340 Enzymes: Kinetics of Oxidations /1 8 : I 



except that hydrogen peroxide acts as both S and AH 2 . The reaction 

 may be represented stoichiometrically by the equations 



e — p x k v p 



E + S^E-S 



k, 



■ e"-S + S^ E + Products 



These equations, being somewhat different from the peroxidatic ones, 

 lead to a slightly different set of differential equations, namely 



-ft = k x {e-p)x - k 2 p - k 3 px 



dx (13) 



— = -k 1 (e-p)x - k 3 px + k 2 p 



The quasi-static approximation applied to the first equation of (13) 

 leads to the relationship 



A * — '-f (14) 



1+ fI 



if k 2 is negligible compared to {k x + k 3 )x. This expression for p x is 

 interesting because it does not depend on x. At the start of the reaction, 

 p increases exponentially for large ratios of x fe. In this increasing range, 

 the first equation in (13) predicts that 



-=- ^ 2 , 15 x 



[k 1 + k 3 )x 



It has been shown that the approximation Equation 1 5 can be improved 

 by replacing * with (0.9)x to take account of the decrease of x as p is 

 increasing. 



In a similar fashion, the quasi-static approximation applied to the 

 second equation of (13) leads to the differential equation 



% = -2*3 A* (16) 



Integrating leads to an exponential curve 



x = x e- 2k ^ 1 (17) 



whose half-life is given by 



( - " S (18) 



The three Equations, 14, 15, and 18, allow one to determine the two 



