EFFECTS OF TEMPERATURE: ENZYMES 749 



AH AS 



\nK,^ 



lnK,= 



RT, R 



AH AS 



RTo R 



, ^,. AH 

 m 



K,, R 



1 _ 1 



(15-6) 



If Xj is determined at one temperature, its value at another temperature 

 may be estimated by this equation if JH is known and does not vary mark- 

 edly with the temperature. Once JH is known it is also possible to calcu- 

 late AS from Eq. 15-3. Given K^, and hence JF, at a single temperature, 

 it is impossible to predict what K^ will be at another temperature because 

 from JF alone the temperature dependence of K^ cannot be established. 



A word should be said about the sign conventions in these equations. 

 In the chemical literature the association constant is often used, in which 

 case AF = — RT In K. The signs in Eq. 15-4 to 15-6 are then changed. 

 Since K, is usually expressed as a dissociation constant, the sign convention 

 of Eq. 15-3 has been adopted. However, the thermodynamic quantitaties 

 — JF, JH, and JS — refer to the association of the enzyme and inhibitor. 



The change in the inhibition with temperature in a simple case will 

 thus depend on JH for one thing. The effects of temperature on noncom- 

 petitive inhibition, assuming that JH does not vary with the temperature, 

 are shown in Fig. 15-1 for various values of JH when K^ is 1 mill at 37.5°. 

 These curves indicate the magnitudes of the eifects to be expected under 

 these conditions. In actual inhibitions, however, it is unlikely that JH 

 will remain constant as the temperature is varied, so that this change in 

 JH must be superimposed on the effects indicated by the curves. Since 

 JH may either increase or decrease with a change in the temperature, the 

 variation of the inhibition will be greater or smaller than shown in the 

 figure. 



In case the formation of the EI complex involves a chemical reaction 

 with the enzyme and the attachment of the inhibitor by covalent bonds, 

 the effects of temperature are apt to be marked because of the highly 

 exothermic nature of most of these reactions. Furthermore, the affinity of 

 the enzyme for the inhibitor will usually fall with rise in temperature, 

 resulting in a decrease in the inhibition. Inhibitions by the sulfhydryl- 

 reacting agents probably fall in this category but there is little experimental 

 basis to confirm this. The inhibition of beef heart succinic dehydrogenase 

 by arsenite has been found in the author's laboratory to decrease with 

 rise in the temperature from 17° to 37^ (Sanyal, 1959). 



