KINETICS OF COMPLEX ENZYME REACTION TYPES 47 



general formulation, assuming appropriate relative concentrations and con- 

 stants. One type of activation not included is that in which the activator 

 combines with the substrate instead of the enzyme; the rate equations are 

 complex and are discussed in some detail by Dixon and Webb (1958 p. 459). 



Reactions in Which the Enzyme Undergoes a Cyclic Change 



There are important reactions in which the enzyme is altered in one phase 

 of the cycle and must be regenerated during another phase in order that 

 the process proceed; oxidation-reduction reactions in which the enzyme, 

 or a prosthetic group, is alternately in the oxidized and reduced states would 

 be of this type. 



EA E + A - ^ , EA ^E' + C 



c *-i c^-'-t) 



E'E"" E'+ R ■ , F/R ^E + D 



The rate equation is of the type: 



. = F. ^^^ (2-76) 



"" (A)(B) ^ A',(B) - K^(X) 



where T^,,, = kJc^i'E^^'i'k.^+ki), Ks, = ki{lc_-^-rk2)''ki{h.2+hi), and K^ = 

 k.2ik_3-[-ki)'k3{k2+ki). AVith respect to one substrate this may be rewritten: 



where 7„/ = 7,„ (B)/[(B)+Zb] and K„ = Kj^^li^^K^- Such reac- 

 tions thus conform to the Michaelis-Menten formulation but the constants 

 are complex and depend on the substance restoring the enzyme to its ori- 

 ginal condition. 



The over-all equation for the above reactions is: 



A + B ^ C + D 



and is a transfer with the enzyme functioning as a carrier. In some cases 

 the same substrate may participate in both reactions and the result is a 

 dismutation: 



2 A ii± C + D 



