Food Biochemistry and Food Processing

162 Part II: Water, Enzymology, Biotechnology, and Protein Cross-linking

unit time; it also represents the turnover rate whose
unit is the reciprocal of time. In the Michaelis-
Menten approach, the dissociation of the EP com-
plex is slow, and the kcatcontribution to this rate con-
stant will be equal to the dissociation constant.
However, in the Briggs-Haldane approach, the dis-
sociation rate of ES complex is fast, and the kcat is
equal to k 2. In addition, the values of kcat/Kmare
used not only to compare the efficiencies of different
enzymes but also to compare the efficiencies of dif-
ferent substrates for a specified enzyme.
Deviations of expected hyperbolic reaction are
occasionally found due to such factors as experi-
mental artifacts, substrate inhibition, existence of
two or more enzymes competing for the same sub-
strate, and the cooperativity. They show nonhyper-
bolic behavior that cannot fit well into the Michaelis-
Menten approach. For instance, a second molecule
binds to the ES complex and forms an inactive terna-
ry complex that usually occurs at high substrate
concentrations and is noticed when rate values are
lower than expected. It leads to breakdown of the
Michaelis-Menten equation. It is not only the
Michaelis-Menten plot that is changed to show a
nonhyperbolic behavior; it is also the Lineweaver-
Burk plot that is altered to reveal the nonlinearity of
the curve (see below).
A second example of occasionally occurring non-
hyperbolic reactions is the existence of more than
one enzyme in a reaction that competes for the same
substrate; the conditions usually are realized when
crude or partially purified samples are used. More-
over, the conformational change in the enzymes may
be induced by ligand binding for the regulation of
their activities, as discussed earlier in this chapter;
many of these enzymes are composed of multimeric
subunits and multiple ligand-binding sites in cases
that do not obey the Michaelis-Menten equation.
The sigmoid, instead of the hyperbolic, curve is ob-
served; this condition, in which the binding of a
ligand molecule at one site of an enzyme may influ-
ence the affinities of other sites, is known as coop-
erativity. The increase and decrease of affinities of
enzyme binding sites are the effects of positive and
negative cooperativity, respectively. The number of
potential substrate binding sites on the enzymes can
be quantified by the Hill coefficient, h, and the
degree of cooperativity can be measured by the Hill
equation (see page 164). More detailed illustrations
and explanations of deviations from Michaelis-

Menten behavior can be found in the literatures

(Bell and Bell 1988, Cornish-Bowden 1995).

DATAPRESENTATION

Untransformed Graphics

The values of Kmand Vmaxcan be determined graph-

ically using nonlinear plots by measuring the initial

rate at various substrate concentrations and then

transforming them into different kinetic plots. First,

the substrate stock concentration can be chosen at a

reasonably high level; then a two-fold (stringently)

or five- or 10-fold (roughly) serial dilution can be

made from this stock. After the data obtained has

been evaluated, a Michaelis-Menten plot of rate vias

a function of substrate concentration [S] is subse-

quently drawn, and the values of both Kmand Vmax

can be estimated. Through the plot, one can check if

a hyperbolic curve is observed, and if the values

estimated are meaningful. Both values will appear to

be infinite if the range of substrate concentrations is

low; on the other hand, although the value of Vmax

can be approximately estimated, that of Kmcannot

be determined if the range of substrate concentra-

tions is too high. Generally, substrate concentrations

covering 20–80% of Vmax, which corresponds to a

substrate concentration of 0.25–5.0 Km, is appreci-

ated.

Lineweaver-Burk Plots

Though nonlinear plots are useful in determining the

values of Kmand Vmax, transformed, linearized plots

are valuable in determining the kinetics of multisub-

strate enzymes and the interaction between enzymes

and inhibitors. One of the best known plots is the

double-reciprocal or Lineweaver-Burk plot (Line-

weaver and Burk 1934). Inverting both sides of the

Michaelis-Menten equation gives the Lineweaver-

Burk plot: 1/v(Km/Vmax) (1/[S]) 
1/Vmax(Fig.

7.3). The equation is for a linear curve when one

plots 1/vagainst 1/[S] with a slope of Km/Vmaxand a

yintercept of 1/Vmax. Thus, the kinetic values can

also be determined from the slope and intercept val-

ues of the plot. However, caution should be taken

due to small experimental errors that may be ampli-

fied by taking the reciprocal (the distorting effect),

especially in the measurement of vvalues at low

substrate concentrations. The problem can be solved