Sampling Real-Time Atomic Dynamics in Metal Nanoparticles by Combining Experiments, Simulations, and Machine Learning.

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.

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.

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.

Self-assembly of cyclic peptide monolayers by hydrophobic supramolecular hinges.

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.

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.

Systematic exploration of accessible topologies of cage molecules via minimalistic models.

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.

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.

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).

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.

Machine learning of atomic dynamics and statistical surface identities in gold nanoparticles.

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.

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.

Into the dynamics of rotaxanes at atomistic resolution.

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.

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.

Unsupervised Data-Driven Reconstruction of Molecular Motifs in Simple to Complex Dynamic Micelles.

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.

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).

Supramolecular Semiconductivity through Emerging Ionic Gates in Ion-Nanoparticle Superlattices.

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.

Reconstructing reactivity in dynamic host-guest systems at atomistic resolution: amide hydrolysis under confinement in the cavity of a coordination cage.

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.

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.