Nonequilibrium Assembly Research Articles

Cell-Free Nonequilibrium Assembly for Hierarchical Protein/Peptide Nanopillars.

Cells contain intricate protein nanostructures, but replicating them outside of cells presents challenges. One such example is the vertical fibronectin pillars observed in embryos. Here, we demonstrate the creation of cell-free vertical fibronectin pillar mimics using nonequilibrium self-assembly. Our approach utilizes enzyme-responsive phosphopeptides that assemble into nanotubes. Enzyme action triggers shape changes in peptide assemblies, driving the vertical growth of protein nanopillars into bundles. These bundles, with peptide nanotubes serving as a template to remodel fibronectin, can then recruit collagen, which forms aggregates or bundles depending on their types. Nanopillar formation relies on enzyme-catalyzed nonequilibrium self-assembly and is governed by the concentrations of enzyme, protein, peptide, the structure of the peptide, and peptide assembly morphologies. Cryo-EM reveals unexpected nanotube thinning and packing after dephosphorylation, indicating a complex sculpting process during assembly. Our study demonstrates a cell-free method for constructing intricate, multiprotein nanostructures with directionality and composition.

Proteinaceous Nanoshells with Quasicrystalline Local Order

Among various proteinaceous nanocontainers and nanoparticles, the most promising ones for various applications in nano- and medical science appear to be those whose structures differ fundamentally from icosahedral viral capsids described by the paradigmatic Caspar-Klug model. By analyzing such anomalous assemblies represented in the Protein Data Bank, we identify a series of shells with square-triangular local order and find that most of them originate from short-period approximants of a dodecagonal tiling consisting of square and triangular tiles. Examining the nonequilibrium assembly of such packings, we propose a new method for obtaining periodic square-triangle approximants and then construct the simplest models of tetragonal, octahedral, and icosahedral shells based on cubic and icosahedral nets cut from the approximant structures. Since gluing the nets can change the distances between adjacent vertices of the resulting shell, we introduce an effective energy, the minimization of which equalizes these distances. While the obtained spherical polyhedra reproduce the structures of experimentally observed protein shells and nanoparticles, the principles of protein organization that we lay out, and the ensuing structural models, can help to discover and investigate similar systems in the future. Published by the American Physical Society 2024

Complex Pathways Drive Pluripotent Fmoc-Leucine Self-Assemblies.

Nature uses complex self-assembly pathways to access distinct functional non-equilibrium self-assemblies. This remarkable ability to steer same set of biomolecules into different self-assembly states is done by avoiding thermodynamic pit. In synthetic systems, on demand control over 'Pathway Complexity' to access self-assemblies different from equilibrium structures remains challenging. Here we show versatile non-equilibrium assemblies of the same monomer via alternate assembly pathways. The assemblies nucleate using non-classical or classical nucleation routes into distinct metastable (transient hydrogels), kinetic (stable hydrogels) and thermodynamic structures [(poly)-crystals and 2D sheets]. Initial chemical and thermal inputs force the monomers to follow different assembly pathways and form soft-materials with distinct molecular arrangements than at equilibrium. In many cases, equilibrium structures act as thermodynamic sink which consume monomers from metastable structures giving transiently formed materials. This dynamics can be tuned chemically or thermally to slow down the dissolution of transient hydrogel, or skip the intermediate hydrogel altogether to reach final equilibrium assemblies. If required this metastable state can be kinetically trapped to give strong hydrogel stable over days. This method to control different self-assembly states can find potential use in similar biomimetic systems to access new materials for various applications.

Kinetically Controlled and Nonequilibrium Assembly of Block Copolymers in Solution.

Covalent polymers are versatile macromolecules that have found widespread use in society. Contemporary methods of polymerization have made it possible to construct sequence polymers, including block copolymers, with high precision. Such copolymers assemble in solution when the blocks have differing solubilities. This produces nano- and microparticles of various shapes and sizes. While it is straightforward to draw an analogy between such amphiphilic block copolymers and phospholipids, these two classes of molecules show quite different assembly characteristics. In particular, block copolymers often assemble under kinetic control, thus producing nonequilibrium structures. This leads to a rich variety of behaviors being observed in block copolymer assembly, such as pathway dependence (e.g., thermal history), nonergodicity and responsiveness. The dynamics of polymer assemblies can be readily controlled using changes in environmental conditions and/or integrating functional groups situated on polymers with external chemical reactions. This perspective highlights that kinetic control is both pervasive and a useful attribute in the mechanics of block copolymer assembly. Recent examples are highlighted in order to show that toggling between static and dynamic behavior can be used to generate, manipulate and dismantle nonequilibrium states. New methods to control the kinetics of block copolymer assembly will provide endless unanticipated applications in materials science, biomimicry and medicine.

Non-Equilibrium Assembly of Atomically-Precise Copper Nanoclusters.

Accurate structure control in dissipative assemblies (DSAs) is vital for precise biological functions. However, accuracy and functionality of artificial DSAs are far from this objective. Herein, a novel approach is introduced by harnessing complex chemical reaction networks rooted in coordination chemistry to create atomically-precise copper nanoclusters (CuNCs), specifically Cu11(µ9-Cl)(µ3-Cl)3L6Cl (L = 4-methyl-piperazine-1-carbodithioate). Cu(I)-ligand ratio change and dynamic Cu(I)-Cu(I) metallophilic/coordination interactions enable the reorganization of CuNCs into metastable CuL2, finally converting into equilibrium [CuL·Y]Cl (Y = MeCN/H2O) via Cu(I) oxidation/reorganization and ligand exchange process. Upon adding ascorbic acid (AA), the system goes further dissipative cycles. It is observed that the encapsulated/bridging halide ions exert subtle influence on the optical properties of CuNCs and topological changes of polymeric networks when integrating CuNCs as crosslink sites. CuNCs duration/switch period could be controlled by varying the ions, AA concentration, O2 pressure and pH. Cu(I)-Cu(I) metallophilic and coordination interactions provide a versatile toolbox for designing delicate life-like materials, paving the way for DSAs with precise structures and functionalities. Furthermore, CuNCs can be employed as modular units within polymers for materials mechanics or functionalization studies.

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids.

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Evidence of Size Stratification in Colloidal Glass Microgranules Realized by Rapid Evaporative Assembly.

Evaporation is a ubiquitous phenomenon. Rapid evaporation of the continuous phase from micrometric colloidal droplets can be used to realize nanostructured microgranules, constituting the assembled nanoparticles. One of the important aspects of such nonequilibrium assembly is the nature of the packing of nanoparticles in the microgranules. The present work demonstrates the evidence of size stratification of the nanoparticles in such far-from-equilibrium configurations. Small-angle X-ray scattering, in combination with particle packing simulation, reveals the "large on top"-type stratification in such assembled microgranules, where the larger particles get concentrated at the outer shell of the granules while the smaller particles reside in the core region. It also reveals the presence of local clusters in such a rapid evaporative assembly in aerosolized colloidal droplets.

Cyclic Macroscopic Assembly and Disassembly Driven by Ionic Strength Fuel: A Waste-Free Approach.

Nonequilibrium assembling systems developed so far have relied on chemical fuels to drive the programmable pH cycles, redox reactions, and metastable bond formations. However, these methods often result in the unwanted accumulation of chemical waste. Herein, we present a novel strategy for achieving cyclic and waste-free nonequilibrium assembly and disassembly of macroscopic hydrogels, utilizing an ionic strength-mediated approach. Our strategy involves using ammonium carbonate as a chemical fuel to temporally regulate the attractions between oppositely charged hydrogels via ionic strength-controlled charge screening and hydrogel elasticity changes. This chemical fuel effectively mediates the assembly/disassembly processes and prevents waste accumulation, as ammonium carbonate can completely decompose into volatile chemical waste. The cyclic and reversible assembly process can be achieved without significant damping due to the self-clearance mechanism, as long as the chemical fuel is repeatedly supplied. This concept holds promise for creating macroscopic and microscopic nonequilibrium systems and self-adaptive materials.

Flow Synthesis of Gigantic Porphyrinic Cages: Facile Synthesis of P12L24 and Discovery of Kinetic Product P9L18.

Herein, we report a continuous flow methodology for the facile and high-yielding synthesis of the porphyrin-based self-assembled organic cage, P12L24, along with the serendipitous discovery of a kinetic product, P9L18 cage, which has been characterized by MALDI-TOF MS, NMR, and AFM analysis. A theoretical study suggests a tricapped trigonal prismatic geometry for P9L18. Unlike P12L24, P9L18 is unstable and readily decomposes into monomers and small oligomers. While the batch synthesis produces only the thermodynamic product P12L24, the continuous flow process generates not only the thermodynamic product but also kinetic products, such as P9L18, illustrating the advantages of the continuous flow process for the synthesis of self-assembled cages and the exploration of new non-equilibrium assemblies.

The entropy-controlled strategy in self-assembling systems.

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Microswimmers under the spotlight: interplay between agents with different levels of activity.

The ability of active matter to assemble into reconfigurable nonequilibrium structures has drawn considerable interest in recent years. We investigate how active fluids respond to spatial light patterns through simulations and experiments on light-activated self-propelled colloidal particles. We examine the processes of inverse templated assembly, which involves creating a region without active particles through a bright pattern, and templated assembly, which promotes the formation of dense particle regions through a dark pattern. We identify scaling relations for the characteristic times for both processes that quantify the interplay between the dimension of the applied pattern and the intrinsic properties of the active fluid. We also explore the assembly mechanism and dynamics of large clusters and show how assembly and inverse assembly can be combined to create any arbitrarily complex template. In addition to providing protocols for templated assembly via light patterning, our results demonstrate how the local packing fraction can be fine-tuned by modulation of the light intensity. The protocol so obtained exceeds the capabilities of conventional assembly strategies, in which packing fraction is dictated by thermodynamics, and opens the door to arbitrarily precise and programmable nonequilibrium assembly strategies in active matter.

Optimization of non-equilibrium self-assembly protocols using Markov state models.

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Self-organized lasers from reconfigurable colloidal assemblies

Non-equilibrium assemblies, where units are able to harness available energy to perform tasks, can often self-organize into dynamic materials that uniquely blend structure with functionality and responsiveness to their environment. The integration of similar features in photonic materials remains challenging but is desirable to manufacture active, adaptive and autonomous photonic devices. Here we show the self-organization of programmable random lasers from the reversible out-of-equilibrium self-assembly of colloids. The random lasing originates from the optical amplification of light undergoing multiple scattering within the dissipative colloidal assemblies and therefore depends crucially on their self-organization behaviour. Under external light stimuli, these dynamic random lasers are responsive and present a continuously tuneable laser threshold. They can therefore reconfigure and cooperate by emulating the ever-evolving spatiotemporal relationship between structure and functionality that is typical of many non-equilibrium assemblies. Experiments inspired by the behaviour of active matter show that an external optical stimulus can spatially reconfigure colloidal random lasers and continuously tune their lasing threshold.

Nonequilibrium regulation of interfacial chemistry for transient macroscopic supramolecular assembly

HypothesisMacroscopic nonequilibrium assembly helps to interpret the interfacial assembly mechanism and promotes the creation of self-adaptive chemical systems for potential applications such as controlled release and mass transfer. We propose that the precise macroscopic nonequilibrium assembly can be achieved by rationally integrating pH-responsive hybrid polymer hydrogels with the urea-urease clock reaction. ExperimentsHerein, pH-responsive and urease-containing polyelectrolyte hydrogels were fabricated for achieving macroscopic nonequilibrium assembly. Optical microscopy was used to visualize the interface of the macroscopic assemblies. Tensile tests were performed to investigate the adhesion strength of the assemblies and the modulus of the hydrogels. The charges and electric field distribution at the hydrogel surface were estimated by zeta potential measurements. Furthermore, an in situ sewing-growing method for fabricating hybrid polymer hydrogels with modularized surface chemistry was presented to achieve precise nonequilibrium assembly. FindingsThe realization of precise macroscopic nonequilibrium assembly relies on the transient electrostatic attraction between the hybrid polymer hydrogels, which lays the foundation for yielding transient macroscopic supramolecular devices potentially useful for timed release. The stability and lifetime of the transient assemblies can be controlled by adjusting the hydrogel synthesis parameters and fuel compositions, and the macroscopic nonequilibrium assembly can be repeated by refueling the system.

Optically-assisted thermophoretic reversible assembly of colloidal particles and E. coli using graphene oxide microstructures

Optically-assisted large-scale assembly of nanoparticles have been of recent interest owing to their potential in applications to assemble and manipulate colloidal particles and biological entities. In the recent years, plasmonic heating has been the most popular mechanism to achieve temperature hotspots needed for extended assembly and aggregation. In this work, we present an alternative route to achieving strong thermal gradients that can lead to non-equilibrium transport and assembly of matter. We utilize the excellent photothermal properties of graphene oxide to form a large-scale assembly of silica beads. The formation of the assembly using this scheme is rapid and reversible. Our experiments show that it is possible to aggregate silica beads (average size 385 nm) by illuminating thin graphene oxide microplatelet by a 785 nm laser at low intensities of the order of 50–100 µW/µm2. We further extend the study to trapping and photoablation of E. coli bacteria using graphene oxide. We attribute this aggregation process to optically driven thermophoretic forces. This scheme of large-scale assembly is promising for the study of assembly of matter under non-equilibrium processes, rapid concentration tool for spectroscopic studies such as surface-enhanced Raman scattering and for biological applications.

Nonequilibrium Catalytic Supramolecular Assemblies of Melamine- and Imidazole-Based Dynamic Building Blocks

The development of synthetic nonequilibrium systems has gathered increasing attention due to their potential to illustrate the dynamic, complex, and emergent traits of biological systems. Simple building blocks capable of interacting via dynamic covalent chemistry and physical assembly in a reaction network under nonequilibrium conditions can contribute to our understanding of complex systems of life and its origin. Herein, we have demonstrated the nonequilibrium generation of catalytic supramolecular assemblies from simple heterocycle melamine driven by a thermodynamically activated ester. Utilizing a reversible covalent linkage, an imidazole moiety was recruited by the assemblies to access a catalytic transient state that dissipated energy via accelerated hydrolysis of the activated ester. The nonequilibrium assemblies were further capable of temporally binding to a hydrophobic guest to modulate its photophysical properties. Notably, the presence of an exogenous aromatic base augmented the lifetime of the catalytic microphases, reflecting their higher kinetic stability.

Light-Programmable Assemblies of Isotropic Micromotors.

“Life-like” nonequilibrium assemblies are of increasing significance, but suffering from limited steerability as they are generally based on micro/nanomotors with inherent asymmetry in chemical composition or geometry, of which the vigorous random Brownian rotations disturb the local interactions. Here, we demonstrate that isotropic photocatalytic micromotors, due to the persistent phoretic flow from the illuminated to shadowed side irrespective of their Brownian rotations, experience light-programmable local interactions (reversibly from attraction to repulsion and/or alignment) depending on the direction of the incident lights. Thus, they can be organized into a variety of tunable nonequilibrium assemblies, such as apolar solids (i.e., immobile colloidal crystal), polar liquids (i.e., phototactic colloidal stream), and polar solids (i.e., phototactic colloidal crystal), which can further be “cut” into a predesigned pattern by utilizing the switching motor-motor interactions at superimposed-light edges. This work facilitates the development of active matters and motile functional microdevices.

Feedback-controlled topological reconfiguration of molecular assemblies for programming supramolecular structures

In biology, nonequilibrium assembly is characterized by fuel-driven switching between associating and nonassociating states of biomolecules. This dynamic assembly model has been used routinely to describe the nonequilibrium processes in synthetic systems. Here, we present a G-quartet-based nonequilibrium system based on fuel-driven co-assembly of guanosine 5'-monophosphate disodium salt hydrate and urease. Addition of lanthanum(III) ions to the system caused macroscopic dynamic switching between precipitates and hydrogels. Interestingly, combined analyses of the nonequilibrium systems demonstrated that molecules could switch between two distinct associating states without undergoing a nonassociating state. This finding suggested a nonequilibrium assembly mechanism of topological reconfiguration of molecular assemblies. We detailed quantitatively the nonequilibrium assembly mechanism to precisely control the phase behaviors of the active materials; thus, we were able to use the materials for transient-gel-templated polymerization and transient circuit connection. This work presents a new nonequilibrium system with unusual phase behaviors, and the resultant active hydrogels hold promise in applications such as fluid confinements and transient electronics.

Suppression of self-stratification in colloidal mixtures with high Péclet numbers.

The non-equilibrium assembly of bimodal colloids during evaporative processes is an attractive means to achieve gradient or stratified layers in thick films. Here, we show that the stratification of small colloids on top of large is prevented when the viscosity of the continuous aqueous phase is too high. We propose a model where a too narrow width of the gradient in concentration of small colloids suppresses the stratification.

Nonreciprocity as a generic route to traveling states

We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic cross-diffusivities, provides a generic mechanism for the emergence of traveling patterns in purely diffusive systems with conservative dynamics. In the absence of nonreciprocity, the binary fluid mixture undergoes a phase transition from a homogeneous mixed state to a demixed state with spatially separated regions rich in one of the two components. Above a critical value of the parameter tuning nonreciprocity, the static demixed pattern acquires a finite velocity, resulting in a state that breaks both spatial and time-reversal symmetry, as well as the reflection parity of the static pattern. We elucidate the generic nature of the transition to traveling patterns using a minimal model that can be studied analytically. Our work has direct relevance to nonequilibrium assembly in mixtures of chemically interacting colloids that are known to exhibit nonreciprocal effective interactions, as well as to mixtures of active and passive agents where traveling states of the type predicted here have been observed in simulations. It also provides insight on transitions to traveling and oscillatory states seen in a broad range of nonreciprocal systems with nonconservative dynamics, from reaction-diffusion and prey-predators models to multispecies mixtures of microorganisms with antagonistic interactions.