VALIDITY OF THE MICHAELIS-MENTEN THEORY 23 



duces the substrate concentration appreciably, the Michaelis formulation 

 will not be obeyed and reciprocal plots may not be linear, in which case the 

 treatment can be extended by putting: 



[(S,)] - (ES) [(E,) - (ES)] 

 ^' = (ES) ^^-^^^ 



where (S,) is the total concentration of substrate. The expression for (ES) 

 now is not simple but involves a quadratic equation and the actual deter- 

 mination of (ES) to compare with (S^) requires a knowledge of the enzyme 

 concentration (or specifically the concentration of enzyme active centers). 

 The generalized treatment of Straus and Goldstein (1943) includes this pos- 

 sible reduction in substrate concentration and will be discussed in the follow- 

 ing chapter. 



It will suffice for the present to calculate the expected reduction in sub- 

 strate concentration for a particular case. If one assumes that within the 

 experimental reaction volume the enzyme protein is 10% and the molecular 

 weight for a single reactive site is 62,000, it is found that (E^) is 1.6 X 10~^ M. 

 With a Michaelis constant of 3 X 10~^ M and a substrate concentration of 

 of 10~^ M, it may be calculated that the substrate concentration would 

 be reduced by 30%, a significant amount; if i?^,„ is 3 X 10~* M, the reduction 

 would be 74%. It is particularly important that consideration be given 

 to such effects when correlations are made between results on isolated 

 enzyme systems in homogeneous solution and the same enzyme system 

 within the cell. 



Another reason for a decrease in substrate concentration under experi- 

 mental conditions would be the utilization of the substrate in the reaction, 

 but this difficulty can be avoided most simply by determining only the 

 initial reaction rate before sufficient depletion of substrate has occurred. 



Assumption That the Products Are Released 

 from the Enzyme Rapidly 



Michaelis and Menten postulated that the products formed from the reac- 

 tion of the ES complex were essentially simultaneously set free from the 

 enzyme. It is quite possible in some enzyme reactions that a relatively stable 

 EP complex is formed which dissociates at a sufficiently slow rate to limit 

 the over-all reaction. For this situation the following sequence can be for- 

 mulated: 



E + S ^ ES ^ EP ^ E + P (2-14) 



and it is assumed that v = ^3 (EP). It is found that the rate equation is 



