338 



Enzymes: Kinetics of Oxidations /IS: I 



[The half-time t pl2 is the time for p to increase from any value p a to a 

 second value p b such that 



See Figure 4.] 



(A 



Pa) = 2 (A 



A) 



Arbitrary Units 

 for Both Axes 



14 



16 



Figure 4. This illustrates Equations (8) and (9) given in the 

 text. The numbers above the curve give the value of p m — p. 

 It is seen that for a curve of this nature the half-time t ll2 does 

 not depend on the region of the curve used to measure it. 



With either ethyl or methyl peroxide, it is possible to set a to zero. 

 Then equilibrium would result in all the measured enzyme being in 

 E-S, that is 



/'max — « for a o = 

 Equation 9 can be rewritten for this case as 



In 2 



1 PI2 ~ i 



ft 1*0 



(10) 



Thus, one can measure k x directly for the alkyl peroxides. 



Numerical studies have shown that k 3 can be approximated by a 

 similar type of expression. If one starts with large enough a and x 

 so that a steady-state region exists, and measures p, a curve such as that 

 in Figure 5 is obtained. The maximum p m of the intermediate complex 

 ES, and the off-time / 1/2 j, until/) decreases to \p m , are related approxi- 

 mately by the expression 



*, = — I— ^ (11) 



Pmhl2l a 



Equations 1 1 and 6 can be combined to yield 



1 



*i^ 



(' - Pm)hm 



(12) 



