768 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



independent of temperature, it may be disregarded. The optimal tempera- 

 ture is found to be: 



Tovt = r "^^.^ ^ (15-37) 



AS + R\tl 



AH ^ 



AH, + AH* 



and is thus related to each enthalpy term and the entropy of the inacti- 

 vation. The relative values of JH, AH ^ and AH* so that a maximum rate 

 will occur may be determined from this equation and the conditions for 

 a maximum in the temperature range studied are defined. 



The optimal temperature is not a very useful value in characterizing 

 an enzyme, as Dixon and Webb (1958) have pointed out, and is often time- 

 dependent, but the effects of inhibition upon it may be of some interest. 

 For example, it has generally been assumed that when an inhibitor lowers 

 T^pi, the inhibitor is facilitating the inactivation of the enzyme. However, 

 from the equation above it may be seen that effects on J^, and AH* 

 may also be involved. It is, after all, a matter of shifting the balance of 

 the temperature dependencies of the constants. A decrease in T^^i will 

 occur if either AH ^ or AH*, or both, is decreased by the inhibitor. Most 

 of the work on shifts in T^^^ due to inhibitors has been done on multienzyme 

 systems or cell metabolism but to interpret such effects it is necessary to 

 understand what can happen to the individual enzymes. These more com- 

 plex systems will be discussed later. 



EFFECTS OF TEMPERATURE: MULTIENZYME SYSTEMS 



Although no quantitative studies of the effects of temperature on multi- 

 enzyme systems have been done, it is possible to formulate certain general 

 principles that will be useful later in discussing the work on cellular meta- 

 bolism. In any multienzyme system there are two or more reactions pro- 

 ceeding simultaneously and the rates of these reactions will generally vary 

 with temperature in different ways. The rates of most enzyme reactions 

 will increase with rising temperature in the i:)hysiological range, but to 

 varying degrees, while in some cases the rate of a particular reaction may 

 actually decrease due to the inactivation of the enzyme. The effects of tem- 

 perature on the behavior of multienzyme systems and on the response of 

 such systems to inhibition will thus depend on the relative changes of the 

 individual rates. It is important to emphasize that the rate changes of 

 enzyme reactions are related not only to the variations in the rate constant 

 k^, and hence to AH*, but also to variations in the Michaelis constant K^^^. 

 In general K^,^ will change with temperature according to the values of AH^^, 

 AH_^, and AH.^*, corresponding to k^, k^^, and ^-g, but if it is the equili- 

 brium constant for the ES complex, the change will depend on AH^, the 

 over-all enthalpy change in the formation of the ES complex. 



