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elementary reactions (1,2,3,4,5) reproduces the experiments and is to be selected for this system.

10.5Summary

The main part of section 10.4 is the application of genetic algorithms to chemical kinetics for determination of the reaction mechanism and rate coefficients for a complex reaction network. We chose the minimal bromate system and developed a computer code that includes the genetic algorithm search method to automate the determination of the reaction mechanisms and (thermodynamically consistent) rate coefficients. For optimization we chose comparison with available experiments on chemical oscillations in this system. The first part of the code incorporates element balance conditions for reactions in steady states to determine possible elementary reaction steps. Then the Horiuti theory [36] is used to determine the possible mechanisms compatible with the overall reaction of this system. Next, we use a genetic algorithm to search which ones of these possible mechanisms have oscillatory domains in the region determined by experiments. The GA with the FKN rate coefficients revealed two groups of oscillatory mechanisms: group I consists of reactions (1,2,4,5), (1,2,4,5,6), and (1,2,4,5,7) in the NFT steps, and group II consists of reactions (1,2,3,4,5) and (1,2,3,4,5,6,7). Group I has nine species (no Br2) with four independent species, whereas group II has ten species with five independent species. On the basis of the forms, domains, and periods of the observed oscillations, we find that the four-step (1,2,4,5) mechanism in group I and the five-step (1,2,3,4,5) mechanism in group II are irreducible sets. Therefore, for both group I and II mechanisms, steps 6 and 7 in NFT steps are not essential for the oscillations. Both mechanisms with the FKN rate coefficients, however, fail to fit well the experimental oscillatory domain. Thus, the last part of the GA code was used to determine the range of rate coefficients to fit the experimental results.

With the use of the FKN equilibrium constants, the four-step (1,2,4,5) mechanism exhibits oscillation, but not in the right range. On the other hand, the five-step (1,2,3,4,5) mechanism yields very good agreement with comparable experiments with determination of the range of the five forward rate coefficients. The five steps (1,2,3,4,5) are made up of the four-step mechanism plus step 3, which indicates that step 3 is essential for reproduction of the experimental results.

With the generality of the procedures discussed in this chapter, it seems reasonable to suggest that GA algorithms are useful and promising for the determination of reaction mechanisms and rate coefficients of complex reaction networks.

Acknowledgments Section 10.2 is based on parts of the article “Genetic-algorithm selection of a regulatory structure that directs flux in a simple metabolic model” by Alex Gilman and John Ross [2]. The retained sections of that article have been rearranged and edited with minor changes in wording.

Section 10.3 is based on parts of the article “Advantages of external periodic events to the evolution of biochemical oscillatory reactions” by Masa Tsuchiya and John Ross [11]. The retained sections of that article have been rearranged and edited with some further interpretations and some changes in wording.

Section 10.4 is based on parts of the article “Application of genetic algorithm to chemical kinetics: determination of reaction mechanism and rate coefficients for a complex reaction

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network” by Masa Tsuchiya and John Ross [27]. The retained sections of that article have been rearranged and edited with some further interpretations and changes in wording.

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