Reaction-diffusion processes at the nano- and microscales

Efficient and scalable prediction of stochastic reaction-diffusion processes using graph neural networks

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction-diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction-diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction-diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.

Repurposing a Catalytic Cycle for Transient Self-Assembly

Life operates out of equilibrium to enable various sophisticated behaviors. Synthetic chemists have strived to mimic biological nonequilibrium systems in such fields as autonomous molecular machines and dissipative self-assembly. Central to these efforts has been the development of new chemical reaction cycles, which drive systems out of equilibrium by conversion of chemical fuel into waste species. However, the construction of reaction cycles has been challenging due to the difficulty of finding compatible reactions that constitute a cycle. Here, we realize an alternative approach by repurposing a known catalytic cycle as a chemical reaction cycle for driving dissipative self-assembly. This approach can overcome the compatibility problem because all steps involved in a catalytic cycle are already known to proceed concurrently under the same conditions. Our repurposing approach is applicable to diverse combinations of catalytic cycles and systems to drive out of equilibrium, which will substantially broaden the scope of out-of-equilibrium systems.

Unveiling Hidden Hyperuniformity: Radial Turing Pattern Formation of Marangoni-Driven SiO2 Nanoparticles on Liquid Metal Surface

Mastering the self-organization of nanoparticle morphologies is pivotal in soft matter physics and film growth. Silicon dioxide (SiO2) nanoparticles are an archetypical model of nanomotor in soft matter. Here, the emphasis is on the self-organizing behavior of SiO2 nanoparticles under extreme conditions. It is unveiled that manipulating the states of the metal substrate profoundly dictates the motion characteristics of SiO2 nanoparticles. This manipulation triggers the emergence of intricate morphologies and distinctive patterns. Employing a reaction-diffusion model, the fundamental roles played by Brownian motion and Marangoni-driven motion in shaping fractal structures and radial Turing patterns are demonstrated, respectively. Notably, these radial Turing patterns showcase hyperuniform order, challenging conventional notions of film morphology. These discoveries pave the way for crafting non-equilibrium morphological materials, poised with the potential for self-healing, adaptability, and innovative applications.

The Role of Hydrogen Bonds in Thermally Responsive Crystallization-Driven Template Autocatalysis

Autocatalysis has been recognized to be involved in the emergence of life and intrinsic to biomolecular replication. Recently, an efficient template autocatalysis driven by solvent-free crystallization has been reported. Herein, we unveil the role of intermolecular hydrogen bonds formed by amides in crystallization-driven template autocatalysis (CDTA), which involves the autocatalytic activity, template selectivity, and thermal responsiveness. We found that the thermal-induced cis-trans isomerization of amides possibly affects the H-bonding-mediated template ability of products for autocatalytic transformation. As a result, CDTA can be reversibly inhibited and activated by tuning the reaction temperatures. Our work sheds light on the significance of noncovalent H-bonding interactions in artificial self-replicators.

Optimizing Binding among Bimolecular Tethered Complexes

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.

Periodic Precipitation in a Confined Liquid Layer

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Enzyme-Inspired Ligand Engineering of Gold Nanoclusters for Electrocatalytic Microenvironment Manipulation

Natural enzymes intricately regulate substrate accessibility through specific amino acid sequences and folded structures at their active sites. Achieving such precise control over the microenvironment has proven to be challenging in nanocatalysis, especially in the realm of ligand-stabilized metal nanoparticles. Here, we use atomically precise metal nanoclusters (NCs) as model catalysts to demonstrate an effective ligand engineering strategy to control the local concentration of CO2 on the surface of gold (Au) NCs during electrocatalytic CO2 reduction reactions (CO2RR). The precise incorporation of two 2-thiouracil-5-carboxylic acid (TCA) ligands within the pocket-like cavity of [Au25(pMBA)18]- NCs (pMBA = para-mercaptobenzoic acid) leads to a substantial acceleration in the reaction kinetics of CO2RR. This enhancement is attributed to a more favorable microenvironment in proximity to the active site for CO2, facilitated by supramolecular interactions between the nucleophilic Nδ- of the pyrimidine ring of the TCA ligand and the electrophilic Cδ+ of CO2. A comprehensive investigation employing absorption spectroscopy, mass spectrometry, isotopic labeling measurements, electrochemical analyses, and quantum chemical computation highlights the pivotal role of local CO2 enrichment in enhancing the activity and selectivity of TCA-modified Au25 NCs for CO2RR. Notably, a high Faradaic efficiency of 98.6% toward CO has been achieved. The surface engineering approach and catalytic fundamentals elucidated in this study provide a systematic foundation for the molecular-level design of metal-based electrocatalysts.

In situ enzymatic control of colloidal phoresis and catalysis through hydrolysis of ATP

The ability to sense chemical gradients and respond with directional motility and chemical activity is a defining feature of complex living systems. There is a strong interest among scientists to design synthetic systems that emulate these properties. Here, we realize and control such behaviors in a synthetic system by tailoring multivalent interactions of adenosine nucleotides with catalytic microbeads. We first show that multivalent interactions of the bead with gradients of adenosine mono-, di- and trinucleotides (AM/D/TP) control both the phoretic motion and a proton-transfer catalytic reaction, and find that both effects are diminished greatly with increasing valence of phosphates. We exploit this behavior by using enzymatic hydrolysis of ATP to AMP, which downregulates multivalent interactivity in situ. This produces a sudden increase in transport of the catalytic microbeads (a phoretic jump), which is accompanied by increased catalytic activity. Finally, we show how this enzymatic activity can be systematically tuned, leading to simultaneous in situ spatial and temporal control of the location of the microbeads, as well as the products of the reaction that they catalyze. These findings open up new avenues for utilizing multivalent interaction-mediated programming of complex chemo-mechanical behaviors into active systems.

From Homogeneity to Turing Pattern: Kinetically Controlled Self-Organization of Transmembrane Protein

Understanding the spatial organization of membrane proteins is crucial for unraveling key principles in cell biology. The reaction-diffusion model is commonly used to understand biochemical patterning; however, applying reaction-diffusion models to subcellular phenomena is challenging because of the difficulty in measuring protein diffusivity and interaction kinetics in the living cell. In this work, we investigated the self-organization of the plasmalemma vesicle-associated protein (PLVAP), which creates regular arrangements of fenestrated ultrastructures, using single-molecule tracking. We demonstrated that the spatial organization of the ultrastructures is associated with a decrease in the association rate by actin destabilization. We also constructed a reaction-diffusion model that accurately generates a hexagonal array with the same 130 nm spacing as the actual scale and informs the stoichiometry of the ultrastructure, which can be discerned only through electron microscopy. Through this study, we integrated single-molecule experiments and reaction-diffusion modeling to surpass the limitations of static imaging tools and proposed emergent properties of the PLVAP ultrastructure.

Cell-Like Synthetic Supramolecular Soft Materials Realized in Multicomponent, Non-/Out-of-Equilibrium Dynamic Systems

Living cells are complex, nonequilibrium supramolecular systems capable of independently and/or cooperatively integrating multiple bio-supramolecules to execute intricate physiological functions that cannot be accomplished by individual biomolecules. These biological design strategies offer valuable insights for the development of synthetic supramolecular systems with spatially controlled hierarchical structures, which, importantly, exhibit cell-like responses and functions. The next grand challenge in supramolecular chemistry is to control the organization of multiple types of supramolecules in a single system, thus integrating the functions of these supramolecules in an orthogonal and/or cooperative manner. In this perspective, the recent progress in constructing multicomponent supramolecular soft materials through the hybridization of supramolecules, such as self-assembled nanofibers/gels and coacervates, with other functional molecules, including polymer gels and enzymes is highlighted. Moreover, results show that these materials exhibit bioinspired responses to stimuli, such as bidirectional rheological responses of supramolecular double-network hydrogels, temporal stimulus pattern-dependent responses of synthetic coacervates, and 3D hydrogel patterning in response to reaction-diffusion processes are presented. Autonomous active soft materials with cell-like responses and spatially controlled structures hold promise for diverse applications, including soft robotics with directional motion, point-of-care disease diagnosis, and tissue regeneration.

Controlling Supramolecular Fiber Formation of Nucleopeptide by Guanosine Triphosphate

Cells use dynamic self-assembly to construct functional structures for maintaining cellular homeostasis. However, using a natural biological small molecule to mimic this phenomenon remains challenging. This work reports the dynamic microfiber formation of nucleopeptide driven by guanosine triphosphate, the small molecule that controls microtubule polymerization in living cells. Deactivation of GTP by enzyme dissociates the fibers, which could be reactivated by adding GTP. Molecular dynamic simulation unveils the mystery of microfiber formation of GBM-1 and GTP. Moreover, the microfiber formation can also be controlled by diffusion-driven GTP gradients across a semipermeable membrane in bulk conditions and the microfluidic method in the defined droplets. This study provides a new platform to construct dynamic self-assembly materials of molecular building blocks driven by GTP.

Artificial Molecular Ratchets: Tools Enabling Endergonic Processes

Non-equilibrium chemical systems underpin multiple domains of contemporary interest, including supramolecular chemistry, molecular machines, systems chemistry, prebiotic chemistry, and energy transduction. Experimental chemists are now pioneering the realization of artificial systems that can harvest energy away from equilibrium. In this tutorial Review, we provide an overview of artificial molecular ratchets: the chemical mechanisms enabling energy absorption from the environment. By focusing on the mechanism type-rather than the application domain or energy source-we offer a unifying picture of seemingly disparate phenomena, which we hope will foster progress in this fascinating domain of science.

Self-Assembly of Structured Colloidal Gels for High-Resolution 3D Micropatterning of Proteins at Scale

Self-assembly, the spontaneous ordering of components into patterns, is widespread in nature and fundamental to generating function across length scales. Morphogen gradients in biological development are paradigmatic as both products and effectors of self-assembly and various attempts have been made to reproduce such gradients in biomaterial design. To date, approaches have typically utilized top-down fabrication techniques that, while allowing high-resolution control, are limited by scale and require chemical cross-linking steps to stabilize morphogen patterns in time. Here, a bottom-up approach to protein patterning is developed based on a novel binary reaction-diffusion process where proteins function as diffusive reactants to assemble a nanoclay-protein composite hydrogel. Using this approach, it is possible to generate scalable and highly stable 3D patterns of target proteins down to sub-cellular resolution through only physical interactions between clay nanoparticles and the proteins and ions present in blood. Patterned nanoclay gels are able to guide cell behavior to precisely template bone tissue formation in vivo. These results demonstrate the feasibility of stabilizing 3D gradients of biological signals through self-assembly processes and open up new possibilities for morphogen-based therapeutic strategies and models of biological development and repair.

The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Turing structuring with multiple nanotwins to engineer efficient and stable catalysts for hydrogen evolution reaction

Low-dimensional nanocrystals with controllable defects or strain modifications are newly emerging active electrocatalysts for hydrogen-energy conversion and utilization; however, a crucial challenge remains in insufficient stability due to spontaneous structural degradation and strain relaxation. Here we report a Turing structuring strategy to activate and stabilize superthin metal nanosheets by incorporating high-density nanotwins. Turing configuration, realized by constrained orientation attachment of nanograins, yields intrinsically stable nanotwin network and straining effects, which synergistically reduce the energy barrier of water dissociation and optimize the hydrogen adsorption free energy for hydrogen evolution reaction. Turing PtNiNb nanocatalyst achieves 23.5 and 3.1 times increase in mass activity and stability index, respectively, compared against commercial 20% Pt/C. The Turing PtNiNb-based anion-exchange-membrane water electrolyser with a low Pt mass loading of 0.05 mg cm-2 demonstrates at least 500 h stability at 1000 mA cm-2, disclosing the stable catalysis. Besides, this new paradigm can be extended to Ir/Pd/Ag-based nanocatalysts, illustrating the universality of Turing-type catalysts.

Cell spheroid creation by transcytotic intercellular gelation

Cell spheroids bridge the discontinuity between in vitro systems and in vivo animal models. However, inducing cell spheroids by nanomaterials remains an inefficient and poorly understood process. Here we use cryogenic electron microscopy to determine the atomic structure of helical nanofibres self-assembled from enzyme-responsive D-peptides and fluorescent imaging to show that the transcytosis of D-peptides induces intercellular nanofibres/gels that potentially interact with fibronectin to enable cell spheroid formation. Specifically, D-phosphopeptides, being protease resistant, undergo endocytosis and endosomal dephosphorylation to generate helical nanofibres. On secretion to the cell surface, these nanofibres form intercellular gels that act as artificial matrices and facilitate the fibrillogenesis of fibronectins to induce cell spheroids. No spheroid formation occurs without endo- or exocytosis, phosphate triggers or shape switching of the peptide assemblies. This study-coupling transcytosis and morphological transformation of peptide assemblies-demonstrates a potential approach for regenerative medicine and tissue engineering.

Orbiting Self-Organization of Filament-Tethered Surface-Active Droplets

Dissipative chemical systems hold the potential to enable life-like behavior in synthetic matter, such as self-organization, motility, and dynamic switching between different states. Here, out-of-equilibrium self-organization is demonstrated by interconnected source and drain droplets at an air-water interface, which display dynamic behavior due to a hydrolysis reaction that generates a concentration gradient around the drain droplets. This concentration gradient interferes with the adhesion of self-assembled amphiphile filaments that grow from a source droplet. The chemical gradient sustains a unique orbiting of the drain droplet, which is proposed to be driven by the selective adhesion of the filaments to the front of the moving droplet, while filaments approaching from behind are destabilized upon contact with the hydrolysis product in the trail of the droplet. Potential applications are foreseen in the transfer of chemical signals amongst communicating droplets in rearranging networks, and the implementation of chemical reactions to drive complex positioning routines in life-like systems.

Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics - rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self-assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states' population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.

Cumulative Effect of pH and Redox Triggers on Highly Adaptive Transient Coacervates

An intricate synergism between multiple biochemical processes and physical conditions determines the formation and function of various biological self-assemblies. Thus, a complex set of variables dictate the far-from-equilibrium nature of these biological assemblies. Mimicking such systems synthetically is a challenging task. We report multi-stimuli responsive transient coacervation of an aldehyde-appended polymer and a short peptide. The coacervates are formed by the disulphide linkages between the peptide molecules and the imine bond between the polymer and the peptide. Imines are susceptible to pH changes and the disulphide bonds can be tuned by oxidation/reduction processes. Thus, the coacervation is operational only under the combined effect of appropriate pH and oxidative conditions. Taking advantage of these facts, the coacervates are transiently formed under a pH cycle (urea-urease/gluconolactone) and a non-equilibrium redox cycle (TCEP/H₂ O₂ ). Importantly, the system showed high adaptability toward environmental changes. The transient existence of the coacervates can be generated without any apparent change in size and shape within the same system through the sequential application of the above-mentioned nonequilibrium reaction cycles. Additionally, the coacervation allows for efficient encapsulation/stabilisation of proteins. Thus, the system has the potential to be used for protein/drug delivery purposes in the future.

Persistent ATP-Concentration Gradients in a Hydrogel Sustained by Chemical Fuel Consumption

We show the formation of macroscopic ATP-concentrations in an agarose gel and demonstrate that these gradients can be sustained in time at the expense of the consumption of a chemical fuel. The approach relies on the spatially controlled activation of ATP-producing and ATP-consuming reactions through the local injection of enzymes in the matrix. The reaction-diffusion system is maintained in a stationary non-equilibrium state as long as chemical fuel, phosphocreatine, is present. The reaction-diffusion system is coupled to a supramolecular system composed of monolayer protected gold nanoparticles and a fluorescent probe. As a result of this coupling, fluorescence signals emerge spontaneously in response to the ATP-concentration gradients. We show that the approach permits the rational formation of complex fluorescence patterns that change over time as a function of the evolution of the ATP-concentrations present in the system.

Formation of Catalytic Hotspots in ATP-Templated Assemblies

The self-assembly of surfactant-based structures that rely for their formation on the combination of a thermodynamically controlled and a dissipative pathway is described. Adenosine triphosphate (ATP) acts as a high-affinity template and triggers assembly formation at low surfactant concentrations. The presence of these assemblies creates the conditions for the activation of a dissipative self-assembly process by a weak-affinity substrate. The substrate-induced recruitment of additional surfactants leads to the spontaneous formation of catalytic hotspots in the ATP-stabilized assemblies that cleave the substrate. As a result of the two self-assembly processes, catalysis can be observed at a surfactant concentration at which low catalytic activity is observed in the absence of ATP.

Reaction-Diffusion Pathways for a Programmable Nanoscale Texture of the Diamond-SiC Composite

The diamond-SiC composite has a low density and the highest possible speed of sound among existing materials except for diamond. The composite is synthesized by a complex exothermic chemical reaction between diamond powder and liquid Si. This makes it an ideal material for protection against impact loading. Experiments show that a system of patterns is formed at the diamond-SiC interface. Modeling of reaction-diffusion processes of composite synthesis proves a formation of ceramic materials with a regular (periodic) interconnected microstructure in a given system. The composite material with interconnected structures at the interface has very high mechanical properties and resistance to impact since its fractioning is intercrystallite.

Priming self-assembly pathways by stacking block copolymers

Block copolymers spontaneously self-assemble into well-defined nanoscale morphologies. Yet equilibrium assembly gives rise to a limited set of structures. Non-equilibrium strategies can, in principle, expand diversity by exploiting self-assembly's responsive nature. In this vein, we developed a pathway priming strategy combining control of thin film initial configurations and ordering history. We sequentially coat distinct materials to form prescribed initial states, and use thermal annealing to evolve these manifestly non-equilibrium states through the assembly landscape, traversing normally inaccessible transient structures. We explore the enormous associated hyperspace, spanning processing (annealing temperature and time), material (composition and molecular weight), and layering (thickness and order) dimensions. We demonstrate a library of exotic non-native morphologies, including vertically-oriented perforated lamellae, aqueduct structures (vertical lamellar walls with substrate-pinned perforations), parapets (crenellated lamellae), and networks of crisscrossing lamellae. This enhanced structural control can be used to modify functional properties, including accessing regimes that surpass their equilibrium analogs.

Controlling the Periodicity of a Reaction-Diffusion Wave in Artificial Cells by a Two-Way Energy Supplier

Reaction-diffusion (RD) waves, which are dynamic self-organization structures generated by nanosize molecules, are a fundamental mechanism from patterning in nano- and micromaterials to spatiotemporal regulations in living cells, such as cell division and motility. Although the periods of RD waves are the critical element for these functions, the development of a system to control their period is challenging because RD waves result from nonlinear physical dynamics under far-from-equilibrium conditions. Here, we developed an artificial cell system with tunable period of an RD-driven wave (Min protein wave), which determines a cell division site plane in living bacterial cells. The developed system is based on our finding that Min waves are generated by energy consumption of either ATP or dATP, and the period of the wave is different between these two energy suppliers. We showed that the Min-wave period was modulated linearly by the mixing ratio of ATP and dATP and that it was also possible to estimate the mixing ratio of ATP and dATP from the period. Our findings illuminated a previously unidentified principle to control the dissipative dynamics of biomolecules and, simultaneously, built an important framework to construct molecular robots with spatiotemporal units.

Effect of the Polarity of Solvents on Periodic Precipitation: Formation of Hierarchical Revert Liesegang Patterns

Liesegang pattern (LP) is one example of self-organized periodic precipitation patterns in nonequilibrium systems. Several studies have demonstrated that the LP morphology can track physicochemical environmental conditions (e.g., temperature); however, the polarity effect has not been explored to date. In this study, a copper chromate system is used to reveal the impact of solvent polarity on the evolving LP structure using water/organic solvent mixtures. In the typical case of using water/dimethyl sulfoxide (DMSO) mixtures, two drastic changes in LP morphology with increasing DMSO contents were found: (i) increasing frequency of the original structure and (ii) formation of a hierarchical pattern with the appearance of another, lower-frequency structure. Furthermore, the simulation model operating with a bimodal size distribution, allowing both homogeneous and heterogeneous precipitations showed good agreement with the experimental results. Therefore, this study demonstrated that LP can be tailored by solvent polarity and can be used for designing hierarchical precipitation patterns in a straightforward manner.

Cell-Size Space Regulates the Behavior of Confined Polymers: From Nano- and Micromaterials Science to Biology

Polymer micromaterials in a liquid or gel phase covered with a surfactant membrane are widely used materials in pharmaceuticals, cosmetics, and foods. In particular, cell-sized micromaterials of biopolymer solutions covered with a lipid membrane have been studied as artificial cells to understand cells from a physicochemical perspective. The characteristics and phase transitions of polymers confined to a microscopic space often differ from those in bulk systems. The effect that causes this difference is referred to as the cell-size space effect (CSE), but the specific physicochemical factors remain unclear. This study introduces the analysis of CSE on molecular diffusion, nanostructure transition, and phase separation and presents their main factors, i.e., short- and long-range interactions with the membrane surface and small volume (finite element nature). This serves as a guide for determining the dominant factors of CSE. Furthermore, we also introduce other factors of CSE such as spatial closure and the relationships among space size, the characteristic length of periodicity, the structure size, and many others produced by biomolecular assemblies through the analysis of protein reaction-diffusion systems and biochemical reactions.

Spatial programming of self-organizing chemical systems using sustained physicochemical gradients from reaction, diffusion and hydrodynamics

Living organisms employ chemical self-organization to build structures, and inspire new strategies to design synthetic systems that spontaneously take a particular form, via a combination of integrated chemical reactions, assembly pathways and physicochemical processes. However, spatial programmability that is required to direct such self-organization is a challenge to control. Thermodynamic equilibrium typically brings about a homogeneous solution, or equilibrium structures such as supramolecular complexes and crystals. This perspective addresses out-of-equilibrium gradients that can be driven by coupling chemical reaction, diffusion and hydrodynamics, and provide spatial differentiation in the self-organization of molecular, ionic or colloidal building blocks in solution. These physicochemical gradients are required to (1) direct the organization from the starting conditions (e.g. a homogeneous solution), and (2) sustain the organization, to prevent it from decaying towards thermodynamic equilibrium. We highlight four different concepts that can be used as a design principle to establish such self-organization, using chemical reactions as a driving force to sustain the gradient and, ultimately, program the characteristics of the gradient: (1) reaction-diffusion coupling; (2) reaction-convection; (3) the Marangoni effect and (4) diffusiophoresis. Furthermore, we outline their potential as attractive pathways to translate chemical reactions and molecular/colloidal assembly into organization of patterns in solution, (dynamic) self-assembled architectures and collectively moving swarms at the micro-, meso- and macroscale, exemplified by recent demonstrations in the literature.

Provenance of life: Chemical autonomous agents surviving through associative learning

We present a benchmark study of autonomous, chemical agents exhibiting associative learning of an environmental feature. Associative learning systems have been widely studied in cognitive science and artificial intelligence but are most commonly implemented in highly complex or carefully engineered systems, such as animal brains, artificial neural networks, DNA computing systems, and gene regulatory networks, among others. The ability to encode environmental information and use it to make simple predictions is a benchmark of biological resilience and underpins a plethora of adaptive responses in the living hierarchy, spanning prey animal species anticipating the arrival of predators to epigenetic systems in microorganisms learning environmental correlations. Given the ubiquitous and essential presence of learning behaviors in the biosphere, we aimed to explore whether simple, nonliving dissipative structures could also exhibit associative learning. Inspired by previous modeling of associative learning in chemical networks, we simulated simple systems composed of long- and short-term memory chemical species that could encode the presence or absence of temporal correlations between two external species. The ability to learn this association was implemented in Gray-Scott reaction-diffusion spots, emergent chemical patterns that exhibit self-replication and homeostasis. With the novel ability of associative learning, we demonstrate that simple chemical patterns can exhibit a broad repertoire of lifelike behavior, paving the way for in vitro studies of autonomous chemical learning systems, with potential relevance to artificial life, origins of life, and systems chemistry. The experimental realization of these learning behaviors in protocell or coacervate systems could advance a new research direction in astrobiology, since our system significantly reduces the lower bound on the required complexity for autonomous chemical learning.

Programmable, Spatiotemporal Control of Colloidal Motion Waves via Structured Light

Traveling waves in a reaction-diffusion system are essential for long-range communication in living organisms and inspire biomimetic materials of similar capabilities. One recent example is the traveling motion waves among photochemically oscillating, silver (Ag)-containing colloids. Being able to manipulate these colloidal waves holds the key for potential applications. Here, we have discovered that these motion waves can be confined by light patterns and that the chemical clocks of silver particles are moved forward by reducing local light intensity. Using these discoveries as design principles, we have applied structured light technology for the precise and programmable control of colloidal motion waves, including their origins, propagation directions, paths, shapes, annihilation, frequency, and speeds. We have also used the controlled propagation of colloidal waves to guide chemical messages along a predefined path to activate a population of micromotors located far from the signal. Our demonstrated capabilities in manipulating colloidal waves in space and time offer physical insights on their operation and expand their usefulness in the fundamental study of reaction-diffusion processes. Moreover, our findings inspire biomimetic strategies for the directional transport of mass, energy, and information at micro- or even nanoscales.

Temporal Stimulus Patterns Drive Differentiation of a Synthetic Dipeptide-Based Coacervate

The fate of living cells often depends on their processing of temporally modulated information, such as the frequency and duration of various signals. Synthetic stimulus-responsive systems have been intensely studied for >50 years, but it is still challenging for chemists to create artificial systems that can decode dynamically oscillating stimuli and alter the systems' properties/functions because of the lack of sophisticated reaction networks that are comparable with biological signal transduction. Here, we report morphological differentiation of synthetic dipeptide-based coacervates in response to temporally distinct patterns of the light pulse. We designed a simple cationic diphenylalanine peptide derivative to enable the formation of coacervates. The coacervates concentrated an anionic methacrylate monomer and a photoinitiator, which provided a unique reaction environment and facilitated light-triggered radical polymerization─even in air. Pulsed light irradiation at 9.0 Hz (but not at 0.5 Hz) afforded anionic polymers. This dependence on the light pulse patterns is attributable to the competition of reactive radical intermediates between the methacrylate monomer and molecular oxygen. The temporal pulse pattern-dependent polymer formation enabled the coacervates to differentiate in terms of morphology and internal viscosity, with an ultrasensitive switch-like mode. Our achievements will facilitate the rational design of smart supramolecular soft materials and are insightful regarding the synthesis of sophisticated chemical cells.

One-Step Patterning of Organic Semiconductors on Gold Electrodes via Capillary-Bridge Manipulation

Patterning organic semiconductors directly on Au electrodes possesses the advantages of eliminating metal atomic penetration effect, compatibility with fine lithography processes, and feasibility of work function modification on electrodes, and it is therefore of value in the commercial manufacturability application of optoelectronic devices with low cost, large scale, and high efficiency. Solution processing, is relatively inexpensive and is scalable to large areas. Nonetheless, conventional solution processing approaches have trade-offs among controllable morphology, regular alignment, precise position, and ordered molecular packing arising from the uncontrollable dewetting kinetics. Here, one-step patterning of 1D polymer nanowire arrays directly on Au source-drain electrodes with precise position, controlled orientation, regulated distribution, and tunable width size were realized by employing a capillary-bridge manipulation method to guide the processes of liquid dewetting and nanowire assembly. Organic field-effect transistors (OFETs) with mobility of 10.1 cm² V^-1 s^-1 and on/off current ratio of 1.9 × 10⁴ were fabricated. Moreover, we verified generality of our method by patterning different solution-processable optoelectronic materials, including small molecules, quantum dot (QD) nanoparticles, and metal-halide perovskites, into ordered structures directly on the target substrate. The work provides a novel insight into efficient manufacturing the regular aligned and precisely positioned 1D organic semiconductors directly on the channel region of prefabricated Au electrodes in one step and facilitates their applications in high-performance electronic devices.

Turing patterns by supramolecular self-assembly of a single salphen building block

In the 1950s, Alan Turing showed that concerted reactions and diffusion of activating and inhibiting chemical species can autonomously generate patterns without previous positional information, thus providing a chemical basis for morphogenesis in Nature. However, access to these patterns from only one molecular component that contained all the necessary information to execute agonistic and antagonistic signaling is so far an elusive goal, since two or more participants with different diffusivities are a must. Here, we report on a single-molecule system that generates Turing patterns arrested in the solid state, where supramolecular interactions are used instead of chemical reactions, whereas diffusional differences arise from heterogeneously populated self-assembled products. We employ a family of hydroxylated organic salphen building blocks based on a bis-Schiff-base scaffold with portions responsible for either activation or inhibition of assemblies at different hierarchies through purely supramolecular reactions, only depending upon the solvent dielectric constant and evaporation as fuel.

Regulating Spatial Localization and Reactivity Biasness of DNAzymes by Metal Ions and Oligonucleotides

Chemical gradient sensing behavior of catalytically active colloids and enzymes is an area of immense interest owing to their importance in understanding fundamental spatiotemporal complexity pattern in living systems and designing of dynamic materials. Herein, we have shown peroxidase activity of DNAzyme (G-quadruplex-hemin complex tagged in a micron-sized glass bead) can be modulated by metal ions and metal ion-binding oligonucleotides. Next we demonstrated both experimentally and theoretically that the localization and product formation ability of the DNAzyme containing particle remains biased to the more catalytically active zone where concentration of metal ion (Hg2+) inhibitor is low. Interestingly, this biased localization can be broken by introduction of Hg2+ binding oligonucleotide in the system. Additionally, macroscopically asymmetric catalytic product distributed zone has also been achieved on this process, showing possibility in regulation in autonomous spatially controlled chemical process. This demonstration of autonomous modulation of the localization pattern and spatially specific enhanced product forming ability of DNAzymes will further enable in designing of responsive nucleic acid-based motile materials and surfaces.

Unraveling the physiochemical nature of colloidal motion waves among silver colloids

Traveling waves are common in biological and synthetic systems, including the recent discovery that silver (Ag) colloids form traveling motion waves in H₂O₂ and under light. Here, we show that this colloidal motion wave is a heterogeneous excitable system. The Ag colloids generate traveling chemical waves via reaction-diffusion, and either self-propel through self-diffusiophoresis ("ballistic waves") or are advected by diffusio-osmotic flows from gradients of neutral molecules ("swarming waves"). Key results include the experimental observation of traveling waves of OH^- with pH-sensitive fluorescent dyes and a Rogers-McCulloch model that qualitatively and quantitatively reproduces the key features of colloidal waves. These results are a step forward in elucidating the Ag-H₂O₂-light oscillatory system at individual and collective levels. In addition, they pave the way for using colloidal waves either as a platform for studying nonlinear phenomena, or as a tool for colloidal transport and for information transmission in microrobot ensembles.

Spatiotemporal Regulation of Hydrogel Actuators by Autocatalytic Reaction Networks

Regulating hydrogel actuators with chemical reaction networks is instrumental for constructing life-inspired smart materials. Herein, hydrogel actuators are engineered that are regulated by the autocatalytic front of thiols. The actuators consist of two layers. The first layer, which is regular polyacrylamide hydrogel, is in a strained conformation. The second layer, which is polyacrylamide hydrogel with disulfide crosslinks, maintains strain in the first layer. When thiols released by the autocatalytic front reduce disulfide crosslinks, the hydrogel actuates by releasing the mechanical strain in the first layer. The autocatalytic front is sustained by the reaction network, which uses thiouronium salts, disulfides of β-aminothiols, and maleimide as starting components. The gradual actuation by the autocatalytic front enables movements such as gradual unrolling, screwing, and sequential closing of "fingers." This actuation also allows the transmission of chemical signals in a relay fashion and the conversion of a chemical signal to an electrical signal. Locations and times of spontaneous initiation of autocatalytic fronts can be preprogrammed in the spatial distribution of the reactants in the hydrogel. To approach the functionality of living matter, the actuators triggered by an autocatalytic front can be integrated into smart materials regulated by chemical circuits.

Iodine clocks: applications and untapped opportunities in materials science

Iodine clocks are fascinating nonlinear chemical systems with a glorious past and a promising future. The dynamic removal of iodine from these systems by different means can have important consequences for their reaction dynamics, and could be exploited for time-controlled autonomous dissipative self-assembly. Here, the untapped opportunities offered by iodine clocks for materials science, especially for the time-programming of supramolecular assembly and sol–gel transition, are reviewed and discussed with the hope of arousing the interest on the subject and stimulating new research directions.

Long-Range-Ordered Assembly of Micro-/Nanostructures at Superwetting Interfaces

On-chip integration of solution-processable materials imposes stringent and simultaneous requirements of controlled nucleation and growth, tunable geometry and dimensions, and long-range-ordered assembly, which is challenging in solution process far from thermodynamic equilibrium. Superwetting interfaces, underpinned by programmable surface chemistry and topography, are promising for steering transport, dewetting, and microfluid dynamics of liquids, thus opening a new paradigm for micro-/nanostructure assembly in solution process. Herein, assembly methods on the basis of superwetting interfaces are reviewed for constructing long-range-ordered micro-/nanostructures. Confined capillary liquids, including capillary bridges and capillary corner menisci realized by controlling local wettability and surface topography, are highlighted for simultaneously attained deterministic patterning and long-range order. The versatility and robustness of confined capillary liquids are discussed with assembly of single-crystalline micro-/nanostructures of organic semiconductors, metal-halide perovskites, and colloidal-nanoparticle superlattices, which lead to enhanced device performances and exotic functionalities. Finally, a perspective for promising directions in this realm is provided.

Solvent-free autocatalytic supramolecular polymerization

Solvent-free chemical manufacturing is one of the awaited technologies for addressing an emergent issue of environmental pollution. Here, we report solvent-free autocatalytic supramolecular polymerization (SF-ASP), which provides an inhibition-free template-assisted catalytic organic transformation that takes great advantage of the fact that the product (template) undergoes a termination-free nucleation-elongation assembly (living supramolecular polymerization) under solvent-free conditions. SF-ASP allows for reductive cyclotetramerization of hydrogen-bonding phthalonitriles into the corresponding phthalocyanines in exceptionally high yields (>80%). SF-ASP requires the growing polymer to form hexagonally packed crystalline fibres, which possibly preorganize the phthalonitriles at their cross-sectional edges for their efficient transformation. With metal oleates, SF-ASP produces single-crystalline fibres of metallophthalocyanines again in exceptionally high yields, which grow in both directions without terminal coupling until the phthalonitrile precursors are completely consumed. By taking advantage of this living nature of polymerization, multistep SF-ASP without/with metal oleates allows for the precision synthesis of multi-block supramolecular copolymers.

Phase separation mechanism for a unified understanding of dissipative pattern formation in a Liesegang system

Dissipative patterns with solid-phase transitions are ubiquitous in nature. Despite their ubiquitous nature, there is no unified understanding of the non-equilibrium self-assembly mechanisms of such pattern formation. The Liesegang pattern (LP) is a typical model that has the potential to describe dissipative pattern formation arising from the nonlinear coupling of directional mass transport of water-soluble substances into a porous media with their solid-phase transition processes. However, the conventional mechanism in a Liesegang system lacks practicality because most of the existing studies have focused only on the transition mechanism of nucleation from the molecular to the solid state. In this study, we demonstrate a novel experimental system based on a phase transition and separation mechanism that does not require nucleation, namely, the pH-induced aggregation of gold nanoparticles modified with 11-mercaptoundecanoic acid (MUA-Au NPs) by H⁺ diffusion in a solid hydrogel. Combined experiments and numerical simulations reveal that pattern formation is driven by the macroscopic phase-separation mechanism. Furthermore, the pattern periodicity obtained from both experiments and simulations follows the classical spacing law of LP, namely, the LP morphology is determined without the need for nucleation. Therefore, we can show that the formation of LPs can be described in a unified mechanism, regardless of whether nucleation occurs. This finding opens the possibility that the chemical Liesegang system can be applied as a practical model for proving the mechanisms of similar dissipative pattern formation.

Progressive Local Accumulation of Self-Assembled Nanoreactors in a Hydrogel Matrix through Repetitive Injections of ATP

Cellular functions are regulated with high spatial control through the local activation of chemical processes in a complex inhomogeneous matrix. The development of synthetic macroscopic systems with a similar capacity allows fundamental studies aimed at understanding the relationship between local molecular events and the emergence of functional properties at the macroscopic level. Here, we show that a kinetically stable inhomogeneous hydrogel matrix is spontaneously formed upon the local injection of ATP. Locally, ATP templates the self-assembly of amphiphiles into large nanoreactors with a much lower diffusion rate compared to unassembled amphiphiles. The local depletion of unassembled amphiphiles near the injection point installs a concentration gradient along which unassembled amphiphiles diffuse from the surroundings to the center. This allows for a progressive local accumulation of self-assembled nanoreactors in the matrix upon repetitive cycles of ATP injection separated by time intervals during which diffusion of unassembled amphiphiles takes place. Contrary to the homogeneous matrix containing the same components, in the inhomogeneous matrix the local upregulation of a chemical reaction occurs. Depending on the way the same amount of injected ATP is administered to the hydrogel matrix different macroscopic distributions of nanoreactors are obtained, which affect the location in the matrix where the chemical reaction is upregulated.

Trade-off between carbohydrates and metal ions regulates the chemotactic directionality of alkaline phosphatase

The role of the Hofmeister interaction in governing the chemotactic behavior of alkaline phosphatase in the presence of carbohydrate and metal ion gradients has been established.

Spatiotemporal dynamics of self-assembled structures in enzymatically induced agonistic and antagonistic conditions

Predicting and designing systems with dynamic self-assembly properties in a spatiotemporal fashion is an important research area across disciplines ranging from understanding the fundamental non-equilibrium features of life to the fabrication of next-generation materials with life-like properties. Herein, we demonstrate a spatiotemporal dynamics pattern in the self-assembly behavior of a surfactant from an unorganized assembly, induced by adenosine triphosphate (ATP) and enzymes responsible for the degradation or conversion of ATP. We report the different behavior of two enzymes, alkaline phosphatase (ALP) and hexokinase (HK), towards adenosine triphosphate (ATP)-driven surfactant assembly, which also results in contrasting spatiotemporal dynamic assembly behavior. Here, ALP acts antagonistically, resulting in transient self-assemblies, whereas HK shows agonistic action with the ability to sustain the assemblies. This dynamic assembly behavior was then used to program the time-dependent emergence of a self-assembled structure in a two-dimensional space by maintaining concentration gradients of the enzymes and surfactant at different locations, demonstrating a new route for obtaining 'spatial' organizational adaptability in a self-organized system of interacting components for the incorporation of programmed functionality.

Phototriggered Spatially Controlled Out-of-Equilibrium Patterns of Peptide Nanofibers in a Self-Sorting Double Network Hydrogel

Out-of-equilibrium patterns arising from diffusion processes are ubiquitous in nature, although they have not been fully exploited for the design of artificial materials. Here, we describe the formation of phototriggered out-of-equilibrium patterns using photoresponsive peptide-based nanofibers in a self-sorting double network hydrogel. Light irradiation using a photomask followed by thermal incubation induced the spatially controlled condensation of peptide nanofibers. According to confocal images and spectroscopic analyses, metastable nanofibers photodecomposed in the irradiated areas, where thermodynamically stable nanofibers reconstituted and condensed with a supply of monomers from the nonirradiated areas. These supramolecular events were regulated by light and diffusion to facilitate the creation of unique out-of-equilibrium patterns, including two lines from a one-line photomask and a line pattern of a protein immobilized in the hydrogel.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

Dissecting Biological and Synthetic Soft-Hard Interfaces for Tissue-Like Systems

Soft and hard materials at interfaces exhibit mismatched behaviors, such as mismatched chemical or biochemical reactivity, mechanical response, and environmental adaptability. Leveraging or mitigating these differences can yield interfacial processes difficult to achieve, or inapplicable, in pure soft or pure hard phases. Exploration of interfacial mismatches and their associated (bio)chemical, mechanical, or other physical processes may yield numerous opportunities in both fundamental studies and applications, in a manner similar to that of semiconductor heterojunctions and their contribution to solid-state physics and the semiconductor industry over the past few decades. In this review, we explore the fundamental chemical roles and principles involved in designing these interfaces, such as the (bio)chemical evolution of adaptive or buffer zones. We discuss the spectroscopic, microscopic, (bio)chemical, and computational tools required to uncover the chemical processes in these confined or hidden soft-hard interfaces. We propose a soft-hard interaction framework and use it to discuss soft-hard interfacial processes in multiple systems and across several spatiotemporal scales, focusing on tissue-like materials and devices. We end this review by proposing several new scientific and engineering approaches to leveraging the soft-hard interfacial processes involved in biointerfacing composites and exploring new applications for these composites.

Chemical engines: driving systems away from equilibrium through catalyst reaction cycles

Biological systems exhibit a range of complex functions at the micro- and nanoscales under non-equilibrium conditions (for example, transportation and motility, temporal control, information processing and so on). Chemists also employ out-of-equilibrium systems, for example in kinetic selection during catalysis, self-replication, dissipative self-assembly and synthetic molecular machinery, and in the form of chemical oscillators. Key to non-equilibrium behaviour are the mechanisms through which systems are able to extract energy from the chemical reactants ('fuel') that drive such processes. In this Perspective we relate different examples of such powering mechanisms using a common conceptual framework. We discuss how reaction cycles can be coupled to other dynamic processes through positive (acceleration) or negative (inhibition) catalysis to provide the thermodynamic impetus for diverse non-equilibrium behaviour, in effect acting as a 'chemical engine'. We explore the way in which the energy released from reaction cycles is harnessed through kinetic selection in a series of what have sometimes been considered somewhat disparate fields (systems chemistry, molecular machinery, dissipative assembly and chemical oscillators), highlight common mechanistic principles and the potential for the synchronization of chemical reaction cycles, and identify future challenges for the invention and application of non-equilibrium systems. Explicit recognition of the use of fuelling reactions to power structural change in catalysts may stimulate the investigation of known catalytic cycles as potential elements for chemical engines, a currently unexplored area of catalysis research.

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.