Category: 3. Enzymes, and their activities

Enzyme kinetics

Enzyme kinetics is the study of factors that determine the speed of enzyme-catalysed reactions. 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 appearance 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 experiments, for convenience we very often use an artificial substrate called a chromogen that yields a brightly coloured product, making the reaction easy to follow using a colorimeter or a spectrophotometer. 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 measured. This would enable us to follow a rapid reaction which, after a few seconds or minutes, might start to slow down, as shown in picture.

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 protons. 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 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

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 sesquisulfide 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 fortunately, 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 the image, 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 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.

How do enzymes work? The broad answer to this question is that they do not alter the equilibrium (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 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:S → P

This is a simplification, as in all cases it is more correct to write this reaction as follows:S ⇌ P

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 isomeraseFructose

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 reaction to occur in the absence of the enzyme. Interestingly, we could also have started this reaction 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 K_eq as follows:Keq=Substrate concentration at end pointSubstrate concentration at end point=0.50.5=1

Thus for a reaction with central equilibrium, K_eq = 1, for an equilibrium ‘to the right’ K_eq is >1, and for an equilibrium ‘to the left’ K_eq is <1.

Therefore if a reaction has a K_eq 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 K_eq 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 equilibrium point, environmental factors such as pH and temperature can and do affect the position of the equilibrium.

It should also be noted that any biochemical reaction which occurs in vivo in a living system does not occur in isolation, but as part of a metabolic pathway, which makes it more difficult 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.

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 polypeptide chains that are folded and bent to form a specific three-dimensional structure, incorporating 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.Figure 1.Representation of substrate binding to the active site of an enzyme molecule.

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 substrate 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 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 substrate 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, manganese, 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).Figure 2.The components of a holoenzyme.

The need for minerals and vitamins in the human diet is partly attributable to their roles within metabolism as cofactors and coenzymes.

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 specificity. 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).

The enormous catalytic activity of enzymes can perhaps best be expressed by a constant, k_cat, that is variously referred to as the turnover rate, turnover frequency or turnover number. This constant 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 (H₂O), into the product, bicarbonate (HCO₃⁻), every second—a truly remarkable achievement.

Table 1.

Turnover rate of some common enzymes showing wide variation.

Enzyme	Turnover rate (mole product s−1 mole enzyme−1)
Carbonic anhydrase	600 000
Catalase	93 000
β–galactosidase	200
Chymotrypsin	100
Tyrosinase	1

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 various 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 physiologist 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 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 catalytic properties. These so-called ‘abzymes’ have significant potential both as novel industrial catalysts 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⇌EnzymeProduct

• Enzymes are “specific.” Each type of enzyme typically only reacts with one, or a couple, of substrates. Some enzymes are more specific than others and will only accept one particular substrate. Other enzymes can act on a range of molecules, as long as they contain the type of bond or chemical group that the enzyme targets.

A substrate entering the active site of the enzyme.

• Enzymes are reusable. Enzymes are not reactants and are not used up during the reaction. Once an enzyme binds to a substrate and catalyzes the reaction, the enzyme is released, unchanged, and can be used for another reaction. This means that for each reaction, there does not need to be a 1:1 ratio between enzyme and substrate molecules.

Enzyme activity can be affected by a variety of factors, such as temperature, pH, and concentration.Enzymes work best within specific temperature and pH ranges, and sub-optimal conditions can cause an enzyme to lose its ability to bind to a substrate.

• Temperature: Raising temperature generally speeds up a reaction, and lowering temperature slows down a reaction. However, extreme high temperatures can cause an enzyme to lose its shape (denature) and stop working.
• pH: Each enzyme has an optimum pH range. Changing the pH outside of this range will slow enzyme activity. Extreme pH values can cause enzymes to denature.
• Enzyme concentration: Increasing enzyme concentration will speed up the reaction, as long as there is substrate available to bind to. Once all of the substrate is bound, the reaction will no longer speed up, since there will be nothing for additional enzymes to bind to.
• Substrate concentration: Increasing substrate concentration also increases the rate of reaction to a certain point. Once all of the enzymes have bound, any substrate increase will have no effect on the rate of reaction, as the available enzymes will be saturated and working at their maximum rate.

Enzymes are catalysts. They are usually proteins, though some RNA molecules act as enzymes too.Enzymes lower the activation energy of a reaction – that is the required amount of energy needed for a reaction to occur. They do this by binding to a substrate and holding it in a way that allows the reaction to happen more efficiently.

Reaction coordinate diagram showing the course of a reaction with and without a catalyst. With the catalyst, the activation energy is lower than without.Image modified from OpenStax, CC BY 3.0.The part of the enzyme where the substrate binds is called the active site. Here, the enzyme changes shape slightly, fitting tightly with the substrate and forming the enzyme/substrate complex.