© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`Essays Biochem. (2015) 59, 1–41: doi: 10.1042/BSE0590001
`
`Enzymes: principles and
`biotechnological applications
`
`Peter K. Robinson1
`College of Science and Technology, University of Central Lancashire, Preston PR1 2HE, U.K.
`
`Abstract
`Enzymes are biological catalysts (also known as biocatalysts) that speed up bio-
`chemical reactions in living organisms, and which can be extracted from cells and
`then used to catalyse a wide range of commercially important processes. This
`chapter covers the basic principles of enzymology, such as classification, struc-
`ture, kinetics and inhibition, and also provides an overview of industrial applica-
`tions. In addition, techniques for the purification of enzymes are discussed.
`
`The nature and classification of enzymes
`Enzymes are biological catalysts (also known as biocatalysts) that speed up biochemical reactions
`in living organisms. They can also be extracted from cells and then used to catalyse a wide range of
`commercially important processes. For example, they have important roles in the production of
`sweetening agents and the modification of antibiotics, they are used in washing powders and vari-
`ous cleaning products, and they play a key role in analytical devices and assays that have clinical,
`forensic and environmental applications. The word ‘enzyme’ was first used by the German physiol-
`ogist Wilhelm Kühne in 1878, when he was describing the ability of yeast to produce alcohol from
`sugars, and it is derived from the Greek words en (meaning ‘within’) and zume (meaning ‘yeast’).
`In the late nineteenth century and early twentieth century, significant advances were made in
`the extraction, characterization and commercial exploitation of many enzymes, but it was not until
`the 1920s that enzymes were crystallized, revealing that catalytic activity is associated with protein
`molecules. For the next 60 years or so it was believed that all enzymes were proteins, but in the
`
`1To whom correspondence should be addressed (email pkrobinson@uclan.ac.uk).
`This article is a reviewed, revised and updated version of the following ‘Biochemistry Across the School
`Curriculum’ (BASC) booklet: Teal A.R. & Wymer P.E.O., 1995: Enzymes and their Role in Technology. For further
`information and to provide feedback on this or any other Biochemical Society education resource, please contact
`education@biochemistry.org. For further information on other Biochemical Society publications, please visit www.
`biochemistry.org/publications.
`
`1
`
`SYNGENTA EXHIBIT 1015
`Syngenta v. FMC, PGR2020-00028
`
`

`

`2
`
`Essays in Biochemistry volume 59 2015
`
`1980s it was found that some ribonucleic acid (RNA) molecules are also able to exert catalytic
`effects. These RNAs, which are called ribozymes, play an important role in gene expression. In the
`same decade, biochemists also developed the technology to generate antibodies that possess cata-
`lytic properties. These so-called ‘abzymes’ have significant potential both as novel industrial cata-
`lysts and in therapeutics. Notwithstanding these notable exceptions, much of classical enzymology,
`and the remainder of this essay, is focused on the proteins that possess catalytic activity.
`As catalysts, enzymes are only required in very low concentrations, and they speed up
`reactions without themselves being consumed during the reaction. We usually describe
`enzymes as being capable of catalysing the conversion of substrate molecules into product
`molecules as follows:
`
`Substrate
`
`Enzyme
`
`(cid:31) (cid:30)(cid:31)(cid:31)(cid:31)(cid:31)(cid:29) (cid:31)(cid:31)(cid:31)(cid:31)(cid:31)
`
`
`
`Product
`
`Enzymes are potent catalysts
`The enormous catalytic activity of enzymes can perhaps best be expressed by a constant, kcat, that
`is variously referred to as the turnover rate, turnover frequency or turnover number. This con-
`stant represents the number of substrate molecules that can be converted to product by a single
`enzyme molecule per unit time (usually per minute or per second). Examples of turnover rate
`values are listed in Table 1. For example, a single molecule of carbonic anhydrase can catalyse the
`conversion of over half a million molecules of its substrates, carbon dioxide (CO2) and water
`−), every second—a truly remarkable achievement.
`(H2O), into the product, bicarbonate (HCO3
`
`Enzymes are specific catalysts
`As well as being highly potent catalysts, enzymes also possess remarkable specificity in that
`they generally catalyse the conversion of only one type (or at most a range of similar types) of
`substrate molecule into product molecules.
`Some enzymes demonstrate group specificity. For example, alkaline phosphatase (an
`enzyme that is commonly encountered in first-year laboratory sessions on enzyme kinetics)
`can remove a phosphate group from a variety of substrates.
`Other enzymes demonstrate much higher specificity, which is described as absolute speci-
`ficity. For example, glucose oxidase shows almost total specificity for its substrate, β-D-glucose,
`and virtually no activity with any other monosaccharides. As we shall see later, this specificity
`is of paramount importance in many analytical assays and devices (biosensors) that measure a
`specific substrate (e.g. glucose) in a complex mixture (e.g. a blood or urine sample).
`
`Table 1. Turnover rate of some common enzymes showing wide variation.
`
`Enzyme
`
`Turnover rate (mole product s−1 mole enzyme−1)
`
`Carbonic anhydrase
`
`Catalase
`
`β–galactosidase
`
`Chymotrypsin
`
`Tyrosinase
`
`600 000
`
`93 000
`
`200
`
`100
`
`1
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`3
`
`Enzyme names and classification
`Enzymes typically have common names (often called ‘trivial names’) which refer to the reaction
`that they catalyse, with the suffix -ase (e.g. oxidase, dehydrogenase, carboxylase), although individ-
`ual proteolytic enzymes generally have the suffix -in (e.g. trypsin, chymotrypsin, papain). Often
`the trivial name also indicates the substrate on which the enzyme acts (e.g. glucose oxidase, alco-
`hol dehydrogenase, pyruvate decarboxylase). However, some trivial names (e.g. invertase, diastase,
`catalase) provide little information about the substrate, the product or the reaction involved.
`Due to the growing complexity of and inconsistency in the naming of enzymes, the
`International Union of Biochemistry set up the Enzyme Commission to address this issue. The first
`Enzyme Commission Report was published in 1961, and provided a systematic approach to the
`naming of enzymes. The sixth edition, published in 1992, contained details of nearly 3 200 different
`enzymes, and supplements published annually have now extended this number to over 5 000.
`Within this system, all enzymes are described by a four-part Enzyme Commission (EC)
`number. For example, the enzyme with the trivial name lactate dehydrogenase has the EC
`number 1.1.1.27, and is more correctly called l–lactate: NAD+ oxidoreductase.
`The first part of the EC number refers to the reaction that the enzyme catalyses (Table 2).
`The remaining digits have different meanings according to the nature of the reaction identified
`by the first digit. For example, within the oxidoreductase category, the second digit denotes the
`hydrogen donor (Table 3) and the third digit denotes the hydrogen acceptor (Table 4).
`Thus lactate dehydrogenase with the EC number 1.1.1.27 is an oxidoreductase (indicated
`by the first digit) with the alcohol group of the lactate molecule as the hydrogen donor (second
`digit) and NAD+ as the hydrogen acceptor (third digit), and is the 27th enzyme to be catego-
`rized within this group (fourth digit).
`
`Table 2. Enzyme Classification: Main classes of enzymes in EC system.
`
`First EC digit
`
`Enzyme class
`
`Reaction type
`
`1.
`
`2.
`
`3.
`
`4.
`
`5.
`
`6.
`
`Oxidoreductases
`
`Oxidation/reduction
`
`Transferases
`
`Atom/group transfer (excluding other classes)
`
`Hydrolases
`
`Hydrolysis
`
`Lyases
`
`Group removal (excluding 3.)
`
`Isomerases
`
`Isomerization
`
`Ligases
`
`Joining of molecules linked to the breakage of
`a pyrophosphate bond
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`4
`
`Essays in Biochemistry volume 59 2015
`
`Table 3. Enzyme Classification: Secondary classes of oxidoreductase enzymes
`in EC system.
`
`Oxidoreductases:
`second EC digit
`
`Hydrogen or electron donor
`
`1.
`
`2.
`
`3.
`
`4.
`
`5.
`
`6.
`
`Alcohol (CHOH)
`
`Aldehyde or ketone (C═O)
`
`─CH─CH─
`
`+)
`Primary amine (CHNH2 or CHNH3
`
`Secondary amine (CHNH)
`
`NADH or NADPH (when another redox catalyst is the acceptor)
`
`Table 4. Enzyme Classification: Tertiary classes of oxidoreductase enzymes in
`EC system.
`
`Oxidoreductases: third EC digit
`
`Hydrogen or electron acceptor
`
`1.
`
`2.
`
`3.
`
`4.
`
`NAD+ or NADP+
`
`Fe3+ (e.g. cytochromes)
`
`O2
`
`Other
`
`Fortunately, it is now very easy to find this information for any individual enzyme using
`the Enzyme Nomenclature Database (available at http://enzyme.expasy.org).
`
`Enzyme structure and substrate binding
`Amino acid-based enzymes are globular proteins that range in size from less than 100 to more
`than 2 000 amino acid residues. These amino acids can be arranged as one or more polypep-
`tide chains that are folded and bent to form a specific three-dimensional structure, incorporat-
`ing a small area known as the active site (Figure 1), where the substrate actually binds. The
`active site may well involve only a small number (less than 10) of the constituent amino acids.
`It is the shape and charge properties of the active site that enable it to bind to a single type
`of substrate molecule, so that the enzyme is able to demonstrate considerable specificity in its
`catalytic activity.
`The hypothesis that enzyme specificity results from the complementary nature of the sub-
`strate and its active site was first proposed by the German chemist Emil Fischer in 1894, and
`became known as Fischer’s ‘lock and key hypothesis’, whereby only a key of the correct size and
`shape (the substrate) fits into the keyhole (the active site) of the lock (the enzyme). It is
`astounding that this theory was proposed at a time when it was not even established that
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`5
`
`Figure 1. Representation of substrate binding to the active site of an enzyme
`molecule.
`
`enzymes were proteins. As more was learned about enzyme structure through techniques such
`as X-ray crystallography, it became clear that enzymes are not rigid structures, but are in fact
`quite flexible in shape. In the light of this finding, in 1958 Daniel Koshland extended Fischer’s
`ideas and presented the ‘induced-fit model’ of substrate and enzyme binding, in which the
`enzyme molecule changes its shape slightly to accommodate the binding of the substrate. The
`analogy that is commonly used is the ‘hand-in-glove model’, where the hand and glove are
`broadly complementary in shape, but the glove is moulded around the hand as it is inserted in
`order to provide a perfect match.
`Since it is the active site alone that binds to the substrate, it is logical to ask what is the
`role of the rest of the protein molecule. The simple answer is that it acts to stabilize the
`active site and provide an appropriate environment for interaction of the site with the sub-
`strate molecule. Therefore the active site cannot be separated out from the rest of the protein
`without loss of catalytic activity, although laboratory-based directed (or forced) evolution
`studies have shown that it is sometimes possible to generate smaller enzymes that do retain
`activity.
`It should be noted that although a large number of enzymes consist solely of protein,
`many also contain a non-protein component, known as a cofactor, that is necessary for the
`enzyme’s catalytic activity. A cofactor may be another organic molecule, in which case it is
`called a coenzyme, or it may be an inorganic molecule, typically a metal ion such as iron, man-
`ganese, cobalt, copper or zinc. A coenzyme that binds tightly and permanently to the protein is
`generally referred to as the prosthetic group of the enzyme.
`When an enzyme requires a cofactor for its activity, the inactive protein component is
`generally referred to as an apoenzyme, and the apoenzyme plus the cofactor (i.e. the active
`enzyme) is called a holoenzyme (Figure 2).
`The need for minerals and vitamins in the human diet is partly attributable to their roles
`within metabolism as cofactors and coenzymes.
`
`Enzymes and reaction equilibrium
`How do enzymes work? The broad answer to this question is that they do not alter the equilib-
`rium (i.e. the thermodynamics) of a reaction. This is because enzymes do not fundamentally
`change the structure and energetics of the products and reagents, but rather they simply allow
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`6
`
`Essays in Biochemistry volume 59 2015
`
`Figure 2. The components of a holoenzyme.
`
`the reaction equilibrium to be attained more rapidly. Let us therefore begin by clarifying the
`concept of chemical equilibrium.
`In many cases the equilibrium of a reaction is far ‘to the right’—that is, virtually all of the
`substrate (S) is converted into product (P). For this reason, reactions are often written as
`follows:
`
`P→
`S
`This is a simplification, as in all cases it is more correct to write this reaction as follows:
`
`P(cid:28)
`S
`This indicates the presence of an equilibrium. To understand this concept it is perhaps
`most helpful to look at a reaction where the equilibrium point is quite central.
`For example:
`
`Glucose
`
`Glucose isomerase
`
`(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:30)
`
`
`(cid:29)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)(cid:31)
`
`
`Fructose
`
`In this reaction, if we start with a solution of 1 mol l−1 glucose and add the enzyme, then
`upon completion we will have a mixture of approximately 0.5 mol l−1 glucose and 0.5 mol l−1
`fructose. This is the equilibrium point of this particular reaction, and although it may only
`take a couple of seconds to reach this end point with the enzyme present, we would in fact
`come to the same point if we put glucose into solution and waited many months for the reac-
`tion to occur in the absence of the enzyme. Interestingly, we could also have started this reac-
`tion with a 1 mol l−1 fructose solution, and it would have proceeded in the opposite direction
`until the same equilibrium point had been reached.
`The equilibrium point for this reaction is expressed by the equilibrium constant Keq as
`follows:
`
`=
`
`1
`
`0 5
`0 5
`
`..
`
`=
`
`Substrate concentration at end point
`Substrate concentr
`aation at end point
`
`Keq
`
`=
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`7
`
`Thus for a reaction with central equilibrium, Keq = 1, for an equilibrium ‘to the right’ Keq
`is >1, and for an equilibrium ‘to the left’ Keq is <1.
`Therefore if a reaction has a Keq value of 106, the equilibrium is very far to the right and
`can be simplified by denoting it as a single arrow. We may often describe this type of reaction
`as ‘going to completion’. Conversely, if a reaction has a Keq value of 10−6, the equilibrium is very
`far to the left, and for all practical purposes it would not really be considered to proceed at all.
`It should be noted that although the concentration of reactants has no effect on the equi-
`librium point, environmental factors such as pH and temperature can and do affect the posi-
`tion of the equilibrium.
` It should also be noted that any biochemical reaction which occurs in vivo in a living sys-
`tem does not occur in isolation, but as part of a metabolic pathway, which makes it more diffi-
`cult to conceptualize the relationship between reactants and reactions. In vivo reactions are not
`allowed to proceed to their equilibrium position. If they did, the reaction would essentially
`stop (i.e. the forward and reverse reactions would balance each other), and there would be no
`net flux through the pathway. However, in many complex biochemical pathways some of the
`individual reaction steps are close to equilibrium, whereas others are far from equilibrium, the
`latter (catalysed by regulatory enzymes) having the greatest capacity to control the overall flux
`of materials through the pathway.
`
`Enzymes form complexes with their substrates
`We often describe an enzyme-catalysed reaction as proceeding through three stages as follows:
`
`+ →
`E S
`
`ES complex
`
`
`
`E P→ +
`
`The ES complex represents a position where the substrate (S) is bound to the enzyme (E)
`such that the reaction (whatever it might be) is made more favourable. As soon as the reaction
`has occurred, the product molecule (P) dissociates from the enzyme, which is then free to bind
`to another substrate molecule. At some point during this process the substrate is converted
`into an intermediate form (often called the transition state) and then into the product.
`The exact mechanism whereby the enzyme acts to increase the rate of the reaction differs
`from one system to another. However, the general principle is that by binding of the substrate
`to the enzyme, the reaction involving the substrate is made more favourable by lowering the
`activation energy of the reaction.
`In terms of energetics, reactions can be either exergonic (releasing energy) or endergonic
`(consuming energy). However, even in an exergonic reaction a small amount of energy,
`termed the activation energy, is needed to give the reaction a ‘kick start.’ A good analogy is that
`of a match, the head of which contains a mixture of energy-rich chemicals (phosphorus ses-
`quisulfide and potassium chlorate). When a match burns it releases substantial amounts of
`light and heat energy (exergonically reacting with O2 in the air). However, and perhaps fortu-
`nately, a match will not spontaneously ignite, but rather a small input of energy in the form of
`heat generated through friction (i.e. striking of the match) is needed to initiate the reaction. Of
`course once the match has been struck the amount of energy released is considerable, and
`greatly exceeds the small energy input during the striking process.
`As shown in Figure 3, enzymes are considered to lower the activation energy of a system
`by making it energetically easier for the transition state to form. In the presence of an enzyme
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`8
`
`Essays in Biochemistry volume 59 2015
`
`Figure 3. Effect of an enzyme on reducing the activation energy required to start a
`reaction where (a) is uncatalysed and (b) is enzyme-catalysed reaction.
`
`catalyst, the formation of the transition state is energetically more favourable (i.e. it requires
`less energy for the ‘kick start’), thereby accelerating the rate at which the reaction will proceed,
`but not fundamentally changing the energy levels of either the reactant or the product.
`
`Properties and mechanisms of enzyme
`action
`Enzyme kinetics
`Enzyme kinetics is the study of factors that determine the speed of enzyme-catalysed reac-
`tions. It utilizes some mathematical equations that can be confusing to students when they first
`encounter them. However, the theory of kinetics is both logical and simple, and it is essential
`to develop an understanding of this subject in order to be able to appreciate the role of
`enzymes both in metabolism and in biotechnology.
`Assays (measurements) of enzyme activity can be performed in either a discontinuous or
`continuous fashion. Discontinuous methods involve mixing the substrate and enzyme together
`and measuring the product formed after a set period of time, so these methods are generally easy
`and quick to perform. In general we would use such discontinuous assays when we know little
`about the system (and are making preliminary investigations), or alternatively when we know a
`great deal about the system and are certain that the time interval we are choosing is appropriate.
`In continuous enzyme assays we would generally study the rate of an enzyme-catalysed
`reaction by mixing the enzyme with the substrate and continuously measuring the appear-
`ance of product over time. Of course we could equally well measure the rate of the reaction
`by measuring the disappearance of substrate over time. Apart from the actual direction (one
`increasing and one decreasing), the two values would be identical. In enzyme kinetics experi-
`ments, for convenience we very often use an artificial substrate called a chromogen that yields
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`9
`
`a brightly coloured product, making the reaction easy to follow using a colorimeter or a spec-
`trophotometer. However, we could in fact use any available analytical equipment that has the
`capacity to measure the concentration of either the product or the substrate.
`
`In almost all cases we would also add a buffer solution to the mixture. As we shall see,
`enzyme activity is strongly influenced by pH, so it is important to set the pH at a specific value
`and keep it constant throughout the experiment.
`Our first enzyme kinetics experiment may therefore involve mixing a substrate solution
`(chromogen) with a buffer solution and adding the enzyme. This mixture would then be
`placed in a spectrophotometer and the appearance of the coloured product would be meas-
`ured. This would enable us to follow a rapid reaction which, after a few seconds or minutes,
`might start to slow down, as shown in Figure 4.
`A common reason for this slowing down of the speed (rate) of the reaction is that the
`substrate within the mixture is being used up and thus becoming limiting. Alternatively, it may
`be that the enzyme is unstable and is denaturing over the course of the experiment, or it could
`be that the pH of the mixture is changing, as many reactions either consume or release pro-
`tons. For these reasons, when we are asked to specify the rate of a reaction we do so early on,
`as soon as the enzyme has been added, and when none of the above-mentioned limitations
`
`Figure 4. Formation of product in an enzyme-catalysed reaction, plotted against time.
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`10
`
`Essays in Biochemistry volume 59 2015
`
`apply. We refer to this initial rapid rate as the initial velocity (v0). Measurement of the reaction
`rate at this early stage is also quite straightforward, as the rate is effectively linear, so we can
`simply draw a straight line and measure the gradient (by dividing the concentration change by
`the time interval) in order to evaluate the reaction rate over this period.
`We may now perform a range of similar enzyme assays to evaluate how the initial velocity
`changes when the substrate or enzyme concentration is altered, or when the pH is changed.
`These studies will help us to characterize the properties of the enzyme under study.
`The relationship between enzyme concentration and the rate of the reaction is usually a
`simple one. If we repeat the experiment just described, but add 10% more enzyme, the reaction
`will be 10% faster, and if we double the enzyme concentration the reaction will proceed twice
`as fast. Thus there is a simple linear relationship between the reaction rate and the amount of
`enzyme available to catalyse the reaction (Figure 5).
`This relationship applies both to enzymes in vivo and to those used in biotechnologi-
`cal applications, where regulation of the amount of enzyme present may control reaction
`rates.
`When we perform a series of enzyme assays using the same enzyme concentration,
`but with a range of different substrate concentrations, a slightly more complex relation-
`ship emerges, as shown in Figure 6. Initially, when the substrate concentration is
`increased, the rate of reaction increases considerably. However, as the substrate concentra-
`tion is increased further the effects on the reaction rate start to decline, until a stage is
`reached where increasing the substrate concentration has little further effect on the reac-
`tion rate. At this point the enzyme is considered to be coming close to saturation with
`substrate, and demonstrating its maximal velocity (Vmax). Note that this maximal velocity
`is in fact a theoretical limit that will not be truly achieved in any experiment, although we
`might come very close to it.
`
`Figure 5. Relationship between enzyme concentration and the rate of an enzyme-
`catalysed reaction.
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`11
`
`Figure 6. Relationship between substrate concentration and the rate of an enzyme-
`catalysed reaction.
`
`The relationship described here is a fairly common one, which a mathematician would
`immediately identify as a rectangular hyperbola. The equation that describes such a relation-
`ship is as follows:
`
`x
`b
`
`×+
`
`a
`x
`
`y
`
`=
`
`The two constants a and b thus allow us to describe this hyperbolic relationship, just as
`with a linear relationship (y = mx + c), which can be expressed by the two constants m (the
`slope) and c (the intercept).
`We have in fact already defined the constant a — it is Vmax. The constant b is a little more
`complex, as it is the value on the x-axis that gives half of the maximal value of y. In enzymol-
`ogy we refer to this as the Michaelis constant (Km), which is defined as the substrate concentra-
`tion that gives half-maximal velocity.
`Our final equation, usually called the Michaelis–Menten equation, therefore becomes:
`
`
`
`Initial rate of reaction (v
`
`)=
`
`0
`
`max ×
`V
`Substrate concentration
`m+ K
`SSubstrate concentration
`
`In 1913, Leonor Michaelis and Maud Menten first showed that it was in fact possible to
`derive this equation mathematically from first principles, with some simple assumptions about
`the way in which an enzyme reacts with a substrate to form a product. Central to their deriva-
`tion is the concept that the reaction takes place via the formation of an ES complex which,
`once formed, can either dissociate (productively) to release product, or else dissociate in the
`reverse direction without any formation of product. Thus the reaction can be represented as
`follows, with k1, k−1 and k2 being the rate constants of the three individual reaction steps:
`
`k
` → +
`E P
`2
`
`k
`(cid:31) (cid:30)(cid:31)(cid:31)(cid:29) (cid:31)(cid:31)(cid:31) ES
`k
`
`−1
`
`1
`
`E
`
`+
`
`S
`
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`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`12
`
`Essays in Biochemistry volume 59 2015
`
`The Michaelis–Menten derivation requires two important assumptions. The first assump-
`tion is that we are considering the initial velocity of the reaction (v0), when the product con-
`centration will be negligibly small (i.e. [S] ≫ [P]), such that we can ignore the possibility of
`any product reverting to substrate. The second assumption is that the concentration of sub-
`strate greatly exceeds the concentration of enzyme (i.e. [S] ≫ [E]).
`The derivation begins with an equation for the expression of the initial rate, the rate
`of formation of product, as the rate at which the ES complex dissociates to form product.
`This is based upon the rate constant k2 and the concentration of the ES complex, as
`follows:
`
`
`
`v
`
`0
`
`=
`
`
`d P[ ]
`dt
`
`=
`
`k
`2
`
`×
`
`[ES]
`
`
`
`(1)
`
`Since ES is an intermediate, its concentration is unknown, but we can express it in terms
`of known values. In a steady-state approximation we can assume that although the concentra-
`tion of substrate and product changes, the concentration of the ES complex itself remains con-
`stant. The rate of formation of the ES complex and the rate of its breakdown must therefore
`balance, where:
`
`Rate of ES complex formation
`
`= k1[ ][S]
`E
`
`Rate of ES complex breakdown
`
`=
`
`+−(
`k
`1
`
`k
`2
`
`
`
`
`
`ES)[ ]
`
`Hence, at steady state:
`
`k
`
`1
`
`[ ][ ]E S
`
`=
`
`k
`
`+−
`1
`
`k
`2
`
`
`
`][ES
`
`
`
`This equation can be rearranged to yield [ES] as follows:
`
`(2)
`
`kk
`
`[ ][S]E
`
`1
`2
`+−
`k
`1
`
`=
`
`
`
`][ES
`
`
`
`and
`
`
`
`The Michaelis constant Km can be defined as follows:
`
`K
`
`m =
`
`k
`2
`
`k
`
`+−1
`k
`1
`
`Equation 2 may thus be simplified to:
`
`
`
`
`
`][ES
`
`
`
`[ ][ ]E S
`
`K
`m
`Since the concentration of substrate greatly exceeds the concentration of enzyme (i.e.
`[S] ≫ [E]), the concentration of uncombined substrate [S] is almost equal to the total concen-
`tration of substrate. The concentration of uncombined enzyme [E] is equal to the total enzyme
`
`=
`
`
`
`(3)
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`P.K. Robinson
`
`13
`
`concentration [E]T minus that combined with substrate [ES]. Introducing these terms to
`Equation 3 and solving for ES gives us the following:
`
`]
`[
`ES
`
`=
`
`[ ] [ ]
`E S
`T
`+ K
`[ ]
`S
`m
`
`We can then introduce this term into Equation 1 to give:
`
`v
`
`0
`
`2=
`k
`
`
`
`[ ]TE
`
`
`[ ]S
`+
`K
`
`
`
`[ ]S
`
`m
`
`
`
`
`
`(4)
`
`(5)
`
`The term k2[E]T in fact represents Vmax, the maximal velocity. Thus Michaelis and Menten
`were able to derive their final equation as:
`
`v
`
`0 =
`
`V
`max
`+
`
`S[ ]
`
`
`S[ ]
`K
`m
`
`A more detailed derivation of the Michaelis–Menten equation can be found in many bio-
`chemistry textbooks (see section 4 of Recommended Reading section). There are also some very
`helpful web-based tutorials available on the subject.
`Michaelis constants have been determined for many commonly used enzymes, and are
`typically in the lower millimolar range (Table 5).
`It should be noted that enzymes which catalyse the same reaction, but which are derived
`from different organisms, can have widely differing Km values. Furthermore, an enzyme with
`multiple substrates can have quite different Km values for each substrate.
`A low Km value indicates that the enzyme requires only a small amount of substrate in
`order to become saturated. Therefore the maximum velocity is reached at relatively low sub-
`strate concentrations. A high Km value indicates the need for high substrate concentrations in
`order to achieve maximum reaction velocity. Thus we generally refer to Km as a measure of the
`affinity of the enzyme for its substrate—in fact it is an inverse measure, where a high Km indi-
`cates a low affinity, and vice versa.
`The Km value tells us several important things about a particular enzyme.
`
`Table 5. Typical range of values of the Michaelis constant.
`
`Enzyme
`
`Carbonic anhydrase
`
`Chymotrypsin
`
`Ribonuclease
`
`Tyrosyl-tRNA synthetase
`
`Pepsin
`
`Km (mmol l−1)
`26
`
`15
`
`8
`
`0.9
`
`0.3
`
`© 2015 Authors. This is an open access article published by Portland Press Limited
`and distributed under the Creative Commons Attribution License 3.0.
`
`

`

`14
`
`Essays in Biochemistry volume 59 2015
`
`1. An enzyme with a low Km value relative to the physiological concentration of substrate will
`probably always be saturated with substrate, and will therefore act at a constant rate,
`regardless of variations in the concentration of substrate within the physiological range.
`2. An enzyme with a high Km value relative to the physiological concentration of substrate will
`not be saturated with substrate, and its activity will therefore vary according to the concen-
`tration of substrate, so the rate of formation of product will depend on the availability of
`substrate.
`3. If an enzyme acts on several substrates, the substrate with the lowest Km value is fre-
`quently assumed to be that enzyme’s ‘natural’ substrate, although this may not be true in
`all cases.
`4. If two enzymes (with similar Vmax) in different metabolic pathways compete for the same
`substrate, then if we know the Km values for the two enzymes we can predict the relative
`activity of the two pathways. Essentially the pathway that has the enzyme with the lower Km
`value is likely to be the ‘preferred pathway’, and more substrate will flow through that p