Methods, based on matrix algebra

Many enzyme reactions have more than one intermediate for which King and Altman (1956) devised a method, based on matrix algebra, by establishing the rate equation of a given enzymic reaction simply by inspecting all complexes and the reactions between them. 

In some doublet reactions the same products may be obtained from the same reactants but in different ways. Such reactions were referred to as olistomeric and the structural conditions of their appearance were determined on the basis of the multiplet theory (348). Thus, theoretically two cases of bond fission can take place in esterification, HO—COR + H—OR and H—OCOR HO—R. The tracer method shows that the first case is realized as a rule. The half-doublet scheme expresses such experiments. The doublet indexes for the reactions in solutions disintegrate into such schemes see Balandin (37). A complete system of doublet reactions for C, H, N, 0, S, and Cl (without their isotopes) has been obtained by the author (345). It is much more detailed than Table VII and amounts to 1500 types. It was obtained by exhaustive variation of atoms and bonds in the index by means of a specially developed method based on matrix algebra and combinatorial analysis. The significance of the obtained classification for organic catalysis is similar to that of the complete system of forms in crystallography, which was derived from the groups of symmetry by Fedorov and covers all possible forms (349). 

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