ABSTRACT: In a single-substrate-single-product enzyme reaction, "counter transport', which indicates that the ratio of the forward to the reverse fluxes is less than that expected from the Independence Relationship, is regarded as strong evidence for the free enzyme existing in two states, one of which combines with the substrate and the other with the product, with a slow isomerization between the two conditions. To account for positive and negative co-operativity, found with some enzymes, additional induced-fit reactions bypassing at least part of the isomerization have been proposed. The effects of such additional steps have been examined, using two models: in one, (a), the enzyme passes through an intermediate state during its isomerization, and both substrate and product may react with this state to give rise to the binary complexes; in the other, (b), the substrate may react with the enzyme as soon as the product is released and similarly with the reverse reaction, the isomerization thereby being bypassed completely. In the presence of such additional steps, the following can be concluded. (i) The data should be analysed in terms of the flux ratios, rather than observation of the amount of countertransport. (ii) The additional bypassing steps markedly change the pattern of dependence of the flux ratio on substrate and product concentrations. At high substrate and product concentrations, the ratio remains very dependent on how far the reaction is from equilibrium, and the kinetics are asymmetric. (iii) The mechanism causing the flux ratio to be less than that given by the Independence Relationship differs from that previously described, in that, at least in part, it arises from a 1:1 exchange between substrate and product. (iv) Despite this novel mechanism, there must be two states of the enzyme, combining respectively with substrate and product, and these must not be in rapid exchange. Thus countertransport remains very strong evidence for the existence of two such states. It is no longer a requirement that the enzyme states should be linked by an isomerization step. (v) Under no conditions can the flux ratio exceed that given by the Independence Relationship. (vi) Under unusual conditions the isomerization of the enzyme in model (b) may be undetectable by steady-state kinetics. (vii) Measurements of the coefficients in the flux ratio equations enable limits to be set to certain ratios of the rate constants. In addition to these conclusions, methods are described for (viii) analysing flux ratio data for the presence of induced fit steps and (ix) determining flux ratios from induced transport curves. The derivation of steady state-velocity equations show that: (x) both models may give rise to positive and negative 'co-operativity' and sigmoid substrate-velocity curves, but that, under conditions giving rise to sigmoid curves, the deviation of the flux ratio from that required by the Independence Relationship may be difficult to demonstrate because of the asymmetry of the system. Under all conditions the fluxes at equilibrium should obey hyperbolic kinetics.
