EFFECTS OF TEMPERATURE: ENZYMES 759 



low, or even negative in the case of urethane, when low concentrations were 

 used. Unfortunately the experiments with high and low inhibitor concen- 

 trations were done under somewhat different conditions so that comparison 

 cannot be quantitative. 



The calculation of thermodynamic values from data obtained on slowly 

 acting and partially irreversible inhibitors has occasionally been ambiguous. 

 When the inhibition is determined after a single time interval, it is diffi- 

 cult to know if this represents a rate process or a i^artial equilibrium, or 

 both, and, hence, if the calculated enthalpy change refers to an activated 

 complex or to the final comi)lex. If the enthalpy of activation is required, 

 it is preferable to determine the progress of the inhibition and to use the 

 initial rates at different temperatures. The problem of simidtaneous inhi- 

 bition and inactivation has been discussed in Chapter 12 and the formu- 

 lations presented there may be used as a basis for predicting temperature 

 effects. It may also be pointed out that it is not valid to plot log i against 

 1/T, as w^as done for the inhibition of cholinesterase by urethane (Shukuya, 

 1953), since the inhibition may be expressed by an equation of the type 

 i = 1 — g-^d)' (see Eqs. 12-12 and 12-16), and log i is not proportional to 

 1/T because the rate constant itself is an exponential function of 1/T. 

 One must first plot log (1 — i) against t to determine the values of k at 

 different temperatures, and then plot log k against 1/T to determine the 

 energy of activation, or log {kjT) against 1/T to determine the enthalpy 

 of activation. 



The temperature dependence of the inhibition of cholinesterase by the 

 organoi^hosphorus compounds is complex because at least two steps are 

 involved, the formation of a reversible EI complex and the ensuing chemical 

 reaction of the inhibitor with an enzyme group. Another complicating 

 factor with certain of these inhibitors is the spontaneous hydrolysis of the 

 phosphorylated enzyme, since the rate of this reversal reaction will also 

 be dependent on the temperature. The inhibition of electric organ cholin- 

 esterase by diisopropylfluorophosphate has been found by Nachmansohn 

 et al. (1947, 1948) to develop more rapidly at higher temperatures, but the 

 difference in the rates is not very large. They stated that the inhibition pos- 

 sessed a QiQ of about 2 but Chadwick (1957) recalculated their data and came 

 up with a QiQ between 1.22 and 1.44. Chadwick using fly head cholinesterase 

 found a Q^^ of 1.58, wdiich is similar to the Q^q of 1.34 for the hydrolysis of 

 acetylcholine by this enzyme. Aldridge (1953 b) found that the inhibition 

 of erythrocyte cholinesterase by the slowly reversible E-600 was charac- 

 terized by an energy of activation of 10.6 kcal/mole. This must represent 

 the formation of the activated complex in the phosphorylation o^ the en- 

 zyme. The rate of the reversal of the inhibition by hydrolysis of the phos- 

 phorylated enzyme is associated with an energy of activation of 14.4 kcal/ 

 mole. A rise in the temperature in such a case may involve an increased 

 rate of formation of the initial EI complex (with a low temperature coeffi- 



