A Practical Introduction to Structure, Mechanism, and Data Analysis - Part 6 pot

7.1 INITIAL VELOCITY MEASUREMENTS 7.1.1 Direct, Indirect, and Coupled Assays To measure the velocity of a reaction, it is necessary to follow a signal thatreports product formation or su

Table 6.4 The IUPAC EC classification of enzymes into six general categories according to the reactions they catalyze

First EC

5 Isomerases Changes in arrangements of atoms in molecules

general types of interaction illustrated with the serine proteases also governsubstrate binding and chemical transformations in all the enzymes nature hasdevised

6.5 ENZYMATIC REACTION NOMENCLATURE

The hydrolytic activity illustrated by the serine proteases is but one of a widevariety of bond cleavage and bond formation reactions catalyzed by enzymes.From the earliest studies of these proteins, scientists have attempted tocategorize them by the nature of the reactions they provide Group names havebeen assigned to enzymes that share common reactivities For example,

‘‘protease’’ and ‘‘proteinase’’ are used to collectively refer to enzymes thathydrolyze peptide bonds Common names for particular enzymes are notalways universally used, however, and their application in individual cases canlead to confusion For example, there is a metalloproteinase known by thecommon names stromelysin, MMP-3(for matrix metalloproteinase number 3),transin, and proteoglycanase Some workers refer to this enzyme asstromelysin, others call it MMP-3, and still others call it transin or proteog-lycanase A newcomer to the metalloproteinase field could be quite frustrated

by this confusing nomenclature For this reason, the International Union ofPure and Applied Chemistry(IUPAC) formed the Enzyme Commission (EC)

to develop a systematic numerical nomenclature for enzymes While mostworkers still use common names for the enzymes they are working with,literature references should always include the IUPAC EC designations, whichhave been universally accepted, to let the reader know precisely what enzymesare being discussed The EC classifications are based on the reactions thatenzymes catalyze Six general categories have been defined, as summarized inTable 6.4 Within each of these broad categories, the enzymes are furtherdifferentiated by a second number that more specifically defines the substrates

on which they act For example, 11 types of hydrolase (category 3) can bedefined, as summarized in Table 6.5

Table 6.5 The IUPAC EC subclassifications of the hydrolases

First Two

3.1 Esters, —C(O)—O- - - R, or with S or P replacing C, or

—C(O)—S - - - R 3.2 Glycosyl, sugar—C—O - - - R, or with N or S replacing O

?Hydrolyzed bonds shown as dashed lines.

Table 6.6 Some examples of enzyme common names and their EC designations

The detailed rules for assigning an EC number to a newly discovered

enzyme were set forth in Volume 13 of the series Comprehensive Biochemistry

(Florkin and Stotz, 1973); an updated version of the nomenclature system waspublished nearly 20 years later(Webb, 1992) Most of the enzymes the reader

is likely to encounter or work with already have EC numbers One can oftenobtain the EC designation directly from the literature pertaining to the enzyme

of interest Another useful source for this information is the Medical SubjectHeadings Supplementary Chemical Records, published by the National Li-brary of Medicine(U.S Department of Health and Human Services, Bethesda,

MD) This volume lists the common names of chemicals and reagents ing enzymes) that are referred to in the medical literature covered by the Index

(includ-Medicus(a source book for literature searching of medically related subjects).Enzymes are listed here under their common names(with cross-references forenzymes having more than one common name) and the EC designation is

provided for each Most college and university libraries carry the Index

Medicus and will have this supplement available, or one can purchase the

supplement directly from the National Library of Medicine Yet anotherresource for determining the EC designation of an enzyme is the Enzyme DataBank, which can be accessed on the Internet.* This data bank provides ECnumbers, recommended names, alternative names, catalytic activities, informa-tion on cofactor utilization, and associated diseases for a very large collection

of enzymes A complete description of the data bank and its uses can be found

REFERENCES AND FURTHER READING

Bairoch, A.(1993) Nucl Acid Res 21, 3155.

Bender, M L., Bergeron, R J., and Komiyama, M.(1984) T he Bioorganic Chemistry of Enzymatic Catalysis, Wiley, New York.

Bruice, T C., and Lapinski, R.(1958) J Am Chem Soc 80, 2265.

Cannon, W R., and Benkovic, S J.(1998) J Biol Chem 273, 26257.

Carter, P., and Wells, J A.(1988) Nature, 332, 564.

Fersht, A R.(1974) Proc R Soc L ondon B, 187, 397.

Fersht, A.(1985) Enzyme Structure and Mechanism, Freeman, New York.

Fersht, A R., and Kirby, A J.(1967) J Am Chem Soc 89, 4853, 4857.

*http://192.239.77.6/Dan/proteins/ec-enzyme.html.

Fischer, E.(1894) Berichte, 27, 2985.

Florkin, M., and Stotz, E H.(1973) Comprehensive Biochemistry, Vol 13, Elsevier, New

York.

Goldsmith, J O., and Kuo, L C.(1993) J Biol Chem 268, 18481.

Hammes, G G.(1982) Enzyme Catalysis and Regulation, Academic Press, New York.

Hartley, B S., and Kilby, B A.(1954) Biochem J 56, 288.

Jencks, W P.(1969) Catalysis in Chemistry and Enzymology, McGraw-Hill, New York.

Jencks, W P.(1975) Adv Enzymol 43, 219.

Kirby, A J.(1980) Effective molarity for intramolecular reactions, in Advances in Physical Organic Chemistry, Vol 17, V Gold and D Bethel, Eds., Academic Press, New York,

pp 183 ff.

Koshland, D E.(1958) Proc Natl Acad Sci USA 44, 98.

Leatherbarrow, R J., Fersht, A R., and Winter, G.(1985) Proc Natl Acad Sci USA,

82, 7840.

Lerner, R A., Benkovic, S J., and Schultz, P G.(1991) Science, 252, 659.

Liao, D., Breddam, K., Sweet, R M., Bullock, T., and Remington, S J (1992)

Perona, J J., and Craik, C S.(1995) Protein Sci 4, 337.

Schechter, I., and Berger, A.(1967) Biochem Biophys Res Commun 27, 157.

Schowen, R L.(1978) in Transition States of Biochemical Processes (Grandous, R D.

and Schowen, R L., Eds.), Chapter 2, Plenum, New York.

Segal, I H.(1975) Enzyme Kinetics, Wiley, New York.

So, O.-Y., Scarafia, L E., Mak, A Y., Callan, O H., and Swinney, D C.(1998) J Biol Chem 273, 5801.

Storm, D R., and Koshland, D E.(1970) Proc Natl Acad Sci USA 66, 445.

Walsh, C.(1979) Enzyme Reaction Mechanisms, Freeman, New York.

Webb, E C.(1992) Enzyme Nomenclature, Academic Press, San Diego, CA.

Wison, C., and Agard, D A.(1991) Curr Opin Struct Biol 1, 617.

Wolfenden, R.(1999) Bioorg Med Chem 7, 647.

Yagisawa, S.(1995) Biochem J 308, 305.

EXPERIMENTAL MEASURES OF ENZYME ACTIVITY

Enzyme kinetics offers a wealth of information on the mechanisms of enzymecatalysis and on the interactions of enzymes with ligands, such as substratesand inhibitors Chapter 5 provided the basis for determining the kineticsubstrate concentrations during steady state catalysis The determination ofthese kinetic constants rests on the ability to measure accurately the initialvelocity of an enzymatic reaction under well-controlled conditions

In this chapter we describe some of the experimental methods used todetermine reaction velocities We shall see that numerous strategies have beendeveloped for following over time the loss of substrate or the appearance ofproducts that result from enzyme turnover The velocity of an enzymaticreaction is sensitive to many solution conditions, such as pH, temperature, andsolvent isotopic composition; these conditions must be well controlled ifmeaningful data are to be obtained Controlled changes in these solutionconditions and measurement of their effects on the reaction velocity canprovide useful information about the mechanism of catalysis as well Like allproteins, enzymes are sensitive to storage conditions and can be denaturedeasily by mishandling Therefore we also discuss methods for the properhandling of enzymes to ensure their maximum catalytic activity and stability

7.1 INITIAL VELOCITY MEASUREMENTS

7.1.1 Direct, Indirect, and Coupled Assays

To measure the velocity of a reaction, it is necessary to follow a signal thatreports product formation or substrate depletion over time The type of signalthat is followed varies from assay to assay but usually relies on some unique

188

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Figure 7.1 (A) Absorption of ferrocytochrome c as a function of time after addition of the enzyme cytochrome c oxidase As the cytochrome c iron is oxidized by the enzyme, the

absorption feature at 550 nm decreases (B) Plot of the absorption at 550 nm for the spectra in (A), as a function of time Note that in this early stage of the reaction (
10% of the substrate has been converted), the plot yields a linear relationship between absorption and time The reaction velocity can thus be determined from the slope of this linear function.

physicochemical property of the substrate or product, and/or the analyst’sability to separate the substrate from the product Generally, most enzymeassays rely on one or more of the following broad classes of detection andseparation methods to follow the course of the reaction:

These methods can be used in direct assay: the direct measurement of the

substrate or product concentration as a function of time For example, the

enzyme cytochrome c oxidase catalyzes the oxidation of the heme-containing protein cytochrome c In its reduced (ferrous iron) form, cytochrome c displays

a strong absorption band at 550 nm, which is significantly diminished inintensity when the heme iron is oxidized(ferric form) by the oxidase One canthus measure the change in light absorption at 550 nm for a solution of ferrous

cytochrome c as a function of time after addition of cytochrome c oxidase; the

diminution of absorption at 550 nm that is observed is a direct measure of theloss of substrate(ferrous cytochrome c) concentration (Figure 7.1).

In some cases the substrate and product of an enzymatic reaction do notprovide a distinct signal for convenient measurement of their concentrations.Often, however, product generation can be coupled to another, nonenzymatic,

reaction that does produce a convenient signal; such a strategy is referred to

as an indirect assay Dihydroorotate dehydrogenase(DHODase) provides anexample of the use of an indirect assays This enzyme catalyzes the conversion

of dihydroorotate to orotic acid in the presence of the exogenous cofactorubiquinone During enzyme turnover, electrons generated by the conversion ofdihydroorotate to orotic acid are transferred by the enzyme to a ubiquinonecofactor to form ubiquinol It is difficult to measure this reaction directly, butthe reduction of ubiquinone can be coupled to other nonenzymatic redoxreactions

Several redoxactive dyes are known to change color upon oxidation orreduction Among these, 2,6-dichlorophenolindophenol(DCIP) is a convenientdye with which to follow the DHODase reaction In its oxidized form DCIP

is bright blue, absorbing light strongly at 610 nm Upon reduction, however,this absorption band is completely lost DCIP is reduced stoichiometrically byubiquinol, which is formed during DHODase turnover Hence, it is possible tomeasure enzymatic turnover by having an excess of DCIP present in a solution

of substrate (dihydroorotate) and cofactor (ubiquinone), then following theloss of 610 nm absorption with time after addition of enzyme to initiate thereaction

A third way of following the course of an enzyme-catalyzed reaction is

referred to as the coupled assays method Here the enzymatic reaction of

interest is paired with a second enzymatic reaction, which can be convenientlymeasured In a typical coupled assay, the product of the enzyme reaction ofinterest is the substrate for the enzyme reaction to which it is coupled forconvenient measurement An example of this strategy is the measurement ofactivity for hexokinase, the enzyme that catalyzes the formation of glucose6-phosphate and ADP from glucose and ATP None of these products orsubstrates provide a particularly convenient means of measuring enzymaticactivity However, the product glucose 6-phosphate is the substrate for theenzyme glucose 6-phosphate dehydrogenase, which, in the presence ofNADP>, converts this molecule to 6-phosphogluconolactone In the course of

the second enzymatic reaction, NADP> is reduced to NADPH, and this

cofactor reduction can be monitored easily by light absorption at 340 nm.This example can be generalized to the following scheme:

A T 99; B T‚ 99; C where A is the substrate for the reaction of interest, v is the velocity for this

reaction, B is the product of the reaction of interest and also the substrate for

the coupling reaction, v is the velocity for the coupling reaction, and C is the

product of the coupling reaction being measured Although we are measuring

C in this scheme, it is the steady state velocity v that we wish to study To accomplish this we must achieve a situation in which v is rate limiting (i.e.,

vv) and B has reached a steady state concentration Under these

condi-tions B is converted to C almost instantaneously, and the rate of C production

Figure 7.2 Typical data for a coupled enzyme reaction illustrating the lag phase that precedes the steady state phase of the time course.

is a reflection of v The measured rate will be less than the steady state rate

v, however, until [B] builds up to its steady state level Hence, in any coupled

assay there will be a lag phase prior to steady state production of C (Figure7.2), which can interfere with the measurement of the initial velocity Thus tomeasure the true initial velocity of the reaction of interest, conditions must besought to minimize the lag phase that precedes steady state product formation,and care must be taken to ensure that the velocity is measured during thesteady state phase

The velocity of the coupled reaction, v, follows simple Michaelis—Menten

t %:

Table 7.1 Values of :99% % [B] ss , useful in

designing coupled assays

however, can be controlled by the researcher by adjusting the concentration

[E] Thus by varying [E] one can adjust V, hence the ratio v/V, hence the

lag time for the coupled reaction

Let us say that we can measure the true steady state velocity v after [B]

has reached 99% of [B] How much time is required to achieve this level of

[B]? We can calculate this from Equation 7.3 if we know the values of v and

values of

for [B]: 99% [B] This percentage is usually considered to be optimal for

measuring v in a coupled assay In certain cases this requirement can be

relaxed For example, [B]: 90% [B] would be adequate for use of a coupledassay to screen column fractions for the presence of the enzyme of interest Inthis situation we are not attempting to define kinetic parameters, but merelywish a relative measure of primary enzyme concentration among differentsamples The reader should consult the original paper by Storer and Cornish-Bowden(1974) for additional tables of

Let us work through an example to illustrate how the values in Table 7.1might be used to design a coupled assay Suppose that we adjust the

concentration of our enzyme of interest so that its steady state velocity v is

say that we wish to measure velocity over a 5-minute time period We wish thelag phase to be a small portion of our overall measurement time, say
0.5

minute What value of V would we need to reach these assay conditions? From

Equation 7.3 we have:

0.5 0.2

Rearranging this we find that

require that v/V0.1 Since we know that v is 0.1 mM/min, V must be

coupling enzyme, we could then calculate the concentration of [E] required

to reach the desired value of V.Easterby (1973) and Cleland (1979) have presented a slightly different

method for determining the duration of the lag phase for a coupled reaction.From their treatments we find that as long as the coupling enzyme(s) operateunder first-order conditions

(t) is dependent on the initial velocity v and the lag time () as follows:

To illustrate the use of Equation 7.6, let us consider the following example

100 s\ Let us say that we wish to set up our assay so as to reach 99% of [B]within the first 20 seconds of the reaction time course To reach 0.99 [B]requires 4.6 (Easterby, 1973) Thus :20 s/4.6:4.3 seconds From rearrange-

ment of Equation 7.6 we can calculate that V needed to achieve this desired

lagtime would be 2.30M/s Dividing this by k (100 s\), we find that the

concentration of coupling enzyme required would be 0.023M or 23 nM

If more than one enzyme is used in the coupling steps, the overall lag timecan be calculated as

coupling enzymes, A and B to follow the reaction of the primary enzyme ofinterest, the overall lag time would be given by:

 :K

V;K

Because coupled reactions entail multiple enzymes, these assays present anumber of potential problems that are not encountered with direct or indirectassays For example, to obtain meaningful data on the enzyme of interest incoupled assays, it is imperative that the reaction of interest remain rate limitingunder all reaction conditions Otherwise, any velocity changes that accompanychanges in reaction conditions may not reflect accurately effects on the target

enzyme For example, to use a coupled reaction scheme to determine k  and

rate limiting at the highest values of [A](i.e., substrate for the primary enzyme

of interest)

Use of a coupled assay to study inhibition of the primary enzyme might alsoseem problematic The presence of multiple enzymes could introduce ambigui-ties in interpreting the results of such experiments: for example, which en-zyme(s) are really being inhibited? Easterby (1973) points out, however, thatusing coupled assays to screen for inhibitors makes it relatively easy todistinguish between inhibitors of the primary enzyme and the coupling en-zyme(s) Inhibitors of the primary enzyme would have the effect of diminishing

the steady state velocity v (Figure 7.3A), while inhibitors of the coupling

enzyme(s) would extend the lag phase without affecting v (Figure 7.3B) In

practice these distinctions are clear-cut only when one measures productformation over a range of time points covering significant portions of both thelag phase and the steady state phase of the progress curves (Figure 7.3).Rudolph et al.(1979), Cleland (1979), and Tipton (1992) provide more detaileddiscussions of coupled enzyme assays

7.1.2 Analysis of Progress Curves: Measuring True

Steady State Velocity

In Chapter 5 we introduced the progress curves for substrate loss and productformation during enzyme catalysis(Figures 5.1 and 5.2) We showed that bothsubstrate loss and product formation follow pseudo-first-order kinetics Thefull progress curve of an enzymatic reaction is rich in kinetic information.Throughout the progress curve, the velocity is changing as the substrateconcentration available to the enzyme continues to diminish Hence, through-out the progress curve the instantaneous velocity approximates the initialvelocity for the instantaneous substrate concentration at a particular timepoint Modern computer graphing programs often provide a means of comput-

ing the derivative of the data points from a plot of y versus x, hence one could

determine the instantaneous velocity(v :d[P]/dt:9d[S]/dt) from

derivitiza-tion of the enzyme progress curve At each time point for which the taneous velocity is determined, the instantaneous value of [S] can bedetermined, and so the instantaneous velocity can be replotted as a function of

instan-[S] This replot is hyperbolic and can be fit to the Michaelis—Menten equation

and its limitations have been described by several authors (Cornish-Bowden,

Figure 7.3 Effects of inhibitors on a coupled enzyme reaction: circles, the data points for the enzyme in the absence of inhibitor; squares, the data points when inhibitor is present as some fixed concentration (A) Effect of an inhibitor of the primary enzyme of interest: the lag phase

is unaffected, but the steady state rate (slope) is diminished (B) Effect of an inhibitor of the coupling enzyme: the lag phase is extended, but the steady state rate is unaffected.

1972; Duggleby and Morrison, 1977; Waley, 1982; Kellershohn and Laurent,1985; Duggleby, 1985, 1994) The use of full progress curve analysis has notbecome popular because derivatization of the progress curves was not straight-forward until the use of computers became widespread, and because of some

of the associated problems with this method as described in the referenced literature

above-As we described in Chapter 5, early in the progress curve, the formation ofproduct and the loss of substrate track linearly with time, so that the velocity

can be determined from the slope of a linear fit of these early time point data.For the remainder of this chapter our discussions are restricted to measure-ment at these early times, so that we are evaluating the initial velocity.Nevertheless, it is useful to determine the full progress curve for the enzymaticreaction at least at a few combinations of enzyme and substrate concentrations,

to ensure that the system is well behaved, that the reaction goes to completion(i.e., [P] :[S]), and that measurements truly are being made during thelinear steady state phase of the reaction

The progress curve for a well-behaved enzymatic reaction should appear asthat seen in Figure 5.1 There should be a reasonable time period, early in thereaction, over which substrate loss and product formation are linear with time

As the reaction progresses, one should see curvature and an eventual plateau

as the substrate supply is exhausted

In some situations a lag phase may appear prior to the linear initial velocityphase of the progress curve This occurs in coupled enzyme assays, as discussedabove Lag phases can be observed for a number of other reasons as well Ifthe enzyme is stored with a reversible inhibitor present, some time may berequired for complete dissociation of the inhibitor after dilution into the assaymixture; hence a lag phase will be observed prior to the steady state (seeChapter 10) Likewise, if the enzyme is stored at a concentration that leads tooligomerization, but only the monomeric enzyme form is active, a lag phasewill be observed in the progress curve that reflects the rate of dissociation ofthe oligomers to monomeric enzyme Lag phases are also observed whenreagent temperatures are not well controlled, as will be discussed in Section7.4.3

The linear steady state phase of the reaction may also be preceded by aninitial burst of rapid reaction, as we encountered in Chapter 6 for chymo-

trypsin-catalyzed hydrolysis of p-nitrophenylethyl carbonate (Figure 6.5) Burst

phase kinetics are observed with some enzymes for several reasons First, severe

product inhibition may occur, so that after a few turnovers, the concentration

of product formed by the reaction is high enough to form a ternary ESPcomplex, which undergoes catalysis at a lower rate than the binary EScomplex Hence, at very early times the rate of product formation corresponds

to the uninhibited velocity of the enzymatic reaction, but after a short time thevelocity changes to that reflective of the ESP complex A second cause of burstkinetics is a time-dependent conformational change of the enzyme structurecaused by substrate binding Here the enzyme is present in a highly active formbut converts to a less active conformation upon formation of the ES complex.Third, the overall reaction rate may be limited by a slow release of the productfrom the EP complex The final, and perhaps the most common, cause for burstkinetics is rapid reaction of the enzyme with substrate to form a covalentintermediate, which undergoes slower steady state decomposition to products.Enzymes like the serine proteases, for which the reaction mechanism goesthrough formation of a covalent intermediate, often show burst kineticsbecause the overall reaction is rate-limited by decomposition of the intermedi-

ate species When this occurs, the intermediate builds up rapidly (i.e., beforethe steady state velocity is realized) to a concentration equal to that of activeenzyme molecules in the sample For enzymes that demonstrate burst phasekinetics due to covalent intermediate formation, the concentration of activeenyzme in a sample can be determined accurately from the intercept value of

a linear fit of the data in the steady state portion of the progress curve Forexample, referring back to Figure 6.5, we see that the reaction was performed

at nominal chymotrypsin concentrations of 8, 16, 24, and 32M Linear fitting

of the steady state data for these reactions gave y-intercept values of 5, 10, 15,

and 20M, respectively Thus the ratio of the y-intercept value to the nominal

concentration of enzyme added is a constant of 0.63, suggesting that about63% of the enzyme molecules in these samples are in a form that supports

catalysis This method, referred to as active site titration, can be a powerful

means of determining accurately the active enzyme concentration

There are several points to consider, however, in the use of the active sitetitration method First, one must be sure that the burst phase observed is due

to covalent intermediate formation (see Chapter 6 and Fersht, 1985, formethods to establish that the enzyme reaction goes through a covalentintermediate) Second, the y intercepts must be appreciably greater than zero

so that they can be measured accurately This means that the concentration ofenzyme required for these assays is much higher than is commonly used formost enzymatic assays Colorimetric or fluorometric assays typically requiremicromolar amounts of enzyme to observe a significant burst phase Theamount of enzyme needed can be reduced by use of radiometric detectionmethods, but even here one typically requires high nanomolar or low microm-olar enzyme concentrations Finally, the amplitude of the burst does not give

a precise measure of the active enzyme concentration if the rates for the burstand the steady state phases are not significantly different A minimalist schemefor an enzyme that goes through a covalent intermediate is as follows:

Fersht (1985) has shown that the burst amplitude (i.e., the y-intercept value

from linear fitting of the steady state data: Figure 7.4) can be described asfollows:

 : [E]
k

k; k

(7.9)

where is the burst amplitude From Equation 7.9 we see that if kk, the

rate constant ratio reduces to 1, and so  : [E] If however, k is not insignificant in comparison to k, we will underestimate the value of [E] from

measurement of Hence, the active enzyme concentrations determined from

Figure 7.4 Examples of a progress curve for an enzyme demonstrating burst phase kinetics The dashed line represents the linear fit of the data in the steady state phase of the reaction;

the y intercept from this fitting give an estimate of, as defined here and in the text The solid curve represents the best fit of the entire time course to an equation for a two-step kinetic

process [P] : [1 9 exp(9k b t)] ; v ss t.

active site titration in some cases represent a lower limit on the true activeenzyme concentration This complication can be avoided by use of substratesthat form irreversible covalent adducts with the enzyme (i.e., substrates for

which k:0) Application of these ‘‘suicide substrates’’ for active site titration

of enzymes has been discussed by Schonbaum et al.(1961) and, more recently,

by Silverman(1988)

It is also important to ensure that the reaction goes to completion — that

is, the plateau must be reached when [P]: [S], the starting concentration ofsubstrate In certain situations, the progress curve plateaus well before fullsubstrate utilization The enzyme, the substrate, or both, may be unstableunder the conditions of the assay, leading to a premature termination ofreaction(see Section 7.6 for a discussion of enzyme stability and inactivation).The presence of an enzyme inactivator, or slow binding inhibitor, can alsocause the reaction to curve over or stop prior to full substrate utilization(seeChapter 10) In some cases, the product formed by the enzymatic reaction can

itself bind to the enzyme in inhibitory fashion When such product inhibition is

significant, the buildup of product during the progress curve can lead topremature termination of the reaction Finally, limitations on the detectionmethod used in an assay may restrict the concentration range over which it ispossible to measure product formation Specific examples are described later

in this chapter In summary, before one proceeds to more detailed analysisusing initial velocity measurements, it is important to establish that the fullprogress curve of the enzymatic reaction is well behaved, or at least that thecause of deviation from the expected behavior is understood

As we have stated, in the early portion of the progress curve, substrate andproduct concentrations track linearly with time, and it is this portion of theprogress curve that we shall use to determine the initial velocity Of course, theduration of this linear phase must be determined empirically, and it can varywith different experimental conditions It is thus critical to verify that the timeinterval over which the reaction velocity is to be determined displays goodsignal linearity with time under all the experimental conditions that will beused Changes in enzyme or substrate concentration, temperature, pH, andother solution conditions can change the duration of the linear phase signifi-cantly One cannot assume that because a reaction is linear for some timeperiod under one set of conditions, the same time period can be used under adifferent set of conditions.

7.1.3 Continuous Versus End Point Assays

Once an appropriate linear time period has been established, the researcher hastwo options for obtaining a velocity measurement First, the signal might bemonitored at discrete intervals over the entire linear time period, or some

convenient portion thereof This strategy, referred to as a continuous assay,

provides the safest means of accurately determining reaction velocity from theslope of a plot of signal versus time

It is not always convenient to assay samples continuously, however, ally when one is using separation techniques, such as high performance liquidchromatography(HPLC) or electrophoresis In such cases a second strategy,

especi-called end point or discontinuous assay, is often employed Having established

a linear time period for an assay, one measures the signal at a single specifictime point within the linear time period(most preferably, a time point near themiddle of the linear phase) The reaction velocity is then determined from thedifference in signal at that time point and at the initiation of the reaction,divided by the time:

v:I

t:IR 9I

where the intensity of the signal being measured at time t and time zero is given

by IR and I, respectively, and t   is the time interval between initiation of

the reaction and measurement of the signal

In many instances it is much easier to take a single reading than to makemultiple measurements during a reaction Inherent in the use of end pointreadings, however, is the danger of assuming that the signal will track linearlywith time over the period chosen, under the conditions of the measurement.Changes in temperature, pH, substrate, and enzyme concentrations, as well asthe presence of certain types of inhibitor (see Chapter 10) can dramaticallychange the linearity of the signal over a fixed time window Hence, end point

readings can be misleading Whenever feasible, then, one should use ous assays to monitor substrate loss or product formation When this isimpractical, end point readings can be used, but cautiously, with carefulcontrols.

continu-7.1.4 Initiating, Mixing, and Stopping Reactions

In a typical enzyme assay, all but one of the components of the reactionmixture are added to the reaction vessel, and the reaction is started at timezero by adding the missing component, which can either be the enzyme or thesubstrate The choice of the initiating component will depend on the details ofthe assay format and the stability of the enzyme sample to the conditions ofthe assay In either case, the other components should be mixed well andequilibrated in terms of pH, temperature, and ionic strength The reactionshould then be initiated by addition of a small volume of a concentrated stocksolution of the missing component A small volume of the initiating component

is used to ensure that its addition does not significantly perturb the conditions(temperature, pH, etc.) of the overall reaction volume Unless the reactionmixture and initiating solutions are well matched in terms of buffer content,

pH, temperature, and other factors, the initiating solution should not be more

than about 5—10% of the total volume of the reaction mixture.

Samples should be mixed rapidly after addition of the initiating solution, butvigorous shaking or vortexmixing is denaturing to enzymes and should beavoided Mixing must, however, be complete; otherwise there will be artifactualdeviations from linear initial velocities as mixing continues during the measure-ments One way to rapidly achieve gentle, but complete, mixing is to add theinitiating solution to the side of the reaction vessel as a ‘‘hanging drop’’ abovethe remainder of the reaction mixture, as illustrated in Figure 7.5 With smallvolumes(say, 50 L), the surface tension will hold the drop in place abovethe reaction mixture At time zero the reaction is initiated by gently invertingthe closed vessel two or three times to mixthe solutions Figure 7.5 illustratesthis technique for a reaction taking place in a microcentrifuge tube It is alsoconvenient to place the initiating solution in the tube cap, which then can beclosed, permitting the solutions to be mixed by inversion as illustrated inFigure 7.5 For optical spectroscopic assays(see Section 7.2.1), the reaction can

be initiated directly in the spectroscopic cuvette by the same technique, using

a piece of Parafilm and one’s thumb to seal the top of the cuvette during theinversions

Regardless of how the reacting and initiating solutions are mixed, the mixingmust be achieved in a short period of time relative to the time interval betweenmeasurements of the reaction’s progress With a little practice one can use theinversion method just described to achieve this mixing in 10 seconds or less.This is usually fast enough for assays in which measurements are to be made

in intervals of 1 minute or longer time A number of parameters, such astemperature and enzyme concentration (see Section 7.4), can be adjusted to

Figure 7.5 A common strategy for initiating an enzymatic reaction in a microcentrifuge tube.

ensure that the reaction velocity is slow enough to allow mixing of thesolutions and making of measurements on a convenient time scale In somerare cases, the enzymatic velocity is so rapid that it cannot be measuredconveniently in this way Then one must resort to specialized rapid mixing anddetection methods, such as stopped-flow techniques (Roughton and Chance,1963; Kyte, 1995); these methods are also used to measure pre—steady stateenzyme kinetics, as described in Chapter 5(Kyte, 1995)

For assays in which samples are removed from the reaction vessel at specifictimes for measurement, one can start the timer at the point of mixing and makemeasurements at known time intervals after the initiation point In manyspectroscopic assays, however, one measures changes in absorption or fluor-escence with time For most modern spectrometers, the detection is initiated

by pressing a button on an instrument panel or depressing a key on a computerkeyboard Thus to start an assay one must mixthe solutions, place the cuvette,

or optical cell, in the holder of the spectrometer, and start the detection bypressing the appropriate button The delay between mixing and actuallystarting a measurement can be as much as 20 seconds Thus the time pointrecorded by the spectrometer as zero will not be the true zero point(i.e., mixingpoint) of the reaction Again, with practice one can minimize this delay time,and in most cases the assay can be set up to render this error insignificant

As we shall see, there should always be two control measurements: one inwhich all the reaction components except the enzyme are present, and aseparate one in which everything but the substrate is present.(In these controls,buffer is added to make up for the volumes that would have been contributed

by the enzyme or substrate solutions.) With these two control measurementsone can calculate what the absorption or fluorscence should be for the reactionmixture at the true time zero If the first spectrometer reading (i.e., the timepoint recorded as time zero by the spectrometer) is significantly different fromthis calculated value, it is necessary to correct the time points recorded by thespectrometer for the time delay between the start of mixing and the initiation

of the detection device A laboratory timer or stopwatch can be used todetermine the time gap

Many nonspectroscopic assays require measurement times that are long incomparison to the rate of the enzymatic reaction being monitored Suppose, forexample, that we wish to measure the amount of product formed every 5minutes over the course of a 30-minute reaction and assay for product by an

HPLC method The HPLC measurement itself might take 20—30 minutes to

complete If the enzymatic reaction is continuing during the measurement time,the amount of product produced during specific time intervals cannot bedetermined accurately In such cases it is necessary to quench or stop thereaction at a specific time, to prevent further enzymatic production of product

or utilization of substrate

Methods for stopping enzymatic reactions usually involve denaturation ofthe enzyme by some means, or rapid freezing of the reaction solution

Examples of quenching methods include immersion in a dry ice—ethanol slurry

to rapidly freeze the solution, and denaturation of the enzyme by addition ofstrong acid or base, addition of electrophoretic sample buffer, or immersion in

a boiling water bath In addition to these methods, reagents can be added thatinterfere in a specific way with a particular enzyme For example, the activity

of many metalloenzymes can be quenched by adding an excess of a metalchelating agent, such as ethylenediaminetetraacetic acid(EDTA)

Three points must be considered in choosing a quenching method for anenzymatic reaction First, the technique used to quench the reaction must notinterfere with the subsequent detection of product or substrate Second, it must

be established experimentally that the quenching technique chosen does indeedcompletely stop the reaction Finally, the volume change that occurs uponaddition of the quenching reagent to the reaction mixture must be accountedfor Similarly, measurement of product or substrate concentration must becorrected to compensate for the dilution effects of quencher addition

7.1.5 The Importance of Running Controls

Regardless of the detection method used to follow an enzymatic reaction, it isalways critical to perform control measurements in which enzyme and sub-strate are separately left out of the reaction mixture These control experimentspermit the analyst to correct the experimental data for any time-dependentchanges in signal that might occur independent of the action of the enzymeunder study, and to correct for any static signal due to components in thereaction mixture To illustrate these points, let us follow a hypothetical

Table 7.2 Volumes of stock solutions to prepare experimental and control samples for a hypothetical enzyme-catalyzed reaction

wave-Figure 7.6A illustrates the time courses we might see for the hypotheticalsolutions from Table 7.2 For our experimental run, the true absorptionreadings are displaced by about 0.1 unit, as a result of the absorption of theenzyme itself (‘‘No substrate’’ trace in Figure 7.6A) To correct for this, wesubtract this constant value from all our experimental data points If we were

to now determine the slope of our corrected experimental trace, however, wewould be overestimating the velocity of our reaction because such a slopewould reflect both the catalytic conversion of substrate to product and thespontaneous absorption change seen in our ‘‘No enzyme’’ control trace Tocorrect for this, we subtract these control data points from the experimentalpoints at each measurement time to yield the difference plot in Figure 7.6B.Measuring the slope of this difference plot yields the true reaction velocity

As illustrated in Figure 7.6A, the correction for the spontaneous absorptionchange may appear at first glance to be trivial However, the velocity measuredfor the uncorrected data differs from the corrected velocity by more than 10%

in this example In some cases the background signal change is even moresubstantial Hence, the types of control measurement discussed here areessential for obtaining meaningful velocity measurements for the catalyzedreaction under study