B

where here A is the activator and B the inhibitor. The k3 A2/B term is again autocat-alytic. Koch and Meinhardt (1994) review the applications of the Gierer-Meinhardt reaction diffusion system to biological pattern formation of complex structures. They give an extensive bibliography of applications of this specific model and its variations.

The real empirical substrate-inhibition system studied experimentally by Thomas (1975) and also described in detail in Chapter 6, Volume I, has

F(A, B) = k1 - k2A - H(A, B), G(A, B) = k3 - k4B - H(A, B), k5 AB (2.5)

Here A and B are respectively the concentrations of the substrate oxygen and the enzyme uricase. The substrate inhibition is evident in the H-term via k8A2. Since the H-terms are negative they contribute to reducing A and B; the rate of reduction is inhibited for large enough A. Reaction diffusion systems based on the Field-Koros-Noyes (FKN) model kinetics (cf. Chapter 8, Volume I) is a particularly important example because of its potential for experimental verification of the theory; references are given at the appropriate places below.

Before commenting on the types of reaction kinetics capable of generating pattern we must nondimensionalise the systems given by (2.2) with reaction kinetics from such as (2.3) to (2.5). By way of example we carry out the details here for (2.2) with F and G given by (2.3) because of its algebraic simplicity and our detailed analysis of it in Chapter 7, Volume I. Introduce L as a typical length scale and set

Was this article helpful?

0 0

Post a comment