748 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



General Effects of Temperature on Dissociation Constants 



Temperature changes will alter enzyme reactions or inhibitions by changing 

 the rate constants of each step; for example, the k^ and k_-i^ for the formation 



E+S;i±ES^E + P (15-1) 



k 



E + I ^ EI Ki= k^.jk, (15-2) 



and dissociation of the ES or EI complexes, and the A^g (or any additional 

 rate constants) for the breakdown of the ES complex into products. The 

 resultant of the effects on k^ and k_-^ is manifested by a change in the sub- 

 strate or inhibitor constants, K^ or K^. The Michaelis-Menten constant, 

 Kj,^ = {k_^ + k^jlk^ may be changed in a more complex fashion. The rate 

 constants may be modified by temperature in two basic ways. The num- 

 ber of reactant molecules capable of surmounting the activation energy 

 barrier will change, or the activation energy itself may be changed. Usually 

 both will occur. One other possible mechanism must be mentioned, since 

 it has played an important role in inhibition studies. This is the effect of 

 temperature on the equilibrium between catalytically active and inactive 

 (or denatured) enzyme molecules. The applicability and validity of this 

 mechanism will be discussed in a separate section. 



Although the value of Z^ at any temperature is related to the free energy 

 of inhibitor binding, the change in K, with temperature is dependent on 

 the enthalpy change for the formation of the EI complex, since: 



AF = RT In K, = AH - TAS (15-3) 



(15-4) 



(15-5) 



dT RT^ 



where AH and J*S are the enthalpy and entropy changes for the binding of 

 the inhibitor to the enzyme. Determination of K, at different temperatures 

 allows the calculation of AH since a plot of log Z, against 1/T will give 

 a line with a slope of J///2.303i?. If the plot is linear over the range of 

 temperatures studied, this indicates that AH has not changed appreciably. 

 However, if the plot is curved, the slope at any point will give AH for 

 that temperature. If the temperature range is not too great and the AH 

 is reasonably constant, a useful relationship may be derived: 



