Role of complexing agents in the appearance of Turing patterns

In this paper we study a four-species reaction-diffusion system where Turing patterns are stabilized by the presence of fast reversible reactions between the morphogens and two different mobile complexing agents (CAs) that are not necessarily in excess. We provide a quantitative explanation of how the interaction with the CA changes the size of the Turing space making it possible to observe patterns even in a region where the free diffusion coefficients of the relevant species are equal, as is usually the case in real systems. Our analytical treatment gives a series of mathematical relations that can be helpful for those designing experiments where Turing patterns are expected to appear. We also show how the mobility of CAs affect the characteristic size of the pattern. Finally, we provide an example of biological interest in order to illustrate the main procedures and results.