380 7. INHIBITION IN MULTIENZYME SYSTEMS 



The Concept of the Limiting Rate 



The belief that in any type of sequential reaction there is a step whose 

 rate is slower than that of any other step and hence is limiting the over-all 

 rate has been very common amongst biochemists and biologists for many 

 years. It has been stated in various ways that the over-all kinetics will 

 depend only on those of the limiting step, that effects upon the system will 

 be observed only when the limiting step is altered, that indeed everything 

 from growth rates to temperature coefficients depend predominantly on 

 some limiting step. It is a dangerous concept, unless properly applied, be- 

 cause it is one of the j)rimary means of introducing simplification into a 

 complex system, which, although a laudable goal, is to be deplored if the 

 assumption is incorrect. Warnings have been issued: e.g., .Greenberg (1956) 

 stated "It is apparent ... that in a sequence of enzyme reactions the step 

 with the lowest velocity at saturation with its substrate may not be the 

 limiting reaction in a steady state," and Hinshelwood (1946) emphasized 

 that " The velocity of a series of consecutive reactions is certainly not 

 governed in general by that of the slowest." It is important to understand 

 when this concept is valid and when it is merely an unjustified simpli- 

 fication. 



One of the sources of confusion is the failure to differentiate between the 

 inherent or potential rate of an enzyme and its actual rate under the ex- 

 perimental conditions. If each enzyme of a multienzyme system is isolated 

 and its maximal rate determined, it is not necessary when these en- 

 zymes are operating sequentially that the enzyme with the lowest maximal 

 rate will be limiting, because the concentrations of the initial substrate 

 and the intermediates will determine to a great extent the over-all rate and 

 which enzyme might be considered to be limiting. Thus the first enzyme in 

 a monolinear chain will often be limiting, whatever its potential rate, due 

 to a low concentration of its substrate, and likewise the inability of a par- 

 ticular intermediate to rise sufficiently may impose limitation on an active 

 enzyme. The presence of compartmentalization will thus determine in 

 some cases what step is rate-controlling. 



Another difficulty in thinking about limiting rates has been the lack of 

 a quantitative expression for the degree to which a particular step is con- 

 trolling the formation of the product. The response to enzyme inhibition 

 often depends markedly upon this and thus a simple approach to a quan- 

 titative formulation will be presented. Let us assume that in the monolinear 

 chain, A -^ B -^ C, the concentration of A is such that reaction 1 is pro- 

 ceeding at a rate greater than the maximal rate of reaction 2, Fg. It is 

 evident that E;^ must be inhibited so that t\ falls below Fg before any 

 depression of v^ occurs. The initial yi=Fi(A)/[(A) + ^J and this must be 



