KINETICS OF COMPLEX ENZYME REACTION TYPES 45 



tulated for acetylcholinesterase (Wilson and Cabib, 1956): 



the rate equation was found to be of the Michaelis form 2-11 with F,„ = 

 ^2^'3/(^'2+^'3) and K„, = k^{Jc_i^k2)lki{k.2^k^), i.e., the classic V„, and Z,„ 

 are each altered by the factor ^3/(^'2+^'3)- The constants for this reaction 

 thus depend on the rate constant for the water reaction and an inhibitor 

 could thus modify both F,,, and iC,,, without interfering with the substrate 

 acetylcholine in any way. 



The Enzyme Reaction Involves an Activator 



An activator is a substance, usually inorganic, that is not chemically 

 altered in the reaction but. by its presence, increases the rate of the enzyme 

 catalysis. In many cases the activator probably functions by participating 

 in the binding of the substrates to the enzyme or by the stabilization of 

 one or more of the complexes involved in the reaction sequence. In the 

 simple situation where the presence of the activator on the enzyme is nec- 

 essary for binding and reaction of the substrate: 



E ^ A ;^' EA (2-67) 



^•-3 



^1 k 



EA -f S ;:± EAS -4 EA 4- P (2-68) 



where A is the activator and S is the substrate, the rate equation is: 



"^ (A)(S) + KJA) + K^K„ '" (S) + K,„[l ^ KJ{X)] ^ ^ 



with K^= A-_3/A-3, K„i^ {k_i-rk^'ki, and 7„, the rate when all the enzyme 

 is in the form EAS. It is interesting that the Michaelis constant determined 

 experimentally by reciprocal plotting depends on the activator concentra- 

 tion. In an enzyme preparation with an unrecognized activator (which may 

 have been separated with the enzyme from the tissue or added in the reac- 

 tion medium, and which may be present in variable concentration under 

 different conditions), the Michaelis constant may vary unexpectedly. It 

 is also evident that an inhibitor could slow the rate by increasing either 

 K, or K„. 



