336 



Enzymes: Kinetics of Oxidations /I8 : I 



where E is catalase, S is peroxide, and AH 2 is the substance being 

 oxidized. As was done in the case of the hydrolase reactions discussed 

 in the last chapter, one may rewrite these as the differential equations 



E 



2 

 J 



370 



-£ = k 1 {e-p)x - k 2 p - k 3 ap 



dx 



— = k 1 (e-p)x + k 2 p 



(1) 



da 

 It 



= — k 3 ap 



410 

 A (m(x) 



450 



Figure 3. The spectra of catalase 

 and its two complexes with 

 methyl-hydrogen peroxide. After 

 B. Chance, "Catalase Peroxides 

 Spectra," J. Biol. Chem. 179: 1331 

 (1949). 



The algebra has become slightly more 

 complex because two substances are used 

 up in the reaction, instead of just one. 



The set of equations in (1) are non- 

 linear differential equations; they do 

 not have an exact solution in closed form. 

 Various approximations can be used 

 just as in the case of the hydrolases. 

 First, it should be noted that 



da = dp + dx 



If a quasi-steady state occurs, then/? will 

 have an approximately constant value p x 

 and one may write the equations 



dx da 

 ~dt~~~di 



Under these circumstances, one may 

 talk of a reaction velocity V defined as 



dt 



and -r = -r- 



T/ _ dx da 



~ ~~dt ' ~dt 



k 3 ap, (2) 



The first equation of (1) can be solved 

 to yield, under quasi-static conditions 



Pi = 



ex 



x + 



Ko "T Kr>a 



(3) 



and hence 



*i 



V = 



x + 



(k 3 a)ex 



(4) 



*i 



