INTRODUCTION AND THEORETICAL CONSIDERATIONS 447 



strate are usually employed at concentrations sufficiently high that their 

 utilization by the biological system does not appreciably alter their con- 

 centrations during the experimental period. If the total enzyme concen- 

 tration of the biological system does not vaiy during the course of the 

 experiment, the variables of equation 3 and 4 are not a function of time. 

 Even in a system in which cells are multiplying, the mother and daughter 

 cells have similar composition, and the concentrations of their intra- 

 cellular enzymes would not be expected to vary appreciably. Conse- 

 quently, for both static and growing systems, the enzyme concentration 

 in all its various forms can be assumed to be constant during the course 

 of the experiment and not a function of time. 



Varied concentrations of inhibitor and substrate are established at the 

 outset of the experiment in such a manner that one can determine the 

 critical ratio which will reduce the response of the biological system to a 

 denned quantity after the lapse of a constant period of time. The total 

 response of the organism, then, is a function of the rate of the limiting 

 inhibited enzymatic reaction and of time. In order to obtain the defined 

 response after a constant period of time, the rate of the limiting reaction, 

 r, must be reduced to a value which is specific for this particular selected 

 response. The rate of the inhibited reaction is proportional to the con- 

 centration of the enzyme-substrate complex; hence, to achieve the critical 

 rate which will produce the chosen biological response in a specified time, 

 the concentration of the active complex [ES] must be reduced to a specific 

 value, C E s, at the onset of the process. 



For increasing concentrations of substrate and inhibitor, particularly 

 those approaching enzyme saturation, the value of [E] approaches zero 

 and becomes negligible in comparison with [EI]. If the total enzyme 

 concentration, [E t ], is assumed to be constant for the reasons previously 

 indicated, it is apparent from equation 4 that the concentration of the 

 enzyme-inhibitor complex, [EI], must be essentially a constant value, 

 C E i, since [E t ] and [ES] are constant, and [E] can be neglected. 



By substitution of these constant values, C E i and C E s for [EI] and 

 [ES], respectively, in the general equation 3, one obtains an equation 

 for the molar ratio of analogue to metabolite which must be established 

 to produce the necessary inhibition that will result in the defined response 

 of the biological system under the conditions outlined above. This ratio 

 is a constant, K, the inhibition index. 



[7] KiCei T r ^v 



wr^cTs =K (6) 



The assumption that the intracellular concentration of all the forms of 

 a particular enzyme in a biological system does not vary with changes in 

 the substrate and inhibitor concentrations may not always be valid. The 



