BLBS102-c08 BLBS102-Simpson March 21, 2012 12:8 Trim: 276mm X 219mm Printer Name: Yet to Come
174 Part 2: Biotechnology and EnzymologyFigure 8.7.The Hill plot.1974) are useful in estimating the Michaelis-Menten kinetic
parameters and are the better plots for revealing deviations from
the reaction behavior.Hill PlotThe Hill equation is a quantitative analysis measuring
non–Michaelis-Menten behavior of cooperativity (Hill 1910).
In a case of completely cooperative binding, an enzyme con-
tainshbinding sites that are all occupied simultaneously with
a dissociation constantK=[E][S]h/[ESh], wherehis the Hill
coefficient, which measures the degree of cooperativity. If there
is no cooperativity,h=1; there is positive cooperativity when
h>1, negative cooperativity whenh<1. The rate value can
be expressed asv=Vmax[S]h/(K+[S]h), and the Hill equa-
tion gives a linear log(vi/Vmax−v)=hlog[S]−logK,when
log(v/Vmax−v) is plotted as a function of log[S] with a slope of
hand ayintercept of−logK(Fig. 8.7). However, the equation
will show deviations from linearity when outside a limited range
of substrate concentrations, that is, in the range of [S]=K.FACTORS AFFECTING ENZYME
ACTIVITYAs discussed earlier in this chapter, the rate of an enzymatic reac-
tion is very sensitive to reaction conditions such as temperature,
pH, ionic strength, buffer constitution, and substrate concentra-
tion. To investigate the catalytic mechanism and the efficiency
of an enzyme with changes in the parameters, and to evaluate a
suitable circumstance for assaying the enzyme activity, the con-
ditions should be kept constant to allow reproducibility of data
and to prevent a misleading interpretation.Enzyme, Substrate, and Cofactor
ConcentrationsIn general, the substrate concentration should be kept much
higher than that of enzyme in order to prevent substrate concen-tration dependency of the reaction rate at low substrate concen-
trations. The rate of an enzyme-catalyzed reaction will also show
linearity to the enzyme concentration when substrate concentra-
tion is constant. The reaction rate will not reveal the linearity
until the substrate is depleted, and the measurement in initial rate
will be invalid. Preliminary experiments must be performed to
determine the appropriate range of substrate concentrations over
a number of enzyme concentrations to prevent the phenomenon
of substrate depletion. In addition, the presence of inhibitor, acti-
vator, and cofactor in the reaction mixture also influence enzyme
activity. The enzymatic activity will be low or undetectable in
the presence of inhibitors or in the absence of activators or co-
factors. In the case of cofactors, the activated enzymes will be
proportional to the cofactor concentration added in the reaction
mixture if enzymes are in excess. The rate of reaction will not
represent the total amount of enzyme when the cofactor sup-
plement is not sufficient, and the situation can be avoided by
adding excess cofactors (Tipton 1992). Besides, loss of enzyme
activity may be seen before substrate depletion, as when the
enzyme concentration is too low and leads to the dissociation
of the dimeric or multimeric enzyme. To test this possibility,
addition of the same amount of enzyme can be applied to the
reaction mixture to measure if there is the appearance of another
reaction progression curve.Effects of pHEnzymes will exhibit maximal activity within a narrow range of
pH and vary over a relatively broad range. For an assay of en-
zymatic catalysis, the pH of the solution of the reaction mixture
must be maintained in an optimal condition to avoid pH-induced
protein conformational changes, which lead to diminishment or
loss of enzyme activity. A buffered solution, in which the pH is
adjusted with a component with pKaat or near the desired pH
of the reaction mixture, is a stable environment that provides the
enzyme with maximal catalytic efficiency. Thus, the appropriate
pH range of an enzyme must be determined in advance when
optimizing assay conditions.
To determine if the enzymatic reaction is pH dependent and to
study the effects of group ionizations on enzyme kinetics, the rate
as a function of substrate concentration atdifferentpH conditions
can be measured to simultaneously obtain the effects of pH on the
kinetic parameters. It is known that the ionizations of groups are
of importance, either for the active sites of the enzyme involved
in the catalysis or for maintaining the active conformation of
the enzyme. Plots ofkcat,Km,andkcat/Kmvalues at varying
pH ranges will reflect important information about the roles of
groups of the enzyme. The effect of pH dependence on the value
ofkcatreveals the steps of ionization of groups involved in the
ES complex and provides a pKavalue for the ES complex state;
the value ofKmshows the ionizing groups that are essential
to the substrate-binding step before the reaction. Moreover, the
kcat/Kmvalue reveals the ionizing groups that are essential to
both the substrate-binding and the ES complex–forming steps,
and provides the pKavalue of the free reactant molecules state
(Brocklehurst and Dixon 1977, Copeland 2000). From a plot of
thekcat/Kmvalue on the logarithmic scale as a function of pH,