4 on the Measurement of Enzymes and Their Inhibitors

On the Measurement of Enzymes and their inhibitors

Andrew Holt

1. Introduction

It is inevitable that most graduate students and researchers in the neurosciences will, from time to time, be faced with a problem related to enzymes. Tasks such as screening novel compounds for enzyme-inhibitor potency, examining the effects of drug administration on enzyme activities, employing enzymes as mark- ers of disease state or cell fractionation, and elucidation of metabolic pathways for psychiatric drugs, are carried out on a regular basis. Yet few topics engender such anxiety and confusion for students of the neurosciences as does enzymology, with the conse- quence that relatively straightforward experiments can take weeks to complete, and results obtained are often misinterpreted or might even be meaningless. Most researchers doing enzyme assays are not enzymologists who deal with enzymes on a daily basis. Rather, they are following an assay protocol described in a manuscript or textbook, with no apparent necessity to understand the funda- mentals of how enzymes and their inhibitors work in order to obtain results. More often than not, the researcher alters the original protocol slightly to suit the materials and apparatus available or to address a different question from that which the assay was designed to answer. Perhaps the enzyme has been obtained from another species or tissue source, or has been isolated and prepared in a manner different to that described. The original substrate may have been replaced by a cheaper or more readily obtainable alternative. The assay temperature or buffer pH might be substantially different. These, and many other factors, can contribute to

From Neuromethods, vol 33 Cell Neurob,o/ogy Techniques

Eds A A Boulton, C B Baker, and A N Bateson Q Humana Press Inc

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production of misleading or incorrect data, or a failure to obtain any results whatsoever. Unfortunately, a lack of familiarity with basic concepts in enzymology may result in the failure of researchers to recognise flawed results or, in the event that the experiment has not worked, the inability to identify and address the cause of the problem.

Many excellent texts are available that describe the processes and kinetics of enzymes and their inhibitors in great detail. How- ever, these imposing volumes are directed more towards enzymologists and are of limited use as bench-top guides to setting up and understanding simple enzyme assays. More general biochemistry textbooks tend to give an overview of Michaelis-Menten kinetics without relating the concepts discussed to the practicalities of assay design. Few reference texts are available that give the neuroscience student a basic understanding of how enzymes function as well as providing guidance in assay design, data analysis, and avoiding problems. This chapter attempts to fill this void and is directed towards the occasional user of enzymes in the neuroscience laboratory. A basic introduction to enzyme terminology will be followed by an appraisal of the types of questions that are often asked by neuroscientists with regard to enzymes. The relation between basic enzyme kinetics and bench-top assays of enzyme activity will then be discussed, with emphasis on where errors might be introduced as a result of a lack of familiarity with kinetic principles. Following a general comparison of continuous assay methods with discontinuous alternatives, the use of spectrophotometry and radiometry for determining initial velocities is described. Finally, an overview of some mechanisms of enzyme inhibition is presented, along with notes on how these might be distinguished experimentally. Many of the examples given in the text are taken from experiments with amine oxidase enzymes, that being the field of research in which the author is involved.

Having read the following chapter, the student may wish to look further into one or more aspects of enzymology, and several texts are particularly useful. Enzyme Assays in the Pract~al Approach series (IRL Press, Oxford), and Enzymology Ldg%x in the LaErfax series (Academic, San Diego, CA) are excellent publications that provide a more comprehensive coverage of many of the topics described herein, while remaining understandable to the novice enzymologist. Rather more detailed examinations of the kinetics of enzymes and their inhibitors are published by Segel(1975) and

Enzyme and InhIbitor Measurement 133

Dixon and Webb (1979). Specialized topics are considered in those volumes of the Methods in Enzymology series edited by D. L. Purich, namely volumes 63,64,87, and 249.

1.1. Enzymes, Enzyme Nomenclature, and the EC System of Classifica fion

Enzymes are biological catalysts and are involved in virtually all biological processes. The word enzyme comes from the Greek, meaning in yeast, the term having been devised by Kuhne in 1878 following his observation that a constituent of yeast was responsible for the hydrolysis of sucrose to glucose and fructose in a fermentation mixture. Enzymes are proteins with molecular weights in the tens or hundreds of thousands, and may be composed of several identical, or different, subunits. Each enzyme molecule has at least one catalytic center, or active site, and enzymes composed of several subunits may have several active sites. An active site is a pocket formed either on the surface of, or deep within the protein molecule, that is complementary in shape and size to the substrate molecule and contains amino acid sidechains appropriate for electronic interaction with specific groups on the substrate molecule. It is interesting to note that the vast majority of biological substrates contain at least one nitrogen bound to three other atoms. The unpaired electrons of nitrogen thus allow binding to one of several possible charged active site groups.

The catalytic activity of many enzymes depends upon the presence of a cofactor (Engel, 1996a), also called a coenzyme or pros- thetic group, that may be an altered amino acid within the peptide backbone, or a separate molecule or metal ion bound covalently or reversibly within, or close to, the active site of the enzyme. Assays of enzymes with loosely-bound cofactors may require the inclusion of extra cofactor in the reaction mixture, to minimize dialysis of bound cofactor from the enzyme into bulk solvent. The cofactor may confer catalytic activity upon an otherwise in- active protein (termed the apoenzyme) in one of several ways (Dixon and Webb, 1979), although the most common involvement is as a carrier molecule, removing part of the donor substrate and transferring it to the acceptor substrate within the active site.

As a catalyst, the function of an enzyme is to lower the activation energy necessary for a chemical reaction to take place (Segel, 1975). This is achieved by binding of one or more substrates within

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the active site, such that the orientation of substrates with respect to each other is optimal for the reaction to take place. In addition, substrate binding may cause some distortion of a susceptible bond within the substrate, producing an activated transition state. The combination of these factors can result in an increase in the rate of a chemical reaction by a factor of as much as 1015.

Enzymes are named and classified according to the recommendations of the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology (see NC-IUBMB, 1992). Each enzyme is given an EC (Enzyme Commission) number based on the type of reaction catalyzed, as well as a recommended name for general use and a systematic name describing the reaction process in more detail (Cornish-Bowden, 1996). For example:

EC number. EC 2.6.1.19 Recommended name: 4-Aminobutyrate transaminase (also

called GABA transaminase or GABA aminotransferase)

Systematic name: 4-Aminobutanoate. 2-oxoglutarate transaminase

In general, the recommended name indicates the preferred substrate or type of substrate, and the type of reaction catalyzed. The EC number conveys several important pieces of information:

2. Belonging to the enzyme class, “transferases.” 6. Belonging to the subclass of transferases that transfers

nitrogenous groups. 1. Belonging to the sub-subclass that transfers ammo groups

19. The serial number of the enzyme in sub-subclass 2.6.1.

The systematic name of GABA transaminase indicates the donor (4-aminobutanoate), the acceptor (2-oxoglutarate) and the class (transaminase). Systematic names may include further terms in parentheses to help distinguish between enzymes of similar function or to describe a secondary process that takes place in the reaction. For example, the systematic name for monoamine oxidase (EC 1.4.3.4) is Amine: oxygen oxidoreductase (deaminatmg) (flavin-containing).

Enzyme activity is most often quoted in hternational LTnrts (IU), or simply Unzts (W. One unit of enzyme activity is defined as that which metabolizes 1 umol of substrate (or forms 1 umol of product) m 1 min (see Tipton, 1993). Clearly, this is not a defmitive value,

Enzyme and Inhibitor Measurement 135

since the number of units of enzyme activity present in a sample will change with variations in factors such as temperature and pH, and, of course, with different substrates. If the conditions under which activity was determined are always defined, then quoting enzyme activity in ZU allows comparisons to be made between different laboratories under the stated conditions. The specific activity of an enzyme is simply the number of IU per mg protein. Thus, the common practice of quoting enzyme activity in units such as pmol h-’ (mg protein)-’ (see Section 2.1.) is merely a lengthier way of stating specific activity in U mg-I. The unit of enzyme activity recommended by the Nomenclature Committee of the International Union of Biochemistry and Molecular Biol- ogy is the Katal (Kat), corresponding to metabolism of 1 mol of substrate in 1 s. It is rarely, if ever, used in the neuroscientific literature, since workers prefer to work in 2.7 and mZJ rather than nKat and pKat.

1.2. Enzymology in fhe Neuroscience Laboratory;

Common Quesfions

A variety of enzymes from several classes and subclasses are of interest to neuroscientists, including oxidases, reductases, transferases, dehydrogenases, hydroxylases, decarboxylases, transami- nases, cholinesterases, synthetases, ATPases, kinases, and cytochromes I’450 (see vol 5, Neuromethods series). Questions asked with regard to such enzymes are equally numerous, but can be grouped together under three general headings.

1.2.1. Is The Enzyme of Interest Present

rn a Particular Cell Type, Tissue, Organ, or Specres?

In order to answer this question, an appropriate assay for the enzyme must be available. The Methods in Enzymology series is recommended as a starting point for a method search, while searches of computer databases such as Medline or the Chemical Abstracts Service (CAS) are also often successful. Otherwise, it may be necessary to design a novel assay. To minimize experimental error, and particularly when substrates with high K,n values are being used, it is generally preferable to assay for the appearance of a product rather than for the disappearance of a substrate. Designing an assay from scratch should not be considered until literature sources have been searched exhaustively, if an enzyme activity can be measured without too much difficulty,

it is likely that someone has already done it. Unfortunately, the reverse is also true; if a simple assay method has not been published, it may not have been for lack of trying!

If a suitable assay system has been found, it will then be necessary to determine the extent to which the enzyme must be purified from the host tissue to allow quantitative measurement of substrate turnover (Lowe and Thomas, 1996). Some familiarity with the physical properties of the enzyme is thus essential (Brocklehurst, 1996), such as stability in different buffer systems and buffers of different pH values, stability over a range of temperatures, resistance to degradation by proteases, whether or not carbohydrates are present on the protein surface, and the effects of freezing and thawing. Knowledge of the subcellular location of the enzyme will also assist in purification. In general, if the source of the enzyme is a solid tissue, then unless the tissue contains relatively high concentrations of enzyme or the assay system is sensitive to the production of picomoles of product, some purification and concentration of the enzyme will be required. However, one should bear in mind that removal of a membrane-bound enzyme from its hydro- phobic environment, perhaps with the use of a detergent, may alter the physical and catalytic properties of the enzyme.

It is often possible to assay soluble enzymes from blood or plasma without further purification, and cultured cells might also be used in this way. However, the presence of alternative metabolic pathways, or routes for removal of the metabolite of interest, must be considered when such impure preparations are employed (see following page). Differential centrifugation of tissue homogenates can be used to separate soluble enzymes from insoluble cellular material, which forms a pellet. The constituents of the pellet can be separated by sucrose density-gradient centrifugation, in which cellular organelles with different densities separate into distinct bands as they migrate down a sucrose gradient. Sucrose density-gradient centrifugation is often preceded by rate-zonal centrifugation, in which cellular constituents can be separated on the basis of their different sedimentation coefficients. For example, centrifugation of a filtered homogenate at 6008 for 10 mm yields a pellet (conventionally referred to as Pl) containing cell nuclei. Centrifugation of the supernatant (Sl) at 15,OOOg for 5 min gives a I’2 pellet consisting of mitochondria, synapto- somes (pinched-off nerve terminals), receptors, and, depending on the tissue type and homogenization conditions, myelin frag-

Enzyme and inhibitor Measurement 137

ments. Centrifugation of the S2 supernatant at 100,OOOg for 1 h gives a P3 pellet containing plasma membrane and microsomal material, and an S3 supernatant containing ribosomes and soluble cytoplasmic material (see Graham, 1984, for an excellent review on the use of centrifugation in the preparation of organelles and membrane fractions). Thus, it is usually relatively straightforward to complete an initial, crude purification and this is often all that is necessary to allow a quantitative assay to be done. Purification beyond these most basic steps requires more complicated techniques such as ion-exchange and affinity chromatography, and most laboratories are not equipped to carry out such procedures efficiently.

Most assay protocols provide information on how best to har- vest and purify the enzyme in question so that the assay can be made successfully. It is advisable to follow such purification protocols as closely as possible, or at least to ensure that the enzyme is purified to a similar degree by an alternative means. In cases in which some degree of purification is necessary, this is generally to remove some constituent of the raw homogenate that might interfere with detection of the assay product. An example of this might be in the measurement of monoamine oxidase type B (MAO-B) in animal tissues, as might be done during studies of antiparkinsonian drug efficacy. MAO-B can oxidize the synthetic amine, benzylamine, to benzaldehyde, which absorbs strongly at 254 nm (E x 12,000 M-l cm-l at neutral pH) (Tabor et al., 1954). Whereas continuous monitoring at 254 nm of benzaldehyde production is a useful measure of MAO-B activity when isolated mitochondria are used as the enzyme source, the assay does not work when a raw homogenate of liver or brain tissue is used, because other enzymes are present that further metabolize benzaldehyde to benzoic acid and benzyl alcohol. Furthermore, the presence of substantial amounts of particulate protein can mask the absorbance of benzaldehyde at 254 nm, since peptide link- ages, carbonyl groups, and aromatic amino acids absorb strongly over a range of wavelengths between 180 and 300 nm. Background noise caused by obstruction of the light path through the cuvet by such particulate matter can further diminish the sensitivity of this assay. Partial purification of MAO-B, by isolating the mitochondria in which this enzyme is found, will prevent secondary metabolism of benzaldehyde, and will reduce the amount of protein present. However, isolation of mitochondria may be

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undesirable, for example in larger studies, in which tissues are obtained from a number of animals. It might then be necessary to consider an alternative assay protocol. A discontinuous radiochemical assay for benzaldehyde formation by MAO-B (Lyles and Callingham, 1982) is unaffected by interfering enzymes and is thus suitable for use with raw homogenates, but is also relatively expensive and generates radioactive waste products. Alternatively, an inexpensive, continuous spectrophotometric assay exists that requires a minimum of enzyme purification and that is unaffected by further metabolism of benzaldehyde (Halt et al., 1997). How- ever, this assay is less sensitive than the others mentioned here and may be unable to detect benzylamine turnover in tissues containing low concentrations of MAO-B. One further approach would be to inhibit interfering enzymes with appropriate, selective inhibitors, although such experiments demand careful con- trols to account for any effects these inhibitors might have on MAO-B function. This example illustrates the choices, based on sensitivity, convenience, and cost, which face the researcher, and all of these aspects must be considered when alternative assay protocols are being compared.

It is important that, for any particular tissue type, the researcher is aware of the metabolic pathways in which the enzyme participates. Of equal importance is that the researcher understands the biochemical basis of the chosen assay method. If an established protocol is being followed, the significance of every assay constituent, and of each individual step in the protocol, should be clear to the student beforehand. An awareness of all of these points will reduce substantially the likelihood of unnecessary delays, cost, and frustration.

1.2.2. Does the Enzyme of Interest Metabolize a Particular Substrate or Group of Substrates?

Once the presence of an enzyme in a tissue or cell type has been established unequivocally, the potential role of the enzyme m that tissue might be addressed by considering the substrate specificity of the enzyme. This question might be approached in one of two ways.

In an in vitro study, the interaction between an enzyme and a potential substrate takes place in an artificial environment out- side the body, such as in a test tube or cuvet. This is the most common manner in which enzymes are studied, and the data

Enzyme and lnhrbitor Measurement 139

obtained can be used to calculate kinetic constants (K,,, VI,,,; see Section 2.1.) for metabolism of a particular substrate by a particular enzyme. Such values are useful when comparisons are made between substrates, or the effects of inhibitors are being studied, but are of limited use in determining the extent to which an enzyme is responsible for the physiological turnover of a substrate in the whole body.

In this respect, perfused organ experiments may prove to be more useful than experiments with isolated enzymes or homogenates. These in vitro studies involve the removal of an organ and its associated vasculature from an anesthetized animal and perfusion, usually via the arterial supply, with an appropriate buffer solution. In this way, compounds of interest can be perfused through organs such as the liver or blood vessel plexi, and the perfusate can be collected and analyzed for metabolites. Although kinetic data are more difficult to obtain by this method, such studies provide valuable information concerning the ability of substrates and metabolites to cross membranes, as well as allowing other enzymes present to influence substrate turnover. Similar information can be obtained from experiments with intact cultured cells suspended in an isotonic buffered medium, to which the substrate is added. Such studies may indicate whether or not a compound metabolized in a test tube can still access the enzyme and act as a substrate in a more physiological setting.

If in vitro experiments support the role of an enzyme in the metabolism of a particular substrate, the researcher might consider following up with an in vivo approach. Substrates are administered to the animal and samples of urine, blood, and tissue can be analyzed for metabolite content after a predetermined time. Information obtained is more usually used to assess the effects of administration of selective enzyme inhibitors, but the researcher is cautioned against using the presence of one or more metabolites to confirm participation of a particular enzyme in turnover of the administered substrate. For example, the presence in the urine of benzaldehyde, or derivatives of benzaldehyde such as hippuric acid, following administration of benzylamine to the whole animal does not alone confirm the involvement of MAO-B in benzylamine metabolism. Another amine oxidase, classed as EC 1.4.3.6 and usually referred to as semicarbazide- sensitive amine oxidase, also oxidizes benzylamine to benzaldehyde in vascular tissue, and the relative contributions of the two

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enzymes can only be resolved by the use of selective inhibitors This example illustrates the problematic nature of in vivo enzymology, and such experiments are perhaps best used as a supple- ment to in vitro studies, rather than as the sole means by which conclusive results might be obtained.

It is important in any enzyme assay to ensure that substrates are pure. Purity might be assessed semiquantitatively by thin-layer chromatography, whereas quantitative data can be obtained by analytical HPLC and related techniques. At best, the presence of impurities will introduce errors in estimations of kinetic constants. A more serious situation occurs when impurities, perhaps break- down products caused by substrate degradation, inhibit the enzyme. Many physiological substrates are relatively unstable in solution, and it is thus good practice to prepare substrate solutions freshly. A number of biogenic amines, such as tyramine and noradrenaline, oxidize readily in warm aqueous solutions of neutral pH. The rate of auto-oxidation is reduced substantially by keeping substrates on ice prior to experimentation, and by includ- mg an antioxidant mixture of ascorbic acid (120 pM) and EDTA (40 pM) in the substrate solution (Iversen, 1963). However, these antioxidants have been shown to affect sensitivity in some assays (Holt et al., 1997), and the researcher must quantify the effects on the enzyme of any such reagents included in the incubation

1.2.3 Is the Enzyme of Interest Inhibited

or Otherwise Affected by a Particular Drug or Chemical?

This is the question which, in the field of enzymology, 1s perhaps most often asked in the neuroscience laboratory. The primary action of many pharmaceutical agents is to inhibit an enzyme or group of enzymes, while some of the side effects of a significant number of drugs can also be attributed to enzyme inhibition. Drugs can inhibit enzyme activity in several ways, and a variety of methods are available to determine the mechanism of action of the inhibitor vs the enzyme of interest. The various classes of inhibitors and the methods used to differentiate between them are described in Section 4, below. However, to understand fully the manner in which inhibitors affect enzyme activity, a familiarity with the basic concepts of enzyme kinetics is essential. The following section attempts to acquaint the researcher with these concepts, and to describe how one might set up an appropriate assay to obtain kinetic constants.


2, Enzyme Kinetics Explained

2.1. Steady-State Kinetics

We shall consider here the kinetics of a unireactant enzyme reaction, that being the simplest model to explain the kinetic properties of most enzymes. This model, which assumes that a single substrate (S) is metabolized to a single product (P) via an intermediate complex (ES) formed between the enzyme 0.3 and substrate, is represented by the equation:

E+S w ES AE+P (1)

k -1

The rates of the forward and back reactions for the interaction between E and S are given by the rate constants, k, and k-,, respectively, while the rate of product formation from ES is given by the rate constant, k,. In steady-state kinetics, it is assumed that during a short initial period of equilibration, the concentration of ES builds up to a constant, steady-state level. For most enzymes, ES decomposes to E + P extremely rapidly and so the rate of product formation is directly proportional to [ES].

Most students are familiar with the Michaelis-Menten equation to some degree. This equation describes the kinetic behavior of enzymes in a steady-state system. The Michaelis-Menten equation can be derived from Eq. (1) rather easily, if a number of basic assumptions are made, and the derivation is described adequately in most basic biochemistry textbooks. This derivation shall not be reiterated here; rather, the equation shall be examined with respect to its influence on a bench-top enzyme assay.

The Michaelis-Menten equation can be written as follows:

v / vlll*x = ISII~K,,, + lS1) (2)

The individual components of the equation are:

[S] Substrate concentration. Units M (molar). z, This is the initial reaction velocity at any given substrate con-

centration. From Eq. (2), it is clear that if Vn,,, and K,” are constants, then an increase or reduction in [Sl, the substrate

142 Holt

concentration, will cause an increase or reduction in v, the reaction velocity, unless [S] is very much larger than K,, in which case small changes in [S] will have a negligible effect on v. Methods for the determination of v values are discussed in Sections 2.3. and 3.

V max The maximum possible reaction velocity, that occurs when all of the enzyme active sites are saturated with substrate. This is true when [S] is very much larger than K,,,, and so u/Vnlax = 1. Thus, [ES] is maximal and the rate of product formation, which is directly proportional to [ES] (see previous page), is maximal. However, if the amount of enzyme present is altered, then the maximum possible value of [ES] is altered, thereby changing v,,,,* The maximum possible reaction velocity is thus directly proportional to the amount (or concentration) of enzyme. The units of Vmax, and of v, are expressed as amount of substrate metabolized or product formed per unit time per amount of enzyme. In practice, the amount of enzyme is often unknown, and the rate is often expressed in terms of tissue protein content or a similar parameter. For example, umol h-’ (mg protein)-’ or nmol min-’ (mL plasma)-l.

Km This is the Michaelis constant. An analysis of the derivation of the Michaelis-Menten equation reveals that, for all intents and purposes:

Km = (km, + k&k1 = [El [SI/[ESl (3)

From Eq. (31, it can be seen that K,” can be expressed in units of concentration, M. From Eq. (2), it is clear that if [S] = K,,, then v / V,,,,, = 0.5. In other words, the Km value, which is specific for a particular substrate interacting with a particular enzyme under a defined set of conditions, is that concentration of substrate at which the enzyme is operating at half of the maximum possible velocity (V,J.

What sort of kinetic behavior is predicted by the Michaelis- Menten equation? As an example, the enzyme, penicillinase (EC 3.5.2.6) metabolizes benzylpenicillin with a Km of approx 50 PM. For a fixed concentration of peniclllinase, the Michaelis-Menten equation predicts that at concentrations of benzylpenicillin very much less than 50 pM, v will increase almost linearly with increasing [Sl and the reaction exhibitsfirst-order kinetics. However, when the concentration of benzylpenicillin is much greater than 50 PM,


PI WV

Fig 1. The effect of substrate concentration on the rate of benzylpem- cillm metabohsm by penicillinase. As [Sl is increased, the initial reaction rate, ~1, increases m a hyperbolic fashion, to a maxrmum rate of V,,,,, at mfimtely hrgh values of IS]. When z, = 0.5 x V,,,nl. then tS1 = K,,, For this reaction, K,,, z 50 uM Note the difficulty m determining VINny, and thus Kill, from such a plot

variations in [S] will have a negligible effect on v, since penicillinase is operating at, or close to, V,,,,, and the reaction exhibits zero-order kinetics. In fact, there is a hyperbolic relation between v and [S], as illustrated in Fig. 1.

When considering the metabolism of a substrate, or group of substrates, as discussed in Section 1.2.2. above, the researcher is most often interested in obtaining values for K,,, and V,na,. For many enzymes, where k-, is significantly larger than kp, the K,, provides an indication of the affinity between E and S; a low K,,# indicates a high affinity for the substrate, and vice versa. Unfortunately, in the neuroscience laboratory, information with regard to rate constants and enzyme concentration is rarely available. Nevertheless, Km values are still highly useful in comparative situations; knowledge of K,,, values for a particular substrate allows the researcher to compare enzymes obtained from different tissues or species, Similarly, calculation of Km values for a panel of substrates with a single enzyme provides information on which modifications to substrate structure most affect the suitability of the compound to act as a substrate for the enzyme. The Km also provides a ballpark

144 Holt

estimation for the concentration of substrate likely to be present physiologically. It would not make sense for an endogenous substrate to be present at a concentration substantially below the K,,,, since the enzyme would be operating at a fraction of V,,,,,. On the other hand, at concentrations significantly higher than the K,,,, the enzyme can operate no more than twice as fast as it can at the Km concentration of substrate, while the ability of the cell to react to changing substrate concentrations is seriously compromised. Fi- nally, knowledge of the K,,, allows the researcher to do assays in vitro under conditions in which the enzyme is operating close to V,,, and product formation is thus linear with time

It is apparent that, while useful in making comparisons, the significance of the K,,, value is a little unclear in the absence of other rate constants. At first glance, the V,,,,, value seems to provide the researcher with a more concrete indication of the efficiency of the enzyme in metabolizing a particular substrate. Would not the substrate exhibiting the higher V,na, value be metabolized most rapidly? The answer, of course, is yes- but only at saturating substrate concentrations, and that depends on the value of Kin. In other words, after obtaining both K,,, and V,,, values, the researcher can make meaningful comparisons with regard to which substrate is turned over most efficiently, or which enzyme turns over a particular substrate most efficiently. Generally, a compound with a low K,,, and a high Vm,, is considered a better substrate than one with a high Km and low Vm,x.

One further kinetic constant which is closely related to V,,,* and which may be of interest is the turnover number. This has already been mentioned, as kp in Eq. (1) and (3). The turnover number is the number of moles of substrate metabolized per min per mole of enzyme (or per mole of active site) at saturating substrate concentration Put even more simply, it is the number of substrate molecules metabolized in 1 min by one enzyme molecule at saturating substrate concentration. The units of k are (min-‘>, and values of k, range from 50 to approx lo7 min- 1 Fhe reciprocal of the . turnover number is the time taken for a single substrate molecule to undergo metabolism. The turnover is linked to V,,,,, by the equation:

where [E,] is the total concentration of enzyme. If a mechanism- based or active-site-directed irreversible inhibitor of the enzyme


is available (see Section 4.3., below), it may be possible to determine [E,] in a tissue homogenate (Lowe and Thomas, 1996). This has been done with radiolabeled clorgyline, to determine the concentration of MAO-A active sites in a suspension of rat heart mitochondria (Fowler and Callingham, 1979). Thereafter, the substrate kp value can be calculated from Eq. (4). Whereas knowledge of the enzyme concentration is necessary to calculate k,, a number of graphical methods exist whereby K,,, and V,,,, can be determined easily from basic experimental data, and these are discussed below in Section 2.2.

The above discussion has centered upon unireactant reaction mechanisms. In reality, most enzymes catalyze reactions between two or more substrates, giving rise to two or more products. Each substrate will have its own K,,, and V,,,a, values for the enzyme. However, these can no longer be considered as constants, since their values usually depend upon the concentration of the other substrate. True Km and Vntax values for a substrate are obtained when the other substrate(s) is present at a saturating concentration in the assay. Note that the second substrate may be some- thing as simple as O,, as is the case with MAO. In this case, the researcher should ensure that kinetic assays of amine substrates are performed under conditions of saturating 0,. If this simple rule is followed, satisfactory estimates for K,n and V,,,, can be obtained for almost any enzyme-substrate combination.

For many multisubstrate systems, precise kinetic data can not be obtained by following the above procedures, since some of the assumptions made in the derivation of the Michaelis-Menten equation may be invalid. In such cases, more complicated models are required to describe enzyme behavior, and these have been summarized by King and Altman (19561, Cleland (1963a-c), and Engel (1996b). However, these models are beyond the scope of this introductory text, and virtually all enzymology problems m the neuroscience laboratory can be solved satisfactorily by following the straightforward procedures described herein.

2.2. Graphical Determimtion of Kinetic Consfanfs

Since the z, vs [S] curve (Fig. 1) is a hyperbola, it is extremely difficult to determine K,,, and V,,,, values directly without the use of a computer. However, the same data can be plotted in one of several alternative ways so that a straight line or series of straight lines, rather than a hyperbola, can be drawn through the data

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points, greatly facilitating determination of K,n and Vmax values To be able to construct a hyperbola for D vs [S], the substrate, at several concentrations, must be incubated with enzyme, at a single concentration, and z, (the initial reaction velocity) is determined at each concentration of substrate. Note that it would not be possible to construct a hyperbola if D had not been determined at several substrate concentrations on either side of the Km concentration. This is an important point to consider when choosing the substrate concentration range for the assay. The minimum range for [S] is between 0.5 x & and 5 x Km (Henderson, 1993), although a wider range, from 0.2 x Km to 8 x Km is preferable. If most or all of the chosen values of [S] lie below K,,, it 1s difficult to determine V mdy, and therefore K,,,, with any certainty. Likewise, an accurate value for Km can not be determined from data points which all lie above K,,,, and if all [S] values are significantly higher than K,,!, the reaction will exhibit kinetics which are zero-order.

If an approximate value for Kin is not known when choosing the concentration range for S, a suck-and-see assay should be done. Since most K,,, values lie between 1O-7 M and 1O-2 M, the substrate should be prepared at several concentrations covering that range (see Sec- tion 2.3.3. below), with consecutive concentrations separated by less than one order of magnitude. For example, an appropriate choice of concentrations would be (PM): 0.2,1,5,10,50,100,500, 1000,5000, and 10,000. Limited availability of the substrate, poor solubility, or cost may preclude use of the highest concentrations. Plotting ZI vs [S] will then provide an estimation of the K,,, and thus the substrate range that should be used m a more comprehensive assay. When the substrate concentration range covers more than two orders of magnitude, as would be the case in the suck-and-see assay described above, plotting [S] values on a log,, scale will prevent bunching of data at the lower end of the [S] axis. The hyperbolic function is transformed to a sigmoid function, and the K,,! value can be estimated by determining [S] at the point of inflexion (Fig. 2).

Having obtained z, values at several concentrations of S sur- rounding the K,, the data can be plotted in one of several different ways to obtain best-fit kinetic constants for substrate turnover (Engel, 1996b). The first three methods discussed below are derived from simple transformations of the Michaelis-Menten equation (Eq. [Zl) to give equations yielding a straight line (y = rnX + c). Kinetic constants can then be obtained from slopes and intercepts of the best-fit straight line.

Enzyme and lnhrbltor Measurement 147

L

g 80- 5 2 $

60-

z 2. 40-

b

0 t I 1 I 1 , I

-7 -6 -5 -4 -3 -2

WloPl WI

Fig 2. “Suck-and-see” plots to estimate K,,t values prior to full kmetic assays. Plotting [S] on a logarrthmic scale allows a wide concentration range to be examined and transforms hyperbolic data to a sigmoidal form Approximate Km values can be obtained from visual or computer- assisted determination of [S] at the points of mflexion. In this example, K,,, values for two different substrates were 5 PM (crrcles) and 500 pM (triangles).

2.2.1. The Hanes- Woolf Plot ([51/v vs [S])

This is the preferred method by which data are analyzed to obtain best-fit values for K,,, and Vmax (Henderson, 1993). The intercept with the x-axis has the value -Km, whereas the slope of the line has the value 1 /V,nax (Fig. 3A). Compared with the Hofstee and Lmeweaver-Burk plots (see Sections 2.2.2. and 2.2.3.1, plot- tmg of data on these axes causes least distortion of the experimental error on each point and thus yields perhaps the most reproducible values for kinetic constants, and those closest to values that might be obtained from computerized analysis of the hyperbola or a direct linear plot.

2.2.2. The Hofstee Plot

(or Woolf-Augustinsson-Hofstee plot; v vs v/[S])

This plot provides excellent confirmation that the data obtained can be fitted to a straight line (Fig. 3B) and that the enzyme-substrate interaction thus follows Michaelis-Menten kinetics (Dowd

148 Ho/t

A 6- Q5- .S

w flS] (arbitrary units)

Figs. 3 A,B

and Riggs, 1965). This might be explained partly by the fact that the experimental variable, D, appears on both axes, magnifying errors arising from poor experimental technique and thus increasing the requirement for care and precision on the part of the researcher. However, as a result of the distortion of errors that occurs during data transformation, linear regression by least- squares analysis may not be used to find the best-fit straight line (Henderson, 1993). Consequently, this plot is used infrequently in presentations of kinetic data.


I I I I iJ ,

-300 -200 -100 0 100

-PI (PM)

Fig. 3. Linear kinetic plots for the determination of IX,,, and V,,,,, values: (A), Hanes-Woolf plot; (B), Hofstee plot; (C), Lmeweaver-Burk plot; (D), direct linear plot.

2.2.3. The Lineweaver-Burk (Double Reciprocal) Plot (l/v vs l/[.Sl)

This is the most popular plot from which kinetic constants are derived. The intercept with the x-axis has the value -l/K,, whereas the y-intercept has the value 1 /V,,, (Fig. 30. In addition, the effects on kinetic constants of competitive and noncompetitive

150 Ho/t

inhibitors are strikingly obvious when data are plotted in this way (see Section 4.2.). However, there exist several arguments against the use of the Lineweaver-Burk plot to obtain Km and V,naz values.

The largest relative errors in the measured variable, z), tend to occur at substrate concentrations below the K,,,, when the enzyme 1s working at a rate significantly below Vm,,. This merely exacer- bates the effect of plotting reciprocals of the data, that being to place more weight on data points obtained at the lowest values of ZI and [S]. Figure 3C clearly shows how the reciprocals of a set of substrate concentrations that were chosen to have relatively even spacing on the [Sl axis of Fig. 3A (12.5, 25, 37.5, 50, 75, 100, 125, 150,175,200,250,375, and 500 PM) become concentrated towards the left of the graph (high u and [Sl). Whether the best-fit straight lme is determined by eye, or by least-squares linear regression, more significance will be given to the one or two data points on the right derived from low ZI and [S] combinations. In this way, it is possible to fit a straight line of excellent fit (r2 > 0.99) to very poor experimental data. As observed by Henderson (1993), the fact that the Lineweaver-Burk plot can conceal a poor fit between the data and a straight line may be the reason for its popularity.

Whereas careful choice of substrate concentrations can provide reciprocal points of equal spacing on the l/ [Sl axis, this still does not address the fact that the largest errors occur in reciprocals of the lowest values of ZI. In order to obtain reliable kinetic constants from a Lineweaver-Burk plot, careful choice of substrate concentration must be coupled with use of an appropriate method to determine the best- fit line that gives more weighting to those transformed data points with smallest errors. When all is said and done, it is both safer and more straightforward to use the Hanes-Woolf plot.

Regardless of which of the above methods is used to analyze kinetic data, it is desirable, though not crucial, to use a linear regression program that gives more weight to those values of D obtained at higher substrate concentrations, since these have the smallest associated relative errors. However, the careful experi- menter will mmimize such errors, thus obviating the need for weighted linear regression, and results obtained will not differ significantly from those generated by weighted regression analysis.

2.2.4. The Direct linear Plot This is perhaps the best means by which Kin and V”,,, can be

determined from kinetic data. Values of [S] are plotted on a nega-


tive horizontal axis and experimentally determined values of v are plotted on a vertical axis (Fig. 3D). If this is done for two or more pairs of ([S], V) values, straight lines drawn through corresponding [S] and v points intersect at [S]=K, and u=Vmar (Eisenthal and Cornish-Bowden, 1974). Smce no transformation of the data takes place, no distortion of errors occurs and no weighting is necessary. In practrce, a single point of intersection will not be obtained when several pairs of ([S], V) values are plotted. Rather, several intersections, yielding several values for Km and Vmax, will be seen; the best-fit values in this case are the median values.

Despite its apparent advantages, the direct linear plot is rarely used when kinetic data are published in graphical form. Whereas other methods such as the Hanes-Woolf and Lineweaver-Burk plots allow several groups of data to be displayed clearly on a single graph, such as may be required in some inhibitor studies (see Section 4.2., below), the direct linear plot becomes congested and confusing. In addrtion, whereas alternative plots require that data can be fitted to a straight line if the enzyme complies with Michaelis-Menten kinetics, any deviation from the behavior predicted by Eq. (2) may not be apparent on a direct linear plot.

In summary, the Hofstee and Hanes-Woolf plots are most useful if confirmation of Michaelis-Menten kinetics is required There- after, kinetic constants are best obtained from a direct linear plot, or from a Hanes-Woolf plot, and data are most clearly displayed on a Hanes-Woolf or, with care, on a Lineweaver-Burk plot. In particular, the effects of inhibitors are perhaps most clearly displayed by the Lineweaver-Burk method, but it is advisable to use an alternative approach to calculate values for kinetic constants, including inhibitor constants, which are to be reported.

2.3. Practical Considerations in Obtaining Initial Reaction Velocities (v)

The above text has discussed the usefulness of knowing kinetic constants and how these are most easily obtained from an appropriate set of (v, [S]) values. One assumption that is always made, and that must be ensured, is that [Sl is correct. There is no substitute for good laboratory technique and care in the preparation of stock solutions and serial dilutions of substrates. The experimental variable is thus V, and an appropriate analysis of experimental data must be made if correct values for D, and thus Km and V,,,,

152 Ho/t

are to be determined. It is during this analysis that errors most often occur, although these are largely preventable if the following points are taken into consideratron.

2.3.1. Multiple Measurements

The influence of experimental errors can be reduced by making several measurements of u at each concentration of substrate and then taking a mean value for D. In most cases, it is acceptable to make triplicate measurements, although at least five measurements are recommended if standard deviations and/or standard errors are to be calculated (Storer et al., 1975). A kinetic plot should be made up of measurements at no fewer than five different substrate concentrations; in the experience of the author, careful measurements made at between six and eight concentrations of substrate are almost always adequate.

2.3.2. Continuous and Discontinuous Assays

A continuous assay is one in which the disappearance of substrate or appearance of product-in other words the progress of the reaction-is monitored continuously (Engel, 1996b). For example, benzaldehyde absorbs strongly at 254 nm and so conversion of benzylamine to benzaldehyde by MAO can be followed continuously in a spectrophotometer at 254 nm (see Section 1.2.1.). This is a direct continuous assay, since one of the reaction species is monitored directly. The reduction of pyruvate to lactate by lactic acid dehydrogenase (EC 1 .l. 1.27) is accompanied by oxidation of NADH, which absorbs at 340 nm, and the decrease in absorbance at 340 nm is thus a direct continuous measure of lactic acid dehydrogenase activity (Kornberg, 1955). In comparison, acetylcho- linesterase (EC 3.1.1.7) can be measured continuously by following hydrolysis of acetylthiocholine. However, this is an lndzrect assay because the thiocholine product must first participate in an exchange reaction with Ellman’s reagent (dithio-bis-(2-nitrobenzoic acid)), which is included in the assay mixture, to release the yellow nitrothiobenzoate ion, which absorbs at 412 nm.

All of these are examples of assays that allow contintlous monitoring of the reaction. Consider now the data that would be obtained from such a continuously monitored assay. Fig. 4 illustrates three reaction progress curves for the metabolism of benzylamine by rat liver MAO-B. The reaction was monitored continuously at 254 nm for a period of 15 min, with the absor-


ESO-

5 50- 8 E40-

g 30- w g 20-

a lo-

Time (minutes)

Fig. 4. Contmuous measurement of benzylamine metabolism by ml- tochondrial MAO-B. Benzylamme at 750 PM (A), 75 PM (B) or 15 pM (C) was incubated with isolated rat liver mitochondria and the increase in absorbance caused by benzaldehyde formation was followed at 254 nm for 15 min Tangents to the initial rates are indicated by dashed lines. Values for v, obtained from the slopes of the tangents, were (nmol min-9; 4.55 (A), 2.5 (B), and 0.83 (C). The K, for benzylamine metabolism by rat liver MAO-B is approx 75 PM.

bance change indicating the rate of production of benzaldehyde, and thus the rate of metabolism of benzylamine. Absorbance readings were converted to nanomole values by application of the Beer- Lambert law (see Section 3.1., below). Three different initial concentrations of benzylamine were used: 750 pM, 75 pM, and 15 PM; the K,,, for benzylamine with this enzyme is approx 75 PM. Each assay contained 0.005 IU of MAO-B activity.

At an initial substrate concentration of 750 pM, the reaction proceeded linearly for the entire period of measurement (plot (A) on Fig. 4). The reason for this becomes apparent when one com- pares the substrate concentration with the K,,, value. With [Sl initially equal to 10 x K,,,, the enzyme operates at 91% of Vmoy (from Eq. [2J), with benzylamine metabolized at a rate of 4.55 nmol min-I. During the 15-min measurement period, 70 nmol of substrate were metabolized, reducing the substrate concentration to approx 680 nM. If this value is then substituted into Eq. (2), it can be seen that the final reaction velocity is still at 90% of V,,,,,. Thus, the reduc-

154 Ho/t

tion in the rate of reaction over the period of measurement was negligible, and the kinetics are zero-order. The initial rate of reaction, v, is equal to the slope of the straight line.

When an initial substrate concentration of 75 pM was used, a rather different progress curve was seen (plot (B) on Fig. 4). The rate of reaction was seen to decrease constantly throughout the period of measurement, and was not linear for any portion of the reaction. With [S] initially equal to Km, the enzyme operates at 0.5 x Vmax (2.5 nmol min-‘1. The curvature of the plot can be explained by the fact that, although only approx 30 nmol of substrate were metabolized during the 15-min measurement period, this caused the reaction rate to decrease from 0.5 x V,,, to approx 0.38 x V,,,,, (from Eq. [2]). In the absence of an initial linear period of metabolism, the initial rate is determined from the slope of the tangent to the progress curve with the point of contact at t = 0, shown as a dashed line on Fig. 4.

The last substrate concentration used was 15 pM, representing 0.2 x K,,, (plot (C) on Fig. 4). The initial rate, calculated from Eq. (2) and determined experimentally from the tangent to the progress curve at t = 0, was 0.17 x V,,x (0.83 nmol min-I). Around half of the available substrate had been consumed over the 15-min measurement period, with the result that the progress curve was almost horizontal by the end of this period.

The above example illustrates that calculation of v from contmuous data is a straightforward procedure. Initial velocity values can be plotted by one of the methods described above to obtain K,,, and Vm,, values for the metabolism of benzylamine by MAO-B. Provided that adequate attention is given to careful experimental technique, and appropriate blank assays are conducted (see Sec- tion 2.3.3., below), the continuous approach represents that most likely to yield reproducible, error-free kinetic data.

A discontinuous assay is one in which the enzymatic reaction must be terminated before a measurement of the amount of substrate used, or product formed, can be made. For example, the radiochemical assay of [‘“Cl benzylamine metabolism by MAO-B (Lyles and Callingham, 1982) requires that the reaction be stopped by the addition of acid, followed by separation of [‘“Cl benzylamine from [14C] benzaldehyde, and counting radioactivity associated with [‘“Cl benzaldehyde in a liquid scintillation spectrometer. This assay can only be done discontinuously because the radioactive product must be separated from the radioactive sub-


strate prior to a measurement being made, since the spectrometer can not differentiate between the two. Similarly, the radiochemical assay for GABA transaminase (4-aminobutyrate transaminase; EC 2.6.1.19) must be done discontinuously because the product ([‘“Cl succinate) must be separated from the substrate V4Cl GABA) before it can be measured in a scintillation spectrometer (Tunnicliff, 1986). The chromogenic compound, 2,2’-azino-bis(3-ethylbenzthiazoline- 6-sulphonic acid) (ABTS), reacts with hydrogen peroxide in the presence of peroxidase to form an intense blue-green dye that absorbs at 414 nm. It can be used in assays of MAO activity (Szutowicz et al., 1984), since hydrogen peroxide is a product of amine metabolism. However, ABTS inhibits MAO, and it absorbs strongly only under conditions of low pH. Thus, it can not be included in the reaction mixture, but rather is added, along with hydrochloric acid, after a specified incubation period. It is thus for a different reason that this assay must be done discontinuously.

An understanding of the manner in which v values are calculated from discontinuous data is of crucial importance to the researcher, if costly errors are to be avoided. The principle on which such assays are based is the same, regardless of which enzyme or assay method is involved. Substrate metabolism is allowed to proceed for a predetermined time, known as the incubation period, and the reaction is terminated (see Fig. 6 and related text, below). The amount, or concentration, of product (or remaining substrate) is then determined, and this value is used to determine the “initial rate” of the reaction. For example, if it was determined that 50 nmol of product had been formed over an incubation period of 10 min, the rate of product formation (v) would be calculated as 5 nmol min-‘. One very important assumption is made here, that being that the rate of product formation was linear for the duration of the incubation period. In fact, this must never be assumed without having verified experimentally that the assumption is valid. This is done by repeating the assay at several incubation times and plotting a reaction progress curve (product vs time) to determine the length of incubation for which product formation remains linear at the substrate concentration being studied. Only then should an appropriate incubation time be chosen.

The consequences of failing to perform this crucial preliminary study each time assay conditions are changed are illustrated in Fig. 5. The experiment that generated the continuous data

156 Holt

z 60-

s 50- al s40-

$ 30- w 5 20- m

IO-

Fig. 5 Drscontinuous measurement of benzylamine metabolism by mltochondrlal MAO-B Benzylamme at 750 pM (A), 75 pM (8) or 15 pM (C) was incubated with isolated rat liver mitochondrra for 15 min before the reaction was terminated and the absorbance at 254 nm due to benzaldehyde was determined. Apparent initial rates were calculated from the slopes of lines loming points at t = 0 and t = 15, following the incorrect assumption that product formatron had been linear for the entire incubation period. True initial rates were determined from the tangents to the continuous data presented in Fig. 4, shown here as dashed lines. Whereas the rate determined discontmuously at [Sl = 750 pM was not different from that measured continuously, discontinuous measurement caused v to be underestimated by 24% and 39% at [Sl = 75 PM and 15 PM, respectively

displayed in Fig. 4 was repeated under identical conditions. How- ever, the concentration of benzaldehyde was not measured continuously, but rather was determined from a single absorbance measurement at the end of a 15-min incubation period. It is clear that, whereas the chosen incubation period was appropriate for the highest substrate concentration and gave a value for o in agree- ment with that obtained from continuous measurement, initial rates at the lower substrate concentrations were substantially underestimated. The dashed lines indicate the tangents, and thus true initial rates, determined from the contmuous data in Fig. 4. Comparison with the solid lines indicates that, if the experiment was done discontinuously under the conditions described above, the initial rates at 75 pM and 15 pM would be underestimated by


24% and 39%, respectively. In turn, this would lead to the determination of kinetic constants that may differ markedly from those calculated from continuous data. One should note that the largest discrepancies would occur at the lowest substrate concentrations, and these errors would be magnified if data were then plotted by the Lineweaver-Burk method (see Section 2.2.3.).

If one follows this line of thought a little further, it becomes apparent that a discontinuous assay will always underestimate v when [Sl is around, or below, the K,,, concentration, since the rate of product formation is Yteper linear in such cases. In particular, at substrate concentrations of 0.5 x Km or less, the reaction kinetics are approaching first-order, so that any reduction in [S] will lower the reaction rate by an equivalent degree. A compromise must therefore be reached, and reaction and incubation conditions should be chosen which minimize the degree of substrate depletion. It is generally accepted that discontinuous conditions under which less than 10% of available substrate is used will yield an acceptable approximation for v at low substrate concentrations, although in some situations this approach may not be valid (Tipton, 1993).

In order to minimize substrate depletion, the researcher has two options. The first is to reduce the incubation period to a minimum. However, other sources of error become more important at short incubation times, such as how to ensure the precision of the length of incubation period. Assays done in large volumes (>200 PL) may take an appreciable time to warm to the desired assay temperature, particularly if the assay is being done in a polystyrene or polythene vessel with poor heat conducting properties. Simi- larly, if the assay is stopped by chilling the reaction mixture, the problem of delayed cooling may occur. For example, Fig. 6 shows the times taken for 500 PL of water in a polythene microcentrifuge tube (A) and 200 ~.I,L of water in a polystyrene 96-well microtiter plate (B) to rise to maximum temperature from 0°C when placed in a water bath at 37.O”C. Whereas the contents of the microcentrifuge tube had climbed to 30°C in 45 s and reached a maximum of 36.3”C shortly thereafter, the water in the plate well took almost 4 min to climb to 3O”C, and the maximum temperature of 34.O”C was not reached for almost 10 min. Clearly, the errors introduced by poor heat transfer in the latter case could be substantial, particularly in kinetic experiments with short incubation times.

158 Holt

OL I * 1 c 1 * 1 ( 1% 1

0 120 240 360 460 600 Time (seconds)

Fig 6 Rates of heat transfer from a water bath to the contents of two plastic reaction vessels. Water at 0°C was placed in a polythene mrcrocentrlfuge tube (500 pL, circles) or in one well of a 96-well microtlter plate (200 uL, triangles). The microcentrlfuge tube was partially sub- merged in a water bath at a temperature of 37.O”C, while the mlcrotlter plate was floated on the water surface The temperatures of the vessel contents were monitored with a thermocouple device until a maximum, steady temperature had been reached This was, for the contents of the mlcrocentrifuge tube, 36 3”C, and for the contents of the microtiter plate well, 34 0°C Values are the means of two experiments.

The second option is to reduce the reaction rate, by reducing the concentration of enzyme present. The extent to which the concentration of enzyme, and thus reaction rate, can be reduced is dictated by the sensitivity limits of the assay method. The researcher should determine beforehand the lower limits of sensitivity of the assay in question and should then choose the lowest enzyme concentration that gives reproducible measurement of turnover at the lowest substrate concentration being used. The importance of this point can not be overemphasized; if the experiments that produced the data shown in Figs. 4 and 5 had been done with a lo-fold lower concentration of MAO-B present, substrate depletion over the 15-min incubation period would have amounted to approx 5% at 75 pM and 8% at 15 pM, and rates determined discontinuously would have been statistically identical to those obtained by continuous measurement

Enzyme and InhibItor Measurement 159

2.3.3. Settrng Up and Analyzing a Kinetic Assay It should now be apparent that most of the work involved in

obtaining kinetic constants for metabolism of a particular substrate by a particular enzyme takes place prior to doing the actual kinetic assay. The assay itself should then be a straightforward procedure if the following guidelines are adhered to.

1. Substrates should be prepared freshly, whenever possible. Mixing of the stock substrate solutions with other reaction constituents will dilute the substrate. The term, [S], refers to the final concentration present m the assay, and stock solutions should be prepared at concentrations that take account of the dilution factor. An estimate for K,,, should be known beforehand, and at least six different concentrations, ranging from 0.2 x Km to 8 x K,,,, should be assayed.

2. The dilution effect also applies to the enzyme added and the same approach should thus be taken. Since enzymes are generally kept on ice prior to experimentation, it is often useful to prepare enzymes in a concentrated form and to start the assay by adding a comparatively small volume of enzyme to the assay mixture. In this way, the assay temperature is not reduced significantly by adding cold enzyme solution. In tissues containing low concentrations of enzyme, concentrated homogenates may be too thick to pipet accurately. When larger volumes of more dilute enzyme are used, the assay can instead be started by adding substrate.

3. It is important that reaction constituents are mixed rapidly when the last component is added. Mixing can be accom- plished with a pipet if assays are performed individually, such as m spectrophotometer cuvets. If many assays are run in parallel, such as in radiochemical experiments where several hun- dred samples might be incubated simultaneously, an alternative means of rapidly mixing all samples should be found. If the total reaction volume is small (approx 250 PL or less) and the assay is done in a glass testtube or similar vessel with good heat-transfer properties, it may be possible to vortex-mix all reaction constituents thoroughly if tubes are kept chilled in iced water, prior to the incubation period.

4. Many substrates are prepared in water, rather than buffer, since many compounds dissolve poorly in some buffer systems, The researcher should ensure that addition of nonbuffered sub-

160 Ho/t

strates, or other reaction constituents, does not alter the pH of the assay mixture. Some enzymes are also sensitive to changes in ionic strength of the solvent, and so the use of buffers of relatively high ionic strength will minimize fluctuations on addition of substrates or inhibitors.

5. In many assay systems, some interaction takes place between reaction constituents which causes an apparent turnover of substrate in the absence of enzyme, substrate, or other agent necessary for detection of substrate turnover. The causes of such “blank” rates are numerous, but they must be accounted for in the final analysis of data. For example, tissue homogenates often contain endogenous substrates and, unless removed beforehand, these may augment measured rates of metabolism of added substrates. Many radiochemical assays suffer from substantial blank readings, often as a combined result of the inability to achieve perfect separation of substrates from products and the high content of radiolabel in the substrate. It is important that the researcher determines the cause of measured blank rates and includes appropriate blank assays in the experiment, the results of which are then subtracted from those obtained from the assay proper. One should note that, if blank rates are dependent on the presence of substrate, then it may be necessary in kinetic studies to include blank assays at each, or at least several, concentrations of substrate.

3. Common Assay Methods Outlined

3.1. Spectrophotometric Assays

Many chemical species are capable of absorbing light at one or more wavelengths in the UV-visible range (200-700 nm). The wavelength at which the molecule absorbs is determined by the types of atoms and bonds present, and more specifically by the orbital energies of their electrons. Since white light is made up of a spectrum of colors (wavelengths), absorbance at one or more wavelengths will remove one or more of the components of white light and a color will thus be imparted on the solution containing the absorbing species. The color of the solution thus indicates which colors were not absorbed. However, if a solution contains molecules that absorb light only in the UV range (200-400 nm), it will still appear colorless since light at wavelengths below approx 400 nm is invisible to the human eye. Note that regular optical


glass will not transmit UV light, and cuvets made from quartz glass or a UV-transmitting plastic should be used at wavelengths below 360 nm.

The fraction of incident light transmitted by a solution is termed the transmittance (T) of that solution, with T normally expressed as a percentage.

T = I/I, (5)

The symbols, I and IO, refer to the intensities of transmitted light and incident light, respectively. A far more useful measure is absorbance (A), which is a function of T:

A = -log,, T = log,,, 1,/I (6)

The absorbance of a solution is directly related to the concentration of the absorbing species present by Beer’s Law, or the Beer- Lambert equation:

A=&cl (7)

The components of Eq. (7) are:

A

C

1

E

The absorbance of the solution. Absorbance has no units as such, since it is a ratio, but the absorbance of a solution is often quoted in “absorbance units”, or AU. The concentration of the absorbing species in solution. Units M (molar, or mol L-l). The pathlength of the light beam passing through the absorbing solution. Units cm. Almost all spectrophotometer cuvets are designed with pathlength 1 cm, although the pathlength in microtiter plates depends on the assay volume. If assays are done in microtiter plates, the assay volume should be maxl- mized to reduce error. A typical plate well volume is 300 pL, giving a pathlength of between 0.85 and 1 cm, depending on the manufacturer. The molar absorption coefficient, or molar absorptivity, of the absorbing species. This value indicates the theoretical absorbance if a 1 M solution of the absorbing species is measured m a cuvet of pathlength 1 cm. Units M-km-l, or L cm-lmol-*. The value of E is usually quoted for the wavelength at which the species absorbs most strongly, and is a constant for that species under a specified set of experimental conditions. Many

762 Ho/t

published assay protocols will state the value of E. However, it is advisable to determine E separately under the prevailing conditions, this being achieved simply by measuring the absorbance of a known concentration of the species and determining E from the Beer-Lambert equation.

It is clear that, under any given set of conditions, E and I remain constant, and thus A increases linearly with increasing c. Thus, it is a simple matter to determine c by measuring A, if E and 2 are known. In practice, the relationship between A and c often devi- ates from linearity at high values of A. Most modern spectrophotometers can determine absorbance in a range from O-3, and it is thus advisable to design experiments so that measured absorbance values lie between 0.01 and 1.

The underlying principle behind spectrophotometric assays of enzyme activity is that either the substrate, or the product, absorb strongly (E > 1000 M-km-‘) at a particular wavelength and that either the appearance or disappearance of product or substrate can therefore be followed at that wavelength in a spectrophotometer, or similar device. If none of the products themselves absorb light sufficiently well, it may be possible to include some reagent(s) that will interact with the product to yield an absorbing species, m an indirect assay of enzyme rate. The measurement of acetyl- cholinesterase (see Section 2.3.2.1, which involves reaction of the thiocholine product with Ellman’s reagent to produce a yellow color, is a good example of an indirect absorbance measurement. A more specialized type of indirect assay is the coupled assay, in which one of the products is metabolized further by a second COU- pling enzyme to yield an absorbing species. The continuous and discontinuous assays for MAO activity, described by Holt et al. (1997) and Szutowicz et al. (19841, respectively, rely on further metabolism of hydrogen peroxide, a product of amine oxidation, by horseradish peroxidase (EC l-11.1.7) to generate colored species that can be measured spectrophotometrically. Such coupled assays must be designed carefully to ensure that the coupling steps are not rate limiting in the overall reaction.

The application of spectrophotometry to enzyme kinetic assays is illustrated in the following example:

Benzylamine is converted to benzaldehyde by MAO-B. A solution of benzaldehyde (10 PM) in buffer pH 7.2, was scanned and was found to have an absorbance peak at 254 nm. The absorbance


of this solution at 254 nm, in a quartz cuvet of pathlength 1 cm, was found to be 0.125. Thus, from Eq. (71, E = 12,500 M-‘cm-l.

When benzylamine (750 PM) was incubated with purified rat liver MAO-B in a quartz cuvette, at pH 7.2 and in a volume of 1 mL, and the increase in absorbance due to production of benzaldehyde was followed continuously at 254 nm, the initial rate (v) was found to be 0.025 AU min-‘. The rate of change of concentration can then be determined:

c =A/(& I) = 0 025/12,500x 1=2 pM (from Eq. [71)

Thus, the rate of change of concentration is 2 pM min-I. In a volume of 1 mL, this is equivalent to the production of 2 nmol benzaldehyde every minute. Furthermore, since 1 U of enzyme activity metabolizes 1 pmol of substrate per min, then the assay contained 2 mU of MAO-B. Finally, if the protein content of the assay mixture is known, the specific activity of the enzyme can be calculated in U mg-‘. As the purity of an enzyme increases, then assuming the enzyme retains its activity during purification, the specific activity will increase with purification to a maximum value that is specific for that enzyme under the stated conditions.

Spectrophotometric measurement is the most common means by which enzyme activity is routinely measured. Most modern spectrophotometers have a split-beam or dual beam system whereby sample and blank assays can be run in parallel, in separate cuvet holders, and the blank rate is subtracted automatically from the sample rate. In single-beam machines, a blank rate must be determined beforehand, and then subtracted manually or automatically from subsequent readings. Some models with multiple cuvet holders allow monitoring of several slow reactions at one time. Multiwell plate readers allow continuous monitoring of up to 96 assays at one time, although variability of readings tends to be slightly greater than in reactions followed in a spectrophotometer.

3.2. Radiochemical Assays

Radiochemical assay protocols fall under the discontinuous category, and all of the cautionary points detailed earlier with respect to discontinuous measurements must be considered. How- ever, under appropriate conditions, radiochemical assays of enzyme activity represent a powerful technique with several

164 Ho/t

advantages over many nonradiometric methods. In particular, very low enzyme activities can be measured, often without the necessity for purification beforehand.

The basic principle behind most radiochemical enzyme assays is that a radiolabeled substrate is metabolized to a radiolabeled product, and the extent of metabolism is determined by counting radioactivity associated with the product following separation of the product from unreacted substrate. Since many enzyme reactions yield more than one product, the researcher should clarify which product or products retain the radiolabel, as separation and counting of an unlabeled product would be altogether unproductive.

The success of these assays depends very much on the efficiency of the method used to separate substrate from product. Poor separation will result in high radioactive counts even in blank assay tubes, where no metabolism has been allowed to take place. Since it is necessary to generate sufficient product such that the measured radioactivity is at least double the blank value, then high blank readings mean higher amounts of product must be generated. This may preclude working at low concentrations of substrates having low Knr values, or with low concentrations of enzyme that may lose activity in extended incubations. Separation is routinely achieved by an ion-exchange or organic solvent-exchange step. The most common methods of separation, along with many other helpful hints concerning radiochemical assays of enzymes, are discussed by Oldham (1993).

A substrate is radiolabeled by replacement of one or more atoms with a radioactive isotope. Thus, the nonradioactive atoms, ‘H, 12C, 31P, 32S, and 127I, can be replaced by their radioactive iso- topes, 3H (tritium), 14C, 32P, 35S, and 1251, respectively. In most cases, these radiolabeled substrates exhibit the same kinetic behavior as do their unlabeled counterparts. The researcher should be aware of safety precautions appropriate for the isotope being used, and should have some knowledge of its decay characteristics,

Radioactivity can be measured in Curies (Ci), Bequerels (Bq), or counts or decays per min (cpm or dpm). Activity is usually measured in a liquid scintillation spectrometer, which counts flashes of light produced in unit time when emitted radiation interacts with luminescent molecules in the scintillation fluid. The rate of light production is proportional to the amount of radioactivity, and thus product, present in the sample. Radioactive sub-


&rates are supplied in a solution of stated specific activity. Gen- erally, information supplied with the substrate will give the specific activity in units of mCi mmol-‘, or similar, and will state the amount of radioactivity supplied, in mCi, as well as the volume. For example, a stock solution of [14Clbenzylamine hydrochloride for the assay of MAO-B may contain 25 mCi mmol-’ and 6.25 uCi in a volume of 250 uL. Thus, there are 250 run01 of benzylamine in the vial, and the concentration of benzylamine is 1 mM.

It is usually recommended that stock substrate solutions are diluted to an appropriate concentration and specific activity, and then frozen in aliquots. This helps to reduce radiolysis (break- down) of substrates that occurs in concentrated solutions of high specific activity. The use of “diluted” in this context can be misleading. For example, the stock solution of [14C]benzylamine hydrochloride (above) would be diluted by adding unlabeled benzylamine hydrochloride. The specific activity (in mCi mmol-’ benzylamine) is therefore reduced. However, the concentration of the stock substrate solution can actually increase, if desired. For example, it is possible to prepare a working stock containing 10 mM benzylamine with a specific activity of 1 mCi mmol-I, by adding 6 pmol of unlabeled benzylamine hydrochloride to the radiolabeled stock (above), and then making the volume up to 625 PL with water or an appropriate buffer. The specific activity of the original stock has been diluted by a factor of 25, whereas the concentration of substrate has been increased by a factor of 10. There is little need to add that any mistakes at this point in the process could prove very costly, both financially and otherwise, and great care should be taken with calculations of these dilutions.

Why is it desirable to dilute the specific activity of the stock solution with unlabeled substrate? Due to the high cost of most radiolabeled compounds, it makes sense to use the minimum ratio of radioactive to unlabeled substrate necessary to achieve satisfactory measurements. In assay protocols that achieve good separation of substrate from product, it is possible to measure radioactivity associated with product which is only 50 pCi above blank levels. Since 1 nCi = 2220 dpm, this is equivalent to approx 100 dpm above blank. Assuming that 10% of the added substrate is metabolized during the incubation period (see Section 2.3.2., above), then only 500 pCi, or 1110 dpm, of radiolabeled substrate need be included in the assay. Clearly, a manufacturer’s stock solution such as that described above, which contains 55,500 dpm

166 Ho/t

uL-I, has far more radioactivity present than is necessary for measurement of substrate turnover. However, simply diluting the stock with buffer or water will reduce the concentration of substrate present, but not its specific activity.

After a working stock of appropriate concentration and specific activity has been prepared, substrate dilutions are made by the addition of water or buffer, as would be done in a regular enzyme assay. Thus, lower concentrations of substrate will contain lower levels of radioactivity, but ail substrate dilutions will be of identical specific activity. The specific activity chosen for the substrate when preparing the working stock should be chosen so that assay tubes with the lowest concentration of substrate (usually 0.2 x K,,,) contain an absolute mn-umum of 1110 dpm (500 pCi> of radioactivity.

One further reason for reducing the specific activity of the manufacturer’s stock is that the level of radioactivity in blank assay tubes is usually proportional to the amount of radioactive substrate present, and low blank readings impart higher sensitivity. Several types of enzyme assay, including m vitro studies of the effects of inhibitors, require a control assay in which the enzyme is operating close to V,,,. From Eq. (2), a substrate concentration of 2 x Kern will allow the enzyme to operate at 67% of V,,,,, whereas increasing the substrate concentration to 10 x K,,l will increase ZI to 91% of Vmax. However, whereas v was increased only by some 36%, associated blank counts will have increased by approx 500%, since the amount of radioactivity present was increased fivefold. Thus, it may be better in such situations to compromise and lose some enzyme activity in return for blanks which are very much lower (Oldham, 1993).

It is a straightforward matter to obtain ZI from dpm values. Since the specific activity of the substrate (and hence the product) is known (units nCi nmol-‘; 1 nCi = 2220 dpm), then the amount of product generated over the incubation period can be calculated If linearity has been established from control experiments (see Sec- tion 2.3.2., above), then the initial velocity, U, can be determined.

3.3. Ofher Assay Methods

While spectrophotometry and radiometry represent the two most popular techniques used in assays of enzymes, several other established and emerging methods should be mentioned. Like spectrophotometry, fluorimetry illuminates the sample of interest


with light of a predetermined wavelength. However, whereas purely absorbent molecules release the absorbed energy as heat, fluorescent compounds emit a photon of light, of longer wavelength and thus lower energy than the incident beam. The amount of emitted light measured provides an indication of the concentration of the fluorophore. Many enzyme reaction products are fluorescent, or can interact with an added reagent to produce a fluorescent derivative. Whether the assay can be done continuously or must be done discontinuously depends upon the conditions required for fluorescence of the product or its derivative.

Most other available assay methods are only suitable for pro- cessing a small number of samples per day, or only allow a single measurement to be made at any one time. Polarography uses changes in electrical current passing through a reaction solution to indicate changes in concentration of an electro-active product (Weitzman and Watkins, 1993). Perhaps the most popular polaro- graphic measurement is that of oxygen consumption (Clark, 1993) Despite the reduced number of samples that may be processed, polarography is relatively inexpensive and allows continuous measurements to be made.

Chromatography is becoming more popular as a means for the separation and quantification of reaction products. High perfor- mance liquid chromatography (HPLC) is a specialized technique that can be used to isolate, identify, and quantify tiny amounts of product in a reaction mixture, with sensitivity being determined largely by the method of detection used. However, some exper- tise with HPLC operation is necessary, and the technique suffers from the drawbacks of other discontinuous assays. The potential applications of capillary electrophoresis to enzymology are now being considered This most sensitive of techniques for the separation and detection of molecules presently allows the assay of enzyme activities in single cells and has even facilitated measurement of the rate of substrate turnover by a single enzyme molecule (Craig et al., 1996).

4. Enzyme Inhibitors and Inhibition Kinetics

4.1. Enzyme Inhibitors

The primary action of many therapeutic agents is to inhibit one or more enzymes, thereby modulating the metabolic pathway(s) in which the enzyme participates. Centrally acting enzyme inhibi-

168 Ho/t

tors currently prescribed (see Rang et al., 1995) include the MAO- A inhibitor antidepressants, phenelzine, tranylcypromine and moclobemide, the nonopioid antipyretic/analgesics, aspirin and paracetamol (which inhibit cycle-oxygenase I, a component of prostaglandin-endoperoxide synthase), the anticonvulsant valproic acid, (which probably inhibits GABA transaminase and succinate-semialdehyde dehydrogenase), and the antiparkinsonian drugs, selegiline (an MAO-B inhibitor) and carbidopa and benserazide (peripheral dopa-decarboxylase inhibitors). In addition, phosphodiesterase inhibitors are self-administered on a daily basis, as theophylline and caffeine, in tea and coffee. Neuroscien- tists are most often interested in determining whether or not a compound inhibits the activity of an enzyme or group of enzymes and, in the event that some inhibitory efficacy is established, in determining the mechanism of inhibition and assigning some value to the inhibitor that gives an indication of its potency. Such information might then assist the researcher in predicting the effects of administration of the inhibitor to an animal, in explain- ing discrepancies found between in vitro and in vivo inhibition experiments, or in calculating the conditions required in vitro to obtain partial or complete enzyme inhibition, a necessary requirement in several experimental procedures. Consequently, it is important to acquire such information in the correct manner so that published values allow others to use the inhibitor with confidence in their own studies.

There are many different ways in which a compound might interact with an enzyme molecule to prevent substrate turnover. The most basic of these are described in detail below, whereas the more complex mechanisms are mentioned only briefly. The kinetics of inhibition for all but the most basic mechanisms are beyond the introductory nature of this text, but are described clearly by Segel (1975) and Dixon and Webb (1979). Excellent reviews by Tipton (1980, 1996) describe clearly the mathematical basis behind many of the points discussed below.

4.1.1. Reversrble and lrreverslble lnhlbitors

All enzyme inhibitors are classed either as reversible or u-reversible, and most are reversible. Following enzyme inhibition, a reversible inhibitor can be removed from the enzyme by dialysis, dilution, or gel filtration, and enzyme activity is thus recovered. An irreversible inhibitor is usually bound covalently, or at least


very tightly, to the enzyme, and enzyme activity can not be recovered by dialysis and related processes. In some cases, activity is recoverable by dialysis, but the rate of recovery is so slow that inhibition can, for all intents and purposes, be considered irreversible.

Since reversible inhibitors are free to associate and dissociate from the enzyme, an equilibrium exists between bound and unbound enzyme.

E+l 1 El (8)

k -1

Except in the case of slow-binding inhibitors (see Section 4.26, below), this equilibrium is normally established very rapidly and is independent of time, assuming that the inhibitor is stable. Thus, the potency of a reversible inhibitor can be quantified by determining the equilibrium constant (or dissociation constant), k-,/k,, for the reversible interaction between the inhibitor and the enzyme (see Section 4.2., below), which is a measure of the affinity of the inhibitor for the enzyme. The equilibrium constant for an enzyme- inhibitor interaction is more usually called the inhibitor constant, and is given the symbol, K,.

Where irreversible inhibitors are concerned, no equilibrium exists between bound and unbound enzyme. Irreversible inhibitors are often time-dependent; in other words, the degree of inhibition increases with time until a maximum level of inhibition is achieved. Thus, no equilibrium constant exists, and the inhibitor potency must be determined by some other means. Often, a velocity constant is quoted (see Section 4.3., below), which indicates the fraction of total enzyme inhibited per min at a desig- nated concentration of inhibitor.

Prior to any kinetic examination of an inhibitor and in order that kinetic results be interpreted correctly, it is necessary to determine if inhibition is time-dependent, and thereafter if it is reversible or irreversible. To assess time-dependence, an enzyme sample is preincubated, often at 37”C, with a submaximal concentration of inhibitor. In this context, submaximal means that between 10% and 50% of the original enzyme activity should still remain at the point when the degree of inhibition is not seen to

170 Ho/t

increase further with continued preincubation. At predetermined time intervals of 1-5 min, small volume aliquots are removed from the enzyme-inhibitor mixture and added to a comparatively large volume of substrate, and remaining enzyme activity (v) is determined. Remaining activity is then plotted vs the appropriate preincubation time, and the resulting plot indicates the minimum preincubation time necessary for the enzyme to become inactivated (Holt and Baker, 1996). If enzyme activity does not decrease with time, inhibition is not time-dependent and preincubation of enzyme with inhibitor is not necessary in subsequent experiments. In addition, a lack of time-dependence suggests that inhibition is likely to be reversible, although this should still be confirmed by dialysis.

When time-dependence, or a lack thereof, has been established, a sample of enzyme should be mixed with sufficient inhibitor to inhibit at least 90% of the enzyme activity, and, if necessary, preincubated for the appropriate time period. A second enzyme sample, the control, should be treated with the solvent in which the inhibitor is dissolved and thereafter should be submitted to the same treatments as is the authentic inhibitor-treated sample. This will account for any loss of enzyme activity that is not caused by the inhibitor. Aliquots of the samples are then most usually dialyzed for one of several time periods over a period of at least 8 h (Halt et al., 1992; Holt and Baker, 19961, and often for 48 h or more. Following dialysis, remaining enzyme activity is measured and expressed as a fraction of the activity in the corresponding, dialyzed control sample. If extensive dialysis fails to recover most of the enzyme activity, inhibition can be considered irreversible One should bear in mind that dialysis, and similar procedures, might also remove a loosely bound cofactor from the enzyme, thereby preventing the recovery of enzyme activity and thus suggesting irreversible inhibition. In such cases, activity in the control sample will also be lost on dialysis, and addition of excess cofactor prior to the substrate incubation stage should recover activity lost in this way.

Dialysis tubing is available with various pore sizes, or molecular weight cut-off (MWCO) values. Tubing is selected such that the pore size is as large as possible to allow rapid diffusion of the inhibitor while preventing loss of the desired protein The Spectra/POP4 membrane, with a MWCO of 12,000-14,000 Da, is safe to use with enzymes larger than approx 25 kDa, whereas smaller enzymes


can be dialyzed with Spectra/PoPS (MWCO 3,500 Da). The tubu- lar membrane should be washed and checked for leaks before use, and should be double-clamped at one end. The membrane is then filled with the sample to be dialyzed, air is removed carefully, and the open end of the tubing is double-clamped to seal the bag closed, leaving some room for expansion of the bag’s contents. Membrane clamps are available from manufacturers of dialysis membranes, To initiate dialysis, the entire bag is placed in a large beaker filled with an appropriate buffer solution and the buffer is stirred gently with a magnetic stirring device. The volume of the buffer should ideally exceed the volume of the sample by at least ZO-fold, and the buffer should be replaced at least twice during the period of dialysis. For example, a 10 mL sample dialyzed vs 1L of buffer with two buffer changes will dilute any inhibitor present by a factor of 106. While the rate of dialysis usually increases with increasing temperature, loss of enzyme activity caused by instabil- i ty or proteolysis at higher temperatures should also be considered when determining the temperature for dialysis. If proteolysis causes significant loss of enzyme activity over prolonged dialysis periods, it may be appropriate to include one or more proteolytic enzyme inhibitors in the dialysis sample (North, 1989).

Very small volumes of enzyme can be dialyzed by placing the sample in a capless microcentrifuge tube and sealing the tube with a single layer of dialysis membrane, held in place by a small piece of tight-fitting rubber tubing. The tube is inverted and tapped lightly to bring the sample in contact with the membrane, and is then floated in a beaker of dialysis buffer.

High-speed dialysis can be achieved with the aid of centrifugal concentrators. Solute is removed under centrifugation by ultrafiltration through a membrane of known MWCO value. The retained enzyme is resuspended in fresh buffer, thereby diluting any inhibitor present, and ultrafiltration is repeated. Typically, a 500~PL sample can be concentrated to 10 ~.JL in around 30 min, with a membrane of MWCO 10,000. Thus, in less than 2 h, an inhibitor can be diluted by a factor of at least 105. Microcon and Centriplus concentrators are available from the Amicon company (Beverly, MA).

Gel filtration, or size-exclusion chromatography, operates on the principle that large enzymes will pass through a size-exclusion column almost unhindered, whereas small inhibitor molecules can diffuse into the mobile phase and thereafter into the pores of the gel matrix, delaying their passage through the column. Dispos-

772 Ho/t

able columns are available from manufacturers such as Bio-Rad (Hercules, CA).

4.2. Kinetics of Reversible inhibitors

The Langmuir equation (see Rang et al., 1995) shows that the inhibitor constant, K, for the reversible interaction between an enzyme and an inhibitor, is numerically equal to the concentration of inhibitor required to occupy 50% of the enzyme active sites at equilibrium. The higher the affinity of the inhibitor for the enzyme, the lower will be the K, value. For most enzyme inhibitors, the K, value is very much larger than the concentration of enzyme present (enzymes are typically present in tissue homogenates at concentrations in the low picomolar to low nanomolar range). Thus, in order to produce even a small degree of inhibition, the inhibitor must usually be present in vast excess over the enzyme, and binding of inhibitor to enzyme does not appreciably reduce the concentration of unbound inhibitor.

If the ratio of K, to enzyme concentration is less than approx 10, normal Michaelis-Menten kinetics with respect to inhibitors no longer apply (Straus and Goldstein, 1943; Goldstein, 1944). Several drugs have K, values in the low nanomolar to high picomolar range, in the same order as the concentration of enzyme. Such tight-binding inhibitors have very high enzyme affinities and binding of inhibitor to the enzyme can cause a marked reduction in the concentration of unbound drug. Methods for calculation of K, values for tight-binding inhibitors are considered separately m Sec- tion 4.2.6., below. Highly specific tight-binding inhibitors should prove tremendously useful in the therapeutic setting; very low doses of drug can be administered once daily, reducing the likelihood of nonspecific adverse reactions and improving patient compliance.

The followmg five sections refer to the kinetics of reversible inhibitors which are not tight-binding.

4.2.1. Fully Competitive Inhibition

A fully competitive inhibitor binds either at the enzyme active site, thereby preventing binding of substrate, or at a separate allosteric site, binding of the inhibitor at which induces a confor- mational change at the active site that prevents substrate binding. The reverse must also be true, in that binding of substrate at the active site prevents binding of inhibitor, either to the active site or to an allosteric site. Inhibition by a fully competitive inhibitor can


be overcome by increasing the concentration of (competing) substrate. Thus, V,,, is unaltered, whereas the K, of the substrate is apparently increased (to a new value of K,n arp) since a higher substrate concentration is required in the presence of the inhibitor to achieve 0.5 x V,,,,. The effects of a fully competitive inhibitor can be seen clearly in a Lineweaver-Burk plot (Fig. 7A) and in a Hanes- Woolf plot (Fig. 7B).

The inhibitor constant for a fully competitive inhibitor can be determined from a replot of slopes obtained from Lineweaver- Burk plots at several inhibitor concentrations. The slope of each line (corresponding to the value, K /V,,J is plotted against the inhibitor concentration (Fig. 7C) ar?$?he intercept with the x-axis is equal to -K,. In view of the arguments mentioned in Section 2.2.3. with regard to weaknesses in the Lineweaver-Burk plot as a means for obtaining kinetic constants, it may be more acceptable to determine values for K,,,ap /Vmnv from Hanes-Woolf plots and thereafter to plot the artificia f ly-determined “slope” values vs inhibitor concentrations to obtain K,.

For the same reasons that K, values are most accurately determined from substrate concentrations covering a range of at least 0.5 x Km to 5 x Km (Section 2.2.1, K, values should be obtained with at least four separate concentrations of inhibitor covering a range of at least 0.5 x K, to 5 x K,, and a preliminary suck-and-see assay may thus be required to assign a tentative value to K,. The reasoning behind this point may become clearer if one considers that a substrate (A) could act as a competitive inhibitor vs turnover of a second substrate (B) by the same enzyme. Since the K, value for (A), determined by the procedure described above, represents the dissociation constant for the reversible interaction between (A) and the enzyme, then this is also equal to the Km for turnover of (A) by that enzyme. By this approach, it is possible to show that a single enzyme is likely responsible for turnover of two or more substrates (Lyles et al,, 1990). If physical problems are encountered in measuring turnover of a particular substrate, it might also be possible to estimate its K,,, value by obtaining a K, in an assay vs an alternative substrate, the turnover of which is able to be measured without difficulty.

For some competitive inhibitors, equilibrium is established over a period of seconds or minutes as a result of a slow on-rate for the inhibitor binding to the enzyme active site (Morrison, 1982). If a reaction is started by the addition of enzyme to a mixture of sub-

[Inhibitor]

174

Enzyme and lnhrbitor Measurement 175

strate and slow-binding inhibztor, the initial velocity will decrease to a slower steady-state velocity. Conversely, if the reaction is begun by the addition of substrate, the reaction rate will increase to a higher steady-state level as inhibitor is displaced from the enzyme. The steady-state velocity should be the same in both cases. Thus, the initial velocity, v, is not the same as the steady-state velocity, unlike the situation with classical mhibitors where steady- state conditions are established instantaneously. Slow onset of inhibition can be observed in continuous assay systems, but may go undetected in discontinuous procedures. Since steady-state conditions should be used in the determination of the inhibitor constant, as described above, measurement of initial velocities is inappropriate and will lead to an incorrect value for K,. The kinetics of slow-binding inhibition can be analyzed by more complex procedures (Morrison, 19821, but these lie outwith the introductory scope of this text.

4.2.2. Fully Noncompetltwe lnhlbrtion

A fully noncompetitive inhibitor binds to the enzyme at a site separate from the active site. The affinity of the active site for the substrate remains unaffected and substrate may still bind. Simi- larly, an inhibitor may bind to the enzyme even if substrate is bound at the active site. Therefore, unlike the case with fully-competitive inhibitors (above), an ESZ tertiary complex is formed. However, the resulting ES1 complex can not break down to yielt : product. Rather, either inhibitor or substrate can leave the complex, giving ES or El, respectively, and only ES may then go on to yield product. Thus, whereas the K,,, remains unaffected, the net effect of a fully noncompetitive inhibitor is to give the impression that less enzyme is present, by reducing Vm,, (to a new value of

Fig. 7 fopposite page) The effects of a fully competitive inhibitor on reaction rates shown in the form of a Lineweaver-Burk plot (A) or a Hanes-Woolf plot (B). Control plots in the absence of Inhibitor are shown as solid lines. The effect of the competitive inhibitor (dashed lines) is to increase the K,,, to a new value of K”, app, while V,n,, remains unaffected. If the assay 1s made in the presence of several concentrations of inhibitor and results are plotted by the Lineweaver-Burk method, the slopes of the lines can be replotted versus the inhibitor concentration to obtain a K3 value for the inhibitor (C)

176 Ho/t

Lx 1 ). The effects of a fully noncompetitive inhibitor can be seen clear y in a Lineweaver-Burk plot (Fig. 8A) and u-t a Hanes-Woolf plot (Fig. 8B).

The K, value for a fully noncompetitive inhibitor corresponds to the dissociation constant (or equilibrium constant) for the ES1 complex yielding ES + I or for the EI complex yielding E + I. Both constants have the same value since the combination of S does not affect the affinity of the enzyme for the inhibitor. K, for a fully noncompetitive inhibitor can be determined from a replot of y-intercepts obtained from Lineweaver-Burk plots at several inhibitor concentrations. The intercept of each line (corresponding to the value, 1/ V,n,, “yp > is plotted against the inhibitor concentration (Fig. 8C) and the intercept with the x-axis IS equal to 4,. Again, it may be more appropriate to determine V,,,,x spy values by the Hanes-Woolf method, and then to plot reciprocals versus inhibitor concentrations to obtain K,.

4.2.3. Fully Uncompetitive Inhibition A fully uncompetitive inhibitor decreases Km and V,,, to the

same extent. A general scheme suggesting the mechanism by which this might happen is described by Dixon and Webb (1979), m which the inhibitor can only combine with the ES complex and not with free enzyme. As with fully noncompetitive inhibition, the ES1 complex can not break down to yield product. In fact, the ES1 complex is in equilibrium only with ES and I, and product can be derived only from ES. Assuming that fully uncompetitive inhibitors do, in fact, act by this mechanism, then this type of inhibition can be verified from a Lineweaver-Burk plot (Fig. 9A) or a Hanes-Woolf plot (Fig. 9B)

The K, value for a fully uncompetitive inhibitor corresponds to the dissociation constant for the ES1 complex yielding ES + I K, is obtained in a manner identical to that for fully noncompeti-

Fig 8. (opposlfe page) The effects of a fully noncompetitive mhibitor on reaction rates shown in the form of a Lineweaver-Burk plot (A) or a Hanes-Woolf plot (B) Control plots in the absence of inhibitor are shown as solid lines The effect of the noncompetitive inhibitor (dashed lines) is to decrease the V,,lal to a new value of V,,lnxa P, while K,?, remains unaffected If the assay is made m the presence otseveral concentrations of mhibitor and results are plotted by the Lmeweaver-Burk method, the y- intercepts of the lines can be replotted versus the inhibitor concentration to obtain a K, value for the mhibitor (Cl

Enzyme and lnhrbrtor Measurement 177

[Inhibitor]

178 Ho/t

l/V maxapp -/

-l/K

Fig 9 The effects of a fully uncompetitive inhibitor on reactron rates shown in the form of a Lineweaver-Burk plot (A) or a Hanes-Woolf plot (B). Control plots m the absence of inhibitor are shown as solid lines The effect of the uncompetmve inhibitor (dashed lines) is to decrease the K,,, and V,nax values by the same extent, to new values of KlllRllp and V The K, value for a fully uncompetitive inhibitor IS determined m a Ka%ner analogous to that for fully noncompetrtive inhibition (Fig. 8C)

tive inhibition, i.e., from the x-intercept of the y-intercept replot of Lineweaver-Burk data. Of course, in the case of fully uncompetitive inhibition, an x-intercept replot would lead to the same value for K,, since Km and V,n,, are altered to the same extent.

Enzyme and lnhibrtor Measurement 179

4.2.4. Fully Mixed Inhibition

Mechanisms of mixed inhibition are somewhat more complex than the others described thus far, and treatment of kinetic data from mixed inhibition experiments is a little more difficult. Unfortunately, in multisubstrate systems, mixed inhibition 1s a common phenomenon and some familiarity with the concept is thus desirable. The simplest mixed inhibition system, that of fully mixed inhibition, is one in which El has a lower affinity than E for S. As with the other “full” inhibition systems, ES1 can not break down to yield product. While If,,,,, is always decreased by a fully mixed inhibitor, K,,! RPP can be higher or lower than the true Km, measured in the absence of inhibitor. The effects on standard kinetic plots are thus, to an extent, unpredictable, but a fully mixed inhibitor always causes Lineweaver-Burk plots to intersect to the left of the y-axis, and above or below, but not on, the x-axis. Examples of the effects of two fully mixed inhibitors, one causing an increase and the other a decrease in ICI,,, on kinetic plots are shown in Fig. 10A (Lineweaver-Burk plot) and Fig. 10B (Hanes- Woolf plot).

Because binding of S affects the affinity of E for Z, then the dissociation constants for the equilibria between EZ yielding E + I, and ES1 yielding ES + I, are not the same. The inhibitor constant for the former equilibrium remains as K,, whereas that for the latter equilibrium is termed K,‘. From data plotted by the Lineweaver- Burk method, a slope replot will yield a value for K,, analogous to the procedure used with fully competitive inhibitors, whereas a y-axis intercept replot will yield a value for K,‘, analogous to the procedure used with fully noncompetitive inhibitors.

4.2.5. Partial Inhibitors

For each of the fill inhibition systems described above, there exists at least one partzal system, in which the ESZ complex can yield product directly, bypassing the intermediate ES complex. Additionally, in the case of partially competitive inhibition, the inhibitor reduces the affinity of the enzyme for substrate without completely preventing substrate binding, and an ES1 complex can also exist. Thus, in all cases of partial inhibition, product can be derived from two intermediates, ES and ES!. The equations governing the kinetics of partial inhibition are rather more complicated than those for full inhibition (Dixon and Webb, 1979),

180 Ho/t

ISI

Fig. 10. The effects of a fully mixed mhibitor on reaction rates shown m the form of a Lmeweaver-Burk plot (A) or a Hanes-Woolf plot (Bl Control plots in the absence of inhibitor are shown as solid lines The effect of the non-competitive mhibltor is to decrease the V,,,, to a new

value Of Ym qpp However, while Kin is also changed to a new value, K this can be higher or lower than, but not equal to, K,,,. In the case ifl’$ i Lineweaver-Burk plot, the inhibitor plot (dashed lines) can mtersect with the control plot below the x-axis (reduced K,,) or above the x-axis (increased KJ, whereas the y-intercepts of the inhibitor plots are always above that of the control. In the case of the Hanes-Woolf plot, x-intercepts to the right or left of the control intercept indicate increased and decreased K,,, values, respectively, while the slopes of inhibitor plots


although it is still possible to determine inhibitor constants in most cases. Replots of slopes and/or intercepts from Lineweaver-Burk plots of partial inhibition are no longer linear and a more detailed analysis is necessary to extract the required information from the plot.

Fortunately, partial inhibition is encountered much less fre- quently than full inhibition. However, if preliminary kinetic results suggest that partial inhibition is occurring, it is advisable to con- sult a text such as Segel(1975) or Dixon and Webb (1979) and to work carefully through the diagnostic steps described therein.

4.2.6. Tight-Binding Inhibitors and Slow Tight-Binding Inhibitors

As was mentioned in the introduction to Section 4.2., some reversible inhibitors have K, values similar in magnitude to the total concentration of enzyme, [E,]. Thus, the usual assumption that free and total inhibitor concentrations are equal can not be made, since inhibitor binding may markedly deplete the concentration of unbound inhibitor. These compounds, often substrate transition-state analogs, are termed tight-binding when steady-state equilibrium is reached almost instantaneously, and slow tight- bindzng when attainment of equilibrium takes seconds or minutes (Williams and Morrison, 1979; Morrison, 1982; SzedIacsek and Duggleby, 1995).

Obtaining inhibitor constants for tight-binding inhibitors requires a different approach from that taken with inhibitors that are not tight-binding. Some of these procedures cause problems even for more experienced enzymologists, and in the neuroscience laboratory, the best approach is probably one of compromise (see Section 4.4.1.). However, it is important at least to be able to rec- ognize the signs of tight-binding, since application of the kinetic procedures described in Sections 4.2.1.-4.2.5, (above) to a tight- binding system would be inappropriate. Generally, significant enzyme inhibition in tissue homogenates at inhibitor concentrations of 10 nM and below should alert the researcher to the possibility of tight-binding inhibition. Lineweaver-Burk plots in the presence

(Fig. 20 contznuedfvom pvevzous page) are always greater than that of the control, indicating a reduced V,,ray. K, values for fully mixed inhibitors can be determined from slope and y-intercept replots (see text)

182 Holt

of a tight-binding inhibitor have both curved and linear portions, and the slopes do not vary in proportion to [LJ, the total concentration of inhibitor (Morrison, 1982).

Dixon (1972) has proposed a method to estimate K, values for the simplest forms of competitive and noncompetitive tight-binding inhibition. The K, for noncompetitive inhibition can be determined directly from a plot of v vs [I,], whereas a replot of K, app values obtained from the first plot yields a K, for competitive tight- binding inhibition (Segel, 1975; Tipton, 1980). Alternatively, the method of Henderson (1972), as summarized by Tipton (19801, provides a graphical means by which inhibitor constants can be calculated for all four classes of reversible tight-binding inhibitors. Initial rates are measured in the presence (v,) or absence (v) of inhibitor, and an analysis is made of a plot of [a/(1-v,/v> versus v/v,.

4.3. Kinetics of lrreversrble Inhibitors

Irreversible inhibitors bind to an enzyme extremely tightly, so that recovery of activity by dialysis is, at best, very slow. In practice, irreversible inhibition can be implied if negligible reversal of inhibition occurs during the time course of the experiment. Thus, after an initial period during which irreversible inhibition occurs, there is no appreciable reversal of inhibition, and therefore no dissociation constant for the interaction between enzyme and inhibitor. Although an irreversible inhibitor will often yield a kinetic plot which is indistinguishable from that of a noncompetitive inhibitor, in which K, is unaffected but Vm,, is reduced, calculation of a K, value is inappropriate and some alternative means must be found by which the potency of irreversible Inhibitors might be quantified (Tipton, 1980).

Nonspecific irreversible inhibitors act in a manner described by the equation:

k 0”

E+I- EI (9)

These inhibitors usually bind to specific chemical groups on an enzyme, but will bind to any enzyme or other cellular constituent containing that group. For example, hydrazine-type reagents, such as phenelzine and semicarbazide, will inhibit most enzymes with a carbonyl-containing cofactor. Thus, administration of these so- called carbonyl reagents will inhibit pyridoxal phosphate-depen-

Enzyme and lnhrbltor Measurement 183

dent enzymes such as aspartate transaminase (EC 2.6.1.1) and L- aromatic amino acid decarboxylase (EC 4.1.1.28), and quino- proteins such as the EC 1.4.3.6 enzymes, diamine oxidase (Holt and Baker, 1995), plasma amine oxidase (Callingham et al., 1995), semicarbazide-sensi tlve amine oxidase (Halt and Callingham, 1995; Holt et al., 1992), and lysyl oxidase (EC 1.4.3.13; Klmman, 1996). Subsequently, as therapeutic agents at least, nonspecific irreversible inhibitors are of little interest because of their wide- spread effects. The potency of these inhibitors can be described by a pseudo-first-order rate constant (Tipton, 1980), although it is probably sufficient to quote an IC,, value (see Section 4.4.1., below).

A more interesting form of irreversible inhibition, both kineti- cally and therapeutically, is that which can be described by the general equation:

k Dll

E+l, ‘r, EI --+ El’ (30)

k oft

In such a reaction, an initial, reversible interaction takes place at the active site, followed by a second step resulting in irreversible inhibition of the enzyme

Two types of inhibitor comply with this reaction scheme, although distinguishing between them on the basis of steady-state kinetic results is not possible (Tipton, 1980). In the case of affinity labeling agents, or active site-directed inhibitors, a time-dependent interaction of an enzyme nucleophile with EI results in formation of the covalent complex, EI”. Such inhibitors are somewhat reactive and the enzyme is a passive participant m the inhibition process.

In contrast, mechanism-based inhibitors, that are also known as suicide inhibitors or kcat inhibitors (Tipton, 1980, Silverman, 1995), are relatively inert species that are similar in structure to a substrate molecule. Following reversible, competitive binding at the active site, the inhibitor is metabolized by the enzyme to an intermediate, or product, that binds tightly to the enzyme or undergoes an affinity labeling-type interaction with the enzyme to form a covalent, irreversible complex. Essentially, the enzyme causes its own Inhibition, hence the term, “suicide inhibitor.” Eq. (10) can be expanded slightly to take account of the metabolic step:

184 Ho/t

k 0” 4 4

E+I,- El - El’

k off

r

+Er (11)

4

\

E+I

In this scheme, the reactive intermediate is represented by EI’. Since I’ is a product of enzyme action, it is perhaps not surpris-

ing that the enzyme can release I’ as product at a rate k,. Thus, it is not necessary that every inhibitor molecule that reacts with the enzyme active site will cause inhibition. The inhibitor can either leave the active site unchanged, at a rate koff, or can leave in the form of I’, which should not react with the enzyme again. In other words, the inhibitor can be inactivated by the enzyme. The ratio of I’ released to enzyme inhibited (either tightly-bound El’ or covalent El*) is called the partition ratio (Silverman, 1995). Only if the partition ratio is zero will stoichiometric inhibition occur (m which every inhibitor molecule inhibits one enzyme molecule). Affinity labeling agents and nonspecific irreversible inhibitors can, in the absence of nonspecific binding, cause stoichiometric inhibition, although a very prolonged preincubation period might be necessary Release of I’ as product explains why stoichiometric inhibition is not always seen with mechanism-based inhibitors.

In order to show that inhibition is mechanism-based, several criteria must be met. Inhibition must be time-dependent, saturable, initially competitive with respect to substrate, a result of catalysis at the active site, and must not occur as a result of recombination of I’ at the active site or elsewhere. The experiments necessary to prove that an inhibitor meets these requirements are described by Silverman (1995).

The potency of an affinity labeling inhibitor which obeys Eq. (lo), can be expressed in terms of K, for the initial, reversible interaction, along with a rate constant, k,, also termed k,,,,t, that indicates the rate of irreversible inactivation of the enzyme. Concentrated enzyme is preincubated with inhibitor and aliquots are removed at time intervals of 1-5 min and diluted m a large volume of substrate to assess irreversible inhibition (Silverman, 1995). A semilogarithmic plot of activity remaining (%) vs prein-

Enzyme and Inhtbltor Measurement 185

cubation time (Fig. 11A) at several concentrations of inhibitor yields a series of straight lines of slope -k, the rate of irreversible inactivation at each inhibitor concentration (Kitz and Wilson, 1962). A replot of l/k (or of ln2/k, which corresponds to the half- life for u-reversible inhibition) vs 1/[1] (Fig. 11B) gives an x-intercept of -1 /K, and a y-intercept of 1 /k,,,ct (or ln2/k&. The units of kInact are min-‘, indicatmg the fraction of enzyme inactivated per min at saturating inhibitor concentrations.

The potency of mechanism-based inhibitors is expressed m terms of K, and klnact, and these values are determined by the method of Kitz and Wilson (1962) in a manner identical to that described for K, and k,,,,t, above (Fig. 11A and B). The K, term is not simply a ratio of koff/kon, but is a complex mixture of koff, ko,, k,, k, and k, (see Eq. [ll]), and k,nact is a mixture of k,, k, and k, (Silverman, 1995). If k, is rate limiting and k3 approaches zero, then K, = K, and k,,,,t = k,.

4.4. Some Comments on Inhibitor Assays

4.4.7. The IC,, Value

In the neuroscientific literature, inhibitor potencies are often expressed as IC,, (or I,,) values, and are sometimes written in the form of PI,, (-log,, IC,,). The IC,, is the concentration of inhibitor which reduces enzyme activity to 50% of activrty in a control sample, and is usually determined from a sigmoidal plot of v (expressed as a fraction of control) vs log,&] (see Holt and Baker, 1995). For simple, reversible inhibition systems, IC,, is related to K, by the Cheng-Prusoff equation:

K, = IC,,/[l + (lSl/~,)l (12)

Clearly, since K, is a constant, IC,, cannot be constant, and its value depends on [Sl (Cheng and Prusoff, 1973). Thus, for simple, reversible inhibition systems, K, values, and not IC,, values, should be quoted.

From the comments on irreversible inhibition in Section 4.3., it should be clear that the degree of inhibition depends not only on the concentration of inhibitor, but also on the concentration of enzyme. For example, a concentration of irreversible inhibitor sufficient to cause 50% inhibition in a sample containing 1 nM enzyme will only inhibit approx 25% of the activity if the enzyme concentration is increased to 2 I-M. This also holds true in the cases of tight-binding and slow tight-binding inhibitors (see Section 4.2.6.).

786 Holt

Preincubation time

l/[lnhibitor]

Fig. 11. Kitz and Wilson method for the determmation of K, (or K,) and k,,,O,f for time-dependent, n-reversible mhibition Enzyme is premcu- bated with Inhibitor and ahquots are removed and diluted mto a large volume of substrate at regular time-intervals to dialyse any rcverslbly- bound inhibitor from the enzyme. In this way, the time-dependent onset of irreversible inhibition can be measured (see text) The experiment IS repeated at several mhibitor concentrations and activity remammg m each aliquot is plotted on a logarithmic scale vs the appropriate premcubation time, with increasing mhibitor concentrations causing more rapid onset of irreversible inhibition and thus increasingly steeper rate plots (AI The slope of each plot is equal to -k, the rate constant for the onset of mhibition at the concentration of mhibitor piesent The half- life for irreversible mhibition at each mhibitor concentration is equal to


However, in view of the fact that obtaining values for K,, K, and k,,,,t for these classes of inhibitors is a relatively complex process, and that in physiological terms at least, their effects are somewhat homogeneous, then the use of IC,, values is acceptable, provided that the enzyme concentration is also quoted. If the enzyme concentration is unknown, then the activity of the enzyme (in IU), along with its specific activity (in ZU mg-I; Section 1.1,) should be provided instead.

4.4.2. Discontinuous Assays Revisited

The effect of any inhibitor is to reduce the initial rate of substrate turnover, v, to a new value which we shall call v’. Thus, if an inhibitor is stated to reduce the activity of an enzyme by 50%, this means that the value of v’ in the presence of inhibitor is 50% of v measured in a control assay, without inhibitor. In a continuous assay, this 50% reduction in initial rate will be readily apparent, as illustrated in Fig. 12. Also apparent from Fig. 12 is the slowing and eventual stoppage of substrate turnover in both samples, largely as a result of substrate depletion, but with other factors such as product-induced inhibition of the enzyme possibly contributing to the effect. However, since the amount of product ultimately formed in each case will be similar, it is important in discontinuous assay systems to ensure that v and V’ are determined on the linear portion of the progress curve. In this example, determination of v and v’ at t = 2 min will show that U’/V = 0.5 and thus that the inhibitor has inhibited the enzyme by 50% at the concentration used. However, measurement at t = 6 min will give a value of v’/v = 0.75, suggesting that the level of inhibition was only 25% and thereby underestimating quite substantially the potency of the inhibitor. At t = 10 min, a discontmuous procedure would suggest that the compound had almost no inhibitory potency.

4.4.3. Reversible Inhibition Measured ex Vivo

If in vitro experiments have shown that a novel compound has significant inhibitory potency, it may be desirable to determine

(Fzg 12 canfznuedfvom prez~ous page) In 2/k. A double-reciprocal plot of 1 lk ZteYsUs l/U] (B) yields values for K, (active site-directed inhibitors) or K, (mechanism-based inhibitors) as well as klnRc, for both types of mhibltlon (see text)

188 Ho/t

I I I I I I I c 0 2 4 6 8 10 12 14

Incubation time (minutes)

Fig. 12 Slowing and eventual cessation of substrate turnover, largely as a result of substrate depletion, in the absence (solid lure) or presence (dashed line) of a reversible, noncompetrtrve mhrbrtor at a concentration equal to its K, value. Whereas the initial rate of reaction, D, was reduced by 50% m the presence of the inhibitor, similar amounts of product were eventually formed in both cases, illustrating the important point that inhibitors reduce the rate, but not extent, of substrate turnover. Consequently, a comparison of products formed m control and inhrbr- tor-treated samples, made by a drscontmuous assay, at any time-point on the nonlinear portion of the graph would result in an underestrma- tron of the potency of the mhrbrtor.

the effects of the compound in vivo. Usually, the drug is administered to an animal at several doses and tissues are removed some time later to determine the degree of enzyme inhibition m an in vitro assay. Techniques in which drugs are administered to the animal prior to an in vitro examination of their effects are usually referred to as eX viva procedures. Such ex viva examinations of inhibitor potency are most informative when inhibition is irreversible or tight-binding. However, if the compound is a reversible inhibitor that IS not tight-binding, it is usually not possible to estimate the in vrvo degree of inhibition by this method (Green, 1984).

With reversible inhibitors, an equilibrium exists between bound and unbound inhibitor, with the degree of mhibrtion depending on the tissue concentration of the inhibitor as well as the inhibitor


constant, I$. Homogenization of the tissue in buffer will dilute the inhibitor, thus dialyzing some of the inhibitor from the enzyme, with the result that the degree of inhibition measured ex viva will be lower, and perhaps substantially lower, than that existing in vivo. Furthermore, if inhibition is also competitive, then the degree of inhibition depends on [S], and the addition of substrate to assay remaining activity will further reduce the amount of bound inhibitor. As a result, an inhibitor which actually causes 50% inhibition in vivo could appear to have no potency whatsoever ex viva (Green, 1984; Holt and Baker, 1996).

Green (1984) discussed the possibility that the ex viva effects of a reversible, competitive inhibitor might be assessed by measuring levels of product (and perhaps substrate) in tissues from drug- treated animals and comparing results with those obtained from control animals. This might be extended to experiments with perfused organs and tissues, in which both inhibitor and substrate can be included in the perfusing fluid (see Section 1.2.2.). How- ever, in many cases, the effects of interference from other metabolic pathways might prove too difficult to overcome.

Another procedure that can be used to assess reversible inhibition ex viva is the protection experiment, in which administration of the reversible, competitive inhibitor of interest is followed by administration of an irreversible inhibitor (Green, 1984). The degree of irreversible inhibition is then assessed ex zlzzlo and compared with that in animals that were not pretreated with the reversible inhibitor. The degree of protection against irreversible inhibition conferred on the enzyme by the reversible inhibitor indicates the extent of reversible inhibition present in vivo. Clearly, for such an experiment to work, both inhibitors must compete for the same binding site on the enzyme. Furthermore, clearance of unbound irreversible inhibitor from the tissue must be at least five times faster than clearance of the reversible inhibitor if the degree of reversible inhibition is not to be underestimated.

A noncompetitive, reversible inhibitor binds to a site other than the active site. Thus, no protection would be conferred against binding of an active site-directed irreversible inhibitor and an alternative approach is necessary to determine the ex vim effects of a noncompetitive, reversible inhibitor. It is often possible to determine the tissue concentration of inhibitor by gas or liquid chromatography, as well as its K1 value from m vitro kinetic experiments (see Section 4.2.2.). If inhibition is not competitive, it

190 Ho/t

may be acceptable to use this information to estimate the degree of inhibition in viva from the relationship:

n lv = l/L1 + (III/KIN (13) This equation is derived from that describing simple noncompetitive inhibition (Tipton, 19801, in which a term relating K,,, to [S] is necessary in order to relate z, to V,,,,,. Since the value of [S] m vivo is not known, then ‘u and V,,,,, can not be determined as such. How- ever, since the degree of noncompetitive inhibition is mdepen- dent of [S], then the ratio of V’/U can be estimated even if either value alone can not be established.

4.4.4. Genera/ Comments It must be ensured that any reduction m z, in the presence of

an inhibitor results from direct inhibition of the enzyme and not from some other interaction of the inhibitor with the assay system. For example, in coupled-assay systems in which a second (coupling) enzyme is included (see Section 3.1.), it must be shown that there is a negligible effect of the inhibitor on the couplmg enzyme. Blank assays should be made routinely in the presence of the inhibitor if the inhibitor has been shown to have some effect unrelated to simple enzyme inhibition In such cases, if the inhibitor is present at several concentratrons, blank assays should be made at the lowest and highest and at least one mter- mediate concentration of inhibitor so that blanks at all inhibitor concentrations might then be estimated. Fortunately, for the most part, such problems occur rarely, and blank assays need not include inhibitor if it can be established that no such effects occur. It is not uncommon for some inhibitors to cause chemiluminescence in radiochemical assays. However, this can often be reduced substantially by including 100 PL glacial acetic acid in the scintillation vial. Furthermore, most modern liquid scintillation spectrometers automatically correct for chemiluminescence during the conversion of cpm to dpm

When communicating information with respect to inhibitor experiments, quoted inhibitor concentrations should be the effec- tive concentrations present in the assay and not concentrations of stock solutions. Thus, for reversible inhibitors, the concentration of the inhibitor present during assay of substrate turnover should be given, whereas for irreversible inhibition requiring premcubation of inhibitor with enzyme, the inhibitor concentration should refer to that in the preincubation step.


5. Summary

This chapter was written as a beginner’s guide to setting up enzyme assays, While only the most basic systems governing metabolism and inhibition have been considered, an understanding of the kinetic principles underlying these systems should allow the researcher to approach most enzymology problems with some confidence. Similarly, armed with this basic knowledge, textbooks of enzyme kinetrcs, that may once have appeared beyond the com- prehension of most parttime enzymologists, will now seem if not user-friendly, then at least less imposing. The information contained herein is not a substitute for good experimental technique. Rather, a combination of both will save time, money, and no little frustration for graduate students and their supervisors alike. Of course, this chapter may have arrived too late to help some, including the undergraduate who wrote that “MAO-A inhibitors such as clorgyline are called suicide inhibitors because they are antidepressants and therefore prevent suicide.”

Acknowledgments

The author is grateful to Monica M. Palcic and Keith F. Tipton for invaluable discussions of some of the kinetic concepts. The author’s research is currently funded by NSERC (Grant OGP3045 to M.M. Palcic).

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192 Ho/t

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4 on the Measurement of Enzymes and Their Inhibitors

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