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.

Non-Equilibrium Modeling of Concentration-Driven processes with Constant Chemical Potential Molecular Dynamics Simulations.

ConspectusConcentration-driven processes in solution, i.e., phenomena that are sustained by persistent concentration gradients, such as crystallization and surface adsorption, are fundamental chemical processes. Understanding such phenomena is crucial for countless applications, from pharmaceuticals to biotechnology. Molecular dynamics (MD), both in- and out-of-equilibrium, plays an essential role in the current understanding of concentration-driven processes. Computational costs, however, impose drastic limitations on the accessible scale of simulated systems, hampering the effective study of such phenomena. In particular, due to these size limitations, closed system MD of concentration-driven processes is affected by solution depletion/enrichment that unavoidably impacts the dynamics of the chemical phenomena under study. As a notable example, in simulations of crystallization from solution, the transfer of monomers between the liquid and crystal phases results in a gradual depletion/enrichment of solution concentration, altering the driving force for phase transition. In contrast, this effect is negligible in experiments, given the macroscopic size of the solution volume. Because of these limitations, accurate MD characterization of concentration-driven phenomena has proven to be a long-standing simulation challenge. While disparate equilibrium and nonequilibrium simulation strategies have been proposed to address the study of such processes, the methodologies are in continuous development.In this context, a novel simulation technique named constant chemical potential molecular dynamics (CµMD) was recently proposed. CµMD employs properly designed, concentration-dependent external forces that regulate the flux of solute species between selected subregions of the simulation volume. This enables simulations of systems under a constant chemical drive in an efficient and straightforward way. The CµMD scheme was originally applied to the case of crystal growth from solution and then extended to the simulation of various physicochemical processes, resulting in new variants of the method. This Account illustrates the CµMD method and the key advances enabled by it in the framework of in silico chemistry. We review results obtained in crystallization studies, where CµMD allows growth rate calculations and equilibrium shape predictions, and in adsorption studies, where adsorption thermodynamics on porous or solid surfaces was correctly characterized via CµMD. Furthermore, we will discuss the application of CµMD variants to simulate permeation through porous materials, solution separation, and nucleation upon fixed concentration gradients. While presenting the numerous applications of the method, we provide an original and comprehensive assessment of concentration-driven simulations using CµMD. To this end, we also shed light on the theoretical and technical foundations of CµMD, underlining the novelty and specificity of the method with respect to existing techniques while stressing its current limitations. Overall, the application of CµMD to a diverse range of fields provides new insight into many physicochemical processes, the in silico study of which has been hitherto limited by finite-size effects. In this context, CµMD stands out as a general-purpose method that promises to be an invaluable simulation tool for studying molecular-scale concentration-driven phenomena.

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.

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.

Molecular communications in complex systems of dynamic supramolecular polymers.

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.

Porous covalent organic nanotubes and their assembly in loops and toroids.

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.

Classifying soft self-assembled materials via unsupervised machine learning of defects.

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.

Electrostatic co-assembly of nanoparticles with oppositely charged small molecules into static and dynamic superstructures.

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.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study.

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

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.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization.

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.

Solvent-driven chirality for luminescent self-assembled structures: experiments and theory.

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.

Exploring the Potential of Benzene-1,3,5-tricarboxamide Supramolecular Polymers as Biomaterials.

The fast dynamics occurring in natural processes increases the difficulty of creating biomaterials capable of mimicking Nature. Within synthetic biomaterials, water-soluble supramolecular polymers show great potential in mimicking the dynamic behavior of these natural processes. In particular, benzene-1,3,5-tricaboxamide (BTA)-based supramolecular polymers have shown to be highly dynamic through the exchange of monomers within and between fibers, but their suitability as biomaterials has not been yet explored. Herein we systematically study the interactions of BTA supramolecular polymers bearing either tetraethylene glycol or mannose units at the periphery with different biological entities. When BTA fibers were incubated with bovine serum albumin (BSA), the protein conformation was only affected by the fibers containing tetraethylene glycol at the periphery (BTA-OEG4). Coarse-grained molecular simulations showed that BSA interacted with BTA-OEG4 fibers rather than with BTA-OEG4 monomers that are present in solution or that may exchange out of the fibers. Microscopy studies revealed that, in the presence of BSA, BTA-OEG4 retained their fiber conformation although their length was slightly shortened. When further incubated with fetal bovine serum (FBS), both long and short fibers were visualized in solution. Nevertheless, in the hydrogel state, the rheological properties were remarkably preserved. Further studies on the cellular compatibility of all the BTA assemblies and mixtures thereof were performed in four different cell lines. A low cytotoxic effect at most concentrations was observed, confirming the suitability of utilizing functional BTA supramolecular polymers as dynamic biomaterials.

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.

Molecular Factors Controlling the Isomerization of Azobenzenes in the Cavity of a Flexible Coordination Cage.

Photoswitchable molecules are employed for many applications, from the development of active materials to the design of stimuli-responsive molecular systems and light-powered molecular machines. To fully exploit their potential, we must learn ways to control the mechanism and kinetics of their photoinduced isomerization. One possible strategy involves confinement of photoresponsive switches such as azobenzenes or spiropyrans within crowded molecular environments, which may allow control over their light-induced conversion. However, the molecular factors that influence and control the switching process under realistic conditions and within dynamic molecular regimes often remain difficult to ascertain. As a case study, here we have employed molecular models to probe the isomerization of azobenzene guests within a Pd(II)-based coordination cage host in water. Atomistic molecular dynamics and metadynamics simulations allow us to characterize the flexibility of the cage in the solvent, the (rare) guest encapsulation and release events, and the relative probability/kinetics of light-induced isomerization of azobenzene analogues in these host-guest systems. In this way, we can reconstruct the mechanism of azobenzene switching inside the cage cavity and explore key molecular factors that may control this event. We obtain a molecular-level insight on the effects of crowding and host-guest interactions on azobenzene isomerization. The detailed picture elucidated by this study may enable the rational design of photoswitchable systems whose reactivity can be controlled via host-guest interactions.

Computational methods in the study of self-entangled proteins: a critical appraisal.

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.