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. In this Account, we discuss the recent developments for producing stationary pH RD patterns in open spatial reactors. The theoretical analysis of the early experiments anticipated the possibility of finding Turing patterns in a wide range of oscillatory reactions if one could control the kinetic and diffusional rate of some key species. However, no experimentally effective method to produce stationary Turing patterns was attained before 2009, and the number of systems stagnated at two until then. The two precursor reaction systems benefited from unplanned favorable chemical properties of the RD media. Theoretical studies point out that appropriate diffusion rate differences are necessary to produce stationary patterns since a competition between an effective short distance self-activation and a long distance inhibitory process is required. This differential diffusion would naturally lead to differential exchange rates between the RD system and its feed environment, an aspect somewhat overlooked in theoretical and in primal experimental approaches. Our pattern design method takes this aspect into account. A slower diffusion of a self-activated species (here, protons), produced in the RD part of the spatial reactor, generates the accumulation of this species compared to the other species. This accumulation has to be at least partly compensated by an independent scavenging reaction. The above requirement naturally brought us to focus on two-substrate pH oscillatory reactions. Stationary RD patterns are now well documented in six pH driven reaction systems. Furthermore, the coupling with a pH dependent metal ion complexing agent led to stationary patterns in calcium ion concentration. Our effective semiempirical design method does not require a detailed knowledge of the reaction kinetics; thus it is applicable to a broad spectrum of reactions and even to synthetic biological systems. It is based on simple dynamic arguments and on general topological characteristics of a nonequilibrium phase diagram. We first illustrate our method with numerical simulations, based on a realistic but idealized general model of the two-substrate pH-oscillator reaction family, and provide a refined view of the topology of the resulting phase diagrams. Then, we exemplify its effectiveness by observations made in distinct pH self-activated systems. Analogies and differences between experiments and the model calculations are pointed out. Besides standard hexagonal arrays of spots and parallel stripes, hitherto undocumented dynamic phenomena, such as randomly blinking areas and complex dynamic and stationary filamentous structures, were observed. The main challenge, to find low-mobility complexing agents that would selectively and reversibly bind a species controlling the self-activatory kinetic path of the reaction, was readily overcome in multiple ways by anions of weak acids: not only by polymeric substances but in some cases by a pH color indicator or even smaller molecules, depending on their proton binding affinity.