Enzyme kinetics. Systematic generation of valid King-Altman patterns

Abstract

One of the most generally applicable algorithms for the derivation of steady-state rate equations for complex enzyme reaction mechanisms is that of King and Altman. Several modifications of this algorithm have been suggested; however, each requires the generation of numerous valid and invalid patterns and the subsequent elimination of those that are invalid. A method is presented, employing topological theory of linear graphs, for the systematic generation of only those patterns which are valid. This method is readily adaptable to use on a digital computer. An independent method for the calculation of the number of valid patterns is also presented. This calculation can be used to substantiate the accuracy of the patterns obtained. This calculation is also adaptable to computerization. Examples are included to demonstrate both the generation of patterns and the calculation of their number for specific enzyme mechanisms.