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Chapter 7 Measurement of Enzyme Activity
C H A P T E R
S E V E N
Measurement of Enzyme Activity T. K. Harris and M. M. Keshwani Contents 58 58 58 62 64 65 67 69 71 71 71
1. Introduction 2. Principles of Catalytic Activity 2.1. Chemical kinetics 2.2. Basic enzyme kinetics 3. Measurement of Enzyme Activity 3.1. Continuous assays 3.2. Discontinuous assays 4. Formulation of Reaction Assay Mixtures 5. Discussion Acknowledgments References
Abstract To study and understand the nature of living cells, scientists have continually employed traditional biochemical techniques aimed to fractionate and characterize a designated network of macromolecular components required to carry out a particular cellular function. At the most rudimentary level, cellular functions ultimately entail rapid chemical transformations that otherwise would not occur in the physiological environment of the cell. The term enzyme is used to singularly designate a macromolecular gene product that specifically and greatly enhances the rate of a chemical transformation. Purification and characterization of individual and collective groups of enzymes has been and will remain essential toward advancement of the molecular biological sciences; and developing and utilizing enzyme reaction assays is central to this mission. First, basic kinetic principles are described for understanding chemical reaction rates and the catalytic effects of enzymes on such rates. Then, a number of methods are described for measuring enzyme-catalyzed reaction rates, which mainly differ with regard to techniques used to detect and quantify concentration changes of given reactants or products. Finally, short commentary is given toward formulation of reaction mixtures used to measure enzyme activity. Whereas a comprehensive treatment of enzymatic reaction assays is not within Department of Biochemistry and Molecular Biology, Miller School of Medicine, University of Miami, Miami, Florida, USA Methods in Enzymology, Volume 463 ISSN 0076-6879, DOI: 10.1016/S0076-6879(09)63007-X
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2009 Elsevier Inc. All rights reserved.
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T. K. Harris and M. M. Keshwani
the scope of this chapter, the very core principles that are presented should enable new researchers to better understand the logic and utility of any given enzymatic assay that becomes of interest.
1. Introduction One primary goal of biological sciences is to deduce the molecular bases of all chemical processes that take place in living organisms. It is well established that the vast majority of biochemical reactions are governed by protein gene products called enzymes. In this sense, enzymes behave as finely tuned chemical catalysts, which greatly enhance reaction rates with both temporal and spatial resolution. Thus, elucidation of biochemical pathways involving biosynthesis, modification, and degradation of macromolecular, metabolic, and signaling molecules remains ultimately tied to experimental methods for purification, reconstitution, and direct demonstration of enzymes to catalyze specific chemical reactions. The focus of this chapter is to explain the most fundamental principles that must be considered in developing effective methods for measuring the progress of enzymecatalyzed reactions. First, kinetic formulation is described for chemical and enzymatic reaction processes. Next, instructive commentary is given on various experimental methods that are commonly used for measuring enzyme activity; and consideration is given toward numerous procedures and conditions that must be optimized.
2. Principles of Catalytic Activity 2.1. Chemical kinetics Chemical kinetics involves the experimental study of reaction rates in order to infer about the kinetic mechanisms for chemical conversion of reactants (R) into products (P) (Fig. 7.1) (House, 2007; Laidler, 1987). For any given chemical reaction, (i) the mechanism refers to the sequence of elementary steps by which overall chemical change occurs and (ii) an elementary step refers to the passing of a reactant or reaction complex through a singletransition state to a chemical form with a defined and detectable lifetime. If chemical conversion of reactants (R) to products (P) involves more than one elementary step, then the chemical structures that exist after each elementary step preceding final product formation are defined as reaction intermediates (I). Figure 7.1 also shows that each elementary step leading to product is characterized by a forward microscopic rate constant (e.g., kþ 1 and kþ 2). If a particular elementary step is reversible, then a reverse rate
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Measurement of Enzyme Activity
A
R1 + R2
k+1 k−1
I
k+2
P1 + P2
E
Reaction coordinate B
E+S
k+1 k−1
ES
k+2
E +P
Figure 7.1 (A) Basic kinetic mechanism for chemical conversion of two molecular reactants (R1 and R2) into two molecular products (P1 and P2). In this mechanism, an intermediate complex (I) is reversibly formed from reactants (kþ 1 and k 1) but is irreversibly converted to products (kþ 2). (B) Basic kinetic mechanism for enzyme (E)-catalyzed conversion of a molecular substrate (S) into a molecular product (P). In this mechanism, an ES intermediate complex is reversibly formed (kþ 1 and k 1) but is irreversibly converted to product (kþ 2). In this case, the enzyme (E) is regenerated and can undergo subsequent catalytic cycles. For both mechanisms, a free-energy diagram depicts typical energy changes that occur along the reaction coordinate leading to intermediates and products. Ground-state energies for reactants, intermediates, and products are depicted as valleys, whereas transition-state energies for chemical changes are depicted by peaks.
constant is designated (e.g., k 1). The principle of microscopic reversibility states that only one transition state exists for reversible chemical conversion between the species associated with one elementary step (i.e., the transition state for the forward reaction is the same as for the reverse reaction). For any given unidirectional conversion within an elementary step, a rate law is used to describe the mathematical relationship between the reaction rate or velocity and the concentration of each given reactant. For a given chemical reaction step occurring in solution, the instantaneous reaction velocity (v) is defined as the derivative of chemical concentration with respect to time (t); and it is expressed either as (i) a decreasing concentration of a given reactant (v ¼ d[R]/dt) or (ii) an increasing concentration of a given product (v ¼ þ d[P]/dt). The standard international units of reaction velocity are M s 1. The rate law for a single-unidirectional step shows the instantaneous velocity to depend on variable reactant concentration values according to parameter values of (i) a proportionality constant (k) and (ii) the exponent of each concentration term (Table 7.1). The proportionality constant is defined as the forward microscopic rate constant for a given chemical conversion, and its dimensions depend on the overall molecularity or order of the reaction. For the rate laws defined in Table 7.1, the molecularity with respect to a given reactant is given by the exponent in the given concentration term and represents the stoichiometric quantity of reactant involved in the reaction step. The kinetic order of a simple chemical reaction
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T. K. Harris and M. M. Keshwani
Table 7.1 Relationship between rate law, order, and the rate constant, k Rate lawa
Order
Units of k
v¼k v ¼ k[R1]
Zero First order with respect to R1 First order overall Second order with respect to R1 Second order overall First order with respect to R1 First order with respect to R2 Second order overall
M s 1 s 1
v ¼ k[R1]2 v ¼ k[R1][R2]
a
M 1 s 1 s 1
For each rate law, the units of the reaction velocity (v) will always be M s 1. M represents moles per liter (mol l 1).
is usually the same as molecularity, but it is important to emphasize that order refers to the exponent value that relates the experimentally measured reaction rate’s dependence on reactant concentration. The overall molecularity or order of a reaction step is the sum of all the concentration term exponents. In order to more fully understand the dependence of instantaneous velocity on reactant concentration, we will first consider a simple first-order reaction in which one molecule of reactant R forms one molecule of product P (R ! P) according to the rate law given by Eq. (7.1). v¼
d½R d½P ¼ ¼ k½R dt dt
ð7:1Þ
In Eq. (7.1), the instantaneous reaction velocity (v ¼ d[R]/dt ¼ þ d [P]/dt) is directly proportional to the concentration of R raised to the first power. If the velocity for either loss of R or gain of P was measured immediately after initiation of the reaction (Fig. 7.2A), then a secondary plot of this initial velocity versus different initial or starting concentrations of [R] would be linear with a slope equal to the first-order rate constant, k (s 1) (Fig. 7.2B). For such analyses, great care must be taken to ensure measurement of initial velocities. With increasing times past initiation of the reaction, the measured velocity decreases proportionately with depletion of [R]. Thus, it is common and good practice to measure initial velocities for either loss of reactant or gain of product at times corresponding to 5% of product conversion. To better illustrate the decreasing reaction velocity with time, the differential rate Eq. (7.1) can be integrated with respect to [R] to yield the first-order or single-exponential decay function given by Eq. (7.2). The limits of integration correspond to the initial concentration of reactant
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Measurement of Enzyme Activity
A
Slopes = v = d [P]/dt, M s−1
Slope = k = dv/d [R]0, s−1
B
v (d[P]/dt)
3[R]0
[P]
2[R]0 [R]0
Time
[R]0
Figure 7.2 Determination of a first-order rate constant from measuring the initial velocity of product formation at differing concentrations of a reactant. (A) Initial velocities of product formation (slopes ¼ v ¼ d[P]/dt, M s 1) are measured for different starting concentrations of reactant (i.e., [R]0, 2[R]0, or 3[R]0). (B) The measured initial velocities are then plotted versus the different starting concentrations of reactant. The slope of this dependence yields the first-order rate constant for conversion of reactant into product (slope ¼ k ¼ dv/d[R]0, s 1).
ð ½R
d½R ¼ k ½R0 ½R
½R ln ½R0
ðt dt 0
¼ kt
½R ¼ ½R0 ekt
ð7:2Þ
when the reaction is initiated (i.e., [R] ¼ [R]0 at t ¼ 0) and the concentration of reactant at a given time after the reaction has started. Figure 7.3A shows the relationship between measuring instantaneous velocity (i.e., v ¼ d[R]/dt, where Dt is very small) according to Eq. (7.1) and measuring overall time progress (i.e., either [R] or [P] versus t, where Dt is very large) according to Eq. (7.2) for the simple first-order conversion of reactant to product. The derivative in Eq. (7.1) is simply the slope of the tangent for the concentration curve at a specific time. If no product is present at t ¼ 0, the sum of reactant and product concentrations at any time must be equal to [R]0 (i.e., [R] þ [P] ¼ [R]0). Using this relationship, ([R]0 [P]) may be substituted for [R] in Eq. (7.2) and rearranged to yield the first-order rate Eq. (7.3) that describes the corresponding increasing product concentration with time (Fig. 7.3B). ½P ¼ ½R0 ð1 ekt Þ
ð7:3Þ
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B
[P]
[R]
A
Time
Time
Figure 7.3 (A) Time progress for decreasing reactant concentration [R] in a first-order reaction. It can be seen that the instantaneous velocity at any given reactant concentration (lines) decreases with decreasing reactant concentration [R]. (B) Corresponding time progress curve for increasing product concentration [P] in the same first-order reaction.
2.2. Basic enzyme kinetics Measurement of enzyme activity is actually a measurement of catalytic activity (Cook and Cleland, 2007; Cornish-Bowden, 1995; Segel, 1975). An enzyme or catalyst participates in chemical reactions by increasing the reaction velocity without itself appearing in the end products. In this case, an enzyme (E) first combines with or binds one or more chemical reactants or substrates (S) (Fig. 7.1B, kþ 1 and k 1). The resulting enzyme–substrate (ES) complex is an intermediate species from which catalytic conversion of substrate to product (P) takes place, ultimately releasing the intact enzyme so that it may catalyze a subsequent reaction (Fig. 7.1B, kþ 2). Since the kþ 2 proportionality constant typically comprises all processes or chemical steps involving conversion of the ES complex to release of products, it is a ‘‘pseudo’’ first-order rate constant (s 1). It is more commonly referred to as the turnover number, kcat, which is the maximum number of substrate molecules converted to product per active site per unit time. Thus, the instantaneous enzyme-catalyzed reaction velocity (v ¼ þ d[P]/dt) is directly proportional to the concentration of the ES complex according to kcat in Eq. (7.4). v¼
d½P ¼ kcat ½ES dt
ð7:4Þ
Equation (7.4) is rendered impractical to the experimentalist, because the differential rate expression that describes the time-dependent concentration of ES complex includes terms for both its formation (kþ 1[E][S]) and decay (k 1[ES] þ kcat[ES]) according to Eq. (7.5). Furthermore, d½ES ¼ kþ1 ½E½S k1 ½ES kcat ½ES dt
ð7:5Þ
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Measurement of Enzyme Activity
Equation (7.5) requires expressions for the time-dependent concentrations of E and S. To overcome the difficulty of integrating all differential rate expressions, the very useful steady-state approximation is applied to the concentration of ES. In cases where the reaction velocity is measured to be approximately constant over a time interval (e.g., measuring the initial velocity), then it follows that the concentration of ES does not vary appreciably. Thus, Eq. (7.5) is equated to zero and rearranged to obtain the Eq. (7.6) expression for [ES] in terms of [E] and [S]. ½ES ¼
kþ1 ½E½S ½E½S ¼ k1 þ kcat Km
ð7:6Þ
In Eq. (7.6), the rate constants are grouped to form a composite constant [Km ¼ (k 1 þ kcat)/kþ 1], which is referred to as the Michaelis constant. When the initial velocity of an enzyme-catalyzed reaction is measured under steady-state conditions, the time-dependent [S] in Eq. (7.6) is approximated by its initial concentration, [S]0, since the amount of product formed is substantially less than the amount of remaining substrate (i.e., [S] [S]0 since ½P ½S). Since the time-dependent [E] cannot be approximated by its initial concentration, [E]0, the law of conservation of mass is used, whereby [E] ¼ [E]0 [ES] is further substituted into Eq. (7.6) to yield Eq. (7.7), which is rearranged to give the Eq. (7.8) expression for [ES]. Now, this expression is substituted back into Eq. (7.4) to yield the familiar Michaelis–Menten Eq. (7.9), ½ES ¼
ð½E0 ½ESÞ½S0 Km
ð7:7Þ
½E0 ½S0 Km þ ½S0
ð7:8Þ
½ES ¼ v¼
kcat ½E0 ½S0 Vmax ½S0 d½P ¼ ¼ kcat ½ES ¼ Km þ ½S0 Km þ ½S0 dt
ð7:9Þ
which shows the initial velocity of product formation to be directly proportional to the total concentration of enzyme, [E]0. Equation (9) further shows the initial velocity of product formation to vary in a hyperbolicdependent manner with regard to the initial concentration of substrate according to the composite Michaelis constant, Km. Here, the Km ¼ (k 1 þ kcat)/kþ 1 values represents the substrate concentration at which halfmaximum initial velocity is attained, and Vmax (M s 1) ¼ kcat[E]0 represents the maximum initial velocity of product formation. In the limiting case where catalytic conversion to products is much slower than dissociation of
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the substrate (i.e., kcat k1 ), the Km value approximates the true dissociation constant for the ES complex, Kd ¼ k 1/kþ 1; and the system is described as being in rapid equilibrium. If the measured initial velocity is then normalized to amount of enzyme in the reaction mixture, then Eq. (7.9) takes the form of Eq. (7.10), whereby the activity of the enzyme is defined Activity ðs1 Þ ¼
v kcat ½S0 ¼ ½E0 Km þ ½S0
ð7:10Þ
as the instantaneous enzyme-catalyzed reaction velocity normalized to the amount of enzyme (v/[E]0). In this case, enzyme activity is measured as a function of substrate concentration to obtain values of the turnover number, kcat, and the Michaelis constant, Km. The ratio of kcat/Km (M 1 s 1) is termed the specificity constant, which is an apparent second-order rate constant that refers to the properties and reactions of the free enzyme leading to the first irreversible step. It is important to point out that the above activity definition pertains to cases in which the enzyme active site concentration (moles per volume) in the reaction mixture is known (e.g., assay of a purified homogeneous form of the enzyme). When enzyme activity measurements are carried out in the presence of other proteins such as crude cell lysates or partially purified enzyme preparations, the measured initial velocity is normalized to the total protein concentration in the assay. In this case, total protein concentration is measured and expressed as weight per volume. As such, when the molar concentration units of initial velocity (mol l 1 s 1) are divided by weight concentration units of total protein (g l 1), the volume terms cancel so that specific enzyme activity is expressed as the number of moles of product converted per unit time per weight of protein. Specific activity expressed in this manner is most often reported as mmol min 1 mg 1. When one unit (U) is defined as conversion of 1 mmol of substrate per minute, then enzyme activity is also commonly expressed as units per milligram of protein (U mg 1). The following sections describe a number of initial considerations and experimental methods for proper development of enzymatic assays.
3. Measurement of Enzyme Activity In order to measure an enzyme’s catalytic activity, it is essential to first identify the chemical changes involving conversion of substrate(s) to product(s). To date, the textual accounting of the incredible variety of enzymatic activities is most typically managed by grouping enzymes according to the
Measurement of Enzyme Activity
65
types of chemical reactions they catalyze (e.g., oxidation–reductions, group transfers, eliminations, isomerizations, rearrangements, condensations, carboxylations, etc.) (Frey and Hegeman, 2007). Further, considerations should take into account whether mechanistically similar chemistry (i) involves either small molecule substrates or larger macromolecular proteins or nucleic acids, (ii) occurs readily in solution or requires membranebound components, and (iii) proceeds to any extent in the reverse direction. In any case, the enzymatic assay is designed around the ability to distinguish between the physicochemical properties of a given substrate with respect to those of a given product in a quantifiable manner (Eisenthal and Danson, 2002; Rossomando, 1990). To a large degree, similar methods of measuring activity have been applied to various enzymes categorized within such subgroups; and it would be prudent to first consider devising assays on the basis of those already well established for either (i) homologous enzymes from different organisms or (ii) different enzymes that catalyze a related chemical reaction. The central theme among all enzyme activity measurements is to ensure measurement of initial velocities. To reiterate this all important point, it is common and good practice to measure initial velocities for either loss of reactant or gain of product at times corresponding to 5% of product conversion. This gives the best approximation for the initial velocity at the starting or initial substrate concentration.
3.1. Continuous assays After surveying the literature for applicable enzymatic assays, one may find a number of suitable methods, which may be initially distinguished according to whether a ‘‘continuous’’ or a ‘‘discontinuous’’ assay is employed. Continuous assays are defined by the ability to continuously monitor either disappearance or appearance of a given substrate or product, respectively; and they most often rely on spectroscopic techniques such as electronic ultraviolet–visible absorption and fluorescence emission. For absorption spectroscopy, molar absorbance extinction coefficients (e) can be gravimetrically determined for any number of compounds with conjugated bond systems. According to the Lambert–Beer relationship (A ¼ ecl ), absorbance (A, unitless) is directly proportional to (i) the molar extinction coefficient (e, M 1 cm 1), (ii) the concentration of the compound (c, M), and (iii) the path length of the cuvette (l, cm) used for the measurement (Segal, 1976). Thus, the molar change in concentration with time or initial velocity (v ¼ d[S]/dt or d[P]/dt) is directly calculated from the slope relating the change in spectroscopic signal at a designated wavelength with respect to time (dA/dt) on dividing by el; and the enzyme activity is ultimately obtained by dividing the initial velocity by either the enzyme molar concentration (M) or the weight concentration of total protein in the assay (mg ml 1) according to either Eq. (7.11) or (7.12), respectively.
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T. K. Harris and M. M. Keshwani
Activity ðs1 Þ ¼
v ðdA=dt; s1 Þ ¼ ½E0 ðe; M1 cm1 Þðl; cmÞð½E0 ; MÞ
v ½E0 ðdA=dt; min1 Þ ¼ ðe; ml mmol 1 cm1 Þðl; cmÞð½E0 ; mg ml1 Þ
ð7:11Þ
Activity ðmmol min1 mg1 Þ ¼
ð7:12Þ
Although ultraviolet–visible absorption spectroscopy is (i) convenient for continuous monitoring and (ii) accurate with respect to determining concentration changes, it is limited with respect to both (i) the number of ESs and products that can be detected and (ii) the range of concentrations that can be accurately detected. Alternatively, fluorescence and phosphorescence spectroscopies can be used for continuously monitoring reaction progress; and in most cases provide significantly enhanced sensitivity. However, it must be pointed out that the concentration of the fluorophore cannot be calculated from the measured fluorescence emission by application of a universal constant equivalent to the molar extinction coefficient. Rather, relative changes in fluorescence emission with time are compared. Regardless, fluorescence and phosphorescence spectroscopies are highly suited for use in high-throughput platforms utilized for screening very large numbers of compounds for effects on enzyme activity. For a large number of enzyme drug targets (e.g., particularly protein kinases and proteases), artificial peptide substrates have been chemically modified to contain one or more small molecule fluorophores; and such substrates undergo fluorescence emission changes occur on either phosphorylation or cleavage. Before employing fluorescence- or phosphorescence-based assays, researchers should thoroughly review literature pertaining to such principles, as numerous properties must be considered (e.g., fluorescence lifetime, quantum yields, and inner-filter effects) (Lakowicz, 2004). Finally, it should be pointed out that numerous ‘‘continuous’’ enzymatic assays can and have been developed for reactions involving substrate– product pairs with no spectroscopic properties. In these cases, either one or more additional enzymes are included in the reaction mixture, which serve to ‘‘couple’’ a given product to a reaction that does yield a desirable spectroscopic property (Eisenthal and Danson, 2002). For the most part, such coupled continuous assays have been applied to metabolic enzymes for which a given product may either be oxidized or reduced by chromogenic coenzymes such as NADH. If the product is not a direct substrate for such a reaction, then an additional enzyme may be included to convert the first product to a second product that undergoes the chromogenic reaction. In any case, it must be ensured that the reaction mixture contains adequate
Measurement of Enzyme Activity
67
amounts of all additional components to ensure that the reaction velocity is solely determined by the enzyme of interest. In other words, the measured reaction velocity should be (i) dependent only on the target substrate(s) and enzyme concentration and (ii) independent or zero order with respect to the concentration of each and every component added to facilitate the coupled reaction.
3.2. Discontinuous assays Discontinuous assays are defined by the inability to continuously and selectively monitor concentration changes of either substrate or product, such as when a given substrate–product pair exhibits either similar or no spectroscopic properties. Rather, the enzymatic reaction must be manually stopped or ‘‘quenched’’ at different times. The quenched samples are then subjected to some method whereby the product can be efficiently separated from the substrate so that the change in concentration of either can be determined for each individual time point. In setting up a discontinuous enzymatic assay, it is crucial to devise methods for both (i) efficiently stopping or ‘‘quenching’’ an enzyme-catalyzed reaction at designated time points and (ii) efficiently separating the large amount of unreacted substrate (95%) from the very small amount of formed product (5%) required for measuring initial velocities. These two methodological points must be considered as a pair, since the ‘‘quenched’’ reaction solution conditions must be amenable to subsequent procedures required for fractionation of substrate and product molecules. Since a large number of enzymes can be rapidly inactivated under a wide variety of conditions (e.g., addition of acid, base, or metal chelators), substrate–product fractionation is foremost considered. High-performance liquid chromatography (HPLC) offers extensive ranges in both resolution capabilities and detection sensitivity (McMaster, 2007). For example, a great variety of mixtures containing either small molecules or macromolecules can be resolved on the basis of differential retention when passed over a column containing a given stationary phase (e.g., ion-exchange, size-exclusion, or reversed-phase chromatography). In addition, HPLC systems can be fixed with any number of detectors so that a compound with a given spectroscopic property can be detected as it elutes from the column, which results in a spectroscopic peak. To gauge the amount of product formed, the area of the resolved product peak is integrated and compared with a standard curve prepared from integrated peak areas obtained for range of product concentrations. In cases where the designated product does not exhibit any spectroscopic properties, one may consider possibilities of either (i) chemically modifying the substrate to contain a spectroscopic active compound or (ii) modifying the product in the quenched reaction mixture. In the latter case, it must be established that essentially all product undergoes modification and that the modified
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T. K. Harris and M. M. Keshwani
product can be readily resolved from any remaining unreacted spectroscopic active compound. The determination of enzyme activity is carried out exactly as in Eqs. (7.11) and (7.12) except that dA/dt is obtained as DA/D t (i.e., a single-point determination rather than a slope determined from many points). In cases when a given substrate–product pair exhibits no useful spectroscopic properties, the amount of product at a given time point in a discontinuous assay can be determined by radiometric analysis (Eisenthal and Danson, 2002). In fact, radiometric assays provide the highest degree of sensitivity, as well as exhibit the highest degree of broad scale utility. Almost any conceivable enzyme substrate can be synthesized to contain a radioactive isotopic atom (or radioisotope) in a position that undergoes transfer from the parent substrate, which can be detected in very small amounts. The most commonly used radioisotopes for enzymatic assays are 3H, 14C, 32P, and 35S. In all four cases, the unstable nucleus undergoes slow first-order decay to form a stable isotope with an atomic number one higher and an atomic weight identical to the original radioisotope through a process called beta-particle emission. Scintillation counting of beta-particle emission gives very sensitive determination of the amount of radioactivity present in a sample, which is directly quantified in counts per minute (cpm). The halflife (t1/2) of a radioisotope is the time required for half of the original number of atoms to decay. Half-life values of 3H (t1/2 ¼ 12.3 years), 14C (t1/2 ¼ 5700 years), 32P (t1/2 ¼ 14.3 days), and 35S (t1/2 ¼ 87.1 days) have been well determined. From these values, it can be seen that the amount of radioactivity emitted by 3H and 14C does not appreciably change over the time course of routine laboratory work; whereas the amount of radioactivity emitted by 32P and 35S significantly decreases over such time. Commercial manufacturers incorporate such radioisotopes into designated positions of target molecules to yield radiolabeled substrate molecules, which have a defined specific (radio)activity (SA) (Segal, 1976). The specific activity refers to the amount of radioactivity (cpm) per unit amount of molecule (mol). Typically, one adds a small amount of the highly radioactive ‘‘hot’’ substrate molecule into a much larger amount of the nonradioactive or ‘‘cold’’ substrate. A small volume of a known concentration is then subjected to scintillation counting to determine the specific (radio)activity of the substrate (SAS, cpm/mol 1). By controlling the mixture of hot and cold substrate molecules, a very wide range of specific (radio)activities can be generated so that enzyme activity measurements are possible over an equal range of substrate concentrations. For example, a radiolabeled substrate with SA ¼ 1000 cpm mmol 1 would enable efficient detection for transfer of label to form 1 mmol of product (1000 cpm), whereas generation of a radiolabeled substrate with SA ¼ 1000 cpm pmol 1 would enable efficient detection of 1 pmol of product!
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Most commonly, ion-exchange methods are used in which the product form of the molecule is retained on solid support (e.g., ion-exchange resin, paper, or disk), while the substrate form is not retained. Other methods of separation may include either selective precipitation, solvent extraction, or gel electrophoresis. Before carrying out the enzyme-catalyzed reaction, it is essential to establish that (i) the radiolabeled product is highly resolved from radioactive substrate and (ii) the amount of resolved product closely approximates the amount subjected for resolution. Typically, one finds a point of compromise, whereby a certain minimum amount of ‘‘background’’ substrate radiation is tolerated in the medium or location where product is resolved. For most accurate analysis, the medium containing the purified product is directly analyzed by scintillation counting (e.g., ion-exchange resin, paper, or disk). Although selected gel regions after electrophoresis may be removed for direct counting, it has been more common practice to quantify spatial radioactivity across an entire gel using scintillation plates and computer densitometry analysis. The amount of enzyme-catalyzed product (mol) detected in the aliquot removed for analysis is calculated by dividing the amount of radioactivity detected in the product fraction (cpm) by the specific (radio)activity of the substrate (cpm/mol 1); the concentration of product, [P], is obtained by dividing by the volume of the aliquot (l); and the initial velocity, d[P]/dt, is obtained by further dividing [P] by the time of the reaction (s). Thus, enzyme activity is ultimately obtained by dividing the initial velocity by either (i) the enzyme molar concentration according to Eq. (7.13) or (ii) the total protein concentration according to Eq. (7.14). Activityðs1 Þ ¼
d½P cpm ¼ 1 S dt½E0 ðSA ; cpm=mmol Þðvol; mlÞðt; sÞð½E; mmol=ml1 Þ ð7:13Þ
d½P dt½E0 cpm ¼ ðSAS ; cpm=mmol1 Þðvol; mlÞðt; minÞð½E; mg=ml1 Þ
Activityðmmolmin1 mg1 Þ ¼
ð7:14Þ
4. Formulation of Reaction Assay Mixtures Having established effective methods for resolution, detection, and quantification of reaction species, it is next time to consider preparation of the reaction mixture itself. For continuous spectroscopic assays, total volumes should be selected to accommodate cuvettes made for the given
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spectrometer. For visible absorption (325 nm), 1 ml plastic disposable cuvettes are most widely used due to convenience. Since plastic cuvettes increasingly absorb light of lower wavelengths, quartz cuvettes should be used in this region. Of increasing availability and utility are fluorometers fitted with microplate readers, which simultaneously obtain accurate emission readings from a large number of individual small reactions (50 ml) on a single microtiter plate. For discontinuous enzyme assays, a total volume of the reaction mixture should be selected in which several (3) designated fixed amount aliquots can be removed at varying times for reaction quenching and product analysis. For all enzyme assays, stock concentrations of suitable buffer, substrate(s), and enzyme are prepared so that dilution of each component to its desired concentration can be achieved by adding volumetric amounts that sum to less than the total volume. The remaining volume is occupied by water. The buffer component should have a pKa value 1 of the desired reaction pH, and its concentration should be chosen to exceed any other component that has ionizable groups. The stock buffer solution may also contain additional compounds that may be necessary to maintain enzyme stability and activity such as salts (e.g., NaCl or KCl), osmolytes (e.g., polyethylene glycol, glycerol, or sucrose), and reducing agents (e.g., 2-mercaptoethanol, dithiothreitol, or TCEP). It is very important to include such components in the preparation of the stock buffer, and the final stock buffer mixture should be titrated to its desired pH at the temperature in which the reaction will be carried out. Pay special attention to use of (i) nitrogen containing buffers (such as Tris) whose pKa values are very sensitive to temperature and (ii) phosphate buffers whose pKa values are very sensitive to ionic strength. In fact, dilution of phosphate buffer will change its pH value, so the pH of its stock concentration must be adjusted accordingly. It is best to generate the reaction mixture by first adding nonenzyme components in the following order: (i) designated volume of water, (ii) designated volume of stock buffer mixture, and (iii) designated volume of stock substrate. It is best to prepare a stock concentration of enzyme so that only a relatively small amount (10% volume) is added to bring the mixture to the designated total volume and initiate the reaction. Immediately, after the enzyme has been added to initiate a continuous assay, the cuvette(s) or microtiter plate must be inserted into a spectrometer that is programmed to begin collecting absorption or emission data at the designated wavelength(s). For discontinuous assays, one must be prepared to remove a precise volume of the reaction mixture and mix with a precise volume of the quench reagent; and this must be repeated at precise times. In all enzyme assays, one should always formulate an additional control reaction mixture that does not contain enzyme to determine the ‘‘background’’ amounts of either (i) noncatalyzed product formation or (ii) signal retained from incomplete resolution. Any such background amounts must be subtracted from the signal detected in the presence of enzyme.
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5. Discussion In this chapter, the most fundamental principles of measuring enzyme reaction rates were presented, and it is in no way a complete treatment on the subject. Nevertheless, clear understanding of these principles is absolutely prerequisite toward either (i) effective utilization of well-developed assays or (ii) efficient development of assays for newly discovered enzymes. Over the past century, countless research articles, review articles, book chapters, and even entire books have reported on the development, utilization, and interpretation of enzyme activity measurements. The selection of books and articles cited in this article provide more comprehensive treatments of the various topics related to measuring enzyme activity.
ACKNOWLEDGMENTS This work was supported by NIGMS, National Institutes of Health Grant GM69868 to T. K. H. and a Maytag Fellowship to M. M. K.
REFERENCES Cook, P. F., and Cleland, W. W. (2007). Enzyme Kinetics and Mechanism. Garland Science, Hamden, CT. Cornish-Bowden, A. (1995). Fundamentals of Enzyme Kinetics. Portland Press, Ltd., London, UK. Eisenthal, R., and Danson, M. (2002). Enzyme Assays: A Practical Approach. Oxford University Press, Inc., New York, NY. Frey, P. A., and Hegeman, A. D. (2007). Enzymatic Reaction Mechanisms. Oxford University Press, Inc., New York, NY. House, J. E. (2007). Principles of Chemical Kinetics. 2nd edn. Academic Press, Burlington, MA. Laidler, K. J. (1987). Chemical Kinetics. 3rd edn. Prentice Hall, Upper Saddle River, NJ. Lakowicz, J. R. (2004). Principles of Fluorescence Spectroscopy. 2nd edn. Springer ScienceþBusiness Media, Inc., New York, NY. McMaster, M. C. (2007). HPLC, a Practical Users Guide. 2nd edn. John Wiley & Sons, Inc., Hoboken, NJ. Rossomando, E. F. (1990). Measurement of enzyme activity. Methods Enzymol. 182, 38–49. Segel, I. H. (1975). Enzyme Kinetics. John Wiley & Sons, Inc., New York, NY. Segal, I. H. (1976). Biochemical Calculations. 2nd edn. John Wiley & Sons, Inc., New York, NY.
S E V E N
Measurement of Enzyme Activity T. K. Harris and M. M. Keshwani Contents 58 58 58 62 64 65 67 69 71 71 71
1. Introduction 2. Principles of Catalytic Activity 2.1. Chemical kinetics 2.2. Basic enzyme kinetics 3. Measurement of Enzyme Activity 3.1. Continuous assays 3.2. Discontinuous assays 4. Formulation of Reaction Assay Mixtures 5. Discussion Acknowledgments References
Abstract To study and understand the nature of living cells, scientists have continually employed traditional biochemical techniques aimed to fractionate and characterize a designated network of macromolecular components required to carry out a particular cellular function. At the most rudimentary level, cellular functions ultimately entail rapid chemical transformations that otherwise would not occur in the physiological environment of the cell. The term enzyme is used to singularly designate a macromolecular gene product that specifically and greatly enhances the rate of a chemical transformation. Purification and characterization of individual and collective groups of enzymes has been and will remain essential toward advancement of the molecular biological sciences; and developing and utilizing enzyme reaction assays is central to this mission. First, basic kinetic principles are described for understanding chemical reaction rates and the catalytic effects of enzymes on such rates. Then, a number of methods are described for measuring enzyme-catalyzed reaction rates, which mainly differ with regard to techniques used to detect and quantify concentration changes of given reactants or products. Finally, short commentary is given toward formulation of reaction mixtures used to measure enzyme activity. Whereas a comprehensive treatment of enzymatic reaction assays is not within Department of Biochemistry and Molecular Biology, Miller School of Medicine, University of Miami, Miami, Florida, USA Methods in Enzymology, Volume 463 ISSN 0076-6879, DOI: 10.1016/S0076-6879(09)63007-X
#
2009 Elsevier Inc. All rights reserved.
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T. K. Harris and M. M. Keshwani
the scope of this chapter, the very core principles that are presented should enable new researchers to better understand the logic and utility of any given enzymatic assay that becomes of interest.
1. Introduction One primary goal of biological sciences is to deduce the molecular bases of all chemical processes that take place in living organisms. It is well established that the vast majority of biochemical reactions are governed by protein gene products called enzymes. In this sense, enzymes behave as finely tuned chemical catalysts, which greatly enhance reaction rates with both temporal and spatial resolution. Thus, elucidation of biochemical pathways involving biosynthesis, modification, and degradation of macromolecular, metabolic, and signaling molecules remains ultimately tied to experimental methods for purification, reconstitution, and direct demonstration of enzymes to catalyze specific chemical reactions. The focus of this chapter is to explain the most fundamental principles that must be considered in developing effective methods for measuring the progress of enzymecatalyzed reactions. First, kinetic formulation is described for chemical and enzymatic reaction processes. Next, instructive commentary is given on various experimental methods that are commonly used for measuring enzyme activity; and consideration is given toward numerous procedures and conditions that must be optimized.
2. Principles of Catalytic Activity 2.1. Chemical kinetics Chemical kinetics involves the experimental study of reaction rates in order to infer about the kinetic mechanisms for chemical conversion of reactants (R) into products (P) (Fig. 7.1) (House, 2007; Laidler, 1987). For any given chemical reaction, (i) the mechanism refers to the sequence of elementary steps by which overall chemical change occurs and (ii) an elementary step refers to the passing of a reactant or reaction complex through a singletransition state to a chemical form with a defined and detectable lifetime. If chemical conversion of reactants (R) to products (P) involves more than one elementary step, then the chemical structures that exist after each elementary step preceding final product formation are defined as reaction intermediates (I). Figure 7.1 also shows that each elementary step leading to product is characterized by a forward microscopic rate constant (e.g., kþ 1 and kþ 2). If a particular elementary step is reversible, then a reverse rate
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Measurement of Enzyme Activity
A
R1 + R2
k+1 k−1
I
k+2
P1 + P2
E
Reaction coordinate B
E+S
k+1 k−1
ES
k+2
E +P
Figure 7.1 (A) Basic kinetic mechanism for chemical conversion of two molecular reactants (R1 and R2) into two molecular products (P1 and P2). In this mechanism, an intermediate complex (I) is reversibly formed from reactants (kþ 1 and k 1) but is irreversibly converted to products (kþ 2). (B) Basic kinetic mechanism for enzyme (E)-catalyzed conversion of a molecular substrate (S) into a molecular product (P). In this mechanism, an ES intermediate complex is reversibly formed (kþ 1 and k 1) but is irreversibly converted to product (kþ 2). In this case, the enzyme (E) is regenerated and can undergo subsequent catalytic cycles. For both mechanisms, a free-energy diagram depicts typical energy changes that occur along the reaction coordinate leading to intermediates and products. Ground-state energies for reactants, intermediates, and products are depicted as valleys, whereas transition-state energies for chemical changes are depicted by peaks.
constant is designated (e.g., k 1). The principle of microscopic reversibility states that only one transition state exists for reversible chemical conversion between the species associated with one elementary step (i.e., the transition state for the forward reaction is the same as for the reverse reaction). For any given unidirectional conversion within an elementary step, a rate law is used to describe the mathematical relationship between the reaction rate or velocity and the concentration of each given reactant. For a given chemical reaction step occurring in solution, the instantaneous reaction velocity (v) is defined as the derivative of chemical concentration with respect to time (t); and it is expressed either as (i) a decreasing concentration of a given reactant (v ¼ d[R]/dt) or (ii) an increasing concentration of a given product (v ¼ þ d[P]/dt). The standard international units of reaction velocity are M s 1. The rate law for a single-unidirectional step shows the instantaneous velocity to depend on variable reactant concentration values according to parameter values of (i) a proportionality constant (k) and (ii) the exponent of each concentration term (Table 7.1). The proportionality constant is defined as the forward microscopic rate constant for a given chemical conversion, and its dimensions depend on the overall molecularity or order of the reaction. For the rate laws defined in Table 7.1, the molecularity with respect to a given reactant is given by the exponent in the given concentration term and represents the stoichiometric quantity of reactant involved in the reaction step. The kinetic order of a simple chemical reaction
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T. K. Harris and M. M. Keshwani
Table 7.1 Relationship between rate law, order, and the rate constant, k Rate lawa
Order
Units of k
v¼k v ¼ k[R1]
Zero First order with respect to R1 First order overall Second order with respect to R1 Second order overall First order with respect to R1 First order with respect to R2 Second order overall
M s 1 s 1
v ¼ k[R1]2 v ¼ k[R1][R2]
a
M 1 s 1 s 1
For each rate law, the units of the reaction velocity (v) will always be M s 1. M represents moles per liter (mol l 1).
is usually the same as molecularity, but it is important to emphasize that order refers to the exponent value that relates the experimentally measured reaction rate’s dependence on reactant concentration. The overall molecularity or order of a reaction step is the sum of all the concentration term exponents. In order to more fully understand the dependence of instantaneous velocity on reactant concentration, we will first consider a simple first-order reaction in which one molecule of reactant R forms one molecule of product P (R ! P) according to the rate law given by Eq. (7.1). v¼
d½R d½P ¼ ¼ k½R dt dt
ð7:1Þ
In Eq. (7.1), the instantaneous reaction velocity (v ¼ d[R]/dt ¼ þ d [P]/dt) is directly proportional to the concentration of R raised to the first power. If the velocity for either loss of R or gain of P was measured immediately after initiation of the reaction (Fig. 7.2A), then a secondary plot of this initial velocity versus different initial or starting concentrations of [R] would be linear with a slope equal to the first-order rate constant, k (s 1) (Fig. 7.2B). For such analyses, great care must be taken to ensure measurement of initial velocities. With increasing times past initiation of the reaction, the measured velocity decreases proportionately with depletion of [R]. Thus, it is common and good practice to measure initial velocities for either loss of reactant or gain of product at times corresponding to 5% of product conversion. To better illustrate the decreasing reaction velocity with time, the differential rate Eq. (7.1) can be integrated with respect to [R] to yield the first-order or single-exponential decay function given by Eq. (7.2). The limits of integration correspond to the initial concentration of reactant
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Measurement of Enzyme Activity
A
Slopes = v = d [P]/dt, M s−1
Slope = k = dv/d [R]0, s−1
B
v (d[P]/dt)
3[R]0
[P]
2[R]0 [R]0
Time
[R]0
Figure 7.2 Determination of a first-order rate constant from measuring the initial velocity of product formation at differing concentrations of a reactant. (A) Initial velocities of product formation (slopes ¼ v ¼ d[P]/dt, M s 1) are measured for different starting concentrations of reactant (i.e., [R]0, 2[R]0, or 3[R]0). (B) The measured initial velocities are then plotted versus the different starting concentrations of reactant. The slope of this dependence yields the first-order rate constant for conversion of reactant into product (slope ¼ k ¼ dv/d[R]0, s 1).
ð ½R
d½R ¼ k ½R0 ½R
½R ln ½R0
ðt dt 0
¼ kt
½R ¼ ½R0 ekt
ð7:2Þ
when the reaction is initiated (i.e., [R] ¼ [R]0 at t ¼ 0) and the concentration of reactant at a given time after the reaction has started. Figure 7.3A shows the relationship between measuring instantaneous velocity (i.e., v ¼ d[R]/dt, where Dt is very small) according to Eq. (7.1) and measuring overall time progress (i.e., either [R] or [P] versus t, where Dt is very large) according to Eq. (7.2) for the simple first-order conversion of reactant to product. The derivative in Eq. (7.1) is simply the slope of the tangent for the concentration curve at a specific time. If no product is present at t ¼ 0, the sum of reactant and product concentrations at any time must be equal to [R]0 (i.e., [R] þ [P] ¼ [R]0). Using this relationship, ([R]0 [P]) may be substituted for [R] in Eq. (7.2) and rearranged to yield the first-order rate Eq. (7.3) that describes the corresponding increasing product concentration with time (Fig. 7.3B). ½P ¼ ½R0 ð1 ekt Þ
ð7:3Þ
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T. K. Harris and M. M. Keshwani
B
[P]
[R]
A
Time
Time
Figure 7.3 (A) Time progress for decreasing reactant concentration [R] in a first-order reaction. It can be seen that the instantaneous velocity at any given reactant concentration (lines) decreases with decreasing reactant concentration [R]. (B) Corresponding time progress curve for increasing product concentration [P] in the same first-order reaction.
2.2. Basic enzyme kinetics Measurement of enzyme activity is actually a measurement of catalytic activity (Cook and Cleland, 2007; Cornish-Bowden, 1995; Segel, 1975). An enzyme or catalyst participates in chemical reactions by increasing the reaction velocity without itself appearing in the end products. In this case, an enzyme (E) first combines with or binds one or more chemical reactants or substrates (S) (Fig. 7.1B, kþ 1 and k 1). The resulting enzyme–substrate (ES) complex is an intermediate species from which catalytic conversion of substrate to product (P) takes place, ultimately releasing the intact enzyme so that it may catalyze a subsequent reaction (Fig. 7.1B, kþ 2). Since the kþ 2 proportionality constant typically comprises all processes or chemical steps involving conversion of the ES complex to release of products, it is a ‘‘pseudo’’ first-order rate constant (s 1). It is more commonly referred to as the turnover number, kcat, which is the maximum number of substrate molecules converted to product per active site per unit time. Thus, the instantaneous enzyme-catalyzed reaction velocity (v ¼ þ d[P]/dt) is directly proportional to the concentration of the ES complex according to kcat in Eq. (7.4). v¼
d½P ¼ kcat ½ES dt
ð7:4Þ
Equation (7.4) is rendered impractical to the experimentalist, because the differential rate expression that describes the time-dependent concentration of ES complex includes terms for both its formation (kþ 1[E][S]) and decay (k 1[ES] þ kcat[ES]) according to Eq. (7.5). Furthermore, d½ES ¼ kþ1 ½E½S k1 ½ES kcat ½ES dt
ð7:5Þ
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Measurement of Enzyme Activity
Equation (7.5) requires expressions for the time-dependent concentrations of E and S. To overcome the difficulty of integrating all differential rate expressions, the very useful steady-state approximation is applied to the concentration of ES. In cases where the reaction velocity is measured to be approximately constant over a time interval (e.g., measuring the initial velocity), then it follows that the concentration of ES does not vary appreciably. Thus, Eq. (7.5) is equated to zero and rearranged to obtain the Eq. (7.6) expression for [ES] in terms of [E] and [S]. ½ES ¼
kþ1 ½E½S ½E½S ¼ k1 þ kcat Km
ð7:6Þ
In Eq. (7.6), the rate constants are grouped to form a composite constant [Km ¼ (k 1 þ kcat)/kþ 1], which is referred to as the Michaelis constant. When the initial velocity of an enzyme-catalyzed reaction is measured under steady-state conditions, the time-dependent [S] in Eq. (7.6) is approximated by its initial concentration, [S]0, since the amount of product formed is substantially less than the amount of remaining substrate (i.e., [S] [S]0 since ½P ½S). Since the time-dependent [E] cannot be approximated by its initial concentration, [E]0, the law of conservation of mass is used, whereby [E] ¼ [E]0 [ES] is further substituted into Eq. (7.6) to yield Eq. (7.7), which is rearranged to give the Eq. (7.8) expression for [ES]. Now, this expression is substituted back into Eq. (7.4) to yield the familiar Michaelis–Menten Eq. (7.9), ½ES ¼
ð½E0 ½ESÞ½S0 Km
ð7:7Þ
½E0 ½S0 Km þ ½S0
ð7:8Þ
½ES ¼ v¼
kcat ½E0 ½S0 Vmax ½S0 d½P ¼ ¼ kcat ½ES ¼ Km þ ½S0 Km þ ½S0 dt
ð7:9Þ
which shows the initial velocity of product formation to be directly proportional to the total concentration of enzyme, [E]0. Equation (9) further shows the initial velocity of product formation to vary in a hyperbolicdependent manner with regard to the initial concentration of substrate according to the composite Michaelis constant, Km. Here, the Km ¼ (k 1 þ kcat)/kþ 1 values represents the substrate concentration at which halfmaximum initial velocity is attained, and Vmax (M s 1) ¼ kcat[E]0 represents the maximum initial velocity of product formation. In the limiting case where catalytic conversion to products is much slower than dissociation of
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T. K. Harris and M. M. Keshwani
the substrate (i.e., kcat k1 ), the Km value approximates the true dissociation constant for the ES complex, Kd ¼ k 1/kþ 1; and the system is described as being in rapid equilibrium. If the measured initial velocity is then normalized to amount of enzyme in the reaction mixture, then Eq. (7.9) takes the form of Eq. (7.10), whereby the activity of the enzyme is defined Activity ðs1 Þ ¼
v kcat ½S0 ¼ ½E0 Km þ ½S0
ð7:10Þ
as the instantaneous enzyme-catalyzed reaction velocity normalized to the amount of enzyme (v/[E]0). In this case, enzyme activity is measured as a function of substrate concentration to obtain values of the turnover number, kcat, and the Michaelis constant, Km. The ratio of kcat/Km (M 1 s 1) is termed the specificity constant, which is an apparent second-order rate constant that refers to the properties and reactions of the free enzyme leading to the first irreversible step. It is important to point out that the above activity definition pertains to cases in which the enzyme active site concentration (moles per volume) in the reaction mixture is known (e.g., assay of a purified homogeneous form of the enzyme). When enzyme activity measurements are carried out in the presence of other proteins such as crude cell lysates or partially purified enzyme preparations, the measured initial velocity is normalized to the total protein concentration in the assay. In this case, total protein concentration is measured and expressed as weight per volume. As such, when the molar concentration units of initial velocity (mol l 1 s 1) are divided by weight concentration units of total protein (g l 1), the volume terms cancel so that specific enzyme activity is expressed as the number of moles of product converted per unit time per weight of protein. Specific activity expressed in this manner is most often reported as mmol min 1 mg 1. When one unit (U) is defined as conversion of 1 mmol of substrate per minute, then enzyme activity is also commonly expressed as units per milligram of protein (U mg 1). The following sections describe a number of initial considerations and experimental methods for proper development of enzymatic assays.
3. Measurement of Enzyme Activity In order to measure an enzyme’s catalytic activity, it is essential to first identify the chemical changes involving conversion of substrate(s) to product(s). To date, the textual accounting of the incredible variety of enzymatic activities is most typically managed by grouping enzymes according to the
Measurement of Enzyme Activity
65
types of chemical reactions they catalyze (e.g., oxidation–reductions, group transfers, eliminations, isomerizations, rearrangements, condensations, carboxylations, etc.) (Frey and Hegeman, 2007). Further, considerations should take into account whether mechanistically similar chemistry (i) involves either small molecule substrates or larger macromolecular proteins or nucleic acids, (ii) occurs readily in solution or requires membranebound components, and (iii) proceeds to any extent in the reverse direction. In any case, the enzymatic assay is designed around the ability to distinguish between the physicochemical properties of a given substrate with respect to those of a given product in a quantifiable manner (Eisenthal and Danson, 2002; Rossomando, 1990). To a large degree, similar methods of measuring activity have been applied to various enzymes categorized within such subgroups; and it would be prudent to first consider devising assays on the basis of those already well established for either (i) homologous enzymes from different organisms or (ii) different enzymes that catalyze a related chemical reaction. The central theme among all enzyme activity measurements is to ensure measurement of initial velocities. To reiterate this all important point, it is common and good practice to measure initial velocities for either loss of reactant or gain of product at times corresponding to 5% of product conversion. This gives the best approximation for the initial velocity at the starting or initial substrate concentration.
3.1. Continuous assays After surveying the literature for applicable enzymatic assays, one may find a number of suitable methods, which may be initially distinguished according to whether a ‘‘continuous’’ or a ‘‘discontinuous’’ assay is employed. Continuous assays are defined by the ability to continuously monitor either disappearance or appearance of a given substrate or product, respectively; and they most often rely on spectroscopic techniques such as electronic ultraviolet–visible absorption and fluorescence emission. For absorption spectroscopy, molar absorbance extinction coefficients (e) can be gravimetrically determined for any number of compounds with conjugated bond systems. According to the Lambert–Beer relationship (A ¼ ecl ), absorbance (A, unitless) is directly proportional to (i) the molar extinction coefficient (e, M 1 cm 1), (ii) the concentration of the compound (c, M), and (iii) the path length of the cuvette (l, cm) used for the measurement (Segal, 1976). Thus, the molar change in concentration with time or initial velocity (v ¼ d[S]/dt or d[P]/dt) is directly calculated from the slope relating the change in spectroscopic signal at a designated wavelength with respect to time (dA/dt) on dividing by el; and the enzyme activity is ultimately obtained by dividing the initial velocity by either the enzyme molar concentration (M) or the weight concentration of total protein in the assay (mg ml 1) according to either Eq. (7.11) or (7.12), respectively.
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T. K. Harris and M. M. Keshwani
Activity ðs1 Þ ¼
v ðdA=dt; s1 Þ ¼ ½E0 ðe; M1 cm1 Þðl; cmÞð½E0 ; MÞ
v ½E0 ðdA=dt; min1 Þ ¼ ðe; ml mmol 1 cm1 Þðl; cmÞð½E0 ; mg ml1 Þ
ð7:11Þ
Activity ðmmol min1 mg1 Þ ¼
ð7:12Þ
Although ultraviolet–visible absorption spectroscopy is (i) convenient for continuous monitoring and (ii) accurate with respect to determining concentration changes, it is limited with respect to both (i) the number of ESs and products that can be detected and (ii) the range of concentrations that can be accurately detected. Alternatively, fluorescence and phosphorescence spectroscopies can be used for continuously monitoring reaction progress; and in most cases provide significantly enhanced sensitivity. However, it must be pointed out that the concentration of the fluorophore cannot be calculated from the measured fluorescence emission by application of a universal constant equivalent to the molar extinction coefficient. Rather, relative changes in fluorescence emission with time are compared. Regardless, fluorescence and phosphorescence spectroscopies are highly suited for use in high-throughput platforms utilized for screening very large numbers of compounds for effects on enzyme activity. For a large number of enzyme drug targets (e.g., particularly protein kinases and proteases), artificial peptide substrates have been chemically modified to contain one or more small molecule fluorophores; and such substrates undergo fluorescence emission changes occur on either phosphorylation or cleavage. Before employing fluorescence- or phosphorescence-based assays, researchers should thoroughly review literature pertaining to such principles, as numerous properties must be considered (e.g., fluorescence lifetime, quantum yields, and inner-filter effects) (Lakowicz, 2004). Finally, it should be pointed out that numerous ‘‘continuous’’ enzymatic assays can and have been developed for reactions involving substrate– product pairs with no spectroscopic properties. In these cases, either one or more additional enzymes are included in the reaction mixture, which serve to ‘‘couple’’ a given product to a reaction that does yield a desirable spectroscopic property (Eisenthal and Danson, 2002). For the most part, such coupled continuous assays have been applied to metabolic enzymes for which a given product may either be oxidized or reduced by chromogenic coenzymes such as NADH. If the product is not a direct substrate for such a reaction, then an additional enzyme may be included to convert the first product to a second product that undergoes the chromogenic reaction. In any case, it must be ensured that the reaction mixture contains adequate
Measurement of Enzyme Activity
67
amounts of all additional components to ensure that the reaction velocity is solely determined by the enzyme of interest. In other words, the measured reaction velocity should be (i) dependent only on the target substrate(s) and enzyme concentration and (ii) independent or zero order with respect to the concentration of each and every component added to facilitate the coupled reaction.
3.2. Discontinuous assays Discontinuous assays are defined by the inability to continuously and selectively monitor concentration changes of either substrate or product, such as when a given substrate–product pair exhibits either similar or no spectroscopic properties. Rather, the enzymatic reaction must be manually stopped or ‘‘quenched’’ at different times. The quenched samples are then subjected to some method whereby the product can be efficiently separated from the substrate so that the change in concentration of either can be determined for each individual time point. In setting up a discontinuous enzymatic assay, it is crucial to devise methods for both (i) efficiently stopping or ‘‘quenching’’ an enzyme-catalyzed reaction at designated time points and (ii) efficiently separating the large amount of unreacted substrate (95%) from the very small amount of formed product (5%) required for measuring initial velocities. These two methodological points must be considered as a pair, since the ‘‘quenched’’ reaction solution conditions must be amenable to subsequent procedures required for fractionation of substrate and product molecules. Since a large number of enzymes can be rapidly inactivated under a wide variety of conditions (e.g., addition of acid, base, or metal chelators), substrate–product fractionation is foremost considered. High-performance liquid chromatography (HPLC) offers extensive ranges in both resolution capabilities and detection sensitivity (McMaster, 2007). For example, a great variety of mixtures containing either small molecules or macromolecules can be resolved on the basis of differential retention when passed over a column containing a given stationary phase (e.g., ion-exchange, size-exclusion, or reversed-phase chromatography). In addition, HPLC systems can be fixed with any number of detectors so that a compound with a given spectroscopic property can be detected as it elutes from the column, which results in a spectroscopic peak. To gauge the amount of product formed, the area of the resolved product peak is integrated and compared with a standard curve prepared from integrated peak areas obtained for range of product concentrations. In cases where the designated product does not exhibit any spectroscopic properties, one may consider possibilities of either (i) chemically modifying the substrate to contain a spectroscopic active compound or (ii) modifying the product in the quenched reaction mixture. In the latter case, it must be established that essentially all product undergoes modification and that the modified
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T. K. Harris and M. M. Keshwani
product can be readily resolved from any remaining unreacted spectroscopic active compound. The determination of enzyme activity is carried out exactly as in Eqs. (7.11) and (7.12) except that dA/dt is obtained as DA/D t (i.e., a single-point determination rather than a slope determined from many points). In cases when a given substrate–product pair exhibits no useful spectroscopic properties, the amount of product at a given time point in a discontinuous assay can be determined by radiometric analysis (Eisenthal and Danson, 2002). In fact, radiometric assays provide the highest degree of sensitivity, as well as exhibit the highest degree of broad scale utility. Almost any conceivable enzyme substrate can be synthesized to contain a radioactive isotopic atom (or radioisotope) in a position that undergoes transfer from the parent substrate, which can be detected in very small amounts. The most commonly used radioisotopes for enzymatic assays are 3H, 14C, 32P, and 35S. In all four cases, the unstable nucleus undergoes slow first-order decay to form a stable isotope with an atomic number one higher and an atomic weight identical to the original radioisotope through a process called beta-particle emission. Scintillation counting of beta-particle emission gives very sensitive determination of the amount of radioactivity present in a sample, which is directly quantified in counts per minute (cpm). The halflife (t1/2) of a radioisotope is the time required for half of the original number of atoms to decay. Half-life values of 3H (t1/2 ¼ 12.3 years), 14C (t1/2 ¼ 5700 years), 32P (t1/2 ¼ 14.3 days), and 35S (t1/2 ¼ 87.1 days) have been well determined. From these values, it can be seen that the amount of radioactivity emitted by 3H and 14C does not appreciably change over the time course of routine laboratory work; whereas the amount of radioactivity emitted by 32P and 35S significantly decreases over such time. Commercial manufacturers incorporate such radioisotopes into designated positions of target molecules to yield radiolabeled substrate molecules, which have a defined specific (radio)activity (SA) (Segal, 1976). The specific activity refers to the amount of radioactivity (cpm) per unit amount of molecule (mol). Typically, one adds a small amount of the highly radioactive ‘‘hot’’ substrate molecule into a much larger amount of the nonradioactive or ‘‘cold’’ substrate. A small volume of a known concentration is then subjected to scintillation counting to determine the specific (radio)activity of the substrate (SAS, cpm/mol 1). By controlling the mixture of hot and cold substrate molecules, a very wide range of specific (radio)activities can be generated so that enzyme activity measurements are possible over an equal range of substrate concentrations. For example, a radiolabeled substrate with SA ¼ 1000 cpm mmol 1 would enable efficient detection for transfer of label to form 1 mmol of product (1000 cpm), whereas generation of a radiolabeled substrate with SA ¼ 1000 cpm pmol 1 would enable efficient detection of 1 pmol of product!
Measurement of Enzyme Activity
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Most commonly, ion-exchange methods are used in which the product form of the molecule is retained on solid support (e.g., ion-exchange resin, paper, or disk), while the substrate form is not retained. Other methods of separation may include either selective precipitation, solvent extraction, or gel electrophoresis. Before carrying out the enzyme-catalyzed reaction, it is essential to establish that (i) the radiolabeled product is highly resolved from radioactive substrate and (ii) the amount of resolved product closely approximates the amount subjected for resolution. Typically, one finds a point of compromise, whereby a certain minimum amount of ‘‘background’’ substrate radiation is tolerated in the medium or location where product is resolved. For most accurate analysis, the medium containing the purified product is directly analyzed by scintillation counting (e.g., ion-exchange resin, paper, or disk). Although selected gel regions after electrophoresis may be removed for direct counting, it has been more common practice to quantify spatial radioactivity across an entire gel using scintillation plates and computer densitometry analysis. The amount of enzyme-catalyzed product (mol) detected in the aliquot removed for analysis is calculated by dividing the amount of radioactivity detected in the product fraction (cpm) by the specific (radio)activity of the substrate (cpm/mol 1); the concentration of product, [P], is obtained by dividing by the volume of the aliquot (l); and the initial velocity, d[P]/dt, is obtained by further dividing [P] by the time of the reaction (s). Thus, enzyme activity is ultimately obtained by dividing the initial velocity by either (i) the enzyme molar concentration according to Eq. (7.13) or (ii) the total protein concentration according to Eq. (7.14). Activityðs1 Þ ¼
d½P cpm ¼ 1 S dt½E0 ðSA ; cpm=mmol Þðvol; mlÞðt; sÞð½E; mmol=ml1 Þ ð7:13Þ
d½P dt½E0 cpm ¼ ðSAS ; cpm=mmol1 Þðvol; mlÞðt; minÞð½E; mg=ml1 Þ
Activityðmmolmin1 mg1 Þ ¼
ð7:14Þ
4. Formulation of Reaction Assay Mixtures Having established effective methods for resolution, detection, and quantification of reaction species, it is next time to consider preparation of the reaction mixture itself. For continuous spectroscopic assays, total volumes should be selected to accommodate cuvettes made for the given
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spectrometer. For visible absorption (325 nm), 1 ml plastic disposable cuvettes are most widely used due to convenience. Since plastic cuvettes increasingly absorb light of lower wavelengths, quartz cuvettes should be used in this region. Of increasing availability and utility are fluorometers fitted with microplate readers, which simultaneously obtain accurate emission readings from a large number of individual small reactions (50 ml) on a single microtiter plate. For discontinuous enzyme assays, a total volume of the reaction mixture should be selected in which several (3) designated fixed amount aliquots can be removed at varying times for reaction quenching and product analysis. For all enzyme assays, stock concentrations of suitable buffer, substrate(s), and enzyme are prepared so that dilution of each component to its desired concentration can be achieved by adding volumetric amounts that sum to less than the total volume. The remaining volume is occupied by water. The buffer component should have a pKa value 1 of the desired reaction pH, and its concentration should be chosen to exceed any other component that has ionizable groups. The stock buffer solution may also contain additional compounds that may be necessary to maintain enzyme stability and activity such as salts (e.g., NaCl or KCl), osmolytes (e.g., polyethylene glycol, glycerol, or sucrose), and reducing agents (e.g., 2-mercaptoethanol, dithiothreitol, or TCEP). It is very important to include such components in the preparation of the stock buffer, and the final stock buffer mixture should be titrated to its desired pH at the temperature in which the reaction will be carried out. Pay special attention to use of (i) nitrogen containing buffers (such as Tris) whose pKa values are very sensitive to temperature and (ii) phosphate buffers whose pKa values are very sensitive to ionic strength. In fact, dilution of phosphate buffer will change its pH value, so the pH of its stock concentration must be adjusted accordingly. It is best to generate the reaction mixture by first adding nonenzyme components in the following order: (i) designated volume of water, (ii) designated volume of stock buffer mixture, and (iii) designated volume of stock substrate. It is best to prepare a stock concentration of enzyme so that only a relatively small amount (10% volume) is added to bring the mixture to the designated total volume and initiate the reaction. Immediately, after the enzyme has been added to initiate a continuous assay, the cuvette(s) or microtiter plate must be inserted into a spectrometer that is programmed to begin collecting absorption or emission data at the designated wavelength(s). For discontinuous assays, one must be prepared to remove a precise volume of the reaction mixture and mix with a precise volume of the quench reagent; and this must be repeated at precise times. In all enzyme assays, one should always formulate an additional control reaction mixture that does not contain enzyme to determine the ‘‘background’’ amounts of either (i) noncatalyzed product formation or (ii) signal retained from incomplete resolution. Any such background amounts must be subtracted from the signal detected in the presence of enzyme.
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5. Discussion In this chapter, the most fundamental principles of measuring enzyme reaction rates were presented, and it is in no way a complete treatment on the subject. Nevertheless, clear understanding of these principles is absolutely prerequisite toward either (i) effective utilization of well-developed assays or (ii) efficient development of assays for newly discovered enzymes. Over the past century, countless research articles, review articles, book chapters, and even entire books have reported on the development, utilization, and interpretation of enzyme activity measurements. The selection of books and articles cited in this article provide more comprehensive treatments of the various topics related to measuring enzyme activity.
ACKNOWLEDGMENTS This work was supported by NIGMS, National Institutes of Health Grant GM69868 to T. K. H. and a Maytag Fellowship to M. M. K.
REFERENCES Cook, P. F., and Cleland, W. W. (2007). Enzyme Kinetics and Mechanism. Garland Science, Hamden, CT. Cornish-Bowden, A. (1995). Fundamentals of Enzyme Kinetics. Portland Press, Ltd., London, UK. Eisenthal, R., and Danson, M. (2002). Enzyme Assays: A Practical Approach. Oxford University Press, Inc., New York, NY. Frey, P. A., and Hegeman, A. D. (2007). Enzymatic Reaction Mechanisms. Oxford University Press, Inc., New York, NY. House, J. E. (2007). Principles of Chemical Kinetics. 2nd edn. Academic Press, Burlington, MA. Laidler, K. J. (1987). Chemical Kinetics. 3rd edn. Prentice Hall, Upper Saddle River, NJ. Lakowicz, J. R. (2004). Principles of Fluorescence Spectroscopy. 2nd edn. Springer ScienceþBusiness Media, Inc., New York, NY. McMaster, M. C. (2007). HPLC, a Practical Users Guide. 2nd edn. John Wiley & Sons, Inc., Hoboken, NJ. Rossomando, E. F. (1990). Measurement of enzyme activity. Methods Enzymol. 182, 38–49. Segel, I. H. (1975). Enzyme Kinetics. John Wiley & Sons, Inc., New York, NY. Segal, I. H. (1976). Biochemical Calculations. 2nd edn. John Wiley & Sons, Inc., New York, NY.