760 15. EFFECTS or VARIOUS FACTORS ON INHIBITION 



cient), an increased rate of enzyme phosphorylation (with a higher temper- 

 ature coefficient), and a faster hydrolysis of the inhibited enzyme (with 

 perhax)s an even higher temperature coefficient). In addition, at the higher 

 temperatures there will be progressive thermal inactivation of the enzyme. 

 Davies (1955) has reported that below 35° the inhibition of horse serum 

 cholinesterase by choline shows an enthalpy change of — 9.8 kcal/mole 

 but above 35° there is a rather sudden change to — 54 kcal/mole, indicating 

 a denaturation-type effect. However, Chadwick has questioned if the ac- 

 curacy of the Ki determinations was sufficient to justify these calculations. 



Equilibria between Active and Inactive forms of the Enzyme 



Many temperature studies of enzymes and metabolism have been inter- 

 preted on the basis of the effects of temperature changes on an equilibrium 

 between catalytically active and inactive (or denatured) forms of the en- 

 zyme, particularly by Johnson and his colleagues (Johnson et al., 1954). There 

 has been some confusion about the kinetics of such systems and, indeed, 

 it is evident that the formulations are enzymically incorrect in most in- 

 stances. Reiner (1959, p. 267) has pointed out some of the errors and there 

 are others related more specifically to inhibitions that will be mentioned 

 later. Under the circumstances, it w^ill be better to present the kinetic equa- 

 tions for several possible systems first, rather than to discuss erroneous or 

 inapplicable formulations. The fundamental addition that must be made 

 to the systems discussed in earlier chapters is the equilibrium: 



E„ — E, K = (EJ/(E,) (15-15) 



where E^, is catalytically active enzyme and E^^ is denatured or inactive 

 enzyme. It must be understood that the inactivating structural change 

 need refer only to the active center and that total enzyme denaturation 

 is not implied; in fact, it might be better if the term "denaturation" were 

 not used iri this connection because the structural changes may not be 

 related to what is classically supposed to occur during denaturation. 

 We shall first consider a simple noninhibited enzyme system: 



A' A'j A-., 



. ^, — E„ + S - E„S ^ E, + P (15-16) 



The rate will be given by v = A^2(EgS) and the conservation equation for 

 the enzyme is (E,) = (EJ -f- (E^) + (E,,S). The rate in terms of the sub- 

 strate concentration and the equilibrium constants is then: 



(S) + ^, 1 + 



i 



