Applications of Combinatorics and Graph Theory to the Biological and Social Sciences pp 295-314 | Cite as

# Combinatorial Aspects of Enzyme Kinetics

## Abstract

Two concepts from chemistry, definable in mathematical terms, are the starting point of this paper: A *reaction network* (which is a generalization of a graph) and a *mechanism for a reaction* (which is a generalization of a path from one vertex to another in a graph). Then, as the main result, a statement made in 1964 by P.C. Milner [4] is put into precise terms and proved. To paraphrase Milner’s statement, a mechanism for a reaction r in a given network reduces to the superposition of two or more consistently oriented direct mechanisms for r from the same network, where direct mechanisms are capable of no such reduction. This result is the principal justification of an algorithm, described in this paper, for generating a list of all possible direct mechanisms for a given reaction in a given network. Examples are used to show how these ideas apply to enzyme kinetics studies.

## Keywords

Homology Group Chemical System Reaction Network Elementary Reaction Free Abelian Group## Preview

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