Judit Horváth

An Experimental Design Method Leading to Chemical Turing Patterns

Adding a Turing Pattern Reaction Two chemical-reaction systems can form sustained stationary patterns (Turing patterns) in solution as the result of the movement of a diffusible species and the formation of negative feedback loops—the chlorite-iodide–malonic acid reaction and the ferrocyanide-iodate-sulfite reaction. Horváth et al. (p. 772) set out to find other examples based on three criteria—that the reaction can develop spatial bistability, that independent control of the negative feedback reaction can be achieved, and the activating and inhibiting processes can be decoupled by slowing down the diffusing species with a complexing agent. The thiourea-iodate-sulfite (TuIS) reaction could be developed into a system that produced different stationary patterns, including stripes and hexagonal arrays of spots. Thus, such Turing pattern–generating reactions are not necessarily uncommon. Three design criteria were used to create sustained stationary patterns in the thiourea-iodate-sulfite reaction system. Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

Oscillatory dynamics induced in a responsive gel by a non-oscillatory chemical reaction: experimental evidence

We provide experimental confirmation of the numerical simulations that predicted spontaneous chemo-mechanical oscillations induced by the size-changes of a pH-responsive hydrogel immersed in the proton-autoactivated bromate-sulphite (BS) reaction. The gel swells and shrinks in a constant and uniform non-equilibrium environment, with no external stimuli. Oscillations result neither from a kinetic feedback in the reaction mechanism nor from long-range activation diffusion instability. The dynamics clearly arises from the feedback that the size responsiveness of the hydrogel exerts on the relative stability of two different pH gradient profiles inside the gel. No oscillations occur without - or with insufficient - size-change of the gel. This is opposed to systems where the mechanical changes are merely slaved to the reaction kinetics. The present progress was obtained by considerably enhancing the swelling-deswelling ratio of the pH-responsive gel by tuning its hydrophobicity. We succeeded in producing more than a dozen of chemomechanical oscillations for over 48 h. We also demonstrate that the system is capable of working under mechanical stress, repeatedly lifting an object weighing 10 times the weight of the swollen gel.

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

Many pattern developments in nature are believed to result from the interplay between self-activated (bio)chemical processes and the diffusive transport of constituents. Though the details are difficult to work out, the relevance of reaction-diffusion processes is widely accepted in many aspects of biological development. Due to their easier manipulation and control, aqueous phase chemical reactions are commonly preferred to probe the patterning capacity of reaction-diffusion processes. Nonetheless, sustained patterns of such a type were observed only in reactions involving oxyhalogen compounds. We report on halogen free solution chemistry systems which lead to stationary or oscillatory spatiotemporal pH patterns. They are based on the acid autocatalytic oxidation of sulfite ions by hydrogen peroxide in combination with two significantly different proton consuming feedback reactions. Besides the chemical novelty, yet experimentally and even theoretically undocumented pattern dynamics are uncovered. This success, based on a well-defined method, further paves the way to the discovery of stationary patterns in delicate biochemical reactions.

Sustained Large-Amplitude Chemomechanical Oscillations Induced by the Landolt Clock Reaction

Synergetic chemomechanical oscillators represent a fundamentally new class of oscillators, where a clock reaction, owning no oscillatory chemical kinetics, generates shrinking-swelling cycles in a chemoresponsive gel under appropriate fixed nonequilibrium boundary conditions. Sufficiently large size-changes are a condition for continually switching between a reacted and an unreacted chemical state in the gel through sufficiently large differences in the diffusion time between the environment and the core of the gel. Two former experimental demonstrations with acid autocatalytic reactions were frustrated either by complex behaviors (chlorite-tetrathionate system) or by side reactions with the gel matrix (bromate-sulfite system). With the Landolt (iodate-sulfite) reaction, regular large-amplitude chemomechanical oscillations can be sustained for more than a week. This enabled a fine study of the temperature and stoichiometry range of operation. I have identified several key steps that are experimentally essential to the systematic design of further synergetic oscillators. The robust realization of this type of self-organization in artificial systems is currently unique.

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.

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 Rabais 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.

Interaction of poly(vinyl alcohol) with the Belousov–Zhabotinsky reaction mixture

The Ce catalyst of the BZ reaction was fixed in a poly(vinyl alcohol–co–vinyl sulfate) copolymer network. The prepared gel system is able to support spatial pattern formation. The preparation of the Ce salt of the copolymer and the gelation procedure are described. Spectrophotometric measurements prove that fixing of Ce in the gel matrix occurs due to a complex formation process. The poly(vinyl alcohol) (PVA) matrix interacts with the oscillating BZ mixture and causes partial inhibition of oscillations in batch BZ solutions and a decrease of wave velocities in thin gel layers. The inhibiting effect of PVA was compared to that of the analogous small molecule secondary alcohol, isopropanol. As a probable reason for the inhibition, two possible side reactions of the PVA with single components of the BZ reaction mixture were examined.

Chemically coded time-programmed self-assembly

Dynamic self-assembly is of great interest in the fields of chemistry, physics and materials science and provides a flexible bottom-up approach to build assemblies at multiscale levels. We propose a method to control the time domain of self-assembling systems in a closed system, from molecular to material level using a driving chemical system: methylene glycol–sulfite pH clock reaction coupled to lactone hydrolysis. The time domain of the transient pH state (alkaline) and the time lag between the initialization of the reaction and the pH change can be efficiently fine-tuned by the initial concentration of the reagents and by the chemical composition of the lactone. The self-assembly of pH-responsive building blocks can be dynamically driven by this kinetic system, in which the time course of the pH change is coded in the system. This approach provides a flexible and autonomous way to control the self-assembly of pH responsive building blocks in closed chemical systems far from their thermodynamic equilibrium.

pH mediated kinetics of assembly and disassembly of molecular and nanoscopic building blocks

Self-assembly occurs when building blocks of the system interact with one another through interactions existing between them. Proper temporal control of these interactions can lead to formation of transient self-assembled states. pH mediated self-assembly is one of the powerful tools to stabilize and destabilize structures consisting of different sized building blocks. Here we investigate the kinetics of pH triggered reversible transformation of two building blocks using a relaxation method, reversible vesicle–micelle transformation of oleic acid molecules and dispersion–aggregation of pH sensitive gold nanoparticles. We found significant differences in the characteristic times (two orders of magnitudes) between the disassembly processes—from an ordered structure to a less ordered structure (in the case of oleic acid molecules) or to single building blocks (in the case of nanoparticles)—and the self-assembly processes (bilayer formation or aggregation of nanoparticles). It can be explained by a sophisticated interplay between repulsive (electrostatic) and attractive (van der Waals) interactions.