Kinetics-Controlled Amphiphile Self-Assembly Processes

Markov State Models Reveal How Folding Kinetics Influence Absorption Spectra of Foldamers

Self-assembly of platinum(II) complex foldamers is an essential approach to fabricate advanced luminescent materials. However, a comprehensive understanding of folding kinetics and their absorption spectra remains elusive. By constructing Markov state models (MSMs) from large-scale molecular dynamics simulations, we reveal that two largely similar dinuclear alknylplatinum(II) terpyridine foldamers, Pt-PEG and Pt-PE with slightly different bridges, exhibit distinctive folding kinetics. Particularly, Pt-PEG bears bridge-dominant, plane-dominant, and cooperative pathways, while Pt-PE only prefers the plane-dominant pathway. Such preference originates from their difference in intrabridge electrostatic interactions, leading to contrastive distributions of metastable states. We also found that the bridge-dominant pathway for Pt-PEG becomes more favorable when lowering the temperature. Interestingly, based on the comprehensive conformation ensembles from our MSMs, we reveal the conformation-dependent absorption spectra of Pt-PEG and Pt-PE. Our theoretical spectra not only align with experimental results but also reveal the contributions of diverse conformations to the overall absorption bands explicitly, facilitating the rational design of stimuli-responsive smart luminescent molecules.

Self-assembly morphology transition mechanism of similar amphiphilic molecules

Molecular self-assembly is a powerful synthesis method for nanomaterials. Promoting the development of self-assembly is not only conducive to the efficient preparation of nanomaterials but also promotes progress in other research fields. Therefore, it is necessary to enhance the advancement of molecular self-assembly, and the key is to deepen the understanding of the correlation between molecular characteristics and self-assembly morphologies. However, some similar amphipihlic molecules self-assemble into assemblies with significant morphology difference, which is challenging to clear the mechanism for experimenters. In this work, we explore the microscopic mechanism of six similar molecules by MD simulations, and the influences of molecular conformation, atomic groups, and polycyclic aromatic hydrocarbons on morphologies are discussed in detail. Our findings enrich the design principles of amphiphilic molecules for self-assembly, which promotes the modular design of molecular self-assembly.

GraphVAMPnets for uncovering slow collective variables of self-assembly dynamics

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers, and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenges. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, such as time-structure independent component analysis, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets, which combines graph neural networks with a variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory, which studies Markov processes without forcing detailed balance constraints, which addresses the out-of-equilibrium challenge in the self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: the aggregation of two hydrophobic molecules and the self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely applied to molecular self-assembly.

An Efficient Path Classification Algorithm Based on Variational Autoencoder to Identify Metastable Path Channels for Complex Conformational Changes

Conformational changes (i.e., dynamic transitions between pairs of conformational states) play important roles in many chemical and biological processes. Constructing the Markov state model (MSM) from extensive molecular dynamics (MD) simulations is an effective approach to dissect the mechanism of conformational changes. When combined with transition path theory (TPT), MSM can be applied to elucidate the ensemble of kinetic pathways connecting pairs of conformational states. However, the application of TPT to analyze complex conformational changes often results in a vast number of kinetic pathways with comparable fluxes. This obstacle is particularly pronounced in heterogeneous self-assembly and aggregation processes. The large number of kinetic pathways makes it challenging to comprehend the molecular mechanisms underlying conformational changes of interest. To address this challenge, we have developed a path classification algorithm named latent-space path clustering (LPC) that efficiently lumps parallel kinetic pathways into distinct metastable path channels, making them easier to comprehend. In our algorithm, MD conformations are first projected onto a low-dimensional space containing a small set of collective variables (CVs) by time-structure-based independent component analysis (tICA) with kinetic mapping. Then, MSM and TPT are constructed to obtain the ensemble of pathways, and a deep learning architecture named the variational autoencoder (VAE) is used to learn the spatial distributions of kinetic pathways in the continuous CV space. Based on the trained VAE model, the TPT-generated ensemble of kinetic pathways can be embedded into a latent space, where the classification becomes clear. We show that LPC can efficiently and accurately identify the metastable path channels in three systems: a 2D potential, the aggregation of two hydrophobic particles in water, and the folding of the Fip35 WW domain. Using the 2D potential, we further demonstrate that our LPC algorithm outperforms the previous path-lumping algorithms by making substantially fewer incorrect assignments of individual pathways to four path channels. We expect that LPC can be widely applied to identify the dominant kinetic pathways underlying complex conformational changes.

Exploiting Minimalistic Backbone Engineered γ-Phenylalanine for the Formation of Supramolecular Co-Polymer

Ordered supramolecular hydrogels assembled by modified aromatic amino acids often exhibit low mechanical rigidity. Aiming to stabilize the hydrogel and understand the impact of conformational freedom and hydrophobicity on the self-assembly process, we designed two building blocks based on 9-fluorenyl-methoxycarbonyl-phenylalanine (Fmoc-Phe) gelator which contain two extra methylene units in the backbone, generating Fmoc-γPhe and Fmoc-(3-hydroxy)-γPhe. Fmoc-γPhe spontaneously assembled in aqueous media forming a hydrogel with exceptional mechanical and thermal stability. Moreover, Fmoc-(3-hydroxy)-γPhe, with an extra backbone hydroxyl group decreasing its hydrophobicity while maintaining some molecular flexibility, self-assembled into a transient fibrillar hydrogel, that later formed microcrystalline aggregates through phase transition. Molecular dynamics simulations and single crystal X-ray analyses revealed the mechanism underlying the two residues' distinct self-assembly behaviors. Finally, we demonstrated Fmoc-γPhe and Fmoc-(3-OH)-γPhe co-assembly to form a supramolecular hydrogel with notable mechanical properties. We believe that the understanding of the structure-assembly relationship will enable the design of new functional amino acid-based hydrogels. This article is protected by copyright. All rights reserved.

2D Liquid-Crystallization-Driven Self-Assembly of Rod-Coil Block Copolymers: Living Growth and Self-Similarity

Liquid-crystallization-driven self-assembly (LCDSA) is an emerging methodology, which has been employed to construct controllable 1D nanostructures. However, 2D nanostructures via living LCDSA are rarely reported, and the complicated growth kinetics are not well-known. Herein, we perform Brownian dynamics (BD) simulations to investigate the 2D living growth of disklike micelles via LCDSA of rod-coil block copolymers. The 2D seeded-growth behavior is achieved by incorporating the unimers onto the edges of disklike seeds with smectic-like liquid-crystalline (LC) cores. The fluidity of such LC-like micellar cores is conducive to the chain adjustments of rod blocks during the 2D living growth process. The apparent growth rate and unique self-similarity kinetics are governed by the interplay between the variations in the growth rate coefficient and the reactive sites at the micelle edges. This work provides an in-depth understanding of the 2D living growth of micelles and guidance to construct well-defined 2D hierarchical nanostructures.

Nanoparticle cluster formation mechanisms elucidated via Markov state modeling: Attraction range effects, aggregation pathways, and counterintuitive transition rates

Nanoparticle clusters are promising candidates for developing functional materials. However, it is still a challenging task to fabricate them in a predictable and controllable way, which requires investigation of the possible mechanisms underlying cluster formation at the nanoscale. By constructing Markov state models (MSMs) at the microstate level, we find that for highly dispersed particles to form a highly aggregated cluster, there are multiple coexisting pathways, which correspond to direct aggregation, or pathways that need to pass through partially aggregated, intermediate states. Varying the range of attraction between nanoparticles is found to significantly affect pathways. As the attraction range becomes narrower, compared to direct aggregation, some pathways that need to pass through partially aggregated intermediate states become more competitive. In addition, from MSMs constructed at the macrostate level, the aggregation rate is found to be counterintuitively lower with a lower free-energy barrier, which is also discussed.

Elucidation of the key role of Pt···Pt interactions in the directional self-assembly of platinum(II) complexes

Molecular self-assembly provides a bottom-up platform to design supramolecular functional materials, attracting numerous interests in material sciences. The utilization of platinum(II) complexes as building blocks of supramolecular assemblies opens up the unique noncovalent Pt···Pt interaction as one of the driving forces, imparting the supramolecular materials with rich spectroscopic features. However, the exact role of Pt···Pt interactions in molecular assembly remains elusive. The current study combines experimental and computational techniques to elucidate the role of Pt···Pt interactions in the self-assembly process of a representative amphiphilic platinum(II) complex. This work demonstrates the directional role of Pt···Pt interactions in assisting the molecular assembly in an anisotropic manner, achieving the formation of ordered self-assembled structures.

Here, we report the use of an amphiphilic Pt(II) complex, K[Pt{(O₃SCH₂CH₂CH₂)₂bzimpy}Cl] (PtB), as a model to elucidate the key role of Pt···Pt interactions in directing self-assembly by combining temperature-dependent ultraviolet-visible (UV-Vis) spectroscopy, stopped-flow kinetic experiments, quantum mechanics (QM) calculations, and molecular dynamics (MD) simulations. Interestingly, we found that the self-assembly mechanism of PtB in aqueous solution follows a nucleation-free isodesmic model, as revealed by the temperature-dependent UV-Vis experiments. In contrast, a cooperative growth is found for the self-assembly of PtB in acetone–water (7:1, vol/vol) solution, which is further verified by the stopped-flow experiments, which clearly indicates the existence of a nucleation phase in the acetone–water (7:1, vol/vol) solution. To reveal the underlying reasons and driving forces for these self-assembly processes, we performed QM calculations and show that the Pt···Pt interactions arising from the interaction between the p_z and d_z² orbitals play a crucial role in determining the formation of ordered self-assembled structures. In subsequent oligomer MD simulations, we demonstrate that this directional Pt···Pt interaction can indeed facilitate the formation of linear structures packed in a helix-like fashion. Our results suggest that the self-assembly of PtB in acetone–water (7:1, vol/vol) solution is predominantly driven by the directional noncovalent Pt···Pt interaction, leading to the cooperative growth and the formation of fibrous nanostructures. On the contrary, the self-assembly in aqueous solution forms spherical nanostructures of PtB, which is primarily due to the predominant contribution from the less directional hydrophobic interactions over the directional Pt···Pt and π−π interactions that result in an isodesmic growth.

Theoretical Study of Macrocyclic Host Molecules: From Supramolecular Recognition to Self-Assembly

Supramolecular chemistry focuses on molecular recognition and self-assembly of various building blocks through weak non-covalent interactions, including anion-π, hydrogen bond (HB), hydrophobic interactions, van der Waals (vdW) interactions, etc, which...

The desalting/salting pathway: a route to form metastable aggregates with tuneable morphologies and lifetimes

We investigate the formation/re-dissociation mechanisms of hybrid complexes made from negatively charged PAA_2k coated γ-Fe₂O₃ nanoparticles (NP) and positively charged polycations (PDADMAC) in aqueous solution in the regime of very high ionic strength (I). When the building blocks are mixed at large ionic strength (1 M NH₄Cl), the electrostatic interaction is screened and complexation does not occur. If the ionic strength is then lowered down to a targeted ionic strength I_target, there is a critical threshold I_c = 0.62 M at which complexation occurs, that is independent of the charge ratio Z and the pathway used to reduce salinity (drop-by-drop mixing or fast mixing). If salt is added back up to 1 M, the transition is not reversible and persistent out-of-equilibrium aggregates are formed. The lifetimes of such aggregates depends on I_target: the closer I_target to I_c is, the more difficult it is to dissolve the aggregates. Such peculiar behavior is driven by the inner structure of the complexes that are formed after desalting. When I_target is far below I_c, strong electrostatic interactions induce the formation of dense, compact and frozen aggregates. Such aggregates can only poorly reorganize further on with time, which makes their dissolution upon resalting almost reversible. Conversely, when I_target is close to I_c more open aggregates are formed due to weaker electrostatic interactions upon desalting. The system can thus rearrange with time to lower its free energy and reach more stable out-of-equilibrium states which are very difficult to dissociate back upon resalting, even at very high ionic strength.

Controlled Self-Assembly Mediated by the Complexation of Calixpyridinium: Diverse Assembled Morphology, Solid-State Fluorescence, and Iodine Capture Capacity

It is a great challenge to precisely control the molecules that self-assemble into diverse shapes with diverse properties. Herein, the self-assembled behaviors between calixpyridinium and two pyrenesulfonate guests, 1,3,6,8-pyrenetetrasulfonic acid tetrasodium salt (PyTS) and sodium 1-pyrenesulfonate (PS), were studied. The morphology and property of the two assemblies were quite different. PS guests self-assembled into spherical aggregates upon complexation with calixpyridinium, while the self-assembled rodlike aggregates were formed via the binding between calixpyridinium and PyTS guests. The calixpyridinium-PS supramolecular aggregates could not emit fluorescence in the solid state, while a strong green fluorescence was emitted by the calixpyridinium-PyTS supramolecular aggregates in the solid state. More interestingly and importantly, the solid calixpyridinium-PyTS supramolecular aggregates exhibited an adsorbent ability to iodine in both the aqueous solution and the vapor phase, while the solid calixpyridinium-PS supramolecular aggregates could not capture iodine. The diverse iodine capture capability of the two supramolecular aggregates was determined by the self-assembled structure at the molecular level.

Unusual Two-Step Assembly of a Minimalistic Dipeptide-Based Functional Hypergelator

Self-assembled peptide hydrogels represent the realization of peptide nanotechnology into biomedical products. There is a continuous quest to identify the simplest building blocks and optimize their critical gelation concentration (CGC). Herein, a minimalistic, de novo dipeptide, Fmoc-Lys(Fmoc)-Asp, as an hydrogelator with the lowest CGC ever reported, almost fourfold lower as compared to that of a large hexadecapeptide previously described, is reported. The dipeptide self-assembles through an unusual and unprecedented two-step process as elucidated by solid-state NMR and molecular dynamics simulation. The hydrogel is cytocompatible and supports 2D/3D cell growth. Conductive composite gels composed of Fmoc-Lys(Fmoc)-Asp and a conductive polymer exhibit excellent DNA binding. Fmoc-Lys(Fmoc)-Asp exhibits the lowest CGC and highest mechanical properties when compared to a library of dipeptide analogues, thus validating the uniqueness of the molecular design which confers useful properties for various potential applications.

Guiding the Morphology of Amyloid Assemblies by Electrostatic Capping: from Polymorphic Twisted Fibrils to Uniform Nanorods

Peptides that self-assemble into cross-β-sheet amyloid structures constitute promising building blocks to construct highly ordered proteinaceous materials and nanoparticles. Nevertheless, the intrinsic polymorphism of amyloids and the difficulty of controlling self-assembly currently limit their usage. In this study, the effect of electrostatic interactions on the supramolecular organization of peptide assemblies is investigated to gain insights into the structural basis of the morphological diversities of amyloids. Different charged capping units are introduced at the N-terminus of a potent β-sheet-forming sequence derived from the 20-29 segment of islet amyloid polypeptide, known to self-assemble into polymorphic fibrils. By tuning the charge and the electrostatic strength, different mesoscopic morphologies are obtained, including nanorods, rope-like fibrils, and twisted ribbons. Particularly, the addition of positive capping units leads to the formation of uniform rod-like assemblies, with lengths that can be modulated by the charge number. It is proposed that electrostatic repulsions between N-terminal positive charges hinder β-sheet tape twisting, leading to a unique control over the size of these cytocompatible nanorods by protofilament growth frustration. This study reveals the high susceptibility of amyloid formation to subtle chemical modifications and opens to promising strategies to control the final architecture of proteinaceous assemblies from the peptide sequence.

Composite Nanotube Ring Structures Formed by Two-Step Self-Assembly for Drug Loading/Release

Nanotube rings are barely reported novel structures formed by the self-assembly of soft matter, as compared with nanotube structures and ring structures. The two-step self-assembly of amphiphilic copolymer AB and solvophobic copolymer CDC was studied. We found that nanotube rings can be formed from a certain mass ratio of copolymer CDC to copolymer AB and block D of certain rigidity. More interestingly, we discovered a new strategy for drug loading and release, which is different from the usual strategies reported in the literature. The present study provides a new rationale for the self-assembly of copolymers.

Nucleation and self-assembly dynamics of hierarchical YAlO3:Ce3+ architectures: Nano probe for in vitro dermatoglyphics and anti-mimetic applications

Highly efficient blue emitting YAlO₃:Ce³⁺ (1-11 mol%) nanopowders have been fabricated via bio-surfactant Epigallocatechin Gallate assisted ultrasound irradiated sonochemical route. The nucleation and self-assembly dynamics of solids in solutions influences many straightforward normal processes, hence it plays a vital role in materials engineering applications. Nevertheless, the comprehensive nucleation and self-assembly mechanisms of hierarchical architectures still poorly acknowledged. In the present work, we have been exploring the nucleation and stepwise self-assembly dynamics of the YAlO₃:Ce³⁺ (5 mol%) nanopowders into hierarchical architectures. We found that under ultrasound irradiation, nucleation in the solution forms via multi step process and self-assembly was stimulated by intermolecular forces between the nanopowders and external forces. The optimized YAlO₃:Ce³⁺ (5 mol%) nanopowders used as a luminescent labeling agent for visualization of latent fingerprints on various porous and non-porous surfaces under ultraviolet 254 nm light. The obtained results exhibit well defined ridge details with high sensitivity, selectivity and low background hindrance which showed greater advantages as compared to the conventional powders. Extensive fingerprint details, namely the number and distribution of sweat pores in a ridge were clearly revealed. Further, demonstrated the viability of high-performance security labels using optimized sample for practical anti-mimetic applications. The present work, enabling understanding of ultrasound assisted nucleation and self-assembly of nanopowders which impart dermatoglyphics and anti- mimetic applications.

Structural Polymorphism in a Self-Assembled Tri-Aromatic Peptide System

Self-assembly is a process of key importance in natural systems and in nanotechnology. Peptides are attractive building blocks due to their relative facile synthesis, biocompatibility, and other unique properties. Diphenylalanine (FF) and its derivatives are known to form nanostructures of various architectures and interesting and varied characteristics. The larger triphenylalanine peptide (FFF) was found to self-assemble as efficiently as FF, forming related but distinct architectures of plate-like and spherical nanostructures. Here, to understand the effect of triaromatic systems on the self-assembly process, we examined carboxybenzyl-protected diphenylalanine (z-FF) as a minimal model for such an arrangement. We explored different self-assembly conditions by changing solvent compositions and peptide concentrations, generating a phase diagram for the assemblies. We discovered that z-FF can form a variety of structures, including nanowires, fibers, nanospheres, and nanotoroids, the latter were previously observed only in considerably larger or co-assembly systems. Secondary structure analysis revealed that all assemblies possessed a β-sheet conformation. Additionally, in solvent combinations with high water ratios, z-FF formed rigid and self-healing hydrogels. X-ray crystallography revealed a "wishbone" structure, in which z-FF dimers are linked by hydrogen bonds mediated by methanol molecules, with a 2-fold screw symmetry along the c-axis. All-atom molecular dynamics (MD) simulations revealed conformations similar to the crystal structure. Coarse-grained MD simulated the assembly of the peptide into either fibers or spheres in different solvent systems, consistent with the experimental results. This work thus expands the building block library for the fabrication of nanostructures by peptide self-assembly.

Improving the productivity of monodisperse polyhedral cages by the rational design of kinetic self-assembly pathways

Hollow polyhedral cages hold great potential for application in nanotechnological and biomedical fields. Understanding the formation mechanism of these self-assembled structures could provide guidance for the rational design of the desired polyhedral cages. Here, by constructing kinetic network models from extensive coarse-grained molecular dynamics simulations, we elucidated the formation mechanism of the dodecahedral cage, which is formed by the self-assembly of patchy particles. We found that the dodecahedral cage is formed through increasing the aggregate size followed by structure rearrangement. Based on this mechanistic understanding, we improved the productivity of the dodecahedral cage through the rational design of the patch arrangement of patchy particles, which promotes the structural rearrangement process. Our results demonstrate that it should be a feasible strategy to achieve the rational design of the desired nanostructures via the kinetic analysis. We anticipate that this methodology could be extended to other self-assembly systems for the fabrication of functional nanomaterials.

Harnessing complexity in molecular self-assembly using computer simulations

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.