Introduction and Goals
In the tutorial entitled Bioenergetics, you reviewed the thermodynamic constraints that determine the likelihood of a reaction proceeding. A clear distinction was made between the thermodynamic likelihood of a reaction and the actual rate of the reaction. Consider the hydrolysis of ATP (ATP + H2O -> ADP + Pi), which is a thermodynamically spontaneous reaction (deltaG°' = -7.3 cal/mol); though spontaneous, this reaction occurs very slowly, so ATP in solution (i.e. in water) is quite stable for several days. In this tutorial, we will consider the physical properties that regulate reaction rates. In addition, you will learn how a biological catalyst can function to accelerate the rate of a reaction.
By the end of this tutorial you should know:
- the definition of the energy of activation, and how it regulates the rate of a reaction
- the properties of enzymes as biological catalysts
- the definition and properties of an active site of an enzyme
- the mechanisms of enzyme action during catalysis
- the kinetics of enzyme catalysis
- the effect of temperature and pH on enzyme activity
- the regulation of enzyme activity, including the mechanisms of inhibitors, allosteric regulation and covalent modifications.
The Energy of Activation Determines the Rate of a Reaction
A chemical reaction requires the breaking and making of chemical bonds in order to convert reactants to products. For this to occur, the reactants must have sufficient kinetic energy to overcome an energy barrier termed the energy of activation. For any given chemical reaction, there is a specific energy of activation, greater than the free energy of the reactants, that the reactants must achieve before the reaction can proceed. Paradoxically, this is true for thermodynamically favored reactions in which the change in free energy (deltaG) of the overall reaction is negative, thus indicating that the free energy of products is less than the free energy of reactants. The relationship between the change in free energy of the reaction and the energy of activation is illustrated in Figure 1.
The rate of a reaction is determined by the number of molecules of reactants that have achieved the energy of activation. In solution, molecules have a range of kinetic energies; some reactant molecules have low energy levels, whereas others have high energy levels. The fraction of reactants with the level of energy that equals or surpasses the energy of activation will be converted into products. This is illustrated in Figure 2. Reactants in this state of high energy are considered in the transition state. The transition state of reactants is a short-lived, high-energy intermediate state in which reactants rapidly convert to products. The rate of a reaction is directly proportional to the number of molecules of reactants that have reached the transition state. The rate of a reaction can be increased by increasing the kinetic energy of the reactants, thereby increasing the number of molecules of reactants that achieve the transition state. For a reaction performed in a test tube in the laboratory, this can be achieved by increasing the temperature of the reaction; this shifts the distribution of the kinetic energy of the reactants so that more molecules achieve or exceed the energy of activation (see Figure 2).
Catalysts Increase the Rate of a Reaction by Lowering the Energy of Activation
Thermal activation of reactants is not a feasible mechanism for increasing the rate of a reaction in a cell. An alternative method is to decrease the energy of activation, thereby ensuring that more molecules of reactants achieve the transition state. This is illustrated in Figure 3. Catalystsare compounds that accelerate the rate of a reaction by lowering the energy of activation. Chemical catalysts are usually acids or metals. For example, the decomposition of hydrogen peroxide (H2O2 -> 2H2O + O2) is thermodynamically favored although hydrogen peroxide is fairly stable, indicating that the rate of the reaction is low. In the presence of a catalyst (e.g. ferric ions), the rate of hydrogen peroxide decomposition increases significantly (3 x 104 fold).
Catalysts provide an environment that accelerates a reaction by lowering the energy of activation. Different reactions are enhanced by different catalysts, however, all catalysts share several features. First, all catalysts increase the rate of reaction by lowering the energy of activation. Second, all catalysts form transient complexes with reactants but are never consumed or permanently changed by the reaction, therefore, they are required in small amounts. Third, catalysts never change the equilibrium of a reaction, therefore, they have no effect on the thermodynamic spontaneity of a reaction.
Enzymes Are Biological Catalysts
Virtually all reactions in cells are catalyzed by enzymes, which are generally proteins. Enzymes bind to reactants, referred to as substrates, and mediate the formation of products. Enzymes are biological catalysts and they have all the same properties as chemical catalysts. In addition, proteins have tremendous specificity for the substrates they bind to and the reactions they catalyze. Furthermore, their activity can be regulated to enhance or decrease activity. Often, enzymes are more effective catalysts than chemical catalysts. Reconsider the decomposition of H2O2, which is accelerated 3 x 104 times in the presence of ferric ions and accelerated 1 x 108 times in the presence of the enzyme catalase. Enzymes typically increase the rate of a reaction by 107 - 1014-fold.
The active site
Enzymes function by directly binding to substrates and accelerating the formation of products. The region of an enzyme that binds to a substrate and catalyzes a reaction is termed the active site. Often this is a small pocket in the structure of the protein that accommodates the binding of the substrates and the formation of the enzyme-substrate complex (ES). However, the initial contact between an enzyme's active site and a suitable substrate is a random event. The rate of formation of the ES complex determines the rate of the reaction; this will be discussed in more detail later in this tutorial. The ES complex is formed by noncovalent interactions including hydrogen bonds, electrostatic interactions, and hydrophobic interactions between specific amino acids in the active site and the substrates. Often there are only a few amino acids that interact with the substrates in the active site. They are generally situated at different positions along the length of the polypeptide, but are brought into close proximity when the polypeptide assumes its final conformation. Frequently, active sites include the amino acids cysteine, histidine, serine, aspartate, glutamate and lysine, and the binding of a substrate is mediated by ionic and/or hydrogen bonds. Many active sites also require a small, bound, nonprotein molecule referred to as a prosthetic group or cofactor for activity. These can include small organic molecules derived from vitamins such as thiamine and niacin, or metals such as iron and zinc.
The specificity of an enzyme is also determined by its active site. The shape of the active site and the specific amino acids that comprise it determine the ability of the enzyme to bind one molecule but not another that may be similar. A striking example of specificity involves hexokinase, which catalyzes the first reaction in glycolysis (Glucose + ATP -> ADP + Glucose-6-P). Hexokinase will catalyze the phosphorylation of D-glucose but not its stereoisomer L-glucose. Other enzymes do not have such great specificity; for example, carboxypeptidase is an enzyme that degrades polypeptide chains from the carboxyl end, and it can bind and degrade a variety of different polypeptides.
The analogy of a lock and key has been used to describe the enzyme-substrate interaction, however, this is misleading. Unlike the lock and key, the conformation of both the enzyme and substrate are altered in the enzyme-substrate complex. A more accurate description is the induced-fit model, where both the conformation of the substrate and the enzyme are changed to achieve the enzyme-substrate complex. This is illustrated in Figure 4 for the enzyme hexokinase.
The Mechanisms of Enzyme Catalysis
An enzyme accelerates the rate of a reaction because the ES complex holds the reactants briefly in a high-energy transition state, which facilitates the reaction. This interaction between the enzyme and the substrate in their transition state lowers the energy of activation, thereby increasing the rate of the reaction. In addition to stabilizing the transition state, enzymes increase the reaction rates through a variety of mechanisms that facilitate substrate interactions, increase substrate reactivity, and weaken the substrate's bonds. When substrates bind to the active sites of enzymes, they are brought in close proximity and in fixed orientations (thereby increasing the probability that they will react). This is in contrast to substrates in solution, which are less likely to encounter each other and are therefore free to undergo rotational movement. The reactivity of the substrates is increased by binding to the enzyme. Charged amino acid side chains in the active sites can accept or donate protons to the substrates and increase reactivity. The charged amino acids provide a local pH environment that enhances the substrate interactions by changing the charge of the substrates. Electrostatic interactions are also important for substrate activation. Specific amino acids in the active site, with partially electronegative or electropositive side chains, can form temporary covalent bonds with the appropriate region of the substrate. A partially charged amino acid will attack and cleave a bond in the substrate, forming a transient covalent bond; then, the substrate will be released and the enzyme left unchanged. Often more than one amino acid participates in the electrostatic interaction, as do prosthetic groups that are capable of electron transfer. Finally, by binding to the enzyme surface, the bonds of the substrate become distorted, weakened and more likely to undergo catalytic attack.
Enzyme kinetics is the quantitative analysis of enzyme catalysis, the rate at which an enzyme catalyzes a reaction, and how catalysis is affected by factors such as substrate concentration. The kinetics of a reaction can be determined (under fixed conditions of temperature, pressure and enzyme concentration) by measuring the initial rate of the reaction as a function of increasing substrate concentration. The rate of reaction can be measured by the appearance of product or disappearance of substrate. Most enzymes exhibit an increased rate of reaction with increasing substrate concentration, as is illustrated in Figure 5. As the substrate concentration increases, the increase in the rate of the reaction is reduced (resulting in a hyperbolic curve). The enzyme eventually approaches saturation, a point beyond which increasing the substrate concentration will not change the rate of the reaction. At saturation, increasing the substrate concentration does not change the rate of the reaction because all of the molecules of the enzyme are engaged in catalysis. Saturation is a fundamental characteristic of an enzyme-catalyzed reaction, which distinguishes it from an uncatalyzed reaction.
The relationship between the initial rate of a reaction (v) and the substrate concentration ([S]) is described by a mathematical equation proposed by the two enzymologists Leonor Michaelis and Maud Menten. The Michaelis-Menten equation is written:
The initial rate of a reaction (v) is a function of Vmax multiplied by the substrate concentration ([S]), divided by the substrate concentration plus the Michaelis constant (Km). Vmax is the maximal velocity, or rate of a reaction, at saturating substrate concentrations (see Figure 5). The Michaelis constant (Km) is defined as the substrate concentration when the velocity of the reaction reaches one-half Vmax (see Figure 5). In most cases, Km is a measure of the affinity of the enzyme for the substrates. The Michaelis-Menten equation can be used to generate a plot similar to the one shown in Figure 5for any enzyme that Vmax and Km are defined. Both Vmax and Km are constants for any given enzyme and they are independent of substrate concentration. Vmax is a function of enzyme concentration. At saturation, the enzyme concentration is rate limiting; therefore, if the reaction is run at a higher enzyme concentration, then Vmax will increase.
The values for Vmax and Km can be determined empirically by measuring the initial rates of a reaction at varying substrate concentrations. By plotting the rates of a reaction against substrate concentration, a characteristic hyperbolic curve is generated. This curve can be used to extrapolate the value of Vmax at increasing substrate concentrations, however, it is difficult to do accurately. Alternatively, data can be plotted using the Lineweaver-Burk plot, or double-reciprocal plot, derived from the equation:
Simply, 1/the initial velocity of the reaction is plotted against 1/the substrate concentration. In contrast to the Michaelis-Menten hyperbolic plot, this is a linear plot (see Figure 6). The values for Vmax and Km can be determined by extrapolating the line generated in the double-reciprocal plot to intercept both the Y-axis (1/v) and the X-axis (1/[S]). The intercept on the Y-axis represents 1/Vmax; the intercept on the X-axis, where 1/v equals zero, represents -1/Km.
The Effects of pH and Temperature
Most enzymes function over a broad range of pHs and temperatures but have an optimal pH and temperature for peak activity. In general, enzyme activities increase with increasing temperatures; however, as temperatures get higher, enzymes begin to denature. Most proteins have an optimal temperature that reflects the temperature of the organism that it was derived from (in the case of thermoregulating organisms) or the environment in which that organism generally thrives in. This is illustrated in Figure 7. Most enzymes are also sensitive to pH. The pH affects the level of protonation of key amino acid residues in the active site and elsewhere in the protein, altering its conformation. As with temperature, the optimal pH for an enzyme depends on the environment in which it normally functions. This is also illustrated in Figure 7.
Enzyme inhibitors are molecules that bind to enzymes and inhibit their activity. These can be naturally occurring molecules or ones that have been developed, such as drugs or pesticides. There are two distinct types of inhibitors: irreversible and reversible. As their name suggests, irreversible inhibitors bind to enzymes very tightly, often forming a covalent bond, and inactivate them. An example is the nerve gas agent diisopropylphosphofluoride (DIPF), which is a potent serine protease inhibitor. In cells, DIPF inhibits the enzyme acetylcholinesterase, an enzyme involved in the regulation of the neurotransmitter acetylcholine, which is responsible for muscle contractions. Exposure to DIPF results in high levels of acetylcholine and permanently contracted muscles. Reversible inhibitorsinteract more loosely with enzymes and can be displaced. Inhibitors are also classified as competitive and noncompetitive inhibitors. Competitive inhibitorsbind to the active sites of enzymes but do not form products, hence they compete with substrates for binding. Often, competitive inhibitors are structurally similar to substrates. Noncompetitive inhibitorsbind to a region other than the active site of an enzyme and inactivate it. These two types of inhibitors have very different affects on enzyme kinetics. Competitive inhibitors, at a fixed concentration, do not change the Vmax of an enzyme. Vmax is the velocity (rate of reaction) at saturation. At saturation, there will be more substrate than inhibitor, and therefore, substrate will outcompete inhibitor for binding to the active site. At lower substrate concentrations, however, the inhibitor will be effective at competing with the substrate for binding to the enzyme, lowering the apparent affinity of the enzyme and resulting in a higher Km value. Noncompetitive inhibitors lower the Vmax. They bind to a molecule of enzyme and inactivate it in a fashion that is not dependent on substrate concentrations because this type of inhibitor does not bind to the active site. The affects of competitive and noncompetitive inhibitors on enzyme kinetics are illustrated in Figure 8.
Allosteric Regulation of Enzyme Activity
One of the most important types of regulation of enzyme activity in the cell is allosteric regulation. Allosteric regulation is mediated by changes in the conformation of the enzyme induced by the binding of regulatory molecules, which can be either activators or inhibitors. Allosteric regulators do not bind to an active site, but rather, bind to a regulatory site in an enzyme; however, they will alter the overall shape of an enzyme and affect its ability to bind substrates. Allosteric regulation is most commonly observed with multisubunit enzymes, but it is not limited to these sorts of enzymes. Allosteric enzymes exist in an equilibrium between an active state and an inactive state. The binding of an allosteric activator shifts the equilibrium toward the active state, whereas the binding of an allosteric inhibitor shifts it toward the inactive state.Figure 9is a schematic illustration of allosteric regulation for a hypothetical enzyme. Allosteric regulation is often encountered in enzymes that function in multistep metabolic pathways. (Examples of this will be seen in the tutorial on Glycolysis.) Frequently, metabolic enzymes are regulated by feedback inhibition, where the end-product of the pathway acts as an allosteric inhibitor of an enzyme in one of the early steps of the pathway (see Figure 10). Enzymes can have both allosteric activators and inhibitors, and can have multiple activators and inhibitors.
Cooperativity is a unique type of allosteric regulation observed in proteins composed of multiple identical subunits. Here, the binding of substrates by one subunit induces a conformational change and increases the affinity of other unoccupied subunits for the substrates. One of the best-studied examples of cooperativity is hemoglobin, which binds oxygen in red blood cells. Hemoglobin is composed of four globin chains, each capable of binding oxygen. At low oxygen levels, only one of the four will bind oxygen, and when it does, it will induce a conformational change in the other globin chains to facilitate oxygen binding.
Enzyme Regulation by Covalent Modifications
In addition to activators and inhibitors, some enzymes can be regulated by covalent modifications. The most common mechanism is phosphorylation, the addition to and removal of phosphate groups from specific amino acid residues in the enzyme by proteins termed kinases. Typically, phosphorylation will occur on serines, threonines, and tyrosines. Phosphorylation changes the charge of the protein and will cause a conformational change that affects enzyme activity. It is completely and rapidly reversible through dephosphorylation (removal of the phosphate) by an enzyme termed a phosphatase. Some find it helpful to think of phosphorylation/dephosphorylation as an on/off switch between the active and inactive state of an enzyme. In some instances, phosphorylation will activate a protein, but in other cases, it will inactivate a protein. The regulation of enzyme activity by kinases and phosphatases will be covered in greater detail in a future tutorial (entitled Signal Transduction) covering cell communication.
Another type of modification of some enzymes involves cleavage of an inactive precursor to activate the protein. This is best understood for digestive enzymes. Many digestive enzymes are secreted into the small intestine in an inactive form (e.g. trypsin), but only in the lumen of the small intestine are they cleaved by specific proteases and activated.
The rate of a reaction is determined by the number of molecules of reactants that have high enough levels of kinetic energy to overcome the energy of activation and reach the transition state. Catalysts increase the rate of a reaction by lowering the energy of activation, but they do not shift the equilibrium or change the thermodynamic likelihood of a reaction. Catalysts form transient complexes with the reactants but they are not altered or consumed by the reaction. Enzymes are biological catalysts that have the same properties as chemical catalysts, however, enzyme catalysts are more specific, and generally, more efficient than chemical catalysts. The activities of enzyme catalysts are also highly regulated.
Enzymes bind substrates at the active site, forming the enzyme-substrate (ES) complex. This interaction is mediated by noncovalent interactions between specific amino acids in the active site and the substrates. Many enzymes also have a prosthetic group bound at the active site that participates in substrate binding and catalysis. The precise configuration and interactions at the active site determine the specificity of the enzyme. Upon an enzyme binding a substrate, the conformations of both the enzyme and the substrate are altered. An enzyme lowers the energy of activation and accelerates the rate of a reaction, in part, by binding and stabilizing the transition state. In addition, an enzyme increases the rate of a reaction by increasing the reactivity of the substrates in a variety of ways including bringing substrates together in the correct orientation, altering the local pH of the active site, forming temporary covalent bonds with the substrates, and distorting and weakening the bonds of the reactants.
Enzyme kinetics is the quantitative analysis of the catalysis. For most enzymes, the initial rate of the reaction (v) increases with increasing substrate concentration ([S]) until the enzyme approaches saturation. This relationship is described by the Michaelis-Menten equation, which defines two values (Vmax and Km) that are unique properties of each enzyme. Vmax is the rate of a reaction at saturation. Km is the substrate concentration at 1/2 Vmax, which is a measure of the enzyme's affinity for the substrates. Plotting the rates of reaction versus substrate concentration of a typical reaction results in a characteristic hyperbolic curve, from which one can estimate the values of Vmax and Km. If one plots a double-reciprocal graph (Lineweaver-Burk plot), one can determine the values of Vmax and Km more accurately. There are several factors that can alter enzyme kinetics. Both pH and temperature can alter the efficiency of an enzyme. Inhibitors, either reversible or irreversible, can bind to an enzyme and inhibit activity. Competitive inhibitors bind to an enzyme at the active site and compete with the substrates for binding, whereas noncompetitive inhibitors bind other regions of an enzyme. Most enzymes in cells undergo allosteric regulation, binding either inhibitors or activators that induce conformational changes in the enzymes. Examples of allosteric regulation include feedback inhibition and cooperativity. Finally, enzyme activity can be altered by protein modifications, including activation by cleavage and switching activity on and off by phosphorylation/dephosphorylation.