Tamás Bánsági

Tomography of reaction-diffusion microemulsions reveals three-dimensional turing patterns

Tomography reveals three-dimensional Turing patterns created by the Belousov-Zhabotinsky reaction running in a microemulsion. Spatially periodic, temporally stationary patterns that emerge from instability of a homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for morphogenesis in living systems and have attracted increasing attention in biology, chemistry, and physics. Patterns found to date have been confined to one or two spatial dimensions. We used tomography to study the Belousov-Zhabotinsky reaction in a microemulsion in which the polar reactants are confined to aqueous nanodroplets much smaller than the scale of the stationary patterns. We demonstrate the existence of Turing patterns that can exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns.

Bubble‐Templated and Flow‐Controlled Synthesis of Macroscopic Silica Tubes Supporting Zinc Oxide Nanostructures

Reaction–transport coupling can self-organize inorganic structures with complex, hierarchical architectures that in some cases extend beyond the nanometer scale into the macroscopic world. A simple but nonetheless interesting example is the hollow-tube motif which is found in cement, biomineralized shells of algae, ferrotubes, speleotherms and hydrothermal vents. Arguably one of the best laboratory models for the study of tube formation is a class of reactions known as chemical or silica “gardens”. These reactions produce millimeter-scale precipitation tubes that can grow upward at rates of millimeters per second. Recent studies of these hollow structures have demonstrated applications of metallosilica tubes as Brønsted acid catalysts and simple microfluid devices. Herein, we present the synthesis of similar tubes using a flow injection method with gas bubbles as directional guides and templates. The bubbles are pinned to the interfacial reaction zone of the growing tubes. The resulting materials are very straight tubes consisting of silica-supported zinc oxide nanostructures and show interesting luminescence and photocatalytic properties. The prototypical experiment underlying our investigations consists of crystals seeded into aqueous solutions containing anions such as borates, phosphates, carbonates, or silicates; herein we present experiments involving silicates. Furthermore, many different salts can be used as the seed, with the exception of Group 1 elements. Tube morphogenesis starts with the formation of a colloidal and semipermeable membrane around the dissolving seed. Osmotic pressure differences induce a cross-membrane flux of water and subsequently rupture the membrane. From the breach site a buoyant jet of salt solution is ejected which templates the tube-forming co-precipitation of amorphous silica and metal hydroxides (or oxides). Figure 1a shows a precipitation structure formed from a zinc(II) sulfate crystal seeded into 2.5m silicate solution. The tube is reminiscent of an erratic string of beads. Figure 1b shows a micrograph of a similar tube obtained by scanning electron microscopy (SEM). The average diameter of the tube is about 1 mm. Clearly, such irregular and uncontrolled structures have very limited value as hollow support systems and cannot be extended over long distances. Our method overcomes these limitations by replacing the seed particle with a seed solution injected at constant flow rates. Furthermore, we place a buoyant gas bubble into the initial, colloidal

Temporal Control of Gelation and Polymerization Fronts Driven by an Autocatalytic Enzyme Reaction

Abstract Chemical systems that remain kinetically dormant until activated have numerous applications in materials science. Herein we present a method for the control of gelation that exploits an inbuilt switch: the increase in pH after an induction period in the urease‐catalyzed hydrolysis of urea was used to trigger the base‐catalyzed Michael addition of a water‐soluble trithiol to a polyethylene glycol diacrylate. The time to gelation (minutes to hours) was either preset through the initial concentrations or the reaction was initiated locally by a base, thus resulting in polymerization fronts that converted the mixture from a liquid into a gel (ca. 0.1 mm min−1). The rate of hydrolytic degradation of the hydrogel depended on the initial concentrations, thus resulting in a gel lifetime of hours to months. In this way, temporal programming of gelation was possible under mild conditions by using the output of an autocatalytic enzyme reaction to drive both the polymerization and subsequent degradation of a hydrogel.

pH Wave-Front Propagation in the Urea-Urease Reaction

The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ~3) to base (pH ~9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1-1 mm min(-1). The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH.

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs.

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.

Locking of Turing patterns in the chlorine dioxide–iodine–malonic acid reaction with one-dimensional spatial periodic forcing

We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns with spatial periodic forcing. Wavenumber-locked stripe patterns are the typical resonant structures that labyrinthine patterns exhibit in response to one-dimensional forcing by illumination when images of stripes are projected on a working medium. Our experimental results reveal that segmented oblique, hexagonal and rectangular patterns can also be obtained. However, these two-dimensional resonant structures only develop in a relatively narrow range of forcing parameters, where the unforced stripe pattern is in close proximity to the domain of hexagonal patterns. Numerical simulations based on a model that incorporates the forcing by illumination using an additive term reproduce well the experimental observations. These findings confirm that additive one-dimensional forcing can generate a two-dimensional resonant response. However, such a response is considerably less robust than the effect of multiplicative forcing.

Evidence for Burgers' equation describing the untwisting of scroll rings

We study the dynamics of rotating scroll waves in three-dimensional excitable systems. Experiments are carried out with the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction and wave patterns are measured using optical tomography. We create twisted scroll rings for which the rotation phase varies along their circular rotation backbone and measure the untwisting dynamics of the collapsing structures. Experimental data reveal the formation of an asymmetric, plateau-like phase profile with a growing region of leading phase and a shrinking region of lagging phase. The experimental data support a quantitative description in terms of a nonlinear diffusion equation.

Kinetics of the urea–urease clock reaction with urease immobilized in hydrogel beads

Feedback driven by enzyme catalyzed reactions occurs widely in biology and has been well characterized in single celled organisms such as yeast. There are still few examples of robust enzyme oscillators in vitro that might be used to study nonlinear dynamical behavior. One of the simplest is the urea–urease reaction that displays autocatalysis driven by the increase in pH accompanying the production of ammonia. A clock reaction was obtained from low to high pH in batch reactor and bistability and oscillations were reported in a continuous flow rector. However, the oscillations were found to be irreproducible and one contributing factor may be the lack of stability of the enzyme in solution at room temperature. Here, we investigated the effect of immobilizing urease in thiol-poly(ethylene glycol) acrylate (PEGDA) hydrogel beads, prepared using emulsion polymerization, on the urea–urease reaction. The resultant mm-sized beads were found to reproduce the pH clock and, under the conditions employed here, the stability of the enzyme was increased from hours to days.

Engineering Enzyme-Driven Dynamic Behaviour in Lipid Vesicles

The urea–urease system is a pH dependent enzymatic reaction that was proposed as a convenient model to study pH oscillations in vitro; here, in order to determine the best conditions for oscillations, a two-variable model is used in which acid and substrate, urea, are supplied at rates \(k_h\) and \(k_s\) from an external medium to an enzyme-containing compartment. Oscillations were observed between pH 4 and 8. Thus the reaction appears a good candidate for the observation of oscillations in experiments, providing the necessary condition that \(k_h > k_s\) is met. In order to match these conditions, we devised an experimental system where we can ensure the fast transport of acid to the encapsulated urease, compared to that of urea. In particular, by means of the droplet transfer method, we encapsulate the enzyme, together with a suitable pH indicator, in a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) lipid membrane, where differential diffusion of H\(^+\) and urea is ensured by the different permeability (\(P_m\)) of membranes to the two species. Here we present preliminary tests for the stability of the enzymatic reaction in the presence of lipids and also the successful encapsulation of the enzyme into lipid vesicles.

Helical Turing patterns in the Lengyel-Epstein model in thin cylindrical layers

The formation of Turing patterns was investigated in thin cylindrical layers using the Lengyel-Epstein model of the chlorine dioxide-iodine-malonic acid reaction. The influence of the width of the layer W and the diameter D of the inner cylinder on the pattern with intrinsic wavelength l were determined in simulations with initial random noise perturbations to the uniform state for W < l/2 and D ∼ l or lower. We show that the geometric constraints of the reaction domain may result in the formation of helical Turing patterns with parameters that give stripes (b = 0.2) or spots (b = 0.37) in two dimensions. For b = 0.2, the helices were composed of lamellae and defects were likely as the diameter of the cylinder increased. With b = 0.37, the helices consisted of semi-cylinders and the orientation of stripes on the outer surface (and hence winding number) increased with increasing diameter until a new stripe appeared.