EFFECTS OF TEMPERATURE: ENZYMES 



761 



When K is very high and the enzyme essentially exists completely in the 

 active form, this reduces to the usual Michaelis-Menten rate expression. 

 The effect of temijerature on the rate will now depend on the variation of 

 K with the temperature. It is generally assumed that inactivation of the 

 enzyme increases with temperature and thus K becomes smaller as the 

 temperature is raised, the term in brackets increasing and the rate de- 

 creasing. Equation 15-17 can be used to explain the phenomenon of max- 

 ima in the rate-temperature curves (see following section). 



The inhibitor may combine only with E^^, or only with E^, (competitive or 

 noncompetitive), or with both E^ and E^ (competitive or noncompetitive). 



Case I: inhibitor combines only with E^ 



A'/ A' 



Erfl :;± Ed ;;z± Eq 



E„S 



Ea+P 



(15-18) 



In all cases K/ will indicate the dissociation constant of the complex with 

 inactive enzyme and K, the dissociation constant of the complex with active 

 enzyme. The conservation equation is now (E,) = (E„) — (E^) -\- (E^S) + 

 (E(^I). The rate is given by: 



VJS) 



(S) + K, 



1 



(I) 



KK, 



and the inhibition by 



(15-19) 



(15-20) 



It may be noted that when the enzyme is all in the active form and K = oo, 

 the rate will be that of the system in the absence of the inhibitor and the 

 inhibition will be zero, since there will be no E^^ with which the inhibitor 

 can combine. When the enzyme is mainly in the inactive form, the rate will 

 be low and the inhibition will approach noncompetitive kinetics. However, 

 in the intermediary range the inhibition will depend on the substrate con- 

 centration much as in competitive inhibition. It is difl&cult to distinguish 

 between this situation and true competitive inhibition. Plots of l/Wj against 

 1/(S) give straight lines with slopes of 



K. 



Vr 



1 + 



1 



+ 



(I) 



KK/ 



whose intercepts on the 1/^', axis will not vary with the inhibitor concen- 

 tration. A plot of (I)(l — i)li against (S) will likewise give a straight line 

 indistinguishable from true competitive inhibition, but the slope will now 

 be KK/IKg instead of K,' jK^ and the intercept will be K-{\ -f- K) instead 



