Bistable Functions and Signaling Motifs in Systems Chemistry: Taking the Next Step Toward Synthetic Cells

A key challenge in modern chemistry research is to mimic life-like functions using simple molecular networks and the integration of such networks into the first functional artificial cell. Central to this endeavor is the development of signaling elements that can regulate the cell function in time and space by producing entities of code with specific information to induce downstream activity. Such artificial signaling motifs can emerge in nonequilibrium systems, exhibiting complex dynamic behavior like bistability, multistability, oscillations, and chaos. However, the de novo, bottom-up design of such systems remains challenging, primarily because the kinetic characteristics and energy aspects yielding bifurcation have not yet been globally defined. We herein review our recent work that focuses on the design and functional analysis of peptide-based networks, propelled by replication reactions and exhibiting bistable behavior. Furthermore, we rationalize and discuss their exploitation and implementation as variable signaling motifs in homogeneous and heterogeneous environments.The bistable reactions constitute reversible second-order autocatalysis as positive feedback to generate two distinct product distributions at steady state (SS), the low-SS and high-SS. Quantitative analyses reveal that a phase transition from simple reversible equilibration dynamics into bistability takes place when the system is continuously fueled, using a reducing agent, to keep it far from equilibrium. In addition, an extensive set of experimental, theoretical, and simulation studies highlight a defined parameter space where bistability operates.Analogous to the arrangement of protein-based bistable motifs in intracellular signaling pathways, sequential concatenation of the synthetic bistable networks is used for signal processing in homogeneous media. The cascaded network output signals are switched and erased or transduced by manipulating the order of addition of the components, allowing it to reach "on demand" either the low-SS or high-SS. The pre-encoded bistable networks are also useful as a programming tool for the downstream regulation of nanoscale materials properties, bridging together the Systems Chemistry and Nanotechnology fields. In such heterogeneous cascade pathways, the outputs of the bistable network serve as input signals for consecutive nanoparticle formation reaction and growth processes, which-depending on the applied conditions-regulate various features of (Au) nanoparticle shape and assembly.Our work enables the design and production of various signaling apparatus that feature higher complexity than previously observed in chemical networks. Future studies, briefly discussed at the end of the Account, will be directed at the design and analysis of more elaborate functionality, such as bistability under flow conditions, multistability, and oscillations. We propose that a profound understanding of the design principles facilitating the replication-based bistability and related functions bear implications for exploring the origin of protein functionality prior to the highly evolved replication-translation-transcription machinery. The integration of our peptide-based signaling motifs within future synthetic cells seems to be a straightforward development of the two alternating states as memory and switch elements for controlling cell growth and division and even communication among different cells. We furthermore suggest that such systems can be introduced into living cells for various biotechnology applications, such as switches for cell temporal and spatial manipulations.

Electrostatically Dominated Pre-Organization in Cyclodextrin Metal-Organic Frameworks

Electrostatic interactions between oppositely charged entities play a key role in pre-organizing substrates and stabilizing transition states of reactions in enzymes. The use of electrostatic interactions to pre-organize ions in nanoconfined pores, however, has not been investigated to its full potential. Herein, we describe how carboxylate anions can be pre-organized at the behest of their electrostatic interactions with K+ cations in nanoconfined tunnels present in γ-cyclodextrin metal-organic frameworks, i.e., CD-MOFs. Several carboxylate anions, which are all much smaller than the cavities of the tunnels, were visualized by X-ray crystallography when nanoconfined in CD-MOFs, despite the large voids present in the tunnels. These anions were found to be aligned within a planar array defined by four K+ cations, positioned around the periphery of the tunnels. The strong electrostatic interactions between the carboxylate anions and the K+ cations dictate the orientation of the anions and override the influence of all other possible noncovalent bonding interactions between them and the tunnels. Consequently, the aligned pairs of γ-cyclodextrin rings constituting the tunnels become distorted, resulting in them having lower symmetry and fewer disordered carboxylate anions in the solid state. Our findings offer a transformative strategy for controlling the packing and orientation of ions in nanoconfined environments.

Multiscale Approach for Tuning Communication among Chemical Oscillators Confined in Biomimetic Microcompartments

Inspired by the biological world, new cross-border disciplines and technologies have emerged. Relevant examples include systems chemistry, which offers a bottom-up approach toward chemical complexity, and bio/chemical information and communication technology (bio/chemical ICT), which explores the conditions for propagating signals among individual microreactors separated by selectively permeable membranes. To fabricate specific arrays of microreactors, microfluidics has been demonstrated as an excellent method. In particular, droplet-based microfluidics is a powerful tool for encapsulating biological entities and chemical reagents in artificial microenvironments, mostly water-in-oil microdroplets. In these systems, the interfaces are liquid-liquid, and their physicochemical properties are key factors for tuning the coupling between molecular diffusion. Simple and double emulsions, where aqueous domains are in equilibrium with oil domains through boundary layers of amphiphilic molecules, are organized assemblies with high interfacial-area-to-volume ratios. These membranes can be engineered to obtain different surface charges, single- or multilayer stacking, and a variable degree of defects in molecular packing. Emulsions find application in many fields, including the food industry, pharmaceutics, and cosmetics. Furthermore, micro- and nanoemulsions can be used to model the propagation of chemical species through long distances, which is not only vital for cell signaling but also significant in molecular computing. Here we present in-depth research on the faceted world of solutions confined in restricted environments. In particular, we focused on the multiscale aspects of structure and dynamics from molecular to micro and macro levels. The Belousov-Zhabotinsky chemical reaction, known for its robustness and well-documented oscillatory behavior, was selected to represent a generic signal emitter/receiver confined within microenvironments separated by liquid-liquid interfaces. In this pulse generator, the temporal and spatial progressions are governed by periodic fluctuations in the concentration of chemical species, which act as activatory or inhibitory messengers over long distances. When organized into "colonies" or arrays, these micro-oscillators exhibit emergent dynamical behaviors at the population level. These behaviors can be finely tuned by manipulating the geometrical distribution of the oscillators and the properties of the interfaces at the nanoscale. By carefully selecting the membrane composition, it is possible to drive the system toward either in-phase, antiphase, or mixed synchronization regimes among individual oscillators, depending on messenger molecules. This relatively simple lab-scale model replicates some of the communication strategies commonly found in biological systems, particularly those based on the passive diffusion of chemical and electrical signals. It can help shed light on fundamental life processes and inspire new implementations in molecular computing and smart materials.

Investigation of transient extreme events in a mutually coupled star network of theoretical Brusselator system

In this article, we present evidence of a distinct class of extreme events that occur during the transient chaotic state within network modeling using the Brusselator with a mutually coupled star network. We analyze the phenomenon of transient extreme events in the network by focusing on the lifetimes of chaotic states. These events are identified through the finite-time Lyapunov exponent and quantified using threshold and statistical methods, including the probability distribution function (PDF), generalized extreme value (GEV) distribution, and return period plots. We also evaluate the transitions of these extreme events by examining the average synchronization error and the system's energy function. Our findings, validated across networks of various sizes, demonstrate consistent patterns and behaviors, contributing to a deeper understanding of transient extreme events in complex networks.

Rethinking life and predicting its origin

The definition, origin and recreation of life remain elusive. As others have suggested, only once we put life into reductionist physical terms will we be able to solve those questions. To that end, this work proposes the phenomenon of life to be the product of two dissipative mechanisms. From them, one characterises extant biological life and deduces a testable scenario for its origin. The proposed theory of life allows its replication, reinterprets ecological evolution and creates new constraints on the search for life.

Living cells and biological mechanisms as prototypes for developing chemical artificial intelligence

Artificial Intelligence (AI) is having a revolutionary impact on our societies. It is helping humans in facing the global challenges of this century. Traditionally, AI is developed in software or through neuromorphic engineering in hardware. More recently, a brand-new strategy has been proposed. It is the so-called Chemical AI (CAI), which exploits molecular, supramolecular, and systems chemistry in wetware to mimic human intelligence. In this work, two promising approaches for boosting CAI are described. One regards designing and implementing neural surrogates that can communicate through optical or chemical signals and give rise to networks for computational purposes and to develop micro/nanorobotics. The other approach concerns "bottom-up synthetic cells" that can be exploited for applications in various scenarios, including future nano-medicine. Both topics are presented at a basic level, mainly to inform the broader audience of non-specialists, and so favour the rise of interest in these frontier subjects.

A Role for Bottom-Up Synthetic Cells in the Internet of Bio-Nano Things?

The potential role of bottom-up Synthetic Cells (SCs) in the Internet of Bio-Nano Things (IoBNT) is discussed. In particular, this perspective paper focuses on the growing interest in networks of biological and/or artificial objects at the micro- and nanoscale (cells and subcellular parts, microelectrodes, microvessels, etc.), whereby communication takes place in an unconventional manner, i.e., via chemical signaling. The resulting "molecular communication" (MC) scenario paves the way to the development of innovative technologies that have the potential to impact biotechnology, nanomedicine, and related fields. The scenario that relies on the interconnection of natural and artificial entities is briefly introduced, highlighting how Synthetic Biology (SB) plays a central role. SB allows the construction of various types of SCs that can be designed, tailored, and programmed according to specific predefined requirements. In particular, "bottom-up" SCs are briefly described by commenting on the principles of their design and fabrication and their features (in particular, the capacity to exchange chemicals with other SCs or with natural biological cells). Although bottom-up SCs still have low complexity and thus basic functionalities, here, we introduce their potential role in the IoBNT. This perspective paper aims to stimulate interest in and discussion on the presented topics. The article also includes commentaries on MC, semantic information, minimal cognition, wetware neuromorphic engineering, and chemical social robotics, with the specific potential they can bring to the IoBNT.

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.

Synchronization of Belousov-Zhabotinsky oscillators with electrochemical coupling in a spontaneous process

A passive electrochemical coupling approach is proposed to induce spontaneous synchronization between chemical oscillators. The coupling exploits the potential difference between a catalyst redox couple in the Belousov-Zhabotinsky (BZ) reaction, without external feedback, to induce surface reactions that impact the kinetics of the bulk system. The effect of coupling in BZ oscillators under batch condition is characterized using phase synchronization measures. Although the frequency of the oscillators decreases nonlinearly over time, by a factor of 2 or more within 100 cycles, the coupling is strong enough to maintain synchronization. In such a highly drifting system, the Gibbs-Shannon entropy of the cyclic phase difference distribution can be used to quantify the coupling effect. We extend the Oregonator BZ model to account for the drifting natural frequencies in batch condition and for electrochemical coupling, and numerical simulations of the effect of acid concentration on synchronization patterns are in agreement with the experiments. Because of the passive nature of coupling, the proposed coupling scheme can open avenues for designing pattern recognition and neuromorphic computation systems using chemical reactions in a spontaneous process.

Research progress in self-oscillating polymer brushes

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications. Self-oscillating polymers are anchored on surfaces of certain materials and are coupled with some self-oscillating reactions (with the Belousov–Zhabotinsky (BZ) reaction as an example) to form self-oscillating polymer brushes. As an independent field of stimulus response functional surface research, the development of new intelligent bionic materials has good potential. This article reviews the oscillation mechanisms of self-oscillating polymer brushes and their classifications. First, the oscillation mechanisms of self-oscillating polymer brushes are introduced. Second, the research progress in self-oscillating polymers is discussed in terms of the type of self-oscillation reactions. Finally, possible future developments of self-oscillating polymer brushes are prospected.

Polymer brushes possess unique changes in physical and chemical properties when they are exposed to external stimuli and have a wide range of applications.

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.

Oscillating Motion of Oil Droplets in the Emulsion Near the Air-Water Interface

Numerous living organisms as well as artificially created self-propelled objects can form dissipative structures due to the nonlinear effects and nonequilibrium of the system. Here we present an active oil-in-water emulsion in which the oil droplets take part in the reciprocating motion under the action of Marangoni flow near the air-water interface. The droplet dynamics in the emulsion is governed by the chemical reaction proceeding between quiescent copper particles and ammonia and by the convective mixing of a surfactant. We established that the reciprocating motion of droplets in the emulsion arises as a result of a periodic change in the Marangoni flow direction at the air-water interface. The feature of the considered system is that the reciprocating motion of droplets is realized only when the surface area fraction of droplets in the emulsion is close to the density of a two-dimensional colloid crystal. Oscillations degenerate under the reduction in surface area fraction to the critical value of ∼50% since the existence of oscillations in the emulsion requires a suppression of the surfactant convective mixing between the inner layers of liquid film and the air-water interface.

Selective Photodimerization in a Cyclodextrin Metal-Organic Framework

For the most part, enzymes contain one active site wherein they catalyze in a serial manner chemical reactions between substrates both efficiently and rapidly. Imagine if a situation could be created within a chiral porous crystal containing trillions of active sites where substrates can reside in vast numbers before being converted in parallel into products. Here, we report how it is possible to incorporate 1-anthracenecarboxylate (1-AC^-) as a substrate into a γ-cyclodextrin-containing metal-organic framework (CD-MOF-1), where the metals are K⁺ cations, prior to carrying out [4+4] photodimerizations between pairs of substrate molecules, affording selectively one of four possible regioisomers. One of the high-yielding regioisomers exhibits optical activity as a result of the presence of an 8:1 ratio of the two enantiomers following separation by high-performance liquid chromatography. The solid-state superstructure of 1-anthracenecarboxylate potassium salt (1-ACK), which is co-crystallized with γ-cyclodextrin, reveals that pairs of substrate molecules are not only packed inside tunnels between spherical cavities present in CD-MOF-1, but also stabilized-in addition to hydrogen-bonding to the C-2 and C-3 hydroxyl groups on the d-glucopyranosyl residues present in the γ-cyclodextrin tori-by combinations of hydrophobic and electrostatic interactions between the carboxyl groups in 1-AC^- and four K⁺ cations on the waistline between the two γ-cyclodextrin tori in the tunnels. These non-covalent bonding interactions result in preferred co-conformations that account for the highly regio- and enantioselective [4+4] cycloaddition during photoirradiation. Theoretical calculations, in conjunction with crystallography, support the regio- and stereochemical outcome of the photodimerization.

Oscillating Reactions Meet Polymers at Interfaces

Chemo-mechanical phenomena, including oscillations and peristaltic motions, are widespread in nature-just think of heartbeats-thanks to the ability of living organisms to convert directly chemical energy into mechanical work. Their imitation with artificial systems is still an open challenge. Chemical clocks and oscillators (such as the popular Belousov-Zhabotinsky (BZ) reaction) are reaction networks characterized by the emergence of peculiar spatiotemporal dynamics. Their application to polymers at interfaces (grafted chains, layer-by-layer assemblies, and polymer brushes) offers great opportunities for developing novel smart biomimetic materials. Despite the wide field of potential applications, limited research has been carried out so far. Here, we aim to showcase the state-of-the-art of this fascinating field of investigation, highlighting the potential for future developments and providing a personal outlook.

Microfluidic compartmentalization of diffusively coupled oscillators in multisomes induces a novel synchronization scenario

Multisome compartments encapsulating the Belousov–Zhabotinsky reaction produced by microfluidics arranged in 1D arrays showed a novel type of global synchronization.

Growth and form of a self-constructing tube network

When a small amount of liquid is quickly injected into another liquid with similar density, the fluid jet usually does not propagate very far. However, when the two solutions chemically react to form a flexible membrane at their interface, then structures that are long and branching can form. Here, we describe the tube networks produced when a small amount of AlCl₃ solution is quickly injected into a NaOH solution. Single straight tubes do not occur, but straight tubular "stems" with 2-5 "branches" are observed. The branches emerge relatively symmetrically from the stem at a common branching junction. These structures can have a ratio of propagation distance to stem width as large as 50. The stem and branches grow by the stretching of the membrane sheathing the closed tube system. These tube networks occasionally exhibit the spontaneous creation of new branches at a junction and also the splitting of a branching junction. A model explains why the branches occur, why they are symmetric around the central stem, and why the initial growth speed is insensitive to the flow rate.

Photochemically Excited, Pulsating Janus Colloidal Motors of Tunable Dynamics

Spontaneous periodicity is widely found in many biological and synthetic systems, and designing colloidal motors that mimic this feature may not only facilitate our understanding of how complexity emerges but also enable applications that benefit from a time-varying activity. However, there is so far no report on a colloidal motor system that shows controllable and spontaneous oscillation in speeds. Inspired by previous studies of oscillating silver microparticles, we report silver-poly(methyl methacrylate) microsphere Janus colloidal motors that moved, interacted with tracers, and exhibited negative gravitaxis all in an oscillatory fashion. Its dynamics, including pulsating speeds and magnitude, as well as whether moving forward in a pulsating or continuous mode, can be systematically modulated by varying chemical concentrations, light intensity, and the way light was applied. A qualitative mechanism is proposed to link the oscillation of Janus colloidal motors to ionic diffusiophoresis, while nonlinearity is suspected to arise from a sequence of autocatalytic decomposition of AgCl and its slow buildup in the presence of H₂O₂ and light. The generation of light-absorbing Ag nanoparticles is suspected to be the key. This study therefore establishes a robust model system of chemically driven, oscillatory colloidal motors with clear directionality, good tunability, and an improved mechanism, with which complex, emergent phenomena can be explored.

Complex oscillation modes in the Belousov-Zhabotinsky reaction by weak diffusive coupling

We study the diffusive coupling of oscillating or excitable Belousov-Zhabotinsky reaction units arranged in a square lattice array and show that for certain sizes of the units and for certain distances between the units, complex oscillation modes of individual spots occur, which manifest themselves in multi-periodic, amplitude-modulated, and multi-mode oscillations. This experimental finding can be reproduced in simulations of the FitzHugh-Nagumo model mimicking the experimental setup, suggesting that it is a generic phenomenon in systems of coupled excitable units such as excitable cell tissues or coupled oscillators such as neurons. Further analysis let us conclude that the complex oscillation modes occur close to the transition from quiescent to coupling-induced oscillations states if this transition is taking place at weak coupling strength.

"Cognitive" modes in small networks of almost identical chemical oscillators with pulsatile inhibitory coupling

The Lavrova-Vanag (LV) model of the periodical Belousov-Zhabotinsky (BZ) reaction has been investigated at pulsed self-perturbations, when a sharp spike of the BZ reaction induces a short inhibitory pulse that perturbs the BZ reaction after some time τ since each spike. The dynamics of this BZ system is strongly dependent on the amplitude C_inh of the perturbing pulses. At C_inh > C_cr, a new pseudo-steady state (SS) emerges far away from the limit cycle of the unperturbed BZ oscillator. The perturbed BZ system spends rather long time in the vicinity of this pseudo-SS, which serves as a trap for phase trajectories. As a result, the dynamics of the BZ system changes qualitatively. We observe new modes with packed spikes separated by either long "silent" dynamics or small-amplitude oscillations around pseudo-SS, depending on C_inh. Networks of two or three LV-BZ oscillators with strong pulsatile coupling and self-inhibition are able to generate so-called "cognitive" modes, which are very sensitive to small changes in C_inh. We demonstrate how the coupling between the BZ oscillators in these networks should be organized to find "cognitive" modes.

Directional coupling in spatially distributed nanoreactors

Silica based hollow nanospheres filled with a reactant solution act as nanoreactors. A close packed ensemble of the nanoshells comprise a porous medium through which a chemical front can propagate. The front velocity decreases as the chemical signal, in the shape of a reaction-diffusion front, is transmitted from one sphere to the other due to the high curvature at the contact points. Experiments reveal that front propagation occurs through the cavity of the nanoshells because surface activity of filled nanoparticles itself cannot support chemical front across the medium.

Chemical front propagates through a closed-packed cluster of nanoreactors made of hollow nanoshells filled with reactant solution.

Interaction between amino-functionalized inorganic nanoshells and acid-autocatalytic reactions

Amino-functionalized inorganic silica nanoshells with a diameter of 511 ± 57 nm are efficiently used as hydrogen ion binders with a base dissociation constant of (1.2 ± 0.1) × 10-4. The hydrogen removal has been shown to produce reaction-diffusion fronts of constant propagation velocity in the autocatalytic chlorite-tetrathionate reaction when it is run in thin planar slices of nanoshell-containing agarose gel to exclude all convection related effects. By controlling the exact amount of amino-functionalized hollow nanospheres in the gel matrix it is possible to finely tune the propagation velocity of the chemical front in the 0.1-10 cm h-1 range. Remarkably, this can be achieved with very low amino-functionalized hollow inorganic nanosphere loadings between 0.1-0.01 (m V-1)%. The front width has also been determined experimentally, which increases by a factor of two with one magnitude decrease in the front velocity.

From dynamic self-assembly to networked chemical systems

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components - on scales from (macro)molecular to macroscopic - can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself - instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities - and, to be sure, new challenges - for DySA research.

Aspects of the Belousov-Zhabotinsky Reaction inside a Self-Oscillating Polymer Brush

We have developed a novel polymer brush surface exhibiting autonomous swelling-deswelling changes driven by the Belousov-Zhabotinsky (BZ) reaction, that is, the self-oscillating polymer brush. In this system, the ruthenium tris(2,2'-bipyridine) [Ru(bpy)₃] catalyst-conjugated polymer chains are densely packed on the solid substrate. It is expected that the BZ reaction in the polymer brush would be influenced by the immobilization effect of the catalyst. To clarify the effect of the immobilization of the catalyst on the self-oscillating polymer brush, the self-oscillating behavior of the polymer brush was investigated by comparing it with that of other self-oscillating polymer materials, the free polymer, and the gel particle under various initial substrate concentrations. The initial substrate dependency of the oscillating period for the polymer brush was found to be different from those for the free polymer and the gel particle. Furthermore, the oscillatory waveform was analyzed on the basis of the Field-Körös-Noyes model. These investigations revealed that the dense immobilization of the self-oscillating polymer on the surface restricted accessibility for the Ru(bpy)₃ moiety. These findings would be helpful in understanding the reaction-diffusion mechanism in the polymer brush, which is a novel reaction medium for the BZ reaction.

Dynamical modes of two almost identical chemical oscillators connected via both pulsatile and diffusive coupling

The dynamics of two almost identical chemical oscillators with mixed diffusive and pulsatile coupling are systematically studied.

Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction

The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10^-21 L) or droplets (V ≈ [10^-8-10^-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10^-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.

Chemical communication and dynamics of droplet emulsions in networks of Belousov-Zhabotinsky micro-oscillators produced by microfluidics

Chemical communication leading to synchronization and collective behaviour of dynamic elements, such as cell colonies, is a widespread phenomenon with biological, physical and chemical importance. Such synchronization between elements proceeds via chemical communication by emmision, interdiffusion and reception of specific messenger molecules. On a lab scale, these phenomena can be modeled by encapsulating an oscillating chemical reaction, which serves as a signal (information) sender/receiver element, inside microcompartments such as droplet emulsions, liposomes and polymersomes. Droplets can thus be regarded as single units, able to generate chemical messengers that diffuse in the environment and hence can interact with other compartments. The Belousov-Zhabotinsky (BZ) reaction is a well-known chemical oscillator largely used as a model for complex nonlinear phenomena, including chemical, physical and biological examples. When the BZ-reaction is encapsulated inside microcompartments, its chemical intermediates can serve as messengers by diffusing among different microcompartments, to trigger specific reactions leading to a collective behavior between the elements. The geometry and constitution of the diffusion pathways play an important role in governing the collective behaviour of the system. In this context, microfluidics is not only a versatile tool for mastering the encapsulation process of the BZ-reaction in monodisperse microcompartments, but also for creating geometries and networks with well defined boundaries. The individual compartments can be engineered with selected properties using different surfactants in the case of simple emulsions, or with specific membrane properties in the case of liposomes. Furthermore, it enables the arrangement of these microcompartments in various geometric configurations, where the diffusive coupling pathways between individual compartments are both spatially and chemically well-defined. In this tutorial paper, we review a number of articles reporting various approaches to generate networks of compartmentalized Belousov-Zhabotinsky (BZ) chemical oscillators using microfluidics. In contrast to biological cellular networks, the dynamical characteristics of the BZ-reaction is well-known and, when confined in microcompartments arranged in different configurations with a pure interdiffusive coupling, these communicative microreactors can serve to mimic various types of bio-physical networks, aiding to comprehend the concept of chemical communication.

Chaotic variations of electrical conductance in powdered Pd correlating with oscillatory sorption of D2

A microcalorimetric method has been combined with a potentiostatic method to measure simultaneously the rate of heat evolution and the electrical current in a powdered sample of palladium during thermokinetic oscillations accompanying the sorption of deuterium in the metal. Deterministic chaos has been confirmed in the temporal variations in current (of ca. 1-4 mA) on the onset of both the sorption and the desorption of deuterium from Pd. It has been found that the first derivative of the current in time, dI/dt, turns out to be correlated precisely with the periodicity of thermokinetic oscillations. The dI/dt curves consist of regularly timed outbursts of aperiodic, high frequency (HF) fluctuations, interlinked by calm periods. The calm periods correlate with the descending slopes of thermokinetic oscillations (i.e., with decrease in the rate of heat evolution) and their lengths depend on the frequency of thermokinetic oscillations. In turn, the outbursts of aperiodic HF fluctuations in the dI/dt derivatives correlate with the ascending slopes of thermokinetic oscillations (i.e., with increasing rate of heat production), but their length is practically constant, irrespective of the thermokinetic frequency. We propose a periodic mechanism of sorption including a collective action of adsorbed deuterium taking place on the Pd surface. The periodicity of this mechanism arises from the temporal separation of its two sub-processes. The sub-process (1) involves only the adsorption of molecular D₂ on the Pd surface and proceeds with little heat evolution until a critical coverage of D₂ is achieved. The sub-process (2) initiates the dissociation of the adsorbed D₂ and the penetration of the dissociated atomic D species into the Pd lattice. It is the more energetic of the two, but it only begins after a threshold coverage of D₂ on the Pd surface has been achieved. We suggest that these sub-processes occurring alternatingly may provide a kernel for the oscillatory behavior observed in Pd/H(D) systems.

The nanotechnology of life-inspired systems

For some decades now, nanotechnology has been touted as the 'next big thing' with potential impact comparable to the steam, electricity or Internet revolutions - but has it lived up to these expectations? While advances in top-down nanolithography, now reaching 10-nm resolution, have resulted in devices that are rapidly approaching mass production, attempts to produce nanoscale devices using bottom-up approaches have met with only limited success. We have been inundated with nanoparticles of almost any shape, material and composition, but their societal impact has been far from revolutionary, with growing concerns over their toxicity. Despite nebulous hopes that making hierarchical nanomaterials will lead to new, emergent properties, no breakthrough applications seem imminent. In this Perspective, we argue that the time is ripe to look beyond individual nano-objects and their static assemblies, and instead focus on systems comprising different types of 'nanoparts' interacting and/or communicating with one another to perform desired functions. Such systems are interesting for a variety of reasons: they can act autonomously without external electrical or optical connections, can be dynamic and reconfigurable, and can act as 'nanomachines' by directing the flow of mass, energy or information . In thinking how this systems nanoscience approach could be implemented to design useful - as opposed to toy-model - nanosystems, our choice of applications and our nanoengineering should be inspired by living matter.

CD-MOF: A Versatile Separation Medium

Porous metal-organic frameworks (MOFs) have been studied in the context of a wide variety of applications, particularly in relation to molecular storage and separation sciences. Recently, we reported a green, renewable framework material composed of γ-cyclodextrin (γ-CD) and alkali metal salts--namely, CD-MOF. This porous material has been shown to facilitate the separation of mixtures of alkylaromatic compounds, including the BTEX mixture (benzene, toluene, ethylbenzene, and the regioisomers of xylene), into their pure components, in both the liquid and gas phases, in an energy-efficient manner which could have implications for the petrochemical industry. Here, we report the ability of CD-MOF to separate a wide variety of mixtures, including ethylbenzene from styrene, haloaromatics, terpinenes, pinenes and other chiral compounds. CD-MOF retains saturated compounds to a greater extent than their unsaturated analogues. Also, the location of a double bond within a molecule influences its retention within the extended framework, as revealed in the case of the structural isomers of pinene and terpinine, where the isomers with exocyclic double bonds are more highly retained than those with endocyclic double bonds. The ability of CD-MOF to separate various mono- and disubstituted haloaromatic compounds appears to be controlled by both the size of the halogen substituents and the strength of the noncovalent bonding interactions between the analyte and the framework, an observation which has been confirmed by molecular simulations. Since CD-MOF is a homochiral framework, it is also able to resolve the enantiomers of chiral analytes, including those of limonene and 1-phenylethanol. These findings could lead to cheaper and easier-to-prepare stationary phases for HPLC separations when compared with other chiral stationary phases, such as CD-bonded silica particles.

Tactic, reactive, and functional droplets outside of equilibrium

Droplets subject to non-equilibrium conditions can exhibit a range of biomimetic and “intelligent” behaviors.

Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay

The dynamics of four almost identical pulse coupled chemical oscillators with time delay are systematically studied.

Extended source model for diffusive coupling

Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.

Spatial and Temporal Control of Information Storage in Cellulose by Chemically Activated Oscillations

Chemical oscillations are exploited to achieve self-expiring graphical information on paper-based supports with precise temporal and spatial control. Writing and self-erasing processes are chemically activated by exciting nonoscillating Belousov-Zhabotinsky (BZ) solutions infiltrated in cellulose paper filters. Exhausted supports can be reactivated many times by adding new BZ medium. Different parameters can be independently controlled to program mono- or multipaced information storage.

Arrays of coupled chemical oscillators

Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning.

Celebrating Soft Matter's 10th Anniversary: Approaches to program the time domain of self-assemblies

Self-regulating reconfigurable soft matter systems are of great interest for creating adaptive and active material properties. Such complex functionalities emerge from non-linear and interactive behavior in space and time as demonstrated by a plethora of dynamic, self-organizing biological structures (e.g., the cytoskeleton). In man-made self-assemblies, patterning of the spatial domain has advanced to creating hierarchical structures via precise molecular programming. However, orchestration of the time domain of self-assemblies is still in its infancy and lacks universal design principles. In this Emerging Area article we outline major strategies for programming the time domain of self-assemblies following the concepts of regulatory reaction networks, energy dissipation and kinetic control. Such concepts operate outside thermodynamic equilibrium and pave the way for temporally patterned, dynamic, and autonomously acting functional materials.

From chemical systems to systems chemistry: Patterns in space and time

We present a brief, idiosyncratic overview of the past quarter century of progress in nonlinear chemical dynamics and discuss what we view as the most exciting recent developments and some challenges and likely areas of progress in the next 25 years.

Chemical gardens without silica: the formation of pure metal hydroxide tubes

Contrary to common belief, hollow precipitation tubes form in the absence of silicate if sodium hydroxide solution is injected into solutions of various metal ions. In many cases, the growth speed has a power law dependence on the flow rate. For vanadyl, we observe damped oscillations in the tube height.

Inhibitory and excitatory pulse coupling of two frequency-different chemical oscillators with time delay

Dynamical regimes of two pulse coupled non-identical Belousov-Zhabotinsky oscillators have been studied experimentally as well as theoretically with the aid of ordinary differential equations and phase response curves both for pure inhibitory and pure excitatory coupling. Time delay τ between a spike in one oscillator and perturbing pulse in the other oscillator plays a significant role for the phase relations of synchronous regimes of the 1:1 and 1:2 resonances. Birhythmicity between anti-phase and in-phase oscillations for inhibitory pulse coupling as well as between 1:2 and 1:1 resonances for excitatory pulse coupling have also been found. Depending on the ratio of native periods of oscillations T2/T1, coupling strength, and time delay τ, such resonances as 1:1 (with different phase locking), 2:3, 1:2, 2:5, 1:3, 1:4, as well as complex oscillations and oscillatory death are observed.

A modular approach to self-oscillating polymer systems driven by the Belousov–Zhabotinsky reaction

This review explores the principle, modular construction, integral control and engineering aspects of self-oscillating polymer systems driven by the Belousov–Zhabotinsky reaction.