From the 1920s to the 1950s, there were a number of authors who discussed the concept of rate-limiting steps, also known as master reactions. Several authors have stated that the concept of the rate-limiting step is incorrect. Burton (1936) was one of the first to point out that: "In the steady state of reaction chains, the principle of the master reaction has no application". Hearon (1952) made a more general mathematical analysis and developed strict rules for the prediction of mastery in a linear sequence of enzyme-catalysed reactions. Webb (1963) was highly critical of the concept of the rate-limiting step and of its blind application to solving problems of regulation in metabolism. Waley (1964) made a simple but illuminating analysis of simple linear chains. He showed that provided the intermediate concentrations were low compared to the  values of the enzymes, the following expression was valid:
where  equals the pathway flux, and  and  are functions of the rate constants and intermediate metabolite concentrations. The  terms are proportional to the limiting rate  values of the enzymes. The first point to note from the above equation is that the pathway flux is a function of all the enzymes; there is no need for there to be a rate-limiting step. If, however, all the terms  from  to , are small relative to  then the first enzyme will contribute the most to determining the flux and therefore, could be termed the rate-limiting step.