 initial rates for many enzymatic reactions exhibit bell-shaped curves as a
function of pH
 curves reflect the ionizations of certain amino acid residues that must be
in a specific ionization state for enzyme activity
 following model can account for such pH effects
 it is assumed that only EH and ESH are catalytically active
 Michaelis-Menten equation for this model is:
vo = V'max[S]/(K'M + [S])
where V'max = Vmax/f2
and
f1 = [H+]/KE1 + 1 + KE2/[H+]
and
f2 = [H+]/KES1 + 1 + KES2/[H+]
and
[pH1]
K'M = KM(f1/f2)
 Here, Vmax and KM refer to the active forms of the enzyme, EH and ESH
 At any given pH, equation [pH1] behaves as a simple Michaelis-Menten
equation but because of the pH-dependence of f1 and f2, vo varies with pH in a
bell-shaped manner
 the ionization constants of enzymes that obey equation [pH1] can be evaluated
by the analysis of the curves of log V'max versus pH, which provides values of
KES1 and KES2
 evaluation of a plot of log (V'max/K'M) versus pH yields KE1 and KE2
36
 experimentally, this entails the determination of the enzyme's MichaelisMenten parameters at each of a series of different pH values.
 measured pK's often provide valuable clues as to the identities of the amino
acid residues essential for enzymatic activity
 a pK of ~4 suggests that an Asp or Glu residue is essential to the enzyme
 a pK of~6 suggests the role for an active site His residue
 a pK of ~10 suggests the involvement of an active site Lys
 However, a given acid-base group may vary by as much as several pH units
from its expected value as a consequence of the environment of the group
 e.g., the carboxylate group of a Glu residue forming a salt bridge with a
Lys residue is stabilized by the nearby positive charge and therefore has a
lower pK than it would otherwise have
 it means that it is more difficult to protonate
 conversely, a carboxylate group immersed in a region of low polarity is
less acidic than normal because it attracts protons more strongly than if it
were in a region of higher polarity
 thus, the identification of a kinetically characterized pK with a particular
amino acid residue must therefore be verified by other types of
measurements such as the use of group specific reagents to inactivate a
putative residue (See Table 5-1).
37
(4) Practical Enzymology
(a) Experimental approaches
i Type of assay
- type of assay (continuous, discontinuous, indirect, direct, coupled, etc.)
ii Direct Continuous Assays
-involves measuring a change in a property of the substrate or product per
time (preferably the product)
-changes in absorbance, fluorescence, pH, optical rotation, conductivity,
enthalpy, viscosity, or volume of reaction mixture
- preferred - allows for the observation of the progress curve of the
reaction (anomalous behaviour)
1) spectophotometric assays- accurate and convenient
-fluorescence or absorbance changes
2) Release or uptake of H+ (pH)- directly in buffered or weakly buffered
solutions with a glass electrode
-restricted pH range (enzyme stability)
- indicator which changes its absorbance with protonation state
-pH stat technique-titrate the reaction mixture with either acid or
base to keep the pH constant whilst recording the rate of addition
-ion-selective electrodes or gas electrodes
38
iii Indirect Assays
-involve some further treatment of the reaction mixture either to produce a
measurable product or to increase the sensitivity or convenience of the
assay procedure
-the indirect assay may be used continuously or discontinuously
1) Discontinuous Indirect Assays-also referred to as sampling assays,
involve stopping the reaction after a fixed time and treating the rxn
mixture to separate a product for analysis
-alternatively, the rxn is stopped to produce a change in the
properties of one of the S or P which can then be measured
-examples of the former type of rxn include radiochemical assays,
also the development of HPLC for rapid separation and quantitation
of reactants has allowed many assays to be devised based on this
technique
-measurement of luminescence is a highly sensitive assay
-formation or disappearance of ATP can be determined by
measuring the light emission in the presence of fire-fly luciferase
which catalyses the rxn:
ATP + luciferin + O2  oxyluciferin + PPi + CO2 + AMP + light
- render a P detectable include, adjustment of the pH to alkaline
values to allow the p-nitrophenol, produced by the action of acid
phosphatase on p-nitrophenylphosphate
-with all discontinuous assays, it is important to ensure that the
procedure used to terminate the rxn does so instantaneously
39
-mixing acid or alkali to alter the pH to a value where the enzyme
is inactive are usually effective
-transfer of a rxn to an ice or boiling water bath may be effective
unless the rxn volumes are large
-essential to establish that the method used does stop the rxn
instantaneously
-include "zero-time" control and compare with rxn where one
reactant is omitted or E has been inactivated (inhibitor, heat
treatment, etc)
2) Continuous Indirect Assays
-carrying out manipulations necessary to detect P formation, or P
remaining within an assay mixture so as to allow the change to be
followed continuously as it occurs
-allows progress curve to be determined in a single assay (less errors
from manipulation)
-reagents that react with one of the P of the rxn to form a detectable
compound can be included in the assay mixture
-detection rxn must occur so rapidly that the E-catalyzed rxn is ratelimiting
-reagent used must have no effect on the activity of the E
-reagent must not react with any of the other components of the system
-eg., detection of carnitine acyltransferases
3) Coupled Assays
-initially, there is a lag time for the E under study to produce [P] to its
steady state level to be used as the S for the second E
40
-must only start measuring after lag period is completed but before
[S] becomes limiting for the E under study
-essential that the coupling E used never becomes rate-limiting so that
the measured rate is always determined by the activity of the E under
study
-efficiency of coupling E will depend on its KM value for the
substrate being formed (the lower its KM value, the more efficiently it
will work at low [S])
-lag period can be reduced by increasing the amount of coupling E
present so that it can catalyze the rxn more rapidly at low [S]
-therefore, usually have a very large excess of coupling E present
-must check the performance of the coupled assay to ensure that it
gives an accurate measure of the activity of the E under study
- the measured velocity is not increased by increasing the amount of
the coupling E present and that it is proportional to the amt of the
first E present at all [S] and under all conditions to be tested
iv Automated assay procedures
-automation of E assay can allow large numbers of samples to be
processed rapidly and efficiently
-many involve the determination of P formation after a fixed time
1) flow systems-uses multi-channel pumps to mix reactants and
determine P formation after a fixed time
2) immobilized enzymes-enzymes are attached to a matrix (bead or
surface) and the reactants added, rxn stopped and the extent of rxn
41
determined by reading the change in absorbance of a P for rxn by a
multi-plate reader
3) multi-cuvet holders in spectrometers-allow several rxns to be
followed by determining the absorbance in each sequentially and
repetitively; typically 4-6 samples
4) multi-plate readers-wavelength selection and T control
5) linearly increasing substrate gradient method-use a pumping
system to generate a linearly increasing gradient of [S] which is then
mixed with E and the extent of rxn is measured after a fixed time
-allows the curve for the dependence of velocity upon [S] to be
determined in a single experiment
(b)Choice of Assay Method
-often a variety of different assay methods available for an E
-choice may simply depend on convenience and the availability of the
appropriate materials and apparatus but some general considerations:
i -in the assay of E with high KM values towards their S, it may be necessary
to work at high [S] to ensure a sufficient period of linearity of the rxn
progress curve
-may be more accurate to follow the rxn by determining the extent of P
formation rather than the disappearance of S
ii -many assay types impose some limitations on the assay conditions due
to S instability under some conditions, which makes it difficult to
estimate the rates of the E-catalyzed rxn accurately
-in coupled assays one of the P is continuously removed and thus such
methods will not be suitable for studies on the inhibition of the E
activity by that P.
42
-assays that involve the determination of the formation of a specific P
may become less practical if large amts of that P are added for
inhibition studies
- often necessary to use more than one type of assay in a complete study
of the behavior of an E
-during purification of an E it is convenient to have a procedure that can
rapidly give an estimate of the activity making direct assays more useful
than discontinuous assays which involve time-consuming separations or
detection procedures
-many discontinuous assays are attractive because it is often possible to
perform a large number of incubations at the same time
-however, essential to ensure measurement of initial rates
(c) Practical Considerations
i Enzyme Purity and Nature-the state of purity of an E preparation affects
the ease with which it may be studied
-optical assays may be difficult to perform accurately with impure
preparations which contain large amounts of absorbing, and possibly
particulate, material
-presence of contaminating activities or S may make it difficult to
perform certain assays
-studies on the inhibition by P require that there are no contaminating E
present which might react with the added P
-membrane-bound E pose a particular problem since removal of the E
from its membrane environment can lead to changes in properties
ranging from complete loss of activity to changes in the kinetic
mechanism obeyed
43
ii Enzyme Stability-essential to assay an E preparation at regular intervals
under standard conditions to determine that it remains constant
-if an E is unstable and steadily loses activity with time, it may be
possible to correct all the values obtained to those that existed at the start
of the studies if a series of standard assays have been carried out at
different times to provided a calibration curve of activity against time
-it is a much better practice to try to find conditions under which the
stock E soln may be stored without appreciable loss of activity over the
time involved
iii Substrates-essential that pure S be used
-presence of contaminants will lead to incorrect estimates of the concn of
soln prepared by weight and it will also lead to errors in the
determination of kinetic constants if any of the impurities are inhibitory
-if a S is contaminated by an uncompetitive inhibitor, it will result in a
proportional decrease in both KM and Vmax as shown below:
44
-purity of S soln should be checked chromatographically or
enzymatically
-if the enzymatic test is used then a discrepancy between the Edetermined [S] and that calculated on a weight basis may indicate
whether purification of S is needed
-the stability of S is also important since many biochemical S are
unstable and their breakdown could lead to changes in the true [S]
-important to use freshly prepared soln of S and to assay their concn at
various intervals to check for any changes
-the small quantities of radioactively-labelled substrates used in many
radiochemical assays together with their high cost often leads to the
possibility that they may contain impurities
-to check purity of these radiolabelled substrates: compare the kinetic
behavior obtained from assays where the radioactive S is varied as a
fixed proportion of the unlabelled S (constant specific radioactivity)
with that observed when the amt of radioactivity is kept constant whist
the total [S] is varied (constant radioactivity)
iv Solvents and Buffers-all solvents and buffers used in E assays must be
free from contaminating material that could affect the activity of the E
-heavy metals are inhibitors of many E and great care is necessary to
exclude them
-some S are not readily soluble in water and are added to the E assay
in soln in an organic solvent
-check that the organic solvent doesn't affect the E activity
45
-also check that the addition of other components in the assay does
not change the pH of the mixture
v . Assay Mixtures-for complex assay mixtures it may be possible to
make up a bulk mixture containing all of them except the E to be
assayed
-useful to make such a "cocktail" if a number of assays are to be
performed under identical conditions such as during E purification
-caution is needed because such cocktails may give rise to blank rates
and such mixtures do not allow one to check for blank rates involving
the E in an incomplete rxn mixture
-different components may differ in their stabilities thus,
-only pre-mix those components that are stable under the storage
conditions in order to avoid the expense of having to discard it
before it has all been used
vi. Mixing-if there are no blank rates in any of the incomplete rxn mixtures,
the choice of whether to start the assay by the addition of the E or one
of the S is not important
-if the E is unstable in the assay mixture, then add the E last
-it might be preferable to pre-incubate the E in the incomplete assay
mixture and start by adding one of the S if there were hysteretic
effects resulting from dilution of the E
-often necessary to store E and S on ice because of instability
-may correct for dilution effects if varying the concn of S or E and
having to added various volumes unless the volumes are
insignificantly small compared with the final rxn mixture
46
-ensure that components of the rxn mixture are mixed properly
-do not over mix as some E are denatured by vigorous mixing
vii .
-enzyme stability increases with [protein]
 addition to assay tube dilutes [protein] and may destabilize enzyme.
-Selwyn devised test in 1965:
d[P]
dt
is proportional to [E]o
since [E]o is constant, then:
d[P]
= [E ]o f(P)
dt
where f(P) is a function relating [P] to the reaction rate.
- upon integration:
[E]o t = F(P)
where F(P) is another function related to [P].
In Selwyn's test of inactivation:
(1) assay enzyme activity of 2 or more [E]o (best to use complete
progress curve)
(2) plot [P] (or another measure of the reaction versus [E]ot:
47
(viii) choice of [S] for kinetic experiments
-v approaches Vmax at [S] >> Km
-[S] << KM then 1ST order
-must measure v both above and below Km value!
-best range: 0.5 Km to 5 Km for determination of Km
-if want to ensure measurement of Vmax then use 10 Km for [S]o
48