Mechanism and Phenomenology of an Oscillating Chemical Reaction

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

ConspectusInspired 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.

Experimental studies of spiral wave teleportation in a light sensitive Belousov-Zhabotinsky system

Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium.

Propagating wave merging in a precipitation reaction

Propagating precipitation waves are a remarkable form of spatiotemporal behavior that arise through the coupling of reaction, diffusion, and precipitation. We study a system with a sodium hydroxide outer electrolyte and an aluminum hydroxide inner electrolyte. In a redissolution Liesegang system, a single propagating precipitation band moves down through the gel, with precipitate formed at the band front and precipitate dissolved at the band back. Complex spatiotemporal waves occur within the propagating precipitation band, including counter-rotating spiral waves, target patterns, and annihilation of waves on collision. We have also carried out experiments in thin slices of gel, which have revealed propagating waves of a diagonal precipitation feature within the primary precipitation band. These waves display a wave merging phenomenon in which two horizontally propagating waves merge into a single wave. Computational modeling permits the development of a detailed understanding of the complex dynamical behavior.

Transient chirality inversion during racemization of a helical cobalt(III) complex

SignificanceWe first observed a transient chirality inversion on a simple unimolecular platform during the racemization of a chiral helical complex [LCo₃A₆]³⁺, i.e., the helicity changed from P-rich (right-handed) to M-rich (left-handed), which then racemized to a P/M equimolar mixture in spite of the absence of a reagent that could induce the M helix. This transient chirality inversion was observed only in the forward reaction, whereas the reverse reaction showed a simple monotonic change with an induction time. Consequently, the M helicity appeared only in the forward reaction. These forward and reverse reactions constitute a hysteretic cycle. Compounds showing such unique time responses would be useful for developing time-programmable switchable materials that can control the physical/chemical properties in a time-dependent manner.

Chirality observed in a driven ruthenium-catalyzed Belousov-Zhabotinsky reaction model

Chirality is commonly associated with the spatial geometry of the atoms composing molecules, the biochemistry of living organisms, and spin properties. In sharp contrast, here we report chirality found in numerically computed stability diagrams of a chemical reaction governed by purely classical (that is, not quantum) equations, namely in a photochemically periodically perturbed ruthenium-catalyzed Belousov-Zhabotinsky reaction model. This novel chirality offers opportunities to explore hitherto unsuspected properties of purely classical chemical oscillators.

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.

Instability of the Homogeneous Distribution of Chemical Waves in the Belousov-Zhabotinsky Reaction

Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov–Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.

Novel modes of synchronization in star networks of coupled chemical oscillators

Photochemically coupled micro-oscillators are studied experimentally and computationally in star networks to investigate the modes and mechanisms of synchronization. The micro-oscillators are catalyst-loaded beads that are placed in catalyst-free Belousov-Zhabotinsky (BZ) solutions. The properties of the photochemical coupling between the oscillators are determined by the composition of the BZ reaction mixtures, and both excitatory coupling and inhibitory coupling are studied. Synchronization of peripheral oscillators coupled through a hub oscillator is exhibited at coupling strengths leading to novel modes of synchronization of the hub with the peripheral oscillators. A theoretical analysis provides insights into the mechanism of the synchronization. The heterogeneous peripheral oscillators have different phase velocities that give rise to a phase divergence; however, the perturbation from the hub acts to realign the phases by delaying the faster oscillators more than the slower oscillators.

Analytical approximations for the speed of pacemaker-generated waves

In oscillatory media, waves can be generated by pacemaker regions which oscillate faster than their surroundings. In many chemical and biological systems, such waves can synchronize the whole medium and as such they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of time-scale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [J. Rombouts and L. Gelens, Phys. Rev. Research 2, 043038 (2020)2643-156410.1103/PhysRevResearch.2.043038].

Quint points lattice in a driven Belousov-Zhabotinsky reaction model

We report the discovery of a regular lattice of exceptional quint points in a periodically driven oscillator, namely, in the frequency-amplitude control parameter space of a photochemically periodically perturbed ruthenium-catalyzed Belousov-Zhabotinsky reaction model. Quint points are singular boundary points where five distinct stable oscillatory phases coalesce. While spikes of the activator show a smooth and continuous variation, the spikes of the inhibitor show an intricate but regular branching into a myriad of stable phases that have fivefold contact points. Such boundary points form a wide parameter lattice as a function of the frequency and amplitude of light absorption. These findings revise current knowledge about the topology of the control parameter space of a celebrated prototypical example of an oscillating chemical reaction.

Video colorimetry of single-chromophore systems based on vector analysis in the 3D color space: Unexpected hysteresis loops in oscillating chemical reactions

Colorimetry, the quantitative determination of color, usually of a digital image, has useful applications in diverse areas of research. Many methods have been proposed for translating the RGB data of an image to obtain concentration information. Among the many methods for RGB analysis, we focus on the vector projection method (VP), which is based on a vector analysis in 3D RGB color space. This method has the major advantages of being conceptually intelligible and generalizable to various systems. For solutions with variable concentrations of one chromophore, we will show that the analysis of the trace in RGB color space allows for a judgment about the reliability of the linear concentration dependence of the chromapostasi parameter. We discuss the theoretical underpinnings of the method in two test cases, a simple dye solution and a titration of an organic acid with phenolphthalein indicator. The VP method was then applied to the Ce-catalyzed Belousov-Zhabotinsky reaction with the expectation that the colorimetry would quantify [Ce⁴⁺] oscillations. Surprisingly, the 3D color space analysis revealed hysteresis loops and the origin and implications of this observation are discussed.

Photochemical motion control of surface active Belousov-Zhabotinsky droplets

Photochemical control of the motion of surface active Belousov-Zhabotinsky (BZ) droplets in an oil-surfactant medium is carried out with illumination intensity gradients. Droplet motion is analyzed under conditions of constant uniform illumination and a constant illumination gradient. Control of droplet motion is developed by testing different illumination gradients. Complex hypotrochoid target trajectories are tracked by BZ droplets illuminated with two-dimensional V-shaped gradients.

Designing multifunctional gels with electrical conductivity, mechanical toughness and self-oscillating performance

Self-oscillating polymer gels driven by the Belousov–Zhabotinsky (BZ) oscillating chemical reaction are a new class of functional gels that have potential applications in autonomously functioning membranes and as artificial muscle actuators.

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.

The Tris(2,2'-Bipyridyl)Ruthenium-Catalysed Belousov–Zhabotinsky Reaction

The Belousov – Zhabotinsky (BZ) reaction is the prototypical oscillating chemical reaction. The tris(2,2'-bipyridine)ruthenium-catalysed BZ reaction (often simply referred to as the ruthenium-catalysed BZ reaction) displays photosensitivity and has been widely exploited for examination of the effects of illumination on nonlinear reaction kinetics. In this review, we investigate the behaviour of the ruthenium-catalysed BZ reaction. The mechanism of the reaction is analysed and we examine how light sensitivity is incorporated into kinetic models of the reaction. The temporal dynamics of the photosensitive reaction is presented and, finally, we discuss the extraordinary wealth of behaviour that has been observed in the spatially-distributed system when perturbed by visible light.

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.

Control of chemical chaos through medium viscosity in a batch ferroin-catalysed Belousov–Zhabotinsky reaction

A macroscopic parameter, such as medium viscosity, can be used to fine tune chemical chaos in a reaction–diffusion–convection system.

Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems

This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.

Desynchronization of stochastically synchronized chemical oscillators

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.

Three-dimensional modeling of propagating precipitation waves

A general three-dimensional model for propagating precipitation waves is presented. Structural features identified in experimental studies of propagating waves in the AlCl3/NaOH and NaAl(OH)4/HCl systems are described by the 3D model. Two forms of precipitate with different physical properties play key mechanistic roles in the wave propagation. Experimentally observed circular and spiral waves are simulated by the 3D model, as well as wave annihilation on the collision of two waves.

Robustness of synthetic circadian clocks to multiple environmental changes

A molecular network that mimics circadian clocks from cyanobacteria is constructed in silico. Simulating its oscillatory behaviour under variable conditions reveals its robustness relative to networks of alternative topologies. The principles for synthetic chemical circadian networks to work properly are consequently highlighted.

Coupled Oscillations and Circadian Rhythms in Molecular Replication Networks

Living organisms often display rhythmic and oscillatory behavior. We investigate here a challenge in contemporary Systems Chemistry, that is, to construct "bottom-up" molecular networks that display such complex behavior. We first describe oscillations during self-replication by applying kinetic parameters relevant to peptide replication in an open environment. Small networks of coupled oscillators are then constructed in silico, producing various functions such as logic gates, integrators, counters, triggers, and detectors. These networks are finally utilized to simulate the connectivity and network topology of the Kai proteins circadian clocks from the S. elongatus cyanobacteria, thus producing rhythms whose constant frequency is independent of the input intake rate and robust toward concentration fluctuations. We suggest that this study helps further reveal the underlying principles of biological clocks and may provide clues into their emergence in early molecular evolution.

Study on identification of rice seeds by chemical oscillation fingerprints

A B–Z oscillation reaction can be maintained for several hours without interference from foreign substances. The oscillation reaction process changed when a sample was added, and a characteristic fingerprint was obtained.

Nonchaos-Mediated Mixed-Mode Oscillations in an Enzyme Reaction System

We report numerical evidence of a new type of wide-ranging organization of mixed-mode oscillations (MMOs) in a model of the peroxidase-oxidase reaction, in the control parameter plane defined by the supply of the reactant NADH and the pH of the medium. In classic MMOs, the intervals of distinct periodic oscillations are always separated from each other by windows of chaos. In contrast, in the new unfolding, such windows of chaos do not exist. Chaos-mediated and nonchaos-mediated MMO phases are separated by a continuous transition boundary in the control parameter plane. In addition, for low pH values, we find an exceptionally wide and intricate mosaic of MMO phases that is described by a detailed phase diagram.

Superdiffusive cusp-like waves in the mercuric iodide precipitate system and their transition to regular reaction bands

We report a two-dimensional (2D) reaction-diffusion system that exhibits a superdiffusive propagating wave with anomalous cusp-like contours. This wave results from a leading precipitation reaction (wavefront) and a trailing redissolution (waveback) between initially separated mercuric chloride and potassium iodide to produce mercuric iodide precipitate (HgI2) in a thin sheet of a solid hydrogel (agar) medium. The propagation dynamics is accompanied by continuous polymorphic transformations between the metastable yellow crystals and the stable red crystals of HgI2. We study the dynamics of wavefront and waveback propagation that reveals interesting anomalous superdiffusive behavior without the influence of external enhancement. We find that a transition from superdiffusive to subdiffusive dynamics occurs as a function of outer iodide concentration. Inner mercuric concentrations lead to the transition from the anomalous cusp-like to cusp-free regular bands. While gel concentration affects the speed of propagation of the wave, it has no effect on its shape or on its superdiffusive dynamics. Microscopically, we show that the macroscopic wave propagation and polymorphic transformations are accompanied by an Ostwald ripening mechanism in which larger red HgI2 crystals are formed at the expense of smaller yellow HgI2 crystals.

Chemical communication between liposomes encapsulating a chemical oscillatory reaction

Electrochemical measurements and numerical simulations are employed to understand the chemical communication between liposomes prepared in microfluidics and encapsulating a chemical oscillator.

Propagating precipitation waves: experiments and modeling

Traveling precipitation waves, including counterrotating spiral waves, are observed in the precipitation reaction of AlCl3 with NaOH [Volford, A.; et al. Langmuir 2007, 23, 961 - 964]. Experimental and computational studies are carried out to characterize the wave behavior in cross-section configurations. A modified sol-coagulation model is developed that is based on models of Liesegang band and redissolution systems. The dynamics of the propagating waves is characterized in terms of growth and redissolution of a precipitation feature that travels through a migrating band of colloidal precipitate.

Modulation of the shape and speed of a chemical wave in an unstirred Belousov-Zhabotinsky reaction by a rotating magnet

The objective of this study was to observe whether a rotating magnetic field (RMF) could change the anomalous chemical wave propagation induced by a moderate-intensity gradient static magnetic field (SMF) in an unstirred Belousov-Zhabotinsky (BZ) reaction. The application of the SMF (maximum magnetic flux density = 0.22 T, maximum magnetic flux density gradient = 25.5 T/m, and peak magnetic force product (flux density × gradient) = 4 T(2) /m) accelerated the propagation velocity in a two-dimensional pattern. Characteristic anomalous patterns of the wavefront shape were generated and the patterns were dependent on the SMF distribution. The deformation and increase in the propagation velocity were diminished by the application of an RMF at a rotation rate of 1 rpm for a few minutes. Numerical simulation by means of the time-averaged value of the magnetic flux density gradient or the MF gradient force over one rotation partially supported the experimental observations. These considerations suggest that RMF exposure modulates the chemical wave propagation and that the degree of modulation could be, at least in part, dependent on the time-averaged MF distribution over one rotation. Bioelectromagnetics 34:220-230, 2013. © 2012 Wiley Periodicals, Inc.

Permanganate oxidation of α-amino acids: kinetic correlations for the nonautocatalytic and autocatalytic reaction pathways

The reactions of permanganate ion with seven α-amino acids in aqueous KH(2)PO(4)/K(2)HPO(4) buffers have been followed spectrophotometrically at two different wavelengths: 526 nm (decay of MnO(4)(-)) and 418 nm (formation of colloidal MnO(2)). All of the reactions studied were autocatalyzed by colloidal MnO(2), with the contribution of the autocatalytic reaction pathway decreasing in the order glycine > l-threonine > l-alanine > l-glutamic acid > l-leucine > l-isoleucine > l-valine. The rate constants corresponding to the nonautocatalytic and autocatalytic pathways were obtained by means of either a differential rate law or an integrated one, the latter requiring the use of an iterative method for its implementation. The activation parameters for the two pathways were determined and analyzed to obtain statistically significant correlations for the series of reactions studied. The activation enthalpy of the nonautocatalytic pathway showed a strong, positive dependence on the standard Gibbs energy for the dissociation of the protonated amino group of the α-amino acid. Linear enthalpy-entropy correlations were found for both pathways, leading to isokinetic temperatures of 370 ± 21 K (nonautocatalytic) and 364 ± 28 K (autocatalytic). Mechanisms in agreement with the experimental data are proposed for the two reaction pathways.