34 2. THE KINETICS OF ENZYME REACTIONS 



The Substrate Is Not Immediately Available to the Enzyme 



When the substrate used must penetrate a barrier to reach the enzyme 

 (such barriers may occur in enzyme aggregates, or in mitochondrial and 

 cell membranes) or requires chemical modification before it will react with 

 the enzyme, the following equations describe the situation: 



S ;4 S' (2-23) 



nJ_0 



S' + E ;=± ES' -1 E + P (2-24) 



Four possible cases may be considered. 



(I) Case 1. The formation of S' from S is very slow and limits the over- 

 all rate. If S' reacts as rapidly as it appears or if k_Q is zero: 



V = US) (2-25) 



and the kinetics are not related to the enzyme reaction. 



(II) Case 2. The formation of S' limits the over-all rate but the back 

 reaction of S' -> S cannot be ignored, in which case v = ^o(S) — k_o{S'). 

 This reduces to v = A'o[(S) — (S')] if ko is a permeability constant and 

 diffusion occurs at equal rates in both directions. Best (1955 a) has equated 

 this rate to the enzyme rate inside the barrier to give: 



V = F„. - ,, , t^: , (2-26) 



(A'o/f) (S) - 1 



where F„, is the maximal rate of the enzyme reaction, and has used this 

 equation to obtain permeability constants for glucose and sucrose in yeast, 

 but it is doubtful if this relationship holds except under very limited con- 

 ditions. 



(III) Case 3. The enzyme reaction limits the over-all rate in which case 

 iS') is in complete equilibrium with (S) and (S') = (S)/^' where K' = k_olko. 

 This value of (S') may be substituted in the Michaelis equation to give: 



VJS') VJ8) ^2.27) 



(S') + K,„ (S) + K'K,„ 



so that in this case the determined Michaelis constant is not the true K^ 

 for the enzyme reaction, a fact of possible importance when such constants 

 are determined in complex systems where the concentration of substrate 

 inside the barrier is not necessarily the same as outside. 



