for the phase transition, highlighting some intrinsic resolution limitations in implicit versus explicit solvent FFs.

Understanding the molecular rules behind the dynamics of supramolecular assemblies is fundamentally important for the rational design of responsive assemblies with tunable properties. Herein, we report that the dynamics of temperature-sensitive supramolecular assemblies is not only affected by the dehydration of oligoethylene glycol (OEG) motifs, but also by the thermally-promoted molecular motions. These counteracting features set up a dynamics transition point (DTP) that can be modulated with subtle variations in a small hydrophobic patch on the hydrophilic face of the amphiphilic assembly. Understanding the structural factors that control the dynamics of the assemblies leads to rational design of enzyme-responsive assemblies with tunable temperature responsive profiles.

The development of powerful methods for living covalent polymerization has been a key driver of progress in organic materials science. While there have been remarkable reports on living supramolecular polymerization recently, the scope of monomers is still narrow and a simple solution to the problem is elusive. Here we report a minimalistic molecular platform for living supramolecular polymerization that is based on the unique structure of all-cis 1,2,3,4,5,6-hexafluorocyclohexane, the most polar aliphatic compound reported to date. We use this large dipole moment (6.2 Debye) not only to thermodynamically drive the self-assembly of supramolecular polymers, but also to generate kinetically trapped monomeric states. Upon addition of well-defined seeds, we observed that the dormant monomers engage in a kinetically controlled supramolecular polymerization. The obtained nanofibers have an unusual double helical structure and their length can be controlled by the ratio between seeds and monomers. The successful preparation of supramolecular block copolymers demonstrates the versatility of the approach.

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 Pt II 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., (© 2020 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

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., (© 2020 The Authors. Chemistry - A European Journal published by Wiley-VCH GmbH.)

We present Swarm-CG , a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg ). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG., Competing Interests: The authors declare no competing financial interest., (© 2020 American Chemical Society.)

We describe, for a single platinum complex bearing a dipeptide moiety, a solvent-driven interconversion from twisted to straight micrometric assembled structures with different chirality. The photophysical and morphological properties of the aggregates have been investigated as well as the role of the media and concentration. A real-time visualization of the solvent-driven interconversion processes has been achieved by confocal microscopy. Finally, atomistic and coarse-grained simulations, providing results consistent with the experimental observations, allow to obtain a molecular-level insight into the interesting solvent-responsive behavior of this system.