Page 212 - Instant notes

Physical chemistry 198

By dividing both the numerator and denominator by k 1 and defining (k −1+k 2)/k 1 as K M, the
Michaelis constant, the observed rate of reaction simplifies to:

This rate law is known as the Michaelis-Menten equation and shows that the rate of
enzyme-mediated reaction is first order with respect to enzyme concentration. The
overall rate depends on the concentration of substrate. At low substrate concentrations,
so the rate of reaction is first order in substrate concentration as well as
enzyme concentration:

When the substrate concentration is sufficiently high that , the overall rate of
reaction is zero order in [S]:
v=k 2[E] 0

The rate of reaction is independent of substrate concentration under these conditions
because at any given time all active sites of the enzymes are filled and increasing the
amount of substrate cannot increase the yield of product. The rate determining step is
therefore the rate at which the ES complex reacts to form products. These conditions also
correspond to the maximum rate of reaction:
v max=k 2[E] 0

and k 2 is often termed the maximum turnover number.

Enzyme kinetics: Lineweaver-Burke plots

The Michaelis-Menten equation can be expressed in a different form by taking the
reciprocal of both sides:

Substituting for the maximum rate of reaction, υ max=k 2[E] 0, gives

Therefore, the reciprocal of reaction rate is directly proportional to the reciprocal of
substrate concentration when the total concentration of enzyme is held constant. The
graph of 1/v plotted against 1/[S] is a straight line and is known as a Lineweaver-Burke