794 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



enzyme reaction, which in the general case it is not. Taking the usual ex- 

 pression for enzyme rate: 



(S) + K^ 



(15-54) 



it may be seen that when the enzyme is saturated with substrate and v = 

 A-2(E^), the changes in the rate with temperature will provide // values ref- 

 erable to the rate constant A'g for the breakdown of the ES complex into 

 free enzyme and products. However, under most conditions J^,„ is not neg- 

 ligible and it also can change with temperature. Usually K^^^ will increase 

 with a rise in the temperature, whether it is the general Michaelis constant 

 or the true substrate constant, and thus the rate will not increase as rapidly 

 with temperature as would be exi^ected if only A'a were involved. Finally, 

 according to the modern expressions for the rate constant (see Eq. 15-10), 

 a plot of log k\2 against IjT would not be expected to be exactly linear 

 (whereas a plot of log k^lT against l/T would be). Most of the log v — 1/T 

 plots reported in the literature are actually not straight lines if the experi- 

 mental points are examined, although straight lines are frequently used 

 to represent them. 



The meaning of // in terms of the usual thermodynamic quantities for 

 an enzyme reaction may be derived as follows. Taking the logarithm of 

 Eq. 15-54 and then differentiating with respect to the temperature (assum- 

 ing that K,,i = Kg, one obtains: 



1/7 r 1 1 



(15-55) 



(15-56) 



The temperature characteristic, //, thus is equal to the enthalpy of activa- 

 tion plus the small RT correction plus the third term which represents the 

 possible changes in K^ with the temperature. The expression for dln{vlT)ldT 

 would be the same with the omission of the 1/T term and // would be given 

 by Eq. 15-56 without the RT term. 



When multienzyme or cellular systems are considered, it becomes more 

 difficult to understand the meaning of jti and the significance of its changes. 

 It is true that in some cases (for example, an irreversible monolinear chain) 

 the over-all rate is controlled by one step and the // obtained would refer 

 only to that step, but in most instances this is not true. Most log v — IfT 

 plots from living systems are curves but sometimes they are represented by 

 a series of two or more linear segments, the transition points between one 

 slope and the next being called critical temperatures (and by some, uncriti- 



