How the Dynamics of a Supramolecular Polymer Determines Its Dynamic Adaptivity and Stimuli-Responsiveness: Structure-Dynamics-Property Relationships From Coarse-Grained Simulations

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.

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.

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.

The dynamic structure of supramolecular polymers is challenging to determine both in experiments and in simulations. Here the authors use coarse-grained molecular models to provide a comprehensive analysis of the molecular communication in these complex molecular systems.

Controlling the length of porphyrin supramolecular polymers via coupled equilibria and dilution-induced supramolecular polymerization

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 Zn²⁺-porphyrin-based supramolecular system when going from long, highly cooperative supramolecular polymers to short, disordered aggregates by adding a monotopic Mn³⁺-porphyrin monomer. When mixing the zinc and manganese centered monomers, the Mn³⁺-porphyrins act as chain-cappers for Zn²⁺-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.

Toward Chemotactic Supramolecular Nanoparticles: From Autonomous Surface Motion Following Specific Chemical Gradients to Multivalency-Controlled Disassembly

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.

Controlling Exchange Pathways in Dynamic Supramolecular Polymers by Controlling Defects

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.

Dynamics in supramolecular nanomaterials

Self-assembly of amphiphilic small molecules in water leads to nanostructures with customizable structure-property relationships arising from their tunable chemistries. Characterization of these assemblies is generally limited to their static structures -e.g. their geometries and dimensions - but the implementation of tools that provide a deeper understanding of molecular motions has recently emerged. Here, we summarize recent reports showcasing dynamics characterization tools and their application to small molecule assemblies, and we go on to highlight supramolecular systems whose properties are substantially affected by their conformational, exchange, and water dynamics. This review illustrates the importance of considering dynamics in rational amphiphile design.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

Not only in silico drug discovery: Molecular modeling towards in silico drug delivery formulations

The use of methods at molecular scale for the discovery of new potential active ligands, as well as previously unknown binding sites for target proteins, is now an established reality. Literature offers many successful stories of active compounds developed starting from insights obtained in silico and approved by Food and Drug Administration (FDA). One of the most famous examples is raltegravir, a HIV integrase inhibitor, which was developed after the discovery of a previously unknown transient binding area thanks to molecular dynamics simulations. Molecular simulations have the potential to also improve the design and engineering of drug delivery devices, which are still largely based on fundamental conservation equations. Although they can highlight the dominant release mechanism and quantitatively link the release rate to design parameters (size, drug loading, et cetera), their spatial resolution does not allow to fully capture how phenomena at molecular scale influence system behavior. In this scenario, the "computational microscope" offered by simulations at atomic scale can shed light on the impact of molecular interactions on crucial parameters such as release rate and the response of the drug delivery device to external stimuli, providing insights that are difficult or impossible to obtain experimentally. Moreover, the new paradigm brought by nanomedicine further underlined the importance of such computational microscope to study the interactions between nanoparticles and biological components with an unprecedented level of detail. Such knowledge is a fundamental pillar to perform device engineering and to achieve efficient and safe formulations. After a brief theoretical background, this review aims at discussing the potential of molecular simulations for the rational design of drug delivery systems.

Temperature dependent aggregation mechanism and pathway of lysozyme: By all atom and coarse grained molecular dynamics simulation

Aggregation of protein causes various diseases including Alzheimer's disease, Parkinson's disease, and type II diabetes. It was found that aggregation of protein depends on many factors like temperature, pH, salt type, salt concentration, ionic strength, protein concentration, co solutes. Here we have tried to capture the aggregation mechanism and pathway of hen egg white lysozyme using molecular dynamics simulations at two different temperatures; 300 K and 340 K. Along with the all atom simulations to get the atomistic details of aggregation mechanism, we have used coarse grained simulation with MARTINI force field to monitor the aggregation for longer duration. Our results suggest that due to the aggregation, changes in the conformation of lysozyme are more at 340 K than at 300 K. The change in the conformation of the lysozyme at 300 K is mainly due to aggregation where at 340 K change in conformation of lysozyme is due to both aggregation and temperature. Also, a more compact aggregated system is formed at 340 K.

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.

Coarse-Grained Force Field Calibration Based on Multiobjective Bayesian Optimization to Simulate Water Diffusion in Poly-ε-caprolactone

Molecular dynamics at the atomistic scale is increasingly being used to predict material properties and speed up the material design and development process. However, the accuracy of molecular dynamics predictions is sensitively dependent on the force fields. In the traditional force field calibration process, a specific property, predicted by the model, is compared with the experimental observation and the force field parameters are adjusted to minimize the difference. This leads to the issue that the calibrated force fields are not generic and robust enough to predict different properties. Here, a new calibration method based on multiobjective Bayesian optimization is developed to speed up the development of molecular dynamics force fields that are capable of predicting multiple properties accurately. This is achieved by reducing the number of simulation runs to generate the Pareto front with an efficient sequential sampling strategy. The methodology is demonstrated by generating a new coarse-grained force field for polycaprolactone, where the force field can predict the mechanical properties and water diffusion in the polymer.

Identifying and Tracking Defects in Dynamic Supramolecular Polymers

A central paradigm of self-assembly is to create ordered structures starting from molecular monomers that spontaneously recognize and interact with each other via noncovalent interactions. In recent years, great efforts have been directed toward perfecting the design of a variety of supramolecular polymers and materials with different architectures. The resulting structures are often thought of as ideally perfect, defect-free supramolecular fibers, micelles, vesicles, etc., having an intrinsic dynamic character, which are typically studied at the level of statistical ensembles to assess their average properties. However, molecular simulations recently demonstrated that local defects that may be present or may form in these assemblies, and which are poorly captured by conventional approaches, are key to controlling their dynamic behavior and properties. The study of these defects poses considerable challenges, as the flexible/dynamic nature of these soft systems makes it difficult to identify what effectively constitutes a defect and to characterize its stability and evolution. Here, we demonstrate the power of unsupervised machine-learning techniques to systematically identify and compare defects in supramolecular polymer variants in different conditions, using as a benchmark 5 Å resolution coarse-grained molecular simulations of a family of supramolecular polymers. We show that this approach allows a complete data-driven characterization of the internal structure and dynamics of these complex assemblies and of the dynamic pathways for defects formation and resorption. This provides a useful, generally applicable approach to unambiguously identify defects in these dynamic self-assembled materials and to classify them based on their structure, stability, and dynamics.

How Defects Control the Out-of-Equilibrium Dissipative Evolution of a Supramolecular Tubule

Supramolecular architectures that work out-of-equilibrium or that can change in specific ways when absorbing external energy are ubiquitous in nature. Gaining the ability to create via self-assembly artificial materials possessing such fascinating behaviors would have a major impact in many fields. However, the rational design of similar dynamic structures requires to understand and, even more challenging, to learn how to master the molecular mechanisms governing how the assembled systems evolve far from the equilibrium. Typically, this represents a daunting challenge due to the limited molecular insight that can be obtained by the experiments or by classical modeling approaches. Here we combine coarse-grained molecular models and advanced simulation approaches to study at submolecular (<5 Å) resolution a supramolecular tubule, which breaks and disassembles upon absorption of light energy triggering isomerization of its azobenzene-containing monomers. Our approach allows us to investigate the molecular mechanism of monomer transition in the assembly and to elucidate the kinetic process for the accumulation of the transitions in the system. Despite the stochastic nature of the excitation process, we demonstrate how these tubules preferentially dissipate the absorbed energy locally via the amplification of defects in their supramolecular structure. We find that this constitutes the best kinetic pathway for accumulating monomer transitions in the system, which determines the dynamic evolution out-of-equilibrium and the brittle behavior of the assembly under perturbed conditions. Thanks to the flexibility of our models, we finally come out with a general principle, where defects explain and control the brittle/soft behavior of such light-responsive assemblies.

Insights into the Kinetics of Supramolecular Comonomer Incorporation in Water

Multicomponent supramolecular polymers are a versatile platform to prepare functional architectures, but a few studies have been devoted to investigate their noncovalent synthesis. Here, we study supramolecular copolymerizations by examining the mechanism and time scales associated with the incorporation of new monomers in benzene-1,3,5-tricarboxamide (BTA)-based supramolecular polymers. The BTA molecules in this study all contain three tetra(ethylene glycol) chains at the periphery for water solubility but differ in their alkyl chains that feature either 10, 12 or 13 methylene units. C₁₀BTA does not form ordered supramolecular assemblies, whereas C₁₂BTA and C₁₃BTA both form high aspect ratio supramolecular polymers. First, we illustrate that C₁₀BTA can mix into the supramolecular polymers based on either C₁₂BTA or C₁₃BTA by comparing the temperature response of the equilibrated mixtures to the temperature response of the individual components in water. Subsequently, we mix C₁₀BTA with the polymers and follow the copolymerization over time with UV spectroscopy and hydrogen/deuterium exchange mass spectrometry experiments. Interestingly, the time scales obtained in both experiments reveal significant differences in the rates of copolymerization. Coarse-grained simulations are used to study the incorporation pathway and kinetics of the C₁₀BTA monomers into the different polymers. The results demonstrate that the kinetic stability of the host supramolecular polymer controls the rate at which new monomers can enter the existing supramolecular polymers.

Differentiating the mechanism of self-assembly in supramolecular polymers through computation

The mechanism by which monomers in solution, beyond a certain concentration or below a certain temperature, self-assemble to form one dimensional supramolecular polymers determines much of the bulk properties of the polymer.

The penetration of a charged peptide across a membrane under an external electric field: a coarse-grained molecular dynamics simulation

The processes of single polyarginine (R8) peptide penetration through planar and vesicle membranes under an external electric field are simulated via a coarse-grained molecular dynamics (CGMD) simulation.