Principles of Biochemistry

8.2.3 Factors affecting Enzyme catalysed reactions

 

1. Effect of substrate concentration

 The effect of varying the substrate concentration on the initial rate of an enzyme-catalyzed reaction when enzyme concentration is held constant is as follows: At very low concentrations of substrate the rate of the reaction will increase with an increase in the substrate concentration. At higher substrate concentrations, the rate increases by smaller and smaller amounts. Finally, a point will be reached beyond which there are only vanishingly small increases in the reaction rate with increasing substrate concentration. No matter how high the substrate concentration is raised beyond this point, the reaction rate will approach but never quite reach a plateau. At this plateau, called the maximum rate (Vmax), the enzyme is “saturated” with its substrate and cannot function faster .

 

 Leonor Michaelis and Maud Menten in 1913, postulated that the enzyme E first combines reversibly with its substrate S to form an enzyme-substrate complex ES in a relatively fast reversible reaction.

E + S → ES

 The ES complex then breaks down in a second reversible reaction, which is slower, to yield the reaction product P and the free enzyme E

ES → P + E

 Since the second reaction is the rate-limiting step, the overall rate of the enzyme-catalyzed reaction must be proportional to the concentration of the enzyme-substrate reaction, the enzyme exists in two forms, the free of the catalyzed reaction will obviously be at a maximum when virtually all of the enzyme is present as the ES complex and the concentration of free enzyme E is vanishingly small. This condition will exist at a very high concentration of the substrate, since, by the Law of mass action, the equilibrium of the first reaction will be pushed to the right when we increase the concentration of S

E + S → ES

 If we increase S to high enough levels, essentially all the free enzyme E will have been converted into the ES form. In the second reaction of the catalytic cycle, the ES complex breaks down continuously and rapidly, to yield the product P and the free enzyme. But if the concentration of S is high enough, the free enzyme E will immediately combine with another molecule of S. Under these conditions a steady state is achieved in which the enzyme is always saturated with its substrate and the reaction rate is maximum.

 Thus is the relationship between the substrate concentration and the rate of an enzymatic reaction, it is difficult to say from the closer and closer approach of the reaction rate to the maximum velocity V max exactly what substrate concentration is required to attain V max. However, because the curve expressing this relationship has the same general shape for most enzymes (it is a rectangular hyperbola Fig.13.3). Michaelis and Menten defined a constant, today designated KM that is useful in establishing the precise relationship between the substrate concentration and the velocity of the enzyme-catalyzed reaction. KM, the Michaelis - Menten constant, is defined as the concentration of the specific substrate at which a given enzyme yields one-half its maximum velocity. It is mathematically expressed by the Michaelis - Menten equation.

Vo = -Vmax [S]

 Km + [S]

 where Vo = Intial rate at substrate concentration[S]

 Vmax = Maximum rate

 Km = Michaelis-Menten constant of enzyme for particular substrate

 [S] = substrate concentration

 This equation was derived by Michaelis and Menten starting from the basic hypothesis that the rate-limiting step in enzymatic reactions is the breakdown of the ES complex to from the product and the free enzyme.