Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system

<p>Abstract</p> <p>Background</p> <p>A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.</p> <p>Results</p> <p>Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations.</p> <p>Conclusions</p> <p>This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.</p

From microscopic compartmentalization to hydrodynamic patterns: New pathways for information transport

Can we exploit hydrodynamic instabilities to trigger an efficient, selective and spontaneous flow of encapsulated chemical information? One possible answer to this question is presented in this paper where cross-diffusion, which commonly characterizes compartmentalized dispersed systems, is shown to initiate buoyancy-driven hydrodynamic instabilities. A general theoretical framework allows us to predict and classify cross-diffusion-induced convection in two-layer stratifications under the action of the gravitational field. The related nonlinear dynamics is described by a cross-diffusion-convection (CDC) model where fickian diffusion is coupled to the Stokes equations. We identify two types of hydrodynamic modes (the negative cross-diffusion-driven convection, NCC, and the positive cross-diffusion-driven convection, PCC) corresponding to the sign of the cross-diffusion term dominating the system dynamics. We finally show how AOT water-in-oil reverse microemulsions are an ideal model system to confirm the general theory and to approach experimentally cross-diffusion-induced hydrodynamic scenarios

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 kh and ks 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 kh > ks 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 (Pm) 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

Signal transduction and communication through model membranes in networks of coupled chemical oscillators

In nature, an important example of chemical communication and synchronicity can be found in cell populations where long-range chemical communication takes place over micrometer distance. In vitro laboratory systems can be useful to understand and control such complex biological mechanisms and, in a biomimetic approach, we present in this paper a model based on three basic features, namely (i) the compartmentalization of chemical information (using microfluidics), (ii) a stable emitter of periodic chemical signals inside compartments (Belousov-Zhabotinsky oscillating reaction) and (iii) a suitable spatio-temporal monitoring of the emitted chemical signal. In particular, starting from our recent work on the communication among oscillators via chemical intermediates in networks of lipid-stabilised droplets, we discuss here the role of compartments and of the geometry of the system. We present 3 different experimental configurations, namely liposomes (water-in-water dispersions), double emulsions (water-in-oil-in-water dispersions) and simple emulsions (water-in-oil dispersions) and we show that the global behaviour of networks can be influenced and controlled by several experimental parameters, like the nature of the collecting solvent, the presence of dopants and the network geometry. Numerical models supporting and explaining the experimental findings are also discussed