Pattern formation mechanisms in reaction-diffusion systems

Abstract

In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

“…As insightfully expressed in [68], the advantage of chemical systems over biological ones is that one can perform experiments under controllable conditions and manipulate the relevant parameters in order to generate patterns. Chemical systems can hence offer rigorous experimental validation of the theoretical predictions and can thereby probe fundamental issues about pattern formation.…”

Interaction between the Belousov-Zhabotinsky reaction and lipid membranes: a kinetic investigation

“…One of the processes responsible for the ferriin consumption is its reaction with the bromomalonic acid during the reaction [11,13] 2Fe(phen) 3 3+ + 2BrMA → fBr -+ 2Fe(phen) 3 2+ + other products (2) According to Edelson [14], reaction (2) is the most important step in determining the length of <T>. In fact, in Figure 4 we see that, if we split <T> in <T autocat > and <T inhibit >, the contribution of the latter to the total length of <T> is predominant.…”

“…It represents the catalytic oxidation of an organic substrate with active methylenic hydrogens, generally malonic acid CH 2 (COOH) 2 ,(MA), by bromate ions in a strongly acidic aqueous solution. The general stoichiometry has the form: 2BrO 3 -+ 3MA + 2H + → 2BrMA + 4H 2 O + 3CO 2 (1) where BrMA is bromomalonic acid (BrCH(COOH) 2 ). The most used catalysts are metal redox couples, such as Ce(IV)/Ce(III) or ferriin/ferroin (Fe(phen) 3 3+ /Fe(phen) 3 2+ ).…”

Calcifying tissue regeneration via biomimetic materials chemistry

“…Yeast cells have been complexed with clay nanotubes to form a stable living hybrid [76]. There have been other interesting developments such as construction of calcite nanocrystals into one type of coccolithophore microstructure (figure 6a, creation of semi-autonomous artificial cells-that could be adapted to biomineralization roles-and use of reaction-diffusion organizing media composed of stacked chemical gradients [8,79]). Some chemists are creating synthetic cells although not as yet specially programmed for biomineralization functions [80,81].…”

“…water-in-oil and oil-in-water mixtures) [5], Langmuir monolayers [6], organic frameworks (reused or those generated from bacteria, e.g. [7]) and reaction-diffusion effects [8] to create patterned materials and structures.…”