Sustained self-organizing pH patterns in hydrogen peroxide driven aqueous redox systems

Recent advances in the temporal and spatiotemporal dynamics induced by bromate–sulfite-based pH-oscillators

The bromate–sulfite reaction-based pH-oscillators represent one of the most useful subgroup among the chemical oscillators. They provide strong H+-pulses which can generate temporal oscillations in other systems coupled to them and they show wide variety of spatiotemporal dynamics when they are carried out in different gel reactors. Some examples are discussed. When pH-dependent chemical and physical processes are linked to a bromate–sulfite-based oscillator, rhythmic changes can appear in the concentration of some cations and anions, in the distribution of the species in a pH-sensitive stepwise complex formation, in the oxidation number of the central cation in a chelate complex, in the volume or the desorption-adsorption ability of a piece of gel. These reactions are quite suitable for generating spatiotemporal patterns in open reactors. Many reaction–diffusion phenomena, moving and stationary patterns, have been recently observed experimentally using different reactor configurations, which allow exploring the effect of different initial and boundary conditions. Here, we summarize the most relevant aspects of these experimental and numerical studies on bromate–sulfite reaction-based reaction–diffusion systems.

Insights from chemical systems into Turing-type morphogenesis

In 1952, Alan Turing proposed a theory showing how morphogenesis could occur from a simple two morphogen reaction-diffusion system [Turing, A. M. (1952) Phil. Trans. R. Soc. Lond. A 237, 37-72. (doi:10.1098/rstb.1952.0012)]. While the model is simple, it has found diverse applications in fields such as biology, ecology, behavioural science, mathematics and chemistry. Chemistry in particular has made significant contributions to the study of Turing-type morphogenesis, providing multiple reproducible experimental methods to both predict and study new behaviours and dynamics generated in reaction-diffusion systems. In this review, we highlight the historical role chemistry has played in the study of the Turing mechanism, summarize the numerous insights chemical systems have yielded into both the dynamics and the morphological behaviour of Turing patterns, and suggest future directions for chemical studies into Turing-type morphogenesis. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Development of a Flow-free Gradient Generator Using a Self-Adhesive Thiol-acrylate Microfluidic Resin/Hydrogel (TAMR/H) Hybrid System

Microfluidic gradient generators have been used to study cellular migration, growth, and drug response in numerous biological systems. One type of device combines a hydrogel and polydimethylsiloxane (PDMS) to generate "flow-free" gradients; however, their requirements for either negative flow or external clamps to maintain fluid-tight seals between the two layers have restricted their utility among broader applications. In this work, a two-layer, flow-free microfluidic gradient generator was developed using thiol-ene chemistry. Both rigid thiol-acrylate microfluidic resin (TAMR) and diffusive thiol-acrylate hydrogel (H) layers were synthesized from commercially available monomers at room temperature and pressure using a base-catalyzed Michael addition. The device consisted of three parallel microfluidic channels negatively imprinted in TAMR layered on top of the thiol-acrylate hydrogel to facilitate orthogonal diffusion of chemicals to the direction of flow. Upon contact, these two layers formed fluid-tight channels without any external pressure due to a strong adhesive interaction between the two layers. The diffusion of molecules through the TAMR/H system was confirmed both experimentally (using fluorescent microscopy) and computationally (using COMSOL). The performance of the TAMR/H system was compared to a conventional PDMS/agarose device with a similar geometry by studying the chemorepulsive response of a motile strain of GFP-expressing Escherichia coli. Population-based analysis confirmed a similar migratory response of both wild-type and mutant E. coli in both of the microfluidic devices. This confirmed that the TAMR/H hybrid system is a viable alternative to traditional PDMS-based microfluidic gradient generators and can be used for several different applications.

Designing Stationary Reaction-Diffusion Patterns in pH Self-Activated Systems

Since Alan Turing's 1952 pioneering work, reaction-diffusion (RD) processes are regarded as prototype mechanisms for pattern formation in living systems. Though suspected in many aspects of morphogenetic development, pure RD patterns have not yet been demonstrated in living organisms. The first observations of an autonomous development of stationary chemical patterns were made in the early 1990s. In this Account, we discuss the recent developments for producing stationary pH RD patterns in open spatial reactors. The theoretical analysis of the early experiments anticipated the possibility of finding Turing patterns in a wide range of oscillatory reactions if one could control the kinetic and diffusional rate of some key species. However, no experimentally effective method to produce stationary Turing patterns was attained before 2009, and the number of systems stagnated at two until then. The two precursor reaction systems benefited from unplanned favorable chemical properties of the RD media. Theoretical studies point out that appropriate diffusion rate differences are necessary to produce stationary patterns since a competition between an effective short distance self-activation and a long distance inhibitory process is required. This differential diffusion would naturally lead to differential exchange rates between the RD system and its feed environment, an aspect somewhat overlooked in theoretical and in primal experimental approaches. Our pattern design method takes this aspect into account. A slower diffusion of a self-activated species (here, protons), produced in the RD part of the spatial reactor, generates the accumulation of this species compared to the other species. This accumulation has to be at least partly compensated by an independent scavenging reaction. The above requirement naturally brought us to focus on two-substrate pH oscillatory reactions. Stationary RD patterns are now well documented in six pH driven reaction systems. Furthermore, the coupling with a pH dependent metal ion complexing agent led to stationary patterns in calcium ion concentration. Our effective semiempirical design method does not require a detailed knowledge of the reaction kinetics; thus it is applicable to a broad spectrum of reactions and even to synthetic biological systems. It is based on simple dynamic arguments and on general topological characteristics of a nonequilibrium phase diagram. We first illustrate our method with numerical simulations, based on a realistic but idealized general model of the two-substrate pH-oscillator reaction family, and provide a refined view of the topology of the resulting phase diagrams. Then, we exemplify its effectiveness by observations made in distinct pH self-activated systems. Analogies and differences between experiments and the model calculations are pointed out. Besides standard hexagonal arrays of spots and parallel stripes, hitherto undocumented dynamic phenomena, such as randomly blinking areas and complex dynamic and stationary filamentous structures, were observed. The main challenge, to find low-mobility complexing agents that would selectively and reversibly bind a species controlling the self-activatory kinetic path of the reaction, was readily overcome in multiple ways by anions of weak acids: not only by polymeric substances but in some cases by a pH color indicator or even smaller molecules, depending on their proton binding affinity.

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.

Design of localized spatiotemporal pH patterns by means of antagonistic chemical gradients

Spatially localized moving and stationary pH patterns are generated in two-side-fed reaction-diffusion systems. The patterns are sandwiched between two quiescent zones and positioned by the antagonistic gradients of the reactants of the self-activatory process. Spatial bistability, spatiotemporal oscillations, and formation of stationary Turing patterns have been predicted by numerical simulations and observed in experiments performed by using different hydrogen ion autocatalytic chemical systems. The formation of stationary patterns due to long-range inhibition is promoted by a large molecular weight hydrogen ion binding polymer.

Spatially localized moving and stationary pH patterns are generated in two-side-fed reaction-diffusion systems.

Determination of the diffusion coefficient of hydrogen ion in hydrogels

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H⁺-autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.

Kinetic and Diffusion-Driven Instabilities in the Bromate-Sulfite-Ferrocyanide System

The spatiotemporal dynamics of the bromate-sulfite-ferrocyanide (BSF) reaction-diffusion system in a open one-side-fed reactor (OSFR) is investigated by numerical simulations. The results of the simulations are compared with experiments performed in an annular shape OSFR. Both kinetic and diffusion-driven instabilities are identified in the model. There are two hydrogen ion consuming pathways in the mechanism: the partial oxidation of sulfite to dithionate and the oxidation of ferrocyanide by bromate ions. Their dynamical effects are similar, as they support the same negative feedback loop via sulfite ion. However, the time scale of the oxidation of ferrocyanide by bromate ions can be conveniently controlled by the input feed concentrations, thus it provides a more flexible way to find spatiotemporal oscillations. Long-range activation due to the relative fast diffusion of hydrogen ions compared to the other reactants can also result in oscillations in this mechanism. We show that the spatial extent of the reaction-diffusion medium along the direction of the diffusive feed (the thickness) acts as a general control parameter of the dynamics. Oscillations, either originated in kinetic or in diffusive instabilities, can only develop in a narrow range of the thickness. This property explains the experimentally often observed spatial localization of the oscillations. A reciprocal relationship is found between two main control parameters of the dynamics, which are the thickness and the hydrogen ion input feed concentration.

The Formation and Spatiotemporal Progress of the pH Wave Induced by the Temperature Gradient in the Thin-Layer H2O2-Na2S2O3-H2SO4-CuSO4 Dynamical System

The H2O2-S2O3(2-)-H(+)-Cu(2+) dynamical system exhibits sustained oscillations under flow conditions but reveals only a single initial peak of the indicator electrode potential and pH variation under batch isothermal conditions. Thus, in the latter case, there is no possibility of the coupling of the oscillations and diffusion which could lead to formation of sustained spatiotemporal patterns in this process. However, in the inhomogeneous temperature field, due to dependence of the local reaction kinetics on temperature, spatial inhomogeneities of pH distribution can develop which, in the presence of an appropriate indicator, thymol blue, manifest themselves as the color front traveling along the quasi-one-dimensional reactor. In this work, we describe the experimental conditions under which the above-mentioned phenomena can be observed and present their numerical model based on thermokinetic coupling and spatial coordinate introduced to earlier isothermal homogeneous kinetic mechanism.

Pattern Formation in the Bromate-Sulfite-Ferrocyanide Reaction

Mixed Landolt-type pH oscillators are versatile systems that allow the experimental study of a wide range of nonlinear phenomena including multistability, oscillations, and spatiotemporal patterns. We report on the dynamics of the bromate-sulfite-ferrocyanide reaction operated in a open one-side-fed reactor, where spatial bistability, spatiotemporal oscillations, front and Turing-type patterns have been observed. The role of different experimental parameters, like the input flow concentrations of the hydrogen and the ferrocyanide ions, the temperature and the thickness of the gel medium (which affects the rate of the diffusive feed) have been investigated. We point out that all these parameters can be efficiently used to control the spatiotemporal dynamics. We show that the increase of ionic strength stabilizes the uniform states at the expense of the patterned one. Some general aspects of the spatiotemporal dynamics of mixed Landolt type systems, which are based on the oxidation of sulfite ions by strong oxidants, are emphasized.

Contribution to an effective design method for stationary reaction-diffusion patterns

The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.

Spatiotemporal behavior induced by differential diffusion in Landolt systems

The spatiotemporal dynamics of Landolt type reactions, for instance reactions between sulfite ions and strong oxidants, performed in a medium fed by the diffusion from a boundary is investigated numerically by using a simple general reaction scheme. In these conditions, the model can generate various spatiotemporal phenomena, e.g., spatial bistability, simple and complex oscillations, birhythmicity, and chaos, even though in a spatially homogeneous open reactor only steady-state bistability can develop. The model consists of two reactions, a protonation equilibrium of the reductant and an oxidation step that is autoactivated by hydrogen ions. The rich dynamics is the result of two factors: (i) long-range activation, through the rapidly diffusing hydrogen ions, (ii) the presence of two parallel autocatalytic pathways. Long range activation provides the necessary negative feedback, whereas the dual nature of the autocatalysis leads to the appearance of two different oscillatory modes. The presence of a second-order term in the rate law of the autocatalytic reaction is linked to a large amplitude oscillations that affect the system as a whole, whereas the third-order one gives rise to localized front oscillations. The complex phenomena, like mixed mode and chaotic oscillations are observed at the meeting of these different oscillatory modes.

Generation of spatiotemporal calcium patterns by coupling a pH-oscillator to a complexation equilibrium

Sustained spatiotemporal pH and calcium patterns are produced in a non-equilibrium inorganic reaction-diffusion system by coupling two modules, the bromate-sulfite-ferrocyanide pH-oscillator and the pH-sensitive complexation of Ca(2+) by ethylenediaminetetraacetate. The development of chemical waves is mainly determined by the oscillatory module, however, the formation of the localised stationary patterns results in the synergistic interaction between the modules.

Thermokinetic origin of luminescent traveling fronts in the H2O2-NaOH-SCN(-)-Cu2+ homogeneous oscillator: experiments and model

According to our original discovery, the oscillatory course of the Cu(2+)-catalyzed oxidation of thiocyanate ions with hydrogen peroxide, in nonstirred medium and upon the addition of luminol as an indicator, can be a source of a novel type of dissipative patterns--luminescent traveling waves. The formation of these fronts, contrary to the patterns associated with the Belousov-Zhabotinsky reaction, cannot be explained in terms of coupled homogeneous kinetics and diffusion, and under isothermal conditions. Both experimental studies and numerical simulations of the kinetic mechanism suggest that the spatial progress of these waves requires mainly the temperature gradient in the solution, which affects the local chemical reaction rate (and thus the oscillation period), with practically negligible contribution from diffusion of reagents. As a consequence of this thermokinetic coupling, the observed traveling patterns are thus essentially the phase (or kinematic) waves, formed due to the spatial phase shift of the oscillations caused by differences in chemical reaction rates. The temperature gradient, caused by the significant heat effect of exothermic oxidation of thiocyanate by hydrogen peroxide, can emerge spontaneously as a local fluctuation or can be forced externally, if the control of progress of the luminescent waves is to be achieved.

Chemical morphogenesis: recent experimental advances in reaction-diffusion system design and control

In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.