Turing Patterns and Waves in Closed Two-Layer Gel Reactors.

Reaction-diffusion waves and stationary Turing patterns are observed in closed two-layer gel reactors, where the two compartments are initially filled with complementary sets of reactants of the chlorine dioxide-iodine-malonic acid-poly(vinyl alcohol) reaction. The asymmetrical loading generates concentration gradients and the patterns form at the interface between the two parts. These easy-to-perform experiments allow us to study a wide range of dynamical phenomena without requiring a specific reactor design or the use of sophisticated equipment.

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.

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.

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.

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.

Multiple types of spatio-temporal oscillations induced by differential diffusion in the Landolt reaction.

The acid autoactivated iodate-sulfite redox reaction (Landolt reaction) exhibits bistability but no oscillatory dynamics when operated in a continuous stirred tank reactor (CSTR). However, it has been previously found experimentally that this reaction can exhibit both spatial bistability and oscillations when carried out in a one side diffusely fed spatial reactor. The precise origin of the oscillatory instability remained mainly elusive.

An experimental design method leading to chemical Turing patterns.

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.

Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation.

We revisit the conditions for the development of reaction-diffusion patterns in the ferrocyanide-iodate-sulfite bistable and oscillatory reaction. This hydrogen ion autoactivated reaction is the only example known to produce sustained stationary lamellar patterns and a wealth of other spatio-temporal phenomena including self-replication and localized oscillatory domain of spots, due to repulsive front interactions and to a parity-breaking front bifurcation (nonequilibrium Ising-Bloch bifurcation). We show experimentally that the space scale separation necessary for the observation of stationary patterns is mediated by the presence of low mobility weak acid functional groups.

Patterns of the ferrocyanide-iodate-sulfite reaction revisited: the role of immobilized carboxylic functions.

We experimentally demonstrate that the standing lamella reaction-diffusion patterns initially observed 17 years ago in a gel-filled open spatial reactor operated with the ferrocyanide-iodate-sulfite bistable reaction requires an upper critical concentration of low-mobility species with weak acid functional groups, a parameter that was overlooked at the time and had made observations difficult to reproduce. The present approach enables the control of the space scale separation between activatory and inhibitory processes. It makes the wealth of exotic pattern dynamics observed earlier easier to reproduce and understand.

Sustained spatiotemporal patterns in the bromate-sulfite reaction.

The acid autoactivated bromate-sulfite reaction exhibits spatial bistability, travelling acid-base fronts, and spatiotemporal oscillations when operated in an unstirred one-side-fed spatial reactor. We show that a skeleton kinetic model, recently proposed by Szántó and Rábai, in which we take into account the charge and the actual diffusivity of solvated ions, provides theoretical results in good agreement with experimental observations. The differences with previous observations made with the homologous iodate-sulfite reaction are discussed.

Spatiotemporal dynamics of the Landolt reaction in an open spatial reactor with conical geometry.

In a previous study, the iodate-sulfite proton autoactivated reaction (Landolt reaction) was shown to exhibit spatial bistability and spatiotemporal oscillations when operated in an open spatial reactor with fixed "thickness", i.e., feed boundary to core distance.

Wave patterns driven by chemomechanical instabilities in responsive gels.

The first experimental evidence of a chemomechanical mechanism leading to morphogenetic instabilities is demonstrated experimentally. The system consists of a pH-responsive gel that swells at high pH and shrinks at low pH, and a bistable reaction system exhibiting an acid steady state (pH approximately 2) and an alkaline steady state (pH approximately 10). Within the gel, the steady state selection depends on the gel size.

Turing patterns, spatial bistability, and front interactions in the [ClO2, I2, I-, CH2(COOH)2] reaction.

Recent experiments by Szalai and De Kepper performed in open spatial reactors have shown that the rich variety of dynamic properties of the chlorine dioxide-iodide-chlorite-iodine-malonic acid family of reactions is far from being exhausted: stable inhomogeneous patterns due to front interactions and transient labyrinthine structures are now added to the spatial bistability and Turing patterns as possible spatial behavior. The two latter phenomena, already observed in the chlorine dioxide-iodide (CDI) and the chlorine dioxide-iodide-malonic acid (CDIMA) reactions, respectively, were kept as limiting cases in the new setup. In this paper, we numerically analyze an extension of the most detailed available model of the CDI system (Lengyel et al.

Glycolytic oscillations and waves in an open spatial reactor: Impact of feedback regulation of phosphofructokinase.

An open spatial reactor has been designed for the investigation of spatio-temporal dynamics of glycolysis. The reactor consists of a diffusive layer made of gel-fixed yeast extract which is in contact with a continuously stirred reservoir to supply this layer with substrates. The coupling between reaction and diffusion in the gel layer enables the formation of spatio-temporal patterns.