BioPHYSICAL chemistry

Because the rate-limiting step is the second reaction,

the rate of the overall reaction is determined by the

second step and is proportional to the concentration

of the complex.

Experimentally, enzyme reactions are often probed

by measuring the initial rate,orinitial 9 elocity, which

is denoted byV 0 , when the concentration of the sub-

strate is much greater than the concentration of the

enzyme. The use of the initial velocity allows the

use of the assumption that changes of the substrate

concentration are negligible. The initial velocity

usually has a linear dependence on the substrate

concentration at low substrate concentrations and

approaches an asymptotic value denoted by Vmaxat

high concentrations (Figure 7.15).

This dependence of the initial velocity on the

substrate concentration can be qualitatively under-

stood in terms of the Michaelis–Menten model.

At any given point in time, the enzyme is present

both as a free enzyme and a complex with the sub-

strate. At low substrate concentrations, most of the

enzyme is present in the free form and the rate is

proportional to the substrate concentration because

the complex formation is favored as the substrate

concentration is increased. The maximum velocity is approached at high

substrate concentrations when essentially all of the enzyme is present as

the complex. Under these conditions the enzyme is said to be saturated

with its substrate, so the changes in the substrate concentration have very

little effect.

The dependence can also be quantified using the Michaelis–Menten

model. For simplicity, assume that once the product is released from the

enzyme, rebinding is unlikely and so the back reaction for the second

step, kb 2 , is negligible. The initial velocity is then

determined by the product of the forward

rate constant for the second step, kf 2 , and the

concentration of the complex, [ES]:

V 0 =kf 2 [ES] (7.39)

Since the concentration of the complex is

usually not determined readily,an expres-

sion for this concentration in terms of the

experimental observables must be determined.

The rate of complex formation is given by the

product of the first forward rate constant, kf 1 ,

152 PARTI THERMODYNAMICS AND KINETICS

S

P

E

(ES)

E

Initial velocity,

V^0

Substrate concentration, [S]

Figure 7.14The basis of the Michaelis–
Menten mechanism is the transient formation
of a enzyme–substrate complex, ES.

Figure 7.15The
effect of substrate
concentration on the
initial velocity for an
enzyme-catalyzed
reaction.