Control analysis of single enzyme sequences with abortive complexes and random substrate binding

Single-enzyme reactions involving abortive complexes, and random sequences, respectively, are subjected to control analysis. Explicit analytical expressions are presented which cover these kinetic behaviors. The latter are based (1) on the concept of control coefficients which measure the sensitivity of flux with respect to rate constants, and (2) on the classical steady state rate equations. The methods include both a graph theoretic approach and computer-aided derivation of algebraic expressions. Some conclusions are derived from the analysis of simple models. It is demonstrated (1) that abortive complexes exert no kinetic (as opposed to equilibrium) control over steady state flux; (2) the sum of the paired flux control coefficients for each step in the catalytic cycle, as well as the sum of the flux control coefficients for the unidirectional steps which emanate from each enzyme species, is equal to unity in a random sequence; (3) in the case of a random reaction sequence, the numerator terms of the rate equation exert an effect in the paired flux control coefficients for those steps in the random portion of the reaction sequence.