7 Enzyme Activities 161

a function of substrate concentration is demonstrat-
ed as shown in Figure 7.2C. Three distinct portions
of the plot will be noticed: an initial linear relation-
ship showing first-order kinetic at low substrate con-
centrations; an intermediate portion showing curved
linearity dependent on substrate concentration, and
a final portion revealing no substrate concentra-
tion dependency, i.e., zero-order kinetic, at high sub-
strate concentrations. The interpretation of the phe-
nomenon can be described by the following scheme:

The initial rate will be proportional to the ES com-

plex concentration if the total enzyme concentra-

tion is constant and the substrate concentration

varies. The concentration of the ES complex will be

proportional to the substrate concentration at low

substrate concentrations, and the initial rate will

show a linear relationship and substrate concentra-

tion dependency. All of the enzyme will be in the

ES complex form when substrate concentration is

high, and the rate will depend on the rate of ES

transformation into enzyme-product and the subse-

quent release of product. Adding more substrate

will not influence the rate, so the relationship of

rate versus substrate concentration will approach

zero (Brown 1902).

However, a lag phase in the progress of the reac-
tion will be noticed in coupled assays due to slow or
delayed response of the detection machinery (see
below). Though vcan be determined at any constant
concentration of substrate, it is recommended that
the value of substrate concentration approaching
saturation (high substrate concentration) be used so
that it can approach its limiting value Vmax with
greater sensitivity and prevent errors occurring at
lower substrate concentrations.
Measurement of the rate of enzyme reaction as a
function of substrate concentration can provide
information about the kinetic parameters that char-
acterize the reaction. Two parameters are important
for most enzymes—Km, an approximate measure-
ment of the tightness of binding of the substrate to
the enzyme; and Vmax, the theoretical maximum
velocity of the enzyme reaction. To calculate these
parameters, it is necessary to measure the enzyme
reaction rates at different concentrations of sub-
strate, using a variety of methods, and analyze the
resulting data. For the study of single-substrate
kinetics, one saturating concentration of substrate in
combination with varying substrate concentrations
can be used to investigate the initial rate (v), the cat-

alytic constant (kcat), and the specific constant (kcat/

Km). For investigation of multisubstrate kinetics,

however, the dependence of von the concentration

of each substrate has to be determined, one after

another; that is, by measuring the initial rate at vary-

ing concentrations of one substrate with fixed con-

centrations of other substrates.

A large number of enzyme-catalyzed reactions

can be explained by the Michaelis-Menten equation:

where [E] and [S] are the concentrations of enzyme

and substrate, respectively (Michaelis and Menten

1913). The equation describes the rapid equilibrium

that is established between the reactant molecules (E

and S) and the ES complex, followed by slow for-

mation of product and release of free enzyme. It

assumes that k 2 k-1in the following equation,

and Kmis the value of [S] when vVmax/2.

Briggs and Haldane (1924) proposed another

enzyme kinetic model, called the steady state model;

steady state refers to a period of time when the rate

of formation of ES complex is the same as rate of

formation of product and release of enzyme. The

equation is commonly the same as that of Michaelis

and Menten, but it does not require k 2 k-1, and

Km(k-1
k 2 )/k 1 because [ES] now is dependent on

the rate of formation of the ES complex (k 1 ) and the

rate of dissociation of the ES complex (k-1and k 2 ).

Only under the condition that k 2  k-1willKs

k 1 /k 1 and be equivalent to Km, the dissociation con-

stant of the ES complex {Ksk 1 /k 1 ([E] 

[ES])[S]/[ES]}, otherwise KmKs.

The Km is the substrate concentration at half of the

maximum rate of enzymatic reaction, and it is equal

to the substrate concentration at which half of the

enzyme active sites are saturated by the substrate in

the steady state. So, Km is not a useful measure of ES

binding affinity in certain conditions when Km is not

equivalent to Ks. Instead, the specific constant

(kcat/Km) can be substituted as a measure of substrate

binding; it represents the catalytic efficiency of the

enzyme. The kcat, the catalytic constant, represents

conversion of the maximum number of reactant

molecules to product per enzyme active site per unit

time, or the number of turnover events occurring per

E + S ES E + P

k

k

(^1) k
1
2
−
←⎯⎯⎯→⎯ ⎯→⎯
v
V
K
k
mmK

• max =
  [
  ([
  S]
  S])
  [E] [S]
  ( + [S])
  cat