VALIDITY OF THE MICHAELIS-MENTEN THEORY 25 



tions and iiL,„ and K^ are the corresponding Michaelis constants. These 

 constants have the following values: 



K 



fl—l ~r n^2 ~r K-2 



kiiki + k_2 + ks) k_3(k.i + ki + k_2) 



This reaction, started from either direction, will approach an equilibrium 

 where the relative concentrations of S and P will be determined by the 

 equilibrium constant of the over-all reaction S ^ P. It is interesting to note 

 that this equilibrium constant is related to the kinetic terms in the follow- 

 ing manner: 



(S) k^k^t^ Ks 



where K^p, as above, is the equilibrium constant (ES)/(EP). If an activator 

 or inhibitor of the enzyme alters the affinity of the enzyme for the substrate 

 (i.e. Kg), it is evident that the other dissociation constants must change 

 appropriately since Kq is unaffected by any effect on the enzyme. 



Assumption That One Substrate Molecule Is Bound At One Enzyme Site 



The assumption that only a single substrate molecule is bound to each 

 enzyme active center, or that if there are more than one active center on 

 the enzyme, the binding of substrate to each site is independent, is probably 

 justified for most enzyme reactions but not for all. If the complex consists 

 of more than one substrate molecule as in the sequence: 



'^•i k 



«S + E ^ ES„ 4 E + P (2-20) 



the rate is given by: 



(S)« 



where K,,^ = {k_i+k-2)jki in the general case. The substrate concentration 

 for half the maximal rate is K„^^^" and the reciprocal plot of Ijv against 

 1/(S) will not be linear. Reactions of this type are uncommon and values 

 of n above two are very unlikely. If a plot of 1/v against 1/(S)^ gives a straight 

 line, a reaction involving two substrate molecules may be suspected, but if 

 non-integral values of n are necessary, it is probable that the deviation 

 from linearity is due to other factors. Situations where two different sub- 



