Enzymes

CHAPTER 6 ENZYMES chemical process is thermodynamically favorable, it is very slow. Yet when sucrose is consumed by a human (or almost any other organism), it releases its chemical energy in seconds. The difference is catalysis. Without catalysis, chemical reactions such as sucrose oxidation could not occur on a useful time scale, and thus could not sustain life. Essentially all reactions that occur in cells are, and must be, catalyzed by enzymes, the most remarkable and highly specialized of the proteins. Our discussion of enzymes is organized around five principles: Enzymes are powerful biological catalysts. Rate accelerations by enzymes are oen far greater than those by synthetic or inorganic catalysts. Like all catalysts, enzymes increase reaction rates, lowering reaction activation barriers. Enzymes do not affect the equilibria of reactions. Enzymes exhibit a very high degree of specificity. Each enzyme catalyzes only one chemical reaction, or sometimes a few closely related reactions. Reaction activation barriers are thus lowered selectively. Enzymatic reactions occur in specialized pockets called active sites. These pockets are similar to ligand binding sites, except that a reaction occurs there — the conversion of a substrate, a molecule that is acted on by an enzyme, to a product. Two concepts explain the catalytic power of enzymes. First, enzymes bind most tightly to the transition state of the catalyzed reaction, using binding energy to lower the activation barrier. Second, enzyme active sites are organized by evolution to facilitate multiple mechanisms of chemical catalysis simultaneously. Many enzymes are regulated. Regulatory mechanisms include reversible covalent modification, binding of allosteric modulators, proteolytic activation, noncovalent binding to regulatory proteins, and elaborate regulatory cascades. Enzymes are oen subject to multiple methods of regulation, which allows for exquisite control of every chemical process that occurs in a cell. The study of enzymes has immense practical importance. Some diseases, especially inheritable genetic disorders, are the result of a deficiency or even a total absence of one or more enzymes. Other disease conditions may be caused by excessive activity of an enzyme. Measurements of the activities of enzymes in blood plasma, erythrocytes, or tissue samples are important in diagnosing certain illnesses. Many drugs act through interactions with enzymes. Enzymes are also important practical tools in chemical engineering, food technology, and agriculture. Virtually every process studied in a biochemical laboratory involves one or oen many enzymes. We now turn to a broader description of these remarkable catalysts. 6.1 An Introduction to Enzymes Much of the history of biochemistry is the history of enzyme research. Biological catalysis was first recognized and described in the late 1700s, in studies on the digestion of meat by secretions of the stomach. The science of biochemistry can be traced to an experiment by Eduard Buchner in 1897, which demonstrated that cell-free yeast extracts could ferment sugar to alcohol. Buchner thus proved that fermentation was promoted by molecules that continued to function when removed from cells. This work marked the end of vitalistic notions advanced by Louis Pasteur that biological catalysis was a process inseparable from living systems. Frederick W. Kühne later gave the name enzymes (from the Greek enzymos, “leavened”) to the molecules detected by Buchner. Eduard Buchner, 1860–1917 Not until the late 1920s did it become clear that enzymes were proteins. In 1926, James Sumner provided the first breakthrough, isolating and crystallizing the enzyme urease. Further work by Northrop, Kunitz, and others led to general acceptance of the enzyme-protein association by the early 1930s. Since the latter part of the twentieth century, thousands of enzymes have been purified, their structures elucidated, and their mechanisms explained. The power of enzyme catalysts is oen astonishing. The enzyme orotidine phosphate decarboxylase, an enzyme involved in the biosynthesis of pyrimidine nucleotides, provides a special example, with a rate enhancement of 1017. The uncatalyzed reaction has a half-life of 78 million years. On the enzyme, the reaction occurs on a time scale of milliseconds. Most Enzymes Are Proteins With the exception of a few classes of catalytic RNA molecules (Chapter 26), enzymes are proteins. Their catalytic activity depends on the integrity of their native protein conformation. If an enzyme is denatured or dissociated into its subunits, catalytic activity is usually lost. The catalytic activity of each enzyme is intimately linked to its primary, secondary, tertiary, and quaternary protein structure. Enzymes, like other proteins, have molecular weights ranging from about 12,000 to more than 1 million. Some enzymes require no chemical groups for activity other than their amino acid residues. Others require an additional chemical component called a cofactor — either one or more inorganic ions, such as Fe2+, M g2+, M n2+, or Zn2+ (Table 6-1), or a complex organic or metalloorganic molecule called a coenzyme. Coenzymes act as transient carriers of specific functional groups (Table 6-2). Most are derived from vitamins, organic nutrients required in small amounts in the diet. We consider coenzymes in more detail as we encounter them in the metabolic pathways discussed in Part II. Some enzymes require both a coenzyme and one or more metal ions for activity. A coenzyme or metal ion that is very tightly or even covalently bound to the enzyme protein is called a prosthetic group. A complete, catalytically active enzyme together with its bound coenzyme and/or metal ions is called a holoenzyme. The protein part of such an enzyme is called the apoenzyme or apoprotein. Finally, some enzyme proteins are modified covalently by phosphorylation, glycosylation, and other processes. Many of these alterations are involved in the regulation of enzyme activity. TABLE 6-1 Some Inorganic Ions That Serve as Cofactors for Enzymes Ions Enzymes Cu2+ Cytochrome oxidase Fe2+ or Fe3+ Cytochrome oxidase, catalase, peroxidase K+ Pyruvate kinase M g2+ Hexokinase, glucose 6-phosphatase, pyruvate kinase M n2+ Arginase, ribonucleotide reductase Mo Dinitrogenase Ni2+ Urease Zn2+ Carbonic anhydrase, alcohol dehydrogenase, carboxypeptidases A and B TABLE 6-2 Some Coenzymes That Serve as Transient Carriers of Specific Atoms or Functional Groups Coenzyme Examples of chemical groups transferred Dietary precursor in mammals Biocytin CO2 Biotin (vitamin B7) Coenzyme A Acyl groups Pantothenic acid (vitamin B5) and other compounds 5′- Deoxyadenosylcobalamin (coenzyme B12) H atoms and alkyl groups Vitamin B12 Flavin adenine dinucleotide Electrons Riboflavin (vitamin B2) Lipoate Electrons and acyl groups Not required in diet Nicotinamide adenine dinucleotide Hydride ion (:H−) Nicotinic acid (niacin, vitamin B3) Pyridoxal phosphate Amino groups Pyridoxine (vitamin B6) Tetrahydrofolate One-carbon groups Folate (vitamin B9) Thiamine pyrophosphate Aldehydes Thiamine (vitamin B1) Note: The structures and modes of action of these coenzymes are described in Part II. Enzymes Are Classified by the Reactions They Catalyze Many enzymes have been named by adding the suffix “-ase” to the name of their substrate or to a word or phrase describing their activity. Thus, urease catalyzes hydrolysis of urea, and DNA polymerase catalyzes the polymerization of nucleotides to form DNA. Other enzymes were named by their discoverers for a broad function, before the specific reaction catalyzed was known. For example, an enzyme known to act in the digestion of foods was named pepsin, from the Greek pepsis, “digestion,” and lysozyme was named for its ability to lyse (break down) bacterial cell walls. Still others were named for their source: trypsin, named in part from the Greek tryein, “to wear down,” was obtained by rubbing pancreatic tissue with glycerin. Sometimes the same enzyme has two or more names, or two different enzymes have the same name. To limit ambiguity, biochemists worldwide have adopted a system for naming and classifying enzymes. This system divides enzymes into seven classes, each with subclasses, based on the type of reaction catalyzed (Table 6-3). Each enzyme is assigned a four-part classification number and a systematic name, which identifies the reaction it catalyzes. As an example, the formal systematic name of the enzyme catalyzing the reaction AT P + D-glucose→ AD P + D-glucose 6-phosphate is ATP:D-hexose 6-phosphotransferase, which indicates that it catalyzes the transfer of a phosphoryl group from ATP to glucose. Its Enzyme Commission number (E.C. number) is 2.7.1.1. The first number (2) denotes the class name (transferase); the second number (7), the subclass (phosphotransferase); the third number (1), a phosphotransferase with a hydroxyl group as acceptor; and the fourth number (1), D-glucose as the phosphoryl group acceptor. For many enzymes, a trivial name is more frequently used — in this case, hexokinase. A complete list and description of the thousands of known enzymes is maintained by the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology (www.qmul.ac.uk/sbcs/iubmb). TABLE 6-3 International Classification of Enzymes Class number Class name Type of reaction catalyzed 1 Oxidoreductases Transfer of electrons (hydride ions or H atoms) 2 Transferases Group transfer 3 Hydrolases Hydrolysis (transfer of functional groups to water) 4 Lyases Cleavage of C— C, C— O, C— N, or other bonds by elimination, leaving double bonds or rings, or addition of groups to double bonds 5 Isomerases Transfer of groups within molecules to yield isomeric forms 6 Ligases Formation of C— C, C— S, C— O, and C— N bonds by condensation reactions coupled to cleavage of ATP or similar cofactor 7 Translocases Movement of molecules or ions across membranes or their separation within membranes SUMMARY 6.1 An Introduction to Enzymes Life depends on powerful and specific catalysts: enzymes. Almost every biochemical reaction is catalyzed by an enzyme. With the exception of a few catalytic RNAs, all known enzymes are proteins. Many require nonprotein coenzymes or cofactors for their catalytic function. Enzymes are classified according to the type of reaction they catalyze. All enzymes have formal E.C. numbers and names, and most have trivial names. 6.2 How Enzymes Work The enzymatic catalysis of reactions is essential to living systems. Under biologically relevant conditions, uncatalyzed reactions tend to be slow — most biological molecules are quite stable in the neutral-pH, mild-temperature, aqueous environment inside cells. Reactions required to digest food, send nerve signals, or contract a muscle simply do not occur at a useful rate without catalysis. The distinguishing feature of an enzyme-catalyzed reaction is that it takes place within the confines of a pocket on the enzyme called the active site (Fig. 6-1). The active site provides a specific environment, customized by evolution, in which a given reaction can occur more rapidly. The molecule that is bound in the active site and acted upon by the enzyme is called the substrate. The surface of the active site is lined with amino acid residues with substituent groups that bind the substrate and catalyze its chemical transformation. Oen, the active site encloses a substrate, sequestering it completely from solution. The enzyme-substrate complex is central to the action of enzymes. It is also the starting point for mathematical treatments that define the kinetic behavior of enzyme-catalyzed reactions and for theoretical descriptions of enzyme mechanisms. FIGURE 6-1 Binding of a substrate to an enzyme at the active site. The enzyme chymotrypsin with bound substrate. Some key active-site amino acid residues appear as a red splotch on the enzyme surface. [Data from PDB ID 7GCH, K. Brady et al., Biochemistry 29:7600, 1990.] Enzymes Affect Reaction Rates, Not Equilibria A simple enzymatic reaction might be written E + S⇌ ES⇌ EP ⇌ E + P (6-1) where E, S, and P represent the enzyme, substrate, and product; ES and EP are transient complexes of the enzyme with the substrate and with the product. To understand catalysis, we must first appreciate the important distinction between reaction equilibria and reaction rates. The function of a catalyst is to increase the rate of a reaction. Catalysts do not affect reaction equilibria. (Recall that a reaction is at equilibrium when there is no net change in the concentrations of reactants or products.) Any reaction, such as S ⇌  P, can be described by a reaction coordinate diagram (Fig. 6-2), a picture of the energy changes during the reaction. As discussed in Chapter 1, energy in biological systems is described in terms of free energy, G. In the coordinate diagram, the free energy of the system is plotted against the progress of the reaction (the reaction coordinate). The starting point for either the forward reaction or the reverse reaction is called the ground state, the contribution to the free energy of the system by an average molecule (S or P) under a given set of conditions. FIGURE 6-2 Reaction coordinate diagram. The free energy of the system is plotted against the progress of the reaction S →  P. Such a diagram describes the energy changes during the reaction. The horizontal axis (reaction coordinate) reflects the progressive chemical changes (e.g., bond breakage or formation) as S is converted to P. The activation energies, ΔG‡, for the S →  P and P →  S reactions are indicated. ΔG′° is the overall standard free-energy change in the direction S →  P. KEY CONVENTION To describe the free-energy changes for reactions, chemists define a standard set of conditions (temperature of 298 K; partial pressure of each gas, 1 atm, or 101.3 kPa; concentration of each solute, 1 M), and express the free-energy change for a reacting system under these conditions as Δ G∘, the standard free-energy change. Because biochemical systems commonly involve H+ concentrations far below 1 M, biochemists define a biochemical standard free-energy change, Δ G′°, the standard free-energy change at pH 7.0; we employ this definition throughout the book. A more complete definition of ΔG′° is given in Chapter 13. The equilibrium between S and P reflects the difference in the free energies of their ground states. In the example shown in Figure 6-2, the free energy of the ground state of P is lower than that of S, so ΔG′° for the reaction is negative (the reaction is exergonic) and at equilibrium there is more P than S (the equilibrium favors P). A favorable equilibrium does not mean that the S →  P conversion will occur at a rapid or even detectable rate. The rate of a reaction is instead dependent on an entirely different parameter, the energy barrier between S and P. That barrier consists of the energy required for alignment of reacting groups, formation of transient unstable charges, bond rearrangements, and other transformations required for the reaction to proceed in either direction. This is illustrated by the energy “hill” in Figures 6-2 and 6-3. To undergo reaction, the molecules must overcome this barrier and therefore must be raised to a higher energy level. At the top of the energy hill is a point at which decay to the S or P state is equally probable (it is downhill either way). This is called the transition state, oen symbolized by a double dagger (‡). The transition state is not a chemical species with any significant stability and should not be confused with a reaction intermediate (such as ES or EP). It is simply a fleeting molecular moment in which events such as bond breakage, bond formation, and charge development have proceeded to the precise point at which decay to substrate and decay to product are equally likely. The difference between the energy level of the ground state and the energy level of the transition state is the activation energy, Δ G‡. The rate of a reaction reflects this activation energy: a higher activation energy corresponds to a slower reaction. Lowering the activation energy increases the rate of reaction. Reaction rates can be increased by raising the temperature and/or pressure, thereby increasing the number of molecules with sufficient energy to overcome the energy barrier. Alternatively, the activation energy can be lowered, and reaction rate increased, by adding a catalyst (Fig. 6-3). FIGURE 6-3 Reaction coordinate diagram comparing enzyme-catalyzed and uncatalyzed reactions. In the reaction S →  P, the ES and EP intermediates occupy minima in the energy progress curve of the enzyme- catalyzed reaction. The terms ΔG‡ uncat and ΔG‡ cat correspond to the activation energy for the uncatalyzed reaction and the overall activation energy for the catalyzed reaction, respectively. The activation energy is lower when the enzyme catalyzes the reaction. Catalysts do not affect reaction equilibria. The bidirectional arrows in Equation 6-1 make this important point: any enzyme that catalyzes the reaction S →  P also catalyzes the reaction P →  S. The role of enzymes is to accelerate the interconversion of S and P. The enzyme is not used up in the process, and the equilibrium point is unaffected. However, the reaction reaches equilibrium much faster when the appropriate enzyme is present, because the rate of the reaction is increased. This relationship between reaction rate and activation energy is illustrated by the process introduced at the beginning of the chapter: the conversion of sucrose and oxygen to carbon dioxide and water: C12H22O11+ 12O2 ⇌  12CO2+ 11H2O This conversion, which takes place through a series of separate reactions, has a very large and negative ΔG′°, and at equilibrium the amount of sucrose present is negligible. Yet sucrose is a stable compound, because the activation energy barrier that must be overcome before sucrose reacts with oxygen is quite high. Sucrose can be stored in a container with oxygen almost indefinitely without reacting. In cells, however, sucrose is readily broken down to CO2 and H2O in a series of reactions catalyzed by enzymes. These enzymes not only accelerate the reactions, they organize and control them so that much of the energy released is recovered in other chemical forms and made available to the cell for other tasks. The reaction pathway by which sucrose (and other sugars) is broken down is the primary energy-yielding pathway for cells, and the enzymes of this pathway allow the reaction sequence to proceed on a biologically useful (millisecond) time scale. Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates. A reaction intermediate is any species on the reaction pathway that has a finite chemical lifetime (longer than a molecular vibration, ∼10−13 second). When the S ⇌  P reaction is catalyzed by an enzyme, the ES and EP complexes can be considered intermediates, even though S and P are stable chemical species (Eqn 6-1); the ES and EP complexes occupy valleys in the reaction coordinate diagram (Fig. 6-3). Additional, less-stable chemical intermediates oen exist in the course of an enzyme-catalyzed reaction. The interconversion of two sequential reaction intermediates thus constitutes a reaction step. When several steps occur in a reaction, the overall rate is determined by the step (or steps) with the highest activation energy; this is called the rate-limiting step. In a simple case, the rate-limiting step is the highest-energy point in the diagram for interconversion of S and P. In practice, the rate-limiting step can vary with reaction conditions, and for many enzymes several steps may have similar activation energies, which means they are all partially rate- limiting. i In this chapter, step and intermediate refer to chemical reactions and chemical species in the reaction pathway of a single enzyme-catalyzed reaction. In the context of metabolic pathways involving many enzymes (discussed in Part II), these terms are used somewhat differently: an entire enzymatic reaction is o en referred to as a “step” in a pathway, and the product of one enzymatic reaction (which is the substrate for the next enzyme in the pathway) is referred to as a pathway “intermediate.” Activation energies are energy barriers to chemical reactions. These barriers are crucial to life itself. Without such energy barriers, complex macromolecules would revert spontaneously to much simpler molecular forms, and the complex and highly ordered structures and metabolic processes of cells could not exist. Over the course of evolution, enzymes have developed to lower activation energies selectively, and thus increase rates, for reactions that are needed for cell survival. Reaction Rates and Equilibria Have Precise Thermodynamic Definitions Reaction equilibria are inextricably linked to the standard free-energy change for the reaction, ΔG′°, and reaction rates are linked to the activation energy, ΔG‡. A basic introduction to these thermodynamic relationships is the next step in understanding how enzymes work. An equilibrium such as S ⇌  P is described by an equilibrium constant, Keq, or simply K (p. 23). Under the standard conditions i used to compare biochemical processes, an equilibrium constant is denoted K ′eq (or K ′): K ′eq = (6-2) From thermodynamics, the relationship between K ′eq and ΔG′° can be described by the expression ΔG′°= −RT ln K ′eq (6-3) where R is the gas constant, 8.315 J/mol·K, and T is the absolute temperature, 298 K (25 ∘C). Equation 6-3 is developed and discussed in more detail in Chapter 13. The important point here is that the equilibrium constant is directly related to the overall standard free-energy change for the reaction (Table 6-4). A large negative value for ΔG′° reflects a favorable reaction equilibrium (one in which there is much more product than substrate at equilibrium) — but as already noted, this does not mean the reaction will proceed at a rapid rate. TABLE 6-4 Relationship between K′eq and Δ G′° K′eq ΔG′° (kJ/m ol) 10−6   34.2 [P] [S] 10−5   28.5 10−4   22.8 10−3  17.1 10−2   11.4 10−1     5.7 1     0.0 101   −5.7 102 −11.4 103 −17.1 Note: The relationship is calculated from ΔG′°= −RT ln K ′eq (Eqn 6-3). The rate of any reaction is determined by the concentration of the reactant (or reactants) and by a rate constant, usually denoted by k. For the unimolecular reaction S →  P, the rate (or velocity) of the reaction, V — representing the amount of S that reacts per unit of time — is expressed by a rate equation: V = k[S] (6-4) In this reaction, the rate depends only on the concentration of S. This is called a first-order reaction. The factor k is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature, and so forth). Here, k is a first-order rate constant and has units of reciprocal time, such as s−1. If a first-order reaction has a rate constant k of 0.03 s−1, this may be interpreted (qualitatively) to mean that 3% of the available S will be converted to P in 1 second. A reaction with a rate constant of 2,000 s−1 will be over in a small fraction of a second. If a reaction rate depends on the concentration of two different compounds, or if the reaction is between two molecules of the same compound, the reaction is second order and k is a second-order rate constant, with units of M −1s−1. The rate equation then becomes V = k[S1] [S2] (6-5) From transition-state theory we can derive an expression that relates the magnitude of a rate constant to the activation energy: k=  e−ΔG‡/RT (6-6) where k is the Boltzmann constant and h is Planck’s constant. The important point is that the relationship between the rate constant k and the activation energy ΔG‡ is inverse and exponential. In simplified terms, this is the basis for the statement that a kT h lower activation energy means a faster reaction rate — and lowering activation energies is what enzymes do. Now we turn from what enzymes do to how they do it. A Few Principles Explain the Catalytic Power and Specificity of Enzymes Enzymes are extraordinary catalysts. The rate enhancements they bring about are in the range of 5 to 17 orders of magnitude (Table 6-5). Enzymes are also very specific, readily discriminating between substrates with quite similar structures. How can these enormous and highly selective rate enhancements be explained? What is the source of the energy for the dramatic lowering of the activation energies for specific reactions? TABLE 6-5 Some Rate Enhancements Produced by Enzymes Cyclophilin 105 Carbonic anhydrase 107 Triose phosphate isomerase 109 Carboxypeptidase A 1011 Phosphoglucomutase 1012 Succinyl-CoA transferase 1013 Urease 1014 Orotidine monophosphate decarboxylase 1017 The answer to these questions has two distinct but interwoven parts. The first lies in the noncovalent interactions between enzyme and substrate. What really sets enzymes apart from most other catalysts is the formation of a specific ES complex. The interaction between substrate and enzyme in this complex is mediated by the same forces that stabilize protein structure, including hydrogen bonds, ionic interactions, and the hydrophobic effect (Chapter 4). Formation of each weak interaction in the ES complex is accompanied by release of a small amount of free energy that stabilizes the interaction. The energy derived from noncovalent enzyme-substrate interaction is called binding energy, Δ GB. Its significance extends beyond a simple stabilization of the enzyme-substrate interaction. As we will see, binding energy is a major source of free energy used by enzymes to lower the activation energies of reactions. The second part of the explanation lies in covalent interactions between enzyme and substrate, plus a few additional chemical catalytic mechanisms. Chemical reactions of many types take place between substrates and enzymes’ functional groups (specific amino acid side chains, metal ions, and coenzymes). Catalytic functional groups on an enzyme may form a transient covalent bond with a substrate and activate it for reaction, or a group may be transiently transferred from the substrate to the enzyme. In many cases, these reactions occur only in the enzyme active site. Covalent interactions between enzymes and substrates lower the activation energy (and thereby accelerate the reaction) by providing an alternative, lower-energy reaction path. Metal ions facilitate additional mechanisms of catalysis that do not involve covalent interactions. We now consider noncovalent contributions to catalysis and the additional chemical mechanisms in turn. Noncovalent Interactions between Enzyme and Substrate Are Optimized in the Transition State How does an enzyme use noncovalent binding energy to lower the activation energy for a reaction? Formation of the ES complex is not the explanation in itself, although some of the earliest considerations of enzyme mechanisms began with this idea. Studies on enzyme specificity carried out by Emil Fischer led him to propose, in 1894, that enzymes were structurally complementary to their substrates, so that they fit together like a lock and key (Fig. 6-4). This elegant idea, that a specific (exclusive) interaction between two biological molecules is mediated by molecular surfaces with complementary shapes, has greatly influenced the development of biochemistry. However, the “lock and key” hypothesis can be misleading when applied to enzymatic catalysis. An enzyme completely complementary to its substrate would be a very poor enzyme, as we can demonstrate. FIGURE 6-4 Complementary shapes of a substrate and its binding site on an enzyme. The enzyme dihydrofolate reductase with its substrate NAD P+, unbound and bound; another bound substrate, tetrahydrofolate, is also visible. In this model, the NAD P+ binds to a pocket that is complementary to it in shape and ionic properties, an illustration of Emil Fischer’s “lock and key” hypothesis of enzyme action. In reality, the complementarity between protein and ligand (in this case, substrate) is rarely perfect, as we saw in Chapter 5. [Data from PDB ID 1RA2, M. R. Sawaya and J. Kraut, Biochemistry 36:586, 1997.] Consider an imaginary reaction, the breaking of a magnetized metal stick. The uncatalyzed reaction is shown in Figure 6-5a. Let’s examine two imaginary enzymes — two “stickases” — that could catalyze this reaction, both of which employ magnetic forces as a paradigm for the binding energy used by real enzymes. We first design an enzyme perfectly complementary to the substrate (Fig. 6-5b). The active site of this stickase is a pocket lined with magnets. To react (break), the stick must reach the bent transition state of the reaction. However, the snug fit of the stick in this active site means that magnets hinder the required bending. Such an enzyme impedes the reaction, stabilizing the substrate instead. In a reaction coordinate diagram (Fig. 6-5b), this kind of ES complex would correspond to an energy trough from which the substrate would have difficulty escaping. Such an enzyme would be useless. FIGURE 6-5 An imaginary enzyme (stickase) designed to catalyze breakage of a metal stick. (a) Before the stick is broken, it must first be bent (the transition state). In both stickase examples, magnetic interactions take the place of weak bonding interactions between enzyme and substrate. (b) A stickase with a magnet-lined pocket complementary in structure to the stick (the substrate) stabilizes the substrate. Bending is impeded by the magnetic attraction between stick and stickase. (c) An enzyme with a pocket complementary to the reaction transition state helps to destabilize the stick, contributing to catalysis of the reaction. The binding energy of the magnetic interactions compensates for the increase in free energy required to bend the stick. Reaction coordinate diagrams (right) show the energy consequences of complementarity to substrate versus complementarity to transition state (EP complexes are omitted). ΔGM , the difference between the transition-state energies of the uncatalyzed and catalyzed reactions, is contributed by the magnetic interactions between the stick and stickase. When the enzyme is complementary to the substrate (b), the ES complex is more stable and has less free energy in the ground state than substrate alone. The result is an increase in the activation energy. The modern notion of enzymatic catalysis, first proposed by Michael Polanyi (1921) and J. B. S. Haldane (1930), was elaborated by Linus Pauling in 1946 and by William P. Jencks in the 1970s: in order to catalyze reactions, an enzyme must be complementary to the reaction transition state. This means that optimal interactions between substrate and enzyme occur only in the transition state. Figure 6-5c demonstrates how such an enzyme can work. The metal stick binds to the stickase, but only a few of the possible magnetic interactions are used in forming the ES complex. The bound substrate must still undergo the increase in free energy needed to reach the transition state. Now, however, the increase in free energy required to draw the stick into a bent and partially broken conformation is offset, or “paid for,” by the magnetic interactions that form between our imaginary enzyme and substrate (analogous to the binding energy in a real enzyme) in the transition state. Many of these interactions involve parts of the stick that are distant from the point of breakage; thus, interactions between the stickase and nonreacting parts of the stick provide some of the energy needed to catalyze stick breakage. This “energy payment” translates into a lower net activation energy and a faster reaction rate. Real enzymes work on an analogous principle. Some weak interactions are formed in the ES complex, but the full complement of such interactions between substrate and enzyme is formed only when the substrate reaches the transition state. The free energy (binding energy) released by the formation of these interactions partially offsets the energy required to reach the top of the energy hill. The summation of the unfavorable (positive) activation energy ΔG‡ and the favorable (negative) binding energy ΔGB results in a lower net activation energy (Fig. 6-6). Even on the enzyme, the transition state is not a stable species but a brief point in time that the substrate spends atop an energy hill. However, the enzyme-catalyzed reaction is much faster than the uncatalyzed process because the hill is much smaller. The important principle is that weak binding interactions between the enzyme and the substrate provide a substantial driving force for enzymatic catalysis. The groups on the substrate that are involved in these weak interactions can be at some distance from the bonds that are broken or changed. The weak interactions formed only in the transition state are those that make the primary contribution to catalysis. FIGURE 6-6 Role of binding energy in catalysis. To lower the activation energy for a reaction, the system must acquire an amount of energy equivalent to the amount by which ΔG‡ is lowered. Much of this energy comes from binding energy, ΔGB, contributed by formation of weak noncovalent interactions between substrate and enzyme in the transition state. The role of ΔGB is analogous to that of ΔGM in Figure 6-5. The requirement for multiple weak interactions to drive catalysis is one reason why enzymes (and some coenzymes) are so large. An enzyme must provide functional groups for ionic, hydrogen- bond, and other interactions, and also must precisely position these groups so that binding energy is optimized in the transition state. Adequate binding is accomplished most readily by positioning a substrate in a cavity (the active site) where it is effectively removed from water. The size of proteins reflects the need for superstructure to keep interacting groups properly positioned and to keep the cavity from collapsing. Can we demonstrate quantitatively that binding energy accounts for the huge rate accelerations brought about by enzymes? Yes. As a point of reference, Equation 6-6 allows us to calculate that ΔG‡ must be lowered by about 5.7 kJ/mol to accelerate a first-order reaction by a factor of 10, under conditions commonly found in cells. The energy available from formation of a single weak interaction is generally estimated to be 4 to 30 kJ/mol. The overall energy available from many such interactions is therefore sufficient to lower activation energies by the 60 to 100 kJ/mol required to explain the large rate enhancements observed for many enzymes. The same binding energy that provides energy for catalysis also gives an enzyme its specificity, the ability to discriminate between a substrate and a competing molecule. Conceptually, specificity is easy to distinguish from catalysis, but this distinction is much more difficult to make experimentally, because catalysis and specificity arise from the same phenomenon. If an enzyme active site has functional groups arranged optimally to form a variety of weak interactions with a particular substrate in the transition state, the enzyme will not be able to interact to the same degree with any other molecule. For example, if the substrate has a hydroxyl group that forms a hydrogen bond with a specific Glu residue on the enzyme, any molecule lacking a hydroxyl group at that particular position will be a poorer substrate for the enzyme. In general, specificity is derived from the formation of many weak interactions between the enzyme and its specific substrate molecule. The importance of binding energy to catalysis can be readily demonstrated. For example, the glycolytic enzyme triose phosphate isomerase catalyzes the interconversion of glyceraldehyde 3-phosphate and dihydroxyacetone phosphate: This reaction rearranges the carbonyl and hydroxyl groups on carbons 1 and 2. However, more than 80% of the enzymatic rate acceleration has been traced to enzyme-substrate interactions involving the phosphate group on carbon 3 of the substrate. This was determined by comparing the enzyme-catalyzed reactions with glyceraldehyde 3-phosphate and with glyceraldehyde (no phosphate group at position 3) as substrate. The general principles outlined above can be illustrated by a variety of recognized catalytic mechanisms. These mechanisms are not mutually exclusive, and a given enzyme might incorporate several catalytic strategies in its overall mechanism of action. Consider what needs to occur for a reaction to take place. Prominent physical and thermodynamic factors contributing to ΔG‡, the barrier to reaction, might include (1) the entropy of molecules in solution, which reduces the possibility that they will react together; (2) the solvation shell of hydrogen-bonded water that surrounds and helps to stabilize most biomolecules in aqueous solution; (3) the distortion of substrates that must occur in many reactions; and (4) the need for proper alignment of catalytic functional groups on the enzyme. Binding energy can be used to overcome all these barriers. First, a large restriction in the relative motions of two substrates that are to react, or entropy reduction, is one obvious benefit of binding them to an enzyme. Binding energy constrains the substrates in the proper orientation to react — a substantial contribution to catalysis, because productive collisions between molecules in solution can be exceedingly rare. Substrates can be precisely aligned on the enzyme, with many weak interactions between each substrate and strategically located groups on the enzyme clamping the substrate molecules into the proper positions. Studies have shown that simply constraining the motion of two reactants can produce rate enhancements of many orders of magnitude (Fig. 6-7). FIGURE 6-7 Rate enhancement by entropy reduction. Shown here are reactions of an ester with a carboxylate group to form an anhydride. The R group is the same in each case. (a) For this bimolecular reaction, the rate constant k is second order, with units of M −1s−1. (b) When the two reacting groups are in a single molecule, and thus have less freedom of motion, the reaction is much faster. For this unimolecular reaction, k has units of s−1. Dividing the rate constant for (b) by the rate constant for (a) gives a rate enhancement of about 105 M . (The enhancement has units of molarity because we are comparing a unimolecular reaction and a bimolecular reaction.) Put another way, if the reactant in (b) were present at a concentration of 1 , the reacting groups would behave as though they were present at a concentration of 105 M . Note that the reactant in (b) has freedom of rotation about three bonds (shown with curved arrows), but this still represents a substantial reduction of entropy over (a). If the bonds that rotate in (b) are constrained as in (c), the entropy is reduced further and the reaction exhibits a rate enhancement of 108 M relative to (a). Second, in water, many organic molecules are surrounded by a solvation shell of structured water that can hinder reactions (see Fig. 2-8). Formation of weak bonds between substrate and enzyme results in desolvation of the substrate. Enzyme-substrate interactions replace most or all of the hydrogen bonds between the substrate and water that would otherwise impede reaction. Third, binding energy involving weak interactions that are formed only in the reaction transition state helps to compensate thermodynamically for the unfavorable free-energy change associated with any distortion, primarily electron redistribution, that the substrate must undergo to react. Finally, the enzyme itself usually undergoes a change in conformation when the substrate binds, induced by multiple weak interactions with the substrate. This is referred to as induced fit, a mechanism postulated by Daniel Koshland in 1958. The motions can affect a small part of the enzyme near the active site or can involve changes in the positioning of entire domains. Typically, a network of coupled motions occurs throughout the enzyme that ultimately brings about the required changes in the active site. Induced fit serves to bring specific functional groups on the enzyme into the proper position to catalyze the reaction. The conformational change also permits formation of additional weak bonding interactions in the transition state. In either case, the new enzyme conformation has enhanced catalytic properties. As we have seen, induced fit is a common feature of the reversible binding of ligands to proteins (Chapter 5). Induced fit is also important in the interaction of almost every enzyme with its substrate. Covalent Interactions and Metal Ions Contribute to Catalysis In most enzymes, noncovalent binding energy is just one of several contributors to the overall catalytic mechanism. Once a substrate is bound to an enzyme, properly positioned catalytic functional groups aid in the cleavage and formation of bonds by a variety of mechanisms, including general acid-base catalysis, covalent catalysis, and metal ion catalysis. The first two of these mechanisms are distinct from those based on binding energy, because they generally involve transient covalent interaction with a substrate or group transfer to or from a substrate. General Acid-Base Catalysis Transfer of a proton from one molecule to another is the single most common reaction in biochemistry. One or, oen, many proton transfers occur in the course of most reactions that take place in cells. Many biochemical reactions occur through the formation of unstable charged intermediates that tend to break down rapidly to their constituent reactant species, impeding the forward reaction (Fig. 6-8). Charged intermediates can oen be stabilized by the transfer of protons to form a species that breaks down more readily to products. These protons are transferred between an enzyme and a substrate or intermediate.

FIGURE 6-8 How a catalyst circumvents unfavorable charge development during cleavage of an amide. The hydrolysis of an amide bond, shown here, is the same reaction as that catalyzed by chymotrypsin and other proteases. Charge development is unfavorable and can be circumvented by donation of a proton by H3O+ (specific acid catalysis) or HA (general acid catalysis), where HA represents any acid. Similarly, charge can be neutralized by proton abstraction by OH− (specific base catalysis) or B: (general base catalysis), where B: represents any base. The effects of catalysis by acids and bases are oen studied using nonenzymatic model reactions, in which the proton donors or acceptors are either the constituents of water alone or other weak acids and bases. Catalysis of the type that uses only the H+ (H3O+) or OH− ions present in water is referred to as specific acid-base catalysis. However, a further increase in rate can oen be afforded by the addition of weak acids and bases to the reaction. Many weak organic acids can supplement water as proton donors, or weak organic bases can supplement water as proton acceptors. The term general acid-base catalysis refers to proton transfers mediated by weak acids and bases other than water. General acid-base catalysis becomes crucial in the active site of an enzyme, where water may not be available as a proton donor or acceptor. Several amino acid side chains can and do take on the role of proton donors and acceptors (Fig. 6-9). These groups can be precisely positioned in an enzyme active site to allow proton transfers, providing rate enhancements of the order of 102 to 105. This type of catalysis occurs on the vast majority of enzymes. FIGURE 6-9 Amino acids in general acid-base catalysis. Many organic reactions that are used to model biochemical processes are promoted by proton donors (general acids) or proton acceptors (general bases). The active sites of some enzymes contain amino acid functional groups, such as those shown here, that can participate in the catalytic process as proton donors or proton acceptors. Covalent Catalysis In covalent catalysis, a transient covalent bond is formed between the enzyme and the substrate. Consider the hydrolysis of a bond between groups A and B: A— B   H2O  −−−→ A + B In the presence of a covalent catalyst (an enzyme with a nucleophilic group X:) the reaction becomes A— B + X:→ A— X + B   H2O   −−−→ A + X:+B Formation and breakdown of a covalent intermediate creates a new pathway for the reaction, but catalysis results only when the new pathway has a lower activation energy than the uncatalyzed pathway. Both of the new steps must be faster than the uncatalyzed reaction. Several amino acid side chains, including all those in Figure 6-9, and the functional groups of some enzyme cofactors can serve as nucleophiles in the formation of covalent bonds with substrates. These covalent complexes always undergo further reaction to regenerate the free enzyme. The covalent bond formed between the enzyme and the substrate can activate a substrate for further reaction in a manner that is usually specific to the particular group or coenzyme. Metal Ion Catalysis Metals, whether tightly bound to the enzyme or taken up from solution along with the substrate, can participate in catalysis in several ways. Ionic interactions between an enzyme-bound metal and a substrate can help orient the substrate for reaction or stabilize charged reaction transition states. This use of weak bonding interactions between metal and substrate is similar to some of the uses of enzyme-substrate binding energy described earlier, and it can contribute to enzyme–transition state complementarity. Metals can also mediate oxidation-reduction reactions by reversible changes in the metal ion’s oxidation state. Nearly a third of all known enzymes require one or more metal ions for catalytic activity. Most enzymes combine several catalytic strategies to bring about a rate enhancement. A good example is the use of covalent catalysis, general acid-base catalysis, and transition-state stabilization in the reaction catalyzed by chymotrypsin, detailed in Section 6.4. SUMMARY 6.2 How Enzymes Work Enzymes are highly effective catalysts, commonly enhancing reaction rates by a factor of 105 to 1017. Enzyme-catalyzed reactions are characterized by the formation of a complex between substrate and enzyme (an ES complex). Substrate binding occurs in a pocket on the enzyme called the active site. The function of enzymes and other catalysts is to lower the activation energy, ΔG‡, for a reaction and thereby enhance the reaction rate. The equilibrium of a reaction is unaffected by the enzyme. Reaction equilibria are described by equilibrium constants, Keq , which are related to the biochemical standard free-energy change ΔG′°. Reaction rates are described by rate constants, k, which are related to the activation energy ΔG‡. The extraordinary rate accelerations provided by enzymes are due to noncovalent binding energy supplemented by covalent interactions or metal ion catalysis. Noncovalent binding energy, ΔGB, is maximized in the transition state of the catalyzed reaction. Enzyme–transition state complementarity is a fundamental principle of enzymatic catalysis. Noncovalent interactions may facilitate the path to the transition state, offsetting the energy required for activation, ΔG‡, by lowering substrate entropy, causing substrate desolvation, or causing a conformational change in the enzyme (induced fit). Binding energy also accounts for the exquisite specificity of enzymes for their substrates. General acid-base catalysis and covalent catalysis mechanisms contribute to the catalytic power of enzymes. Covalent interactions between the substrate and the enzyme, group transfers to and from the enzyme, and interactions with metal ions can provide a new, lower-energy reaction path. 6.3 Enzyme Kinetics as an Approachto Understanding Mechanism Biochemists commonly use several approaches to study the mechanism of action of purified enzymes. The three-dimensional structure of the protein provides important information, which is enhanced by traditional protein chemistry and modern methods of site-directed mutagenesis (changing the amino acid sequence of a protein by genetic engineering; see Fig. 9-10). These technologies permit enzymologists to examine the role of individual amino acids in enzyme structure and action. However, the oldest approach to understanding enzyme mechanisms, and one that remains very important, is to determine the rate of a reaction and how it changes in response to changes in experimental parameters, a discipline known as enzyme kinetics. We provide here a basic introduction to the kinetics of enzyme-catalyzed reactions. Substrate Concentration Affects the Rate of Enzyme-Catalyzed Reactions At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms: the free or uncombined form E and the substrate- combined form ES. When the enzyme is first mixed with a large excess of substrate, there is an initial transient period, the pre–steady state, during which the concentration of ES builds up. For most enzymatic reactions, this period is very brief. The pre-steady state is frequently too short to be observed easily, lasting only the time (oen microseconds) required to convert one molecule of substrate to product (one enzymatic turnover). The reaction quickly achieves a steady state in which [ES] (and the concentrations of any other intermediates) remains approximately constant for much of the remainder of the reaction (Fig. 6-10). As most of the reaction reflects the steady state, the traditional analysis of reaction rates is referred to as steady-state kinetics. FIGURE 6-10 The course of an enzyme-catalyzed reaction. In a typical reaction, product will increase as substrate declines. The concentration of free enzyme, E, declines rapidly, as the concentration of the ES complex increases and reaches a steady state. The steady-state concentration of ES remains nearly constant for much of the remainder of the reaction. A key factor affecting the rate of a reaction catalyzed by an enzyme is the concentration of substrate, [S]. However, studying the effects of substrate concentration is complicated by the fact that [S] changes during the course of an in vitro reaction as substrate is converted to product. One simplifying approach is to measure the initial rate (or initial velocity), designated V0 (Fig. 6-11). In a typical reaction, the enzyme may be present in nanomolar quantities, whereas [S] may be five or six orders of magnitude higher. If only the beginning of the reaction is monitored, over a period in which only a small percentage of the available substrate (<2%−3%) is converted to product, [S] can be regarded as constant, to a reasonable approximation. V0 can then be explored as a function of [S], which is adjusted by the investigator. Note that even the initial rate reflects a steady state. FIGURE 6-11 Initial velocities of enzyme-catalyzed reactions. A theoretical enzyme that catalyzes the reaction S ⇌  P is present at a concentration of S sufficient to catalyze the reaction at a maximum velocity, defined as Vmax, of 1 μ /min. The rate observed at a given concentration of S depends on the Michaelis constant, Km, explained in more detail in the next section. Here, the Km is 0.5 μ . Progress curves are shown for substrate concentrations below, at, and above the Km. The rate of an enzyme-catalyzed reaction declines as substrate is converted to product. A tangent to each curve taken at time = 0 (dashed line) defines the initial velocity, V0, of each reaction. The effect on V0 of varying [S] when the enzyme concentration is held constant is shown in Figure 6-12. At relatively low concentrations of substrate, V0 increases almost linearly with an increase in [S]. At higher substrate concentrations, V0 increases by smaller and smaller amounts in response to increases in [S]. Finally, a point is reached beyond which increases in V0 are vanishingly small as [S] increases. This plateau-like V0 region is close to the maximum velocity, Vmax. FIGURE 6-12 Effect of substrate concentration on the initial velocity of an enzyme- catalyzed reaction. The maximum velocity, Vmax, is extrapolated from the plot, because V0 approaches but never quite reaches Vmax. The substrate concentration at which V0 is half-maximal is Km, the Michaelis constant. The concentration of enzyme in an experiment such as this is generally so low that [S]≫[E] even when [S] is described as low or relatively low. The units shown are typical for enzyme-catalyzed reactions and are given only to help illustrate the meaning of V0 and [S]. (Note that the curve describes part of a rectangular hyperbola, with one asymptote at Vmax. If the curve were continued below [S] = 0, it would approach a vertical asymptote at [S]=−Km.) The ES complex is the key to understanding this kinetic behavior, just as it was a starting point for our discussion of catalysis. The kinetic pattern in Figure 6-12 led Victor Henri, following a proposal by Adolphe Wurtz a few decades earlier, to propose in 1903 that the combination of an enzyme with its substrate molecule to form an ES complex is a necessary step in enzymatic catalysis. This idea was expanded into a general theory of enzyme action, particularly by Leonor Michaelis and Maud Menten in 1913. They postulated that the enzyme first combines reversibly with its substrate to form an enzyme-substrate complex in a relatively fast reversible step: E+ S  k1 ⇌k−1  ES (6-7) The ES complex then breaks down in a slower second step to yield the free enzyme and the reaction product P: ES  k2 ⇌k−2  E+ P (6-8) Because the slower second reaction (Eqn 6-8) must limit the rate of the overall reaction, the overall rate must be proportional to the concentration of the species that reacts in the second step — that is, ES. Le : Leonor Michaelis, 1875–1949; Right: Maud Menten, 1879–1960 At low [S], most of the enzyme is in the uncombined form E. Here, the rate is proportional to [S] because the equilibrium of Equation 6-7 is pushed toward formation of more ES as [S] increases. The maximum initial rate of the catalyzed reaction (Vmax) is observed when virtually all the enzyme is present as the ES complex and [E] is vanishingly small. Under these conditions, the enzyme is “saturated” with its substrate, so that further increases in [S] have no effect on rate. This condition exists when [S] is sufficiently high that essentially all the free enzyme has been converted to the ES form. Aer the ES complex breaks down to yield the product P, the enzyme is free to catalyze the reaction of another molecule of substrate (and will do so rapidly under saturating conditions). The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Figure 6-12, and the pattern seen in the figure is sometimes referred to as saturation kinetics. The Relationship between Substrate Concentration and Reaction Rate Can Be Expressed with the Michaelis-Menten Equation The curve expressing the relationship between [S] and V0 (Fig. 6-12) has the same general shape for most enzymes (it approaches a rectangular hyperbola), which can be expressed algebraically by the Michaelis- Menten equation. Michaelis and Menten derived this equation starting from their basic hypothesis that the rate-limiting step in enzymatic reactions is the breakdown of the ES complex to product and free enzyme. The equation is V0= (6-9) This is the Michaelis-Menten equation, the rate equation for a one- substrate enzyme-catalyzed reaction. It is a statement of the quantitative relationship between the initial velocity V0, the maximum velocity Vmax, and the initial substrate concentration [S], all related through a constant, Km, called the Michaelis constant. All these terms — [S], V0, Vmax, and Km — are readily measured experimentally. Here we develop the basic logic and the algebraic steps in a modern derivation of the Michaelis-Menten equation, which includes the steady- state assumption, a concept introduced by G. E. Briggs and J. B. S. Haldane in 1925. The derivation starts with the two basic steps of the formation and breakdown of ES (Eqns 6-7 and 6-8). Early in the reaction, the concentration of the product, [P], is negligible, and we make the simplifying assumption that the reverse reaction, P → S (described by Vmax [S] Km + [S] k−2), can be ignored. This assumption is not critical but it simplifies our task. The overall reaction then reduces to E+ S  k1 ⇌k−1  ES k2 →  E+ P (6-10) V0 is determined by the breakdown of ES to form product, which is determined by [ES]: V0 = k2 [ES] (6-11) Because [ES] in Equation 6-11 is not easily measured experimentally, we must begin by finding an alternative expression for this term. First, we introduce the term [Et], representing the total enzyme concentration (the sum of free and substrate-bound enzyme). Free or unbound enzyme [E] can then be represented by [Et]− [ES]. Also, because [S] is ordinarily far greater than [Et], the amount of substrate bound by the enzyme at any given time is negligible compared with the total [S]. With these conditions in mind, the following steps lead us to an expression for V0 in terms of easily measurable parameters. Step 1 The rates of formation and breakdown of ES are determined by the steps governed by the rate constants k1 (formation) and k−1+ k2 (breakdown to reactants and products, respectively), according to the expressions Rate of ES formation= k1([Et]–[ES])[S] (6-12) Rate of ES breakdown= k−1[ES]+ k2[ES] (6-13) Step 2 We now make an important assumption: that the initial rate of reaction reflects a steady state in which [ES] is constant — that is, the rate of formation of ES is equal to the rate of its breakdown. This is called the steady-state assumption. The expressions in Equations 6-12 and 6-13 can be equated for the steady state, giving k1([Et]− [ES])[S]= k−1[ES]+ k2[ES] (6-14) Step 3 In a series of algebraic steps, we now solve Equation 6-14 for [ES]. First, the le side is multiplied out and the right side simplified to give k1[Et] [S]− k1[ES] [S]= (k−1+ k2) [ES] (6-15) Adding the term k1[ES][S] to both sides of the equation and simplifying gives k1[Et] [S]= (k1[S]+ k−1+ k2) [ES] (6-16) We then solve this equation for [ES]: [ES]= (6-17) This can now be simplified further, combining the rate constants into one expression: [ES]= (6-18) The term (k−1+ k2)/k1 is defined as the Michaelis constant, Km. Substituting this into Equation 6-18 simplifies the expression to [ES]= (6-19) Step 4 We can now express V0 in terms of [ES]. Substituting the right side of Equation 6-19 for [ES] in Equation 6-11 gives V0 = (6-20) This equation can be simplified further. Because the maximum velocity occurs when the enzyme is saturated (that is, when [ES]= [Et]), Vmax k1[Et] [S] k1[S]+ k−1+ k2 [Et] [S] [S]+ (k−1+ k2)/k1 [Et] [S] Km + [S] k2[Et] [S] Km + [S] can be defined as k2[Et]. Substituting this in Equation 6-20 gives Equation 6-9: V0 = Note that Km has units of molar concentration. Does the equation fit experimental observations? Yes; we can confirm this by considering the limiting situations where [S] is very low or very high, as shown in Figure 6-13. FIGURE 6-13 Dependence of initial velocity on substrate concentration. This graph shows the kinetic parameters that define the limits of the curve at low [S] and high [S]. At low [S], Km ≫ [S], and the [S] term in the denominator of the Michaelis- Menten equation (Eqn 6-9) becomes insignificant. The equation simplifies to V0= Vmax[S]/Km, and V0 exhibits a linear dependence on [S], as observed here. At high [S], where [S]≫ Km, the Km term in the denominator of the Michaelis-Menten Vmax[S] Km + [S] equation becomes insignificant and the equation simplifies to V0= Vmax; this is consistent with the plateau observed at high [S]. The Michaelis-Menten equation is therefore consistent with the observed dependence of V0 on [S], and the shape of the curve is defined by the terms Vmax/Km at low [S] and Vmax at high [S]. An important numerical relationship emerges from the Michaelis- Menten equation in the special case when V0 is exactly one-half Vmax (Fig. 6-13). Then = (6-21) On dividing by Vmax, we obtain = (6-22) Solving for Km, we get Km + [S]= 2[S], or Km = [S], when V0= ½Vmax (6-23) This is a very useful, practical definition of Km:Km is equivalent to the substrate concentration at which V0 is one-half Vmax. Vmax 2 Vmax[S] Km + [S] 1 2 [S] Km + [S] Michaelis-Menten Kinetics Can Be Analyzed Quantitatively There are several ways to determine Vmax and Km from a plot relating V0 to [S]. A traditional approach is to algebraically transform the Michaelis- Menten equation into equations that convert the hyperbolic curve in the V0 versus [S] plot into a linear form from which values of Vmax and Km may be obtained by extrapolation. The most common of these approaches takes the reciprocal of both sides of the Michaelis-Menten equation (Eqn 6-9): V0 = = (6-24) Separating the components of the numerator on the right side of the equation gives = + (6-25) which simplifies to = + Vmax[S] Km +   [S] 1 V0 Km + [S] Vmax[S] 1 V0 Km Vmax[S] [S] Vmax[S] 1 V0 Km Vmax[S] 1 Vmax (6-26) This form of the Michaelis-Menten equation is called the Lineweaver- Burk equation. For enzymes obeying the Michaelis-Menten relationship, a plot of 1/V0 versus 1/[S] (the “double reciprocal” of the V0 versus [S] plot we have been using up to this point) yields a straight line (Fig. 6-14). This line has a slope of Km/Vmax, an intercept of 1/Vmax on the 1/V0 axis, and an intercept of −1/Km on the 1/[S] axis. The Lineweaver-Burk plot is a useful way to display data and can provide some mechanistic information, as we will see. However, the double- reciprocal transformation tends to give undue weight to data obtained at low substrate concentration, and can distort errors in the extrapolated values of Vmax and Km.

FIGURE 6-14 A double-reciprocal, or Lineweaver-Burk, plot. Plotting 1/V0 versus 1/[S] puts the data into a linear form. Intercepts on the 1/V0 and 1/[S] axes are 1/Vmax and −1/Km, respectively. More commonly, the parameters Vmax and Km are derived directly from the V0 versus [S] plot via nonlinear regression, using one of a multitude of curve-fitting programs available online. These are generally easy to use and offer accuracy superior to Lineweaver-Burk or related approaches. Kinetic Parameters Are Used to Compare Enzyme Activities It is important to distinguish between the Michaelis-Menten equation and the specific kinetic mechanism on which the equation was originally based. The Michaelis-Menten equation does not depend on the relatively simple two-step reaction mechanism proposed by Michaelis and Menten (Eqn 6-10). All enzymes that exhibit a hyperbolic dependence of V0 on [S] are said to follow Michaelis-Menten kinetics. Many enzymes that follow Michaelis-Menten kinetics have quite different reaction mechanisms, and enzymes that catalyze reactions with six or eight identifiable steps oen exhibit the same steady-state kinetic behavior. The practical rule that Km = [S] when V0= ½Vmax (Eqn 6-23) holds for all enzymes that follow Michaelis-Menten kinetics. The most important exceptions to Michaelis-Menten kinetics are the regulatory enzymes, discussed in Section 6.5. The parameters Km and Vmax can be obtained experimentally for any given enzyme, and their measurement is oen a key first step in enzyme characterization. However, the mechanistic insight they offer is limited. Obtaining information about the number, rates, or chemical nature of discrete steps in the reaction usually requires additional complementary approaches. Steady-state kinetics nevertheless is the standard language through which biochemists compare and characterize the catalytic efficiencies of enzymes. Interpreting Km and Vmax Both the magnitude and the meaning of Km and Vmax can vary greatly from enzyme to enzyme. Km can vary even for different substrates of the same enzyme (Table 6- 6). The term is sometimes used (oen inappropriately) as an indicator of the affinity of an enzyme for its substrate. The actual meaning of Km depends on specific aspects of the reaction mechanism, such as the number and relative rates of the individual steps. For reactions with two steps, Km = (6-27) TABLE 6-6 Km for Some Enzymes and Substrates Enzyme Substrate Km (mM) Hexokinase (brain) ATP -Glucose -Fructose 0.4 0.05 1.5 Carbonic anhydrase HCO−3 26 Chymotrypsin Glycyltyrosinylglycine N-Benzoyltyrosinamide 2.5 k2+ k−1 k1 β -Galactosidase -Lactose 4.0 Threonine dehydratase -Threonine 5.0 When k2 is rate-limiting, k2≪ k−1, and Km reduces to k−1/k1, which is defined as the dissociation constant, Kd, of the ES complex. Where these conditions hold, Km does represent a measure of the affinity of the enzyme for its substrate in the ES complex. However, this scenario does not apply for most enzymes. Sometimes k2≫ k−1, and then Km = k2/k1. In other cases, k2 and k−1 are comparable, and Km remains a more complex function of all three rate constants (Eqn 6-27). The Michaelis-Menten equation and the characteristic saturation behavior of the enzyme still apply, but Km cannot be considered a simple measure of substrate affinity. Even more common are cases in which the reaction goes through several steps aer formation of ES; Km can then become a very complex function of many rate constants. The quantity Vmax depends upon the rate-limiting step of the enzyme- catalyzed reaction. If an enzyme reacts by the two-step Michaelis- Menten mechanism, Vmax = k2[Et], where k2 is rate-limiting. However, the number of reaction steps and the identity of the rate-limiting step(s) can vary from enzyme to enzyme. For example, consider the common situation where product release, EP → E+ P, is rate-limiting. Early in the reaction (when [P] is low), the overall reaction can be adequately described by the scheme E+ S k1  ⇌k−1  ES k2  ⇌k−2  EP k3 →  E+ P (6-28) In this case, most of the enzyme is in the EP form at saturation, and Vmax = k3[Et]. It is useful to define a more general rate constant, kcat, to describe the limiting rate of any enzyme-catalyzed reaction at saturation. If the reaction has several steps, one of which is clearly rate-limiting, kcat is equivalent to the rate constant for that limiting step. For the simple reaction of Equation 6-10, kcat = k2. For the reaction of Equation 6-28, when product release is clearly rate-limiting, kcat = k3. When several steps are partially rate-limiting, kcat can become a complex function of several of the rate constants that define each individual reaction step. In the Michaelis-Menten equation, kcat = Vmax/[Et]. Rearranged, Vmax = kcat[Et], and Equation 6-9 becomes V0= (6-29) The constant kcat is a first-order rate constant and hence has units of reciprocal time. It is also called the turnover number. It is equivalent to the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule when the enzyme is saturated with substrate. The turnover numbers of several enzymes are given in Table 6-7. TABLE 6-7 Turnover Number, kcat, of Some Enzymes Enzyme Substrate kcat (s−1) Catalase H2O2 40,000,000 Carbonic anhydrase HCO−3 400,000 kcat[Et] [S] Km + [S] Acetylcholinesterase Acetylcholine 14,000 β -Lactamase Benzylpenicillin 2,000 Fumarase Fumarate 800 RecA protein (an ATPase) ATP 0.5 Comparing Catalytic Mechanisms and Efficiencies The kinetic parameters kcat and Km are useful for the study and comparison of different enzymes, whether their reaction mechanisms are simple or complex. Each enzyme has values of kcat and Km that reflect the cellular environment, the concentration of substrate normally encountered in vivo by the enzyme, and the chemistry of the reaction being catalyzed. The parameters kcat and Km also allow us to evaluate the kinetic efficiency of enzymes, but either parameter alone is insufficient for this task. Two enzymes catalyzing different reactions may have the same kcat (turnover number), yet the rates of the uncatalyzed reactions may be different and thus the rate enhancements brought about by the enzymes may differ greatly. Experimentally, the Km for an enzyme tends to be similar to the cellular concentration of its substrate. An enzyme that acts on a substrate present at a very low concentration in the cell usually has a lower Km than an enzyme that acts on a substrate that is more abundant. The best way to compare the catalytic efficiencies of different enzymes or the turnover of different substrates by the same enzyme is to compare the ratio kcat/Km for the two reactions. This parameter, sometimes called the specificity constant, is the rate constant for the conversion of E + S to E + P. When [S]≪ Km, Equation 6-29 reduces to the form V0 =  [Et] [S] (6-30) V0 in this case depends on the concentration of two reactants, [Et] and [S], so this is a second-order rate equation, and the constant kcat/Km is a second-order rate constant with units of M −1s−1. There is an upper limit to kcat/Km, imposed by the rate at which E and S can diffuse together in an aqueous solution. This diffusion-controlled limit is 108 to 109 M −1s−1, and many enzymes have a kcat/Km near this range (Table 6-8). Such enzymes are said to have achieved catalytic perfection. Note that different values of kcat and Km can produce the maximum ratio. TABLE 6-8 Enzymes for Which kcat/Km Is Close to the Diffusion- Controlled Limit (108 to 109 M −1 S−1) Enzyme Substrate kcat(S−1) Km(M) kcat/Km(M −1 S−1) Acetylcholinesterase Acetylcholine 1.4× 104 9× 10−5 1.6× 108 Carbonic anhydrase CO2 HCO−3 1× 106 4× 105 1.2× 10−2 2.6× 10−2 8.3× 107 1.5× 107 Catalase H2O2 4× 107 1.1× 100 4× 107 Crotonase Crotonyl-CoA 5.7× 103 2× 10−5 2.8× 108 Fumarase Fumarate Malate 8× 102 9× 102 5× 10−6 2.5× 10−5 1.6× 108 3.6× 107 β -Lactamase Benzylpenicillin 2.0× 103 2× 10−5 1× 108 kcat Km Information from A. Fersht, Structure and Mechanism in Protein Science, p. 166, W. H. Freeman and Company, 1999. WORKED EXAMPLE 6-1 Determination of Km An enzyme is discovered that catalyzes the chemical reaction SAD ⇌  HAPPY A team of motivated researchers sets out to study the enzyme, which they call happyase. They find that the kcat for happyase is 600 s−1 and they carry out several additional experiments. When [Et]= 20 nM and [SAD] = 40 μ M, the reaction velocity, V0, is 9.6 μM  s−1. Calculate Km for the substrate SAD. SOLUTION: We know kcat, [Et], [S], and V0. We want to solve for Km. We will first derive an expression for Km, beginning with the Michaelis-Menten equation (Eqn 6-9). We will calculate Vmax by equating it to kcat[Et]. We can then substitute the known values to calculate Km. V0 = First, multiply both sides by Km + [S]: Vmax[S] (Km + [S])    V0(Km+[S])= Vmax[S] V0Km + V0[S]= Vmax[S] Subtract V0[S] from both sides to give V0Km = Vmax[S]− V0[S] Factor out [S] and divide both sides by V0. Km = Now, equate Vmax to kcat[Et], and substitute the given values to obtain Km . Vmax = kcat[Et]= (600 s−1) 0.02 μM = 12 μM  s−1 Km = (12 μM  s−1− 9.6 μM  s−1) 40 μM  /9.6 μM  s−1 = 96 μM 2 s−1/9.6 μM  s−1 = 10 μM Once you have worked with this equation, you will recognize shortcuts to solve problems like this. For example, rearranging Equation 6-9 by simply dividing both sides by Vmax gives = (Vmax− V0)[S] V0 V0 Vmax [S] Km + [S] Thus, the ratio V0/Vmax = 9.6 μM  s−1/12 μM  s−1= [S]/(Km + [S]). This sometimes simplifies the process of solving for Km, in this case, giving 0.25[S], or 10 μ M. WORKED EXAMPLE 6-2 Determination of [S] In a separate happyase experiment using [Et]= 10 mM , the reaction velocity, V0, is measured as 3 μM  s−1. What is the [S] used in this experiment? SOLUTION: Using the same logic as in Worked Example 6-1 — equating Vmax to kcat[Et] — we see that Vmax for this enzyme concentration is 6 μM  s−1. Note that V0 is exactly half of Vmax. Recall that Km is by definition equal to the [S] at which V0 = ½ Vmax. Thus, in this example, the [S] must be the same as Km, or 10 μ M. If V0 were anything other than ½Vmax, it would be simplest to use the expression V0/Vmax = [S]/(Km + [S]) to solve for [S]. Many Enzymes Catalyze Reactions with Two or More Substrates We have seen how [S] affects the rate of a simple enzymatic reaction with only one substrate molecule (S → P). In most enzymatic reactions, however, two (and sometimes more) different substrate molecules bind to the enzyme and participate in the reaction. Nearly two-thirds of all enzymatic reactions have two substrates and two products. These are generally reactions in which a group is transferred from one substrate to the other, or one substrate is oxidized while the other is reduced. For example, in the reaction catalyzed by hexokinase, ATP and glucose are the substrate molecules, and ADP and glucose 6-phosphate are the products: AT P + glucose→ ADP + glucose 6-phosphate A phosphoryl group is transferred from ATP to glucose. The rates of such bisubstrate reactions can also be analyzed by the Michaelis- Menten approach. Hexokinase has a characteristic Km for each of its substrates (Table 6-6). Enzymatic reactions with two substrates proceed by one of several different types of pathways. In some cases, both substrates are bound to the enzyme concurrently at some point in the course of the reaction, forming a noncovalent ternary complex (Fig. 6-15a); the substrates bind in a random sequence or in a specific order. Ordered binding occurs when binding of the first substrate creates a condition, oen a conformation change, required for the second substrate to bind. In other cases, the first substrate is converted to product and dissociates before the second substrate binds, so no ternary complex is formed. An example of this is the Ping-Pong, or double-displacement, mechanism (Fig. 6-15b). FIGURE 6-15 Common mechanisms for enzyme-catalyzed bisubstrate reactions. (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates can bind in either order. Product dissociation can also be ordered or random. (b) An enzyme-substrate complex forms, a product leaves the complex, the altered enzyme forms a second complex with another substrate molecule, and the second product leaves, regenerating the enzyme. Substrate 1 may transfer a functional group to the enzyme (to form the covalently modified E′), which is subsequently transferred to substrate 2. This is called a Ping- Pong or double-displacement mechanism. (c) Ternary complex formation depicted using Cleland nomenclature. In the ordered bi bi and random bi bi reactions shown here, the release of product follows the same pattern as the binding of substrate — both ordered or both random. (d) The Ping-Pong or double-displacement reaction described with Cleland nomenclature. A shorthand notation developed by W. W. Cleland can be helpful in describing reactions with multiple substrates and products. In this system, referred to as Cleland nomenclature, substrates are denoted A, B, C, and D, in the order in which they bind to the enzyme, and products are denoted P, Q, S, and T, in the order in which they dissociate. Enzymatic reactions with one, two, three, or four substrates are referred to as uni, bi, ter, and quad, respectively. The enzyme is, as usual, denoted E, but if it is modified in the course of the reaction, successive forms are denoted F, G, and so on. The progress of the reaction is indicated with a horizontal line, with successive chemical species indicated below it. If there is an alternative in the reaction path, the horizontal line is bifurcated. Steps involving binding and dissociating substrates and products are indicated with vertical lines. Common reactions with two substrates and two products (bi bi) are described with the shorthand forms illustrated in Figure 6-15c for an ordered bi bi reaction and a random bi bi reaction. In the latter example, the release of product is also random, as indicated by the two sets of bifurcations. Rarely, the binding of substrates is ordered and the release of products is random, or vice versa, eliminating the bifurcation at one end or the other of the progress line. In a Ping-Pong reaction, lacking a ternary complex, the pathway has a transient second form of the enzyme, F (Fig. 6-15d). This is the form in which a group has been transferred from the first substrate, A, to create a transient covalent attachment to the enzyme. As noted above, such reactions are oen called double-displacement reactions, as a group is transferred first from substrate A to the enzyme and then from the enzyme to substrate B. Substrates A and B do not encounter each other on the enzyme. Michaelis-Menten steady-state kinetics can provide only limited information about the number of steps and intermediates in an enzymatic reaction, but the approach can be used to distinguish between pathways that have a ternary intermediate and pathways — including Ping-Pong pathways — that do not (Fig. 6-16). As we will see when we consider enzyme inhibition, steady-state kinetics can also distinguish between ordered and random binding of substrates and products in reactions with ternary intermediates. FIGURE 6-16 Steady-state kinetic analysis of bisubstrate reactions. In these double-reciprocal plots, the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S2], generating several separate lines. (a) Intersecting lines indicate that a ternary complex is formed in the reaction; (b) parallel lines indicate a Ping-Pong (double- displacement) pathway. Enzyme Activity Depends on pH In general, steady-state kinetics provides information required to characterize an enzyme and assess its catalytic efficiency. Additional information can be gained by examination of how the key experimental parameters kcat and kcat/Km change when reaction conditions change, particularly pH. Enzymes have an optimum pH (or pH range) at which their activity is maximal (Fig. 6-17); at higher or lower pH, activity decreases. This is not surprising. Amino acid side chains in the active site may act as weak acids and bases only if they maintain a certain state of ionization. Elsewhere in the protein, removing a proton from a His residue, for example, might eliminate an ionic interaction that is essential for stabilizing the active conformation of the enzyme. A less common cause of pH sensitivity is titration of a group on the substrate.

FIGURE 6-17 The pH-activity profiles of two enzymes. These curves are constructed from measurements of initial velocities when the reaction is carried out in buffers of different pH. Because pH is a logarithmic scale reflecting 10-fold changes in [H+], the changes in V0 are also plotted on a logarithmic scale. The pH optimum for the activity of an enzyme is generally close to the pH of the environment in which the enzyme is normally found. Pepsin, a peptidase found in the stomach, has a pH optimum of about 1.6. The pH of gastric juice is between 1 and 2. Glucose 6- phosphatase of hepatocytes (liver cells), with a pH optimum of about 7.8, is responsible for releasing glucose into the blood. The normal pH of the cytosol of hepatocytes is about 7.2. The pH range over which an enzyme undergoes changes in activity can provide a clue to the type of amino acid residue involved (see Table 3-1). A change in activity near pH 7.0, for example, oen reflects titration of a His residue. The effects of pH must be interpreted with some caution, however. In the closely packed environment of a protein, the pKa of amino acid side chains can be significantly altered. For example, a nearby positive charge can lower the pKa of a Lys residue, and a nearby negative charge can increase it. Such effects sometimes result in a pKa that is shied by several pH units from its value in the free amino acid. In the enzyme acetoacetate decarboxylase, for example, one Lys residue has a pKa of 6.6 (compared with 10.5 in free lysine) due to electrostatic effects of nearby positive charges. Pre–Steady State Kinetics Can Provide Evidence for Specific Reaction Steps The mechanistic insight provided by steady-state kinetics can be augmented, sometimes dramatically, by an examination of the pre– steady state. Consider an enzyme with a reaction mechanism that conforms to the scheme in Equation 6-28, featuring three steps: E+ S  k1 ⇌k−1  ES  k2 ⇌k−2  EP k3 →  E+ P Overall catalytic efficiency for this reaction can be assessed with steady- state kinetics, but the rates of the individual steps cannot be determined in this way, and the slow (rate-limiting) step can rarely be identified. For the rate constants of individual steps to be measured, the reaction must be studied during its pre–steady state. The first turnover of an enzyme- catalyzed reaction oen occurs in seconds or milliseconds, so researchers use special equipment that allows mixing and sampling on this time scale (Fig. 6-18a). Reactions are stopped and protein-bound products are quantified, aer the timed addition and rapid mixing of an acid that denatures the protein and releases all bound molecules. A detailed description of pre–steady state kinetics is beyond the scope of this text, but we can illustrate the power of this approach by a simple example of an enzyme that uses the pathway shown in Equation 6-28. This example also involves an enzyme that catalyzes a relatively slow reaction, so the pre–steady state is more conveniently observed. FIGURE 6-18 Pre–steady state kinetics. The transient phase that constitutes the pre–steady state o en exists for mere seconds or milliseconds, requiring specialized equipment to monitor it. (a) A simple schematic for a rapid-mixing device, called a stopped-flow device. Enzyme (E) and substrate (S) are mixed with the aid of mechanically operated syringes. The reaction is quenched at a programmed time by adding a denaturing acid through another syringe, and the amount of product formed is measured, in this case with a spectrophotometer. (b) Experimental data for an enzyme reaction show the pre–steady state occurring in the first 5 to 10 seconds. This is a relatively slow reaction and is used as an example because the steady state can be conveniently monitored. The slope of the lines a er 15 seconds reflects the steady state. Extrapolating this slope back to zero time (dashed lines) gives the amplitude of the burst phase. The progress of the reaction during the pre–steady state primarily reflects the chemical steps in the reaction (details of which are not shown). The presence of a burst implies that a step following the chemical step that produces P is rate-limiting — in this case, the product-release step. Notice that the extrapolated intercept at time = 0 increases as [E] increases. (c) A plot of burst amplitude (the intercepts from (b)) versus [E] shows that one molecule of P is formed in each active site during the burst (pre–steady state) phase. This provides evidence that product release is the rate-limiting step, because it is the only step following product formation in this simple enzymatic reaction. The enzyme used in this experiment was RNase P, one of the catalytic RNAs described in Chapter 26. [(b, c) Data from J. Hsieh et al., RNA 15:224, 2009.] For many enzymes, dissociation of product is rate-limiting. In this example (Fig. 6-18b, c), the rate of dissociation of the product (k3) is slower than the rate of its formation (k2). Product dissociation therefore dictates the rates observed in the steady state. How do we know that k3 is rate-limiting? A slow k3 gives rise to a burst of product formation in the pre–steady state, because the preceding steps are relatively fast. The burst reflects the rapid conversion of one molecule of substrate to one molecule of product at each enzyme active site. The observed rate of product formation soon slows to the steady-state rate as the bound product is slowly released. Each enzymatic turnover aer the first one must proceed through the slow product-release step. However, the rapid generation of product in that first turnover provides much information. The amplitude of the burst — when one molecule of product is generated per molecule of enzyme present (Fig. 6-18c), measured by extrapolating the steady-state progress line back to zero time — is the highest amplitude possible. This provides one piece of evidence that product release is, indeed, rate-limiting. The rate constant for the chemical reaction step, k2, can be derived from the observed rate of the burst phase. Of course, enzymes do not always conform to the simple reaction scheme of Equation 6-28. Formally, the observation of a burst indicates that a rate-limiting step (typically, product release, or an enzyme conformational change, or another chemical step) occurs aer formation of the product being monitored. Additional experiments and analysis can oen define the rates of each step in a multistep enzymatic reaction. Some examples of the application of pre–steady state kinetics are included in the descriptions of specific enzymes in Section 6.4. Enzymes Are Subject to Reversible or Irreversible Inhibition Enzyme inhibitors are molecules that interfere with catalysis, slowing or halting enzymatic reactions. Enzymes catalyze virtually all cellular processes, so it should not be surprising that enzyme inhibitors are among the most important pharmaceutical agents known. For example, aspirin (acetylsalicylate) inhibits the enzyme that catalyzes the first step in the synthesis of prostaglandins, compounds involved in many processes, including some that produce pain. The study of enzyme inhibitors also has provided valuable information about enzyme mechanisms and has helped define some metabolic pathways. There are two broad classes of enzyme inhibitors: reversible and irreversible. Reversible Inhibition One common type of reversible inhibition is called competitive (Fig. 6- 19a). A competitive inhibitor competes with the substrate for the active site of an enzyme. While the inhibitor (I) occupies the active site, the substrate is excluded, and vice versa. Many competitive inhibitors are structurally similar to the substrate and combine with the enzyme to form an unreactive EI complex. Even fleeting combinations of this type will reduce the efficiency of an enzyme. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the Michaelis-Menten equation (Eqn 6-9) becomes V0 = (6-31) where α= 1+     and    KI= Equation 6-31 describes the important features of competitive inhibition. The experimentally determined variable αKm, the Km observed in the presence of the inhibitor, is oen called the “apparent” Km. Vmax[S] αKm + [S] [I] KI [E] [I] [EI] FIGURE 6-19 Competitive inhibition. (a) Competitive inhibitors bind to the enzyme’s active site; KI is the equilibrium dissociation constant for inhibitor binding to E. (b) Competitive inhibitors affect the observed Km, but not the Vmax. This is readily evident in the plot of V0 versus [S]. (c) In a Lineweaver-Burk plot, the lines generated + and − inhibitor intersect on the y axis, which reflects 1/Vmax. As the observed Km increases in the presence of an inhibitor, the intercept on the x axis (−1/Km) moves to the right. Bound inhibitor does not inactivate the enzyme. When the inhibitor dissociates, substrate can bind and react. Because the inhibitor binds reversibly to the enzyme, the competition can be biased to favor the substrate simply by adding more substrate. When [S] far exceeds [I], the probability that an inhibitor molecule will bind to the enzyme is minimized and the reaction exhibits normal Vmax. However, in the presence of inhibitor, the [S] at which V0 = ½Vmax, the apparent Km, increases in the presence of inhibitor by the factor α (Fig. 6-19b). This effect on apparent Km, combined with the absence of an effect on Vmax, is diagnostic of competitive inhibition and is readily revealed in a double-reciprocal plot (Fig. 6-19c). The equilibrium constant for inhibitor binding, KI, can be obtained from the same plot. A medical therapy based on competition at the active site is used to treat patients who have ingested methanol, a solvent found in gas-line antifreeze. The liver enzyme alcohol dehydrogenase converts methanol to formaldehyde, which is damaging to many tissues. Blindness is a common result of methanol ingestion, because the eyes are particularly sensitive to formaldehyde. Ethanol competes effectively with methanol as an alternative substrate for alcohol dehydrogenase. The effect of ethanol is much like that of a competitive inhibitor, with the distinction that ethanol is also a substrate for alcohol dehydrogenase and its concentration will decrease over time as the enzyme converts it to acetaldehyde. The therapy for methanol poisoning is slow intravenous infusion of ethanol, at a rate that maintains a controlled concentration in the blood for several hours. This slows the formation of formaldehyde, lessening the danger while the kidneys filter out the methanol to be excreted harmlessly in the urine. Two other types of reversible inhibition, uncompetitive and mixed, can be defined in terms of one-substrate enzymes, but in practice are observed only with enzymes having two or more substrates. An uncompetitive inhibitor (Fig. 6-20a) binds at a site distinct from the substrate active site and, unlike a competitive inhibitor, binds only to the ES complex. In the presence of an uncompetitive inhibitor, the Michaelis-Menten equation is altered to V0= (6-32) where α′= 1+     and    K′I= As described by Equation 6-32, at high concentrations of substrate, V0 approaches Vmax/α′. Thus, an uncompetitive inhibitor lowers the measured Vmax. Apparent Km also decreases, because the [S] required to reach one-half Vmax decreases by the factor α′ (Fig. 6-20b, c). This behavior can be explained as follows. Because the enzyme is inactive when the uncompetitive inhibitor is bound, but the inhibitor is not competing with substrate for binding, the inhibitor effectively removes some fraction of the enzyme molecules from the reaction. Given that Vmax depends on [E], the observed Vmax decreases. Given that the Vmax[S] Km + α′[S] [I] K′I [ES] [I] [ESI] inhibitor binds only to the ES complex, only ES (not free enzyme) is deleted from the reaction, so the [S] needed to reach ½Vmax — that is, Km — declines by the same amount. FIGURE 6-20 Uncompetitive inhibition. (a) Uncompetitive inhibitors bind at a separate site, but bind only to the ES complex; K′I is the equilibrium constant for an inhibitor binding to ES. (b) In the presence of an uncompetitive inhibitor, both the Km and the Vmax decline, and by equivalent factors. In the V0 versus [S] plot, the decline in Vmax is somewhat easier to discern than the decline in Km. (c) The Lineweaver- Burk plot for an uncompetitive inhibitor is quite diagnostic, as the lines generated in the presence and absence of an inhibitor are parallel. Note that the lines seen in the presence of an inhibitor are always above the line generated in the absence of an inhibitor, reflecting the decline in both Km and Vmax brought about by the inhibitor (i.e., the intercepts move up on the y axis and to the le on the x axis). A mixed inhibitor (Fig. 6-21a) also binds at a site distinct from the substrate active site, but it binds to either E or ES. The rate equation describing mixed inhibition is V0= (6-33) where α and α′ are defined as above. A mixed inhibitor usually affects both Km and Vmax (Fig. 6-21b, c). Vmax is affected because the inhibitor renders some fraction of the available enzyme molecules inactive, lowering the effective [E] on which Vmax depends. The Km may increase or decrease, depending on which enzyme form, E or ES, the inhibitor binds to most strongly. The special case of α= α′, rarely encountered in experiments, historically has been defined as noncompetitive inhibition. Examine Equation 6-33 to see why a noncompetitive inhibitor would affect the Vmax but not the Km. Vmax[S] αKm + α′[S] FIGURE 6-21 Mixed inhibition. (a) Mixed inhibitors bind at a separate site, but they may bind to either E or ES. (b) The kinetic patterns brought about by a mixed inhibitor are complex. The Vmax always declines. The Km may increase or decrease, depending upon the relative values of α and α′. (c) In a Lineweaver-Burk plot, the lines generated + and − inhibitor always intersect, but not on an axis. The intercepts on the y axis always move up, as the Vmax declines. The lines may intersect either above or below the x axis. When they intersect above, as shown here, α> α′ and the observed Km is increasing. When the lines intersect below the x axis (not shown), α< α′ and the observed Km is decreasing. Equation 6-33 is a general expression for the effects of reversible inhibitors, simplifying to the expressions for competitive inhibition and uncompetitive inhibition when α′= 1.0 or α = 1.0, respectively. From this expression we can summarize the effects of inhibitors on individual kinetic parameters. For all reversible inhibitors, the apparent Vmax= Vmax/α′, because the right side of Equation 6-33 always simplifies to Vmax/α′ at sufficiently high substrate concentrations. For competitive inhibitors, α′= 1.0 and can thus be ignored. Taking this expression for apparent Vmax, we can also derive a general expression for apparent Km to show how this parameter changes in the presence of reversible inhibitors. Apparent Km, as always, equals the [S] at which V0 is one-half apparent Vmax or, more generally, when V0= Vmax/2α′. This condition is met when [S]= αKm/α′. Thus, apparent Km = αKm/α′. The terms α and α′ reflect the binding of inhibitor to E and ES, respectively. Thus, the term αKm/α′ is a mathematical expression of the relative affinity of inhibitor for the two enzyme forms. This expression is simpler when either α or α′ is 1.0 (for uncompetitive or competitive inhibitors), as summarized in Table 6-9. TABLE 6-9 Effects of Reversible Inhibitors on Apparent Vmax and Apparent Km Inhibitor type Apparent Vmax Apparent Km None Vmax Km Competitive Vmax αKm Uncompetitive Vmax/α′ Km/α′ Mixed Vmax/α′ αKm/α′ In practice, uncompetitive inhibition and mixed inhibition are observed only for enzymes with two or more substrates — say, S1 and S2 — and are very important in the experimental analysis of such enzymes. If an inhibitor binds to the site normally occupied by S1, it may act as a competitive inhibitor in experiments in which [S1] is varied. If an inhibitor binds to the site normally occupied by S2, it may act as a mixed or uncompetitive inhibitor of S1. The actual inhibition patterns observed depend on whether the S1- and S2-binding events are ordered or random, and thus the order in which substrates bind and products leave the active site can be determined. Product inhibition experiments in which one of the reaction products is provided as an inhibitor are oen particularly informative. If only one of two reaction products is present, no reverse reaction can take place. However, a product generally binds to some part of the active site and can thus serve as an effective inhibitor. Enzymologists can combine steady-state kinetic studies involving different combinations and amounts of products and inhibitors with pre–steady state analysis to develop a detailed picture of the mechanism of a bisubstrate reaction. WORKED EXAMPLE 6-3 Effect of Inhibitor on Km The researchers working on happyase (see Worked Examples 6-1 and 6- 2) discover that the compound STRESS is a potent competitive inhibitor of happyase. Addition of 1 nM STRESS increases the measured Km for SAD by a factor of 2. What are the values for α and α′ under these conditions? SOLUTION: Recall that the apparent Km, the Km measured in the presence of a competitive inhibitor, is defined as αKm. Because Km for SAD increases by a factor of 2 in the presence of 1 nMSTRESS, the value of α must be 2. The value of α′ for a competitive inhibitor is 1, by definition. Irreversible Inhibition The irreversible inhibitors bind covalently with or destroy a functional group on an enzyme that is essential for the enzyme’s activity, or they form a highly stable noncovalent association. Formation of a covalent link between an irreversible inhibitor and an enzyme is a particularly effective way to inactivate an enzyme. Irreversible inhibitors are another useful tool for studying reaction mechanisms. Amino acids with key catalytic functions in the active site can sometimes be identified by determining which residue is covalently linked to an inhibitor aer the enzyme is inactivated. An example is shown in Figure 6-22. FIGURE 6-22 Irreversible inhibition. Reaction of chymotrypsin with diisopropylfluorophosphate (DIFP) modifies Ser195 and irreversibly inhibits the enzyme. This has led to the conclusion that Ser195 is the key active-site Ser residue in chymotrypsin. A special class of irreversible inhibitors is the suicide inactivators. These compounds are relatively unreactive until they bind to the active site of a specific enzyme. A suicide inactivator undergoes the first few chemical steps of the normal enzymatic reaction, but instead of being transformed into the normal product, the inactivator is converted to a very reactive compound that combines irreversibly with the enzyme. These compounds are also called mechanism-based inactivators, because they hijack the normal enzyme reaction mechanism to inactivate the enzyme. Suicide inactivators play a significant role in rational drug design, an approach to obtaining new pharmaceutical agents in which chemists synthesize novel substrates based on knowledge of substrates and reaction mechanisms. A well-designed suicide inactivator is specific for a single enzyme and is unreactive until it is within that enzyme’s active site, so drugs based on this approach can offer the important advantage of few side effects (Box 6-1). BOX 6-1 MEDICINE Curing African Sleeping Sickness with a Biochemical Trojan Horse African sleeping sickness, or African trypanosomiasis, is caused by protists (single- celled eukaryotes) called trypanosomes (Fig. 1). This disease (and related trypanosome-caused diseases) is medically and economically significant in many developing nations. Until the late twentieth century, the disease was virtually incurable. Vaccines are ineffective because the parasite has a novel mechanism to evade the host immune system. FIGURE 1 Trypanosoma brucei rhodesiense, one of several trypanosomes known to cause African sleeping sickness. The cell coat of trypanosomes is covered with a single protein, which is the antigen to which the human immune system responds. Every so o en, however, by a process of genetic recombination (see Table 28-1), a few cells in the population of infecting trypanosomes switch to a new protein coat, not recognized by the immune system. This process of “changing coats” can occur hundreds of times. The result is a chronic cyclic infection: the human host develops a fever, which subsides as the immune system beats back the first infection; trypanosomes with changed coats then become the seed for a second infection, and the fever recurs. This cycle can repeat for weeks, and the weakened person eventually dies. One approach to treating African sleeping sickness uses pharmaceutical agents designed as mechanism-based enzyme inactivators (suicide inactivators). A vulnerable point in trypanosome metabolism is the pathway of polyamine biosynthesis. The polyamines spermine and spermidine, involved in DNA packaging, are required in large amounts in rapidly dividing cells. The first step in their synthesis is catalyzed by ornithine decarboxylase, an enzyme that requires for its function a coenzyme called pyridoxal phosphate. Pyridoxal phosphate (PLP), derived from vitamin B6, forms a covalent bond with the amino acid substrates of the reactions it is involved in and acts as an electron sink to facilitate a variety of reactions (see Fig. 22-32). In mammalian cells, ornithine decarboxylase undergoes rapid turnover — that is, a rapid, constant round of enzyme degradation and synthesis. In some trypanosomes, however, the enzyme (for reasons not well understood) is stable, not readily replaced by newly synthesized enzyme. An inhibitor of ornithine decarboxylase that binds permanently to the enzyme thus adversely affects the parasite, but has little effect on human cells, which can rapidly replace inactivated enzyme. The first few steps of the normal reaction catalyzed by ornithine decarboxylase are shown in Figure 2. Once CO2 is released, the electron movement is reversed and putrescine is produced (see Fig. 22-32). Based on this mechanism, several suicide inactivators have been designed, one of which is difluoromethylornithine (DFMO). DFMO is relatively inert in solution. When it binds to ornithine decarboxylase, however, the enzyme is quickly inactivated (Fig. 3). The inhibitor acts by providing an alternative electron sink in the form of two strategically placed fluorine atoms, which are excellent leaving groups. Instead of electrons moving into the ring structure of PLP, the reaction results in displacement of a fluorine atom. The —S of a Cys residue at the enzyme’s active site then forms a covalent complex with the highly reactive PLP-inhibitor adduct, in an essentially irreversible reaction. In this way, the inhibitor makes use of the enzyme’s own reaction mechanisms to kill it. FIGURE 2 Mechanism of ornithine decarboxylase reaction. FIGURE 3 Inhibition of ornithine decarboxylase by DFMO. DFMO has proved highly effective in treating African sleeping sickness caused by Trypanosoma brucei gambiense. Approaches such as this show great promise for treating a wide range of diseases. The design of drugs based on enzyme mechanism and structure can complement the more traditional trial-and-error methods of developing pharmaceuticals. An irreversible inhibitor need not bind covalently to the enzyme. Noncovalent binding is enough, if that binding is so tight that the inhibitor dissociates only rarely. How does a chemist develop a tight- binding inhibitor? Recall that enzymes evolve to bind most tightly to the transition states of the reactions that they catalyze. In principle, if one can design a molecule that looks like that reaction transition state, it should bind tightly to the enzyme. Even though transition states cannot be observed directly, chemists can oen predict the approximate structure of a transition state based on accumulated knowledge about reaction mechanisms. Although the transition state is by definition transient and thus unstable, in some cases stable molecules can be designed that resemble transition states. These are called transition-state analogs. They bind to an enzyme more tightly than does the substrate in the ES complex, because they fit into the active site better (that is, they form a greater number of weak interactions) than the substrate itself. The idea of transition-state analogs was suggested by Linus Pauling in the 1940s, and it has been explored using a variety of enzymes. For example, transition-state analogs designed to inhibit the glycolytic enzyme aldolase bind to that enzyme more than four orders of magnitude more tightly than do its substrates (Fig. 6-23). A transition- state analog cannot perfectly mimic a transition state. Some analogs, however, bind to a target enzyme 102 to 108 times more tightly than does the normal substrate, providing good evidence that enzyme active sites are indeed complementary to transition states. The concept of transition-state analogs is important to the design of new pharmaceutical agents. As we shall see in Section 6.4, the powerful anti- HIV drugs called protease inhibitors were designed in part as tight- binding transition-state analogs. FIGURE 6-23 A transition-state analog. In glycolysis, a class II aldolase (found in bacteria and fungi) catalyzes the cleavage of fructose 1,6-bisphosphate to form glyceraldehyde 3-phosphate and dihydroxyacetone phosphate. The reaction proceeds via a reverse aldol-like mechanism. The compound phosphoglycolohydroxamate, which resembles the proposed enediolate transition state, binds to the enzyme nearly 10,000 times better than does the dihydroxyacetone phosphate product. SUMMARY 6.3 Enzyme Kinetics as an Approach to Understanding Mechanism Most enzymes have certain kinetic properties in common. When substrate is added to an enzyme, the reaction rapidly achieves a steady state in which the rate at which the ES complex forms balances the rate at which it breaks down. As [S] increases, the steady-state activity of a fixed concentration of enzyme increases in a hyperbolic fashion to approach a characteristic maximum rate, Vmax, at which essentially all the enzyme has formed a complex with substrate. The Michaelis-Menten equation V0= relates initial velocity to [S] and Vmax through the Michaelis constant, Km . Michaelis-Menten kinetics is also called steady-state kinetics. Km and Vmax have different meanings for different enzymes. However, the Km is always equal to the substrate concentration that results in a reaction rate equal to one-half Vmax. The values of Vmax and Km can be determined by using transformations of the Michaelis-Menten equation that allow linear plotting of data and extrapolation (for example, Lineweaver-Burk), or (more accurately) by using nonlinear regression. The limiting rate of an enzyme-catalyzed reaction at saturation is described by the constant kcat, the turnover number. The ratio kcat/Km provides a good measure of catalytic efficiency. Vmax[S] Km + [S] Most enzymes catalyze reactions involving multiple substrates, with the majority having two substrates and two products. The Michaelis- Menten equation is applicable to bisubstrate reactions, which occur by ternary complex or Ping-Pong (double-displacement) pathways. Every enzyme has an optimum pH (or pH range) at which it has maximal activity. The pH-rate profile can provide mechanistic clues. Pre–steady state kinetics can provide added insight into enzymatic reaction mechanisms. Reversible inhibition of an enzyme may be competitive, uncompetitive, or mixed. Competitive inhibitors compete with substrate by binding reversibly to the active site, but they are not transformed by the enzyme. Uncompetitive inhibitors bind only to the ES complex, at a site distinct from the active site. Mixed inhibitors bind to either E or ES, again at a site distinct from the active site. In irreversible inhibition, an inhibitor binds permanently to an active site by forming a covalent bond or a very stable noncovalent interaction. Inhibition patterns can elucidate mechanism. 6.4 Examples of Enzymatic Reactions Thus far we have focused on the general principles of catalysis and on introducing some of the kinetic parameters used to describe enzyme action. We now turn to several examples of specific enzyme reaction mechanisms. To understand the complete mechanism of action of a purified enzyme, we need to identify all substrates, cofactors, products, and regulators. We also need to know (1) the temporal sequence in which enzyme-bound reaction intermediates form, (2) the structure of each intermediate and each transition state, (3) the rates of interconversion between intermediates, (4) the structural relationship of the enzyme to each intermediate, and (5) the energy that all reacting and interacting groups contribute to the intermediate complexes and transition states. There are still only a few enzymes for which we have an understanding that meets all these requirements. Here we present the mechanisms for three enzymes: chymotrypsin, hexokinase, and enolase. These examples are not intended to cover all possible classes of enzyme chemistry. They have been chosen in part because they are among the best- understood enzymes and in part because they clearly illustrate some general principles outlined in this chapter. We present the chymotrypsin example in order to review some of the conventions used to depict enzyme mechanisms. Much mechanistic detail and experimental evidence is necessarily omitted; no one book could completely document the rich experimental history of these enzymes. In addition, we consider only briefly the special contribution of coenzymes to the catalytic activity of many enzymes. The function of coenzymes is chemically varied, and we describe each coenzyme in detail as it is encountered in our discussion of metabolism in Part II of this book. The Chymotrypsin Mechanism Involves Acylation and Deacylation of a Ser Residue Bovine pancreatic chymotrypsin (Mr 25,191) is a protease, an enzyme that catalyzes the hydrolytic cleavage of peptide bonds. This protease is specific for peptide bonds adjacent to aromatic amino acid residues (Trp, Phe, Tyr). The three-dimensional structure of chymotrypsin is shown in Figure 6-24, with functional groups in the active site emphasized. The reaction catalyzed by this enzyme illustrates the principle of transition- state stabilization and also provides a classic example of general acid-base catalysis and covalent catalysis. FIGURE 6-24 Structure of chymotrypsin. (a) A representation of primary structure, showing disulfide bonds and the amino acid residues crucial to catalysis. The protein consists of three polypeptide chains linked by disulfide bonds. (The numbering of residues in chymotrypsin, with “missing” residues 14, 15, 147, and 148, is explained in Fig. 6-42.) The active-site amino acid residues are grouped together in the three- dimensional structure. (b) A depiction of the enzyme emphasizing its surface. The hydrophobic pocket in which the aromatic amino acid side chain of the substrate is bound is shown in yellow. Key active-site residues, including Ser195, His57, and Asp102, are red. The roles of these residues in catalysis are illustrated in Figure 6-27. (c) The polypeptide backbone as a ribbon structure. Disulfide bonds are yellow; the three chains are colored as in part (a). (d) A close-up of the active site with a substrate (white and yellow) bound. The hydroxyl of Ser195 attacks the carbonyl group of the substrate (the oxygens are red); the developing negative charge on the oxygen is stabilized by the oxyanion hole (amide nitrogens from Ser195 and Gly193, in blue), as explained in Figure 6-27. The aromatic amino acid side chain of the substrate (yellow) sits in the hydrophobic pocket. The amide nitrogen of the peptide bond to be cleaved (protruding toward the viewer and projecting the path of the rest of the substrate polypeptide chain) is shown in white. [(b, c, d) Data from PDB ID 7GCH, K. Brady et al., Biochemistry 29:7600, 1990.] Chymotrypsin enhances the rate of peptide bond hydrolysis by a factor of at least 109. It does not catalyze a direct attack of water on the peptide bond; instead, a transient covalent acyl-enzyme intermediate is formed. The reaction thus has two distinct phases. In the acylation phase, the peptide bond is cleaved and an ester linkage is formed between the peptide carbonyl carbon and the enzyme. In the deacylation phase, the ester linkage is hydrolyzed and the nonacylated enzyme is regenerated. The first evidence for a covalent acyl-enzyme intermediate came from a classic application of pre–steady state kinetics. In addition to its action on polypeptides, chymotrypsin catalyzes the hydrolysis of small esters and amides. These reactions are much slower than hydrolysis of peptides because less binding energy is available with smaller substrates (the pre–steady state is also correspondingly longer), thus simplifying the analysis of the resulting reactions. In their investigations in 1954, B. S. Hartley and B. A. Kilby found that chymotrypsin hydrolysis of the ester p- nitrophenylacetate, as measured by release of p-nitrophenol, proceeds with a rapid burst before leveling off to a slower rate (Fig. 6-25). By extrapolating back to zero time, they concluded that the burst phase corresponded to the release of just under one molecule of p-nitrophenol for every enzyme molecule present (a small fraction of their enzyme molecules were inactive). Recall from Figure 6-18 that a burst implies that the rate-limiting step of catalysis occurs aer release of the product being monitored. Hartley and Kilby interpreted the burst to reflect a rapid release of p-nitrophenol during a rapid acylation of all the enzyme molecules. They suggested that turnover of the enzyme was limited by a subsequent, slower deacylation step. Later work substantiated their hypothesis. The observation of a burst phase provides yet another example of the use of kinetics to break down a reaction into its constituent steps. FIGURE 6-25 Pre–steady state kinetic evidence for an acyl-enzyme intermediate. The hydrolysis of p-nitrophenylacetate by chymotrypsin is measured by release of p-nitrophenol (a colored product). Initially, there is a rapid burst of p-nitrophenol release nearly stoichiometric with the amount of enzyme present. This reflects the fast acylation phase of the reaction. The subsequent rate is slower, because enzyme turnover is limited by the rate of the slower deacylation phase. Researchers have discovered additional features of the chymotrypsin mechanism by analyzing the dependence of the reaction on pH. The rate of chymotrypsin-catalyzed cleavage generally exhibits a bell-shaped pH-rate profile (Fig. 6-26). The rates plotted in Figure 6-26a are obtained at low (subsaturating) substrate concentrations and therefore represent kcat/Km (see Eqn 6-30, p. 193). A more complete analysis of the rates at different substrate concentrations at each pH allows researchers to determine the individual contributions of the kcat and Km terms. Aer obtaining the maximum rates at each pH, one can plot the kcat alone versus pH (Fig. 6-26b); aer obtaining the Km at each pH, researchers can then plot 1/Km versus pH (Fig. 6- 26c). Kinetic and structural analyses have revealed that the change in kcat reflects the ionization state of His57. The decline in kcat at low pH results from protonation of His57 (so that it can no longer extract a proton from Ser195 in the first chemical step of the reaction). This rate reduction illustrates the importance of general acid and general base catalysis in the mechanism for chymotrypsin. The changes in the 1/Km term reflect the ionization of the α -amino group of Ile16 (at the amino-terminal end of one of the enzyme’s three polypeptide chains). This group forms a salt bridge to Asp194, stabilizing the active conformation of the enzyme. When this group loses its proton at high pH, the salt bridge is eliminated, and a conformational change closes the hydrophobic pocket where the aromatic amino acid side chain of the substrate inserts (Fig. 6-24). Substrates can no longer bind properly, which is measured kinetically as an increase in Km.

FIGURE 6-26 The pH dependence of chymotrypsin-catalyzed reactions. (a) The rates of chymotrypsin-mediated cleavage produce a bell-shaped pH-rate profile with an optimum at pH 8.0. The rate (V) plotted here is that at low substrate concentrations and thus reflects the term kcat/Km. The plot can be broken down to its components by using kinetic methods to determine the terms kcat and Km separately at each pH. When this is done (b, c), it becomes clear that the transition just above pH 7 is due to changes in kcat, whereas the transition above pH 8.5 is due to changes in 1/Km. Kinetic and structural studies have shown that the transitions illustrated in (b) and (c) reflect the ionization states of the His57 side chain (when substrate is not bound) and the α -amino group of Ile16 (at the amino terminus of the B chain), respectively. For optimal activity, His57 must be unprotonated and Ile16 must be protonated. The chymotrypsin reaction is detailed in Figure 6-27. The nucleophile in the acylation phase is the oxygen of Ser195. (Proteases with a Ser residue that plays this role in reaction mechanisms are called serine proteases.) The pKa of a Ser hydroxyl group is generally too high for the unprotonated form to be present in significant concentrations at physiological pH. However, in chymotrypsin, Ser195 is linked to His57 and Asp102 in a hydrogen-bonding network referred to as the catalytic triad. When a peptide substrate binds to chymotrypsin, a subtle change in conformation compresses the hydrogen bond between His57 and Asp102, resulting in a stronger interaction, called a low- barrier hydrogen bond. This enhanced interaction increases the pKa of His57 from ∼7 (for free histidine) to >12, allowing the His residue to act as an enhanced general base that can remove the proton from the Ser195 hydroxyl group. Deprotonation prevents development of a highly unstable positive charge on the Ser195 hydroxyl and makes the Ser side chain a stronger nucleophile. At later reaction stages, His57 also acts as a proton donor, protonating the amino group in the displaced portion of the substrate (the leaving group).

MECHANISM FIGURE 6-27 Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps to ), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps to ), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate. *The short-lived tetrahedral intermediate following step and the second tetrahedral intermediate that forms later, following step , are sometimes referred to as transition states, but this terminology can cause confusion. An intermediate is any chemical species with a finite lifetime, “finite” being defined as longer than the time required for a molecular vibration (∼10−13 second). A transition state is simply the maximum-energy species formed on the reaction coordinate, and it does not have a finite lifetime. The tetrahedral intermediates formed in the chymotrypsin reaction closely resemble, both energetically and structurally, the transition states leading to their formation and breakdown. However, the intermediate represents a committed stage of completed bond formation, whereas the transition state is part of the process of reaction. In the case of chymotrypsin, given the close relationship between the intermediate and the actual transition state, the distinction between them is routinely glossed over. Furthermore, the interaction of the negatively charged oxygen with the amide nitrogens in the oxyanion hole, o en referred to as transition-state stabilization, also serves to stabilize the intermediate in this case. Not all intermediates are so short-lived that they resemble transition states. The chymotrypsin acyl-enzyme intermediate is much more stable and more readily detected and studied, and it is never confused with a transition state. As the Ser195 oxygen attacks the carbonyl group of the substrate (Fig. 6-27, step ), a very short-lived tetrahedral intermediate is formed in which the carbonyl oxygen acquires a negative charge. This charge, forming within a pocket on the enzyme called the oxyanion hole, is stabilized by hydrogen bonds contributed by the amide groups of two peptide bonds in the chymotrypsin backbone. One of these hydrogen bonds (contributed by Gly193) is present only in this intermediate and in the transition states for its formation and breakdown; it reduces the energy required to reach these states. This is an example of the use of binding energy in catalysis through enzyme–transition state complementarity. The intermediate collapses in step , breaking the peptide bond. The amino group of the first product is protonated by His57, now acting as a general acid catalyst. Water is the second substrate, entering the active site in step . As water attacks the carbon in the ester linkage in step , and the resulting intermediate collapses to break the ester linkage and generate the second product in step , His57 again acts — first as a general base to deprotonate the water, and then as a general acid to protonate the Ser oxygen as it leaves. Dissociation of the second product (step ) completes the reaction cycle. An Understanding of Protease Mechanisms Leads to New Treatments for HIV Infection New pharmaceutical agents are almost always designed to inhibit an enzyme. The extremely successful therapies developed to treat HIV infection provide a case in point. The human immunodeficiency virus (HIV) is the agent that causes acquired immune deficiency syndrome (AIDS). In 2018, 38 million people worldwide were living with HIV infection, with about 1.7 million new infections that year and approximately 770,000 fatalities. AIDS first surfaced as a worldwide epidemic in the 1980s; HIV was discovered soon aer and was identified as a retrovirus. Retroviruses possess (1) an RNA genome and (2) an enzyme, reverse transcriptase, that is capable of using RNA to direct the synthesis of a complementary DNA. Efforts to understand HIV and develop therapies for HIV infection benefited from decades of basic research, both on enzyme mechanisms and on the properties of other retroviruses. A retrovirus such as HIV has a relatively simple life cycle (see Fig. 26-29). Its RNA genome is converted to duplex DNA in several steps catalyzed by the reverse transcriptase (described in Chapter 26). The duplex DNA is then inserted into a chromosome in the nucleus of the host cell by the enzyme integrase (described in Chapter 25). The integrated copy of the viral genome can remain dormant indefinitely. Alternatively, it can be transcribed back into RNA, which can then be translated into proteins to construct new virus particles. Most of the viral genes are translated into large polyproteins, which are cut by an HIV protease into the individual proteins needed to make the virus (see Fig. 26-30). Only three key enzymes operate in this cycle: the reverse transcriptase, the integrase, and the protease. These enzymes thus represent the most promising drug targets. There are four major subclasses of proteases. The serine proteases, such as chymotrypsin and trypsin, and the cysteine proteases (in which a Cys residue serves a catalytic role similar to that of Ser in the active site) form covalent enzyme-substrate complexes; the aspartyl proteases and metalloproteases do not. The HIV protease is an aspartyl protease. Two active-site Asp residues facilitate the direct attack of a water molecule on the carbonyl group of the peptide bond to be cleaved (Fig. 6-28). The initial product of this attack is an unstable tetrahedral intermediate, much like that in the chymotrypsin reaction. This intermediate is close in structure and energy to the reaction transition state. The drugs that have been developed as HIV protease inhibitors form noncovalent complexes with the enzyme, but they bind to it so tightly that they can be considered irreversible inhibitors. The tight binding is derived in part from their design as transition-state analogs. The success of these drugs makes a point worth emphasizing: the catalytic principles we have studied in this chapter are not simply abstruse ideas to be memorized — their application saves lives. MECHANISM FIGURE 6-28 Mechanism of action of HIV protease. Two active-site Asp residues (from different subunits) act as general acid-base catalysts, facilitating the attack of water on the peptide bond. The unstable tetrahedral intermediate in the reaction pathway is shaded light red. The HIV protease is most efficient at cleaving peptide bonds between Phe and Pro residues. The active site has a pocket that binds an aromatic group next to the bond to be cleaved. Several HIV protease inhibitors are shown in Figure 6-29. Although the structures appear varied, they all share a core structure: a main chain with a hydroxyl group positioned next to a branch containing a benzyl group. This arrangement targets the benzyl group to an aromatic (hydrophobic) binding pocket. The adjacent hydroxyl group mimics the negatively charged oxygen in the tetrahedral intermediate in the normal reaction, providing a transition-state analog that facilitates very tight binding. The remainder of each inhibitor structure was designed to fit into and bind to various crevices along the surface of the enzyme, enhancing overall binding. The availability of these effective drugs has vastly increased the life span and quality of life of millions of people with HIV and AIDS. In 2018, 23.3 million of the 38 million people living with HIV infection were receiving antiretroviral therapy.

FIGURE 6-29 HIV protease inhibitors. The hydroxyl group (red) acts as a transition-state analog, mimicking the oxygen of the tetrahedral intermediate. The adjacent benzyl group (blue) helps to properly position the drug in the active site. Hexokinase Undergoes Induced Fit on Substrate Binding Yeast hexokinase (Mr 107,862) is a bisubstrate enzyme that catalyzes this reversible reaction: ATP and ADP always bind to enzymes as a complex with the metal ion M g2+. In the hexokinase reaction, the γ-phosphoryl of ATP is transferred to the hydroxyl at C-6 of glucose. This hydroxyl is similar in chemical reactivity to water, and water freely enters the enzyme active site. Yet hexo-kinase favors the reaction with glucose by a factor of 106. The enzyme can discriminate between glucose and water because of a conformational change in the enzyme when the correct substrate binds (Fig. 6-30). Hexokinase thus provides a good example of induced fit. When glucose is not present, the enzyme is in an inactive conformation, with the active-site amino acid side chains out of position for reaction. When glucose (but not water) and Mg⋅ATP bind, the binding energy derived from this interaction induces a conformational change in hexokinase to the catalytically active form. FIGURE 6-30 Induced fit in hexokinase. (a) Hexokinase has a U-shaped structure. (b) The ends pinch toward each other in a conformational change induced by binding -glucose. [Data from (a) PDB ID 2YHX, C. M. Anderson et al., J. Mol. Biol. 123:15, 1978. (b) PDB ID 2E2O, modeled with ADP derived from PDB ID 2E2Q, H. Nishimasu et al., J. Biol. Chem. 282:9923, 2007.] This model has been reinforced by kinetic studies. The five- carbon sugar xylose, stereochemically similar to glucose but one carbon shorter, binds to hexokinase but in a position where it cannot be phosphorylated. Nevertheless, addition of xylose to the reaction mixture increases the rate of ATP hydrolysis. Evidently, the binding of xylose is sufficient to induce a change in hexokinase to its active conformation, and the enzyme is thereby “tricked” into phosphorylating water. The hexokinase reaction also illustrates that enzyme specificity is not always a simple matter of binding one compound but not another. In the case of hexokinase, specificity is observed not in the formation of the ES complex but in the relative rates of subsequent catalytic steps. Reaction rates increase greatly in the presence of a substrate, glucose, that is able to accept a phosphoryl group.

Induced fit is only one aspect of the catalytic mechanism of hexokinase — like chymotrypsin, hexokinase uses several catalytic mechanisms. For example, the active-site amino acid residues (those brought into position by the conformational change that follows substrate binding) participate in general acid- base catalysis and transition-state stabilization. The Enolase Reaction Mechanism Requires Metal Ions Another glycolytic enzyme, enolase, catalyzes the reversible dehydration of 2-phosphoglycerate to phosphoenolpyruvate: The reaction provides an example of the use of an enzymatic cofactor, in this case a metal ion (another example of coenzyme function is provided in Box 6-1). Yeast enolase (Mr 93, 316) is a dimer with 436 amino acid residues per subunit. The enolase reaction illustrates one type of metal ion catalysis and provides an additional example of general acid-base catalysis and transition- state stabilization. The reaction occurs in two steps (Fig. 6-31a). First, Lys345 acts as a general base catalyst, abstracting a proton from C-2 of 2-phosphoglycerate; then Glu211 acts as a general acid catalyst, donating a proton to the — OH leaving group. The proton at C-2 of 2-phosphoglycerate is not acidic and thus is quite resistant to its removal by Lys345. However, the electronegative oxygen atoms of the adjacent carboxyl group pull electrons away from C-2, making the attached protons somewhat more labile. In the active site, the carboxyl group of 2-phosphoglycerate undergoes strong ionic interactions with two bound M g2+ ions (Fig. 6-31b), greatly enhancing the electron withdrawal by the carboxyl. Together, these effects render the C-2 protons sufficiently acidic (lowering the pKa) that one proton can be abstracted to initiate the reaction. As the unstable enolate intermediate is formed, the metal ions further act to shield the two negative charges (on the carboxyl oxygen atoms) that transiently exist in close proximity to each other. Hydrogen bonding to other active-site amino acid residues also contributes to the overall mechanism. The various interactions effectively stabilize both the enolate intermediate and the transition state preceding its formation. MECHANISM FIGURE 6-31 Two-step reaction catalyzed by enolase. (a) The mechanism by which enolase converts 2-phosphoglycerate (2-PGA) to phosphoenolpyruvate. The carboxyl group of 2-PGA is coordinated by two M g2+ ions at the active site. (b) The substrate, 2-PGA, in relation to the M g2+, Lys345, and Glu211 in the enolase active site (gray outline). Nitrogen is shown in blue, phosphorus in orange; hydrogen atoms are not shown. [(b) Data from PDB ID 1ONE, T. M. Larsen et al., Biochemistry 35:4349, 1996.] An Understanding of Enzyme Mechanism Produces Useful Antibiotics Penicillin was discovered in 1928 by Alexander Fleming, but another 15 years passed before this relatively unstable compound was understood well enough for it to be used as a pharmaceutical agent to treat bacterial infections. Penicillin interferes with the synthesis of peptidoglycan, the major component of the rigid cell wall that protects bacteria from osmotic lysis. Peptidoglycan consists of polysaccharides and peptides cross-linked in several steps that include a transpeptidase reaction (Fig. 6-32). It is this reaction that is inhibited by penicillin and related compounds (Fig. 6-33a), all of which are irreversible inhibitors of transpeptidase. They bind to the active site of transpeptidase through a segment that mimics one conformation of the D-Ala–D- Ala segment of the peptidoglycan precursor. The peptide bond in the precursor is replaced by a highly reactive β -lactam ring in the antibiotic. When penicillin binds to the transpeptidase, an active-site Ser attacks the carbonyl of the β -lactam ring and generates a covalent adduct between penicillin and the enzyme. The leaving group remains attached, however, because it is linked by the remnant of the β -lactam ring (Fig. 6-33b). The covalent complex irreversibly inactivates the enzyme. This, in turn, blocks synthesis of the bacterial cell wall, and most bacteria die as the fragile inner membrane bursts under osmotic pressure.

FIGURE 6-32 The transpeptidase reaction. This reaction, which links two peptidoglycan precursors into a larger polymer, is facilitated by an active- site Ser and a covalent catalytic mechanism similar to that of chymotrypsin. Note that peptidoglycan is one of the few places in nature where amino acid residues are found. The active-site Ser attacks the carbonyl of the peptide bond between the two Ala residues, creating a covalent ester linkage between the substrate and the enzyme, with release of the terminal Ala residue. An amino group from the second peptidoglycan precursor then attacks the ester linkage, displacing the enzyme and cross-linking the two precursors.

FIGURE 6-33 Transpeptidase inhibition by β -lactam antibiotics. (a) β - Lactam antibiotics have a five-membered thiazolidine ring fused to a four- membered β -lactam ring. The latter ring is strained and includes an amide moiety that plays a critical role in the inactivation of peptidoglycan synthesis. The R group differs with the type of penicillin. Penicillin G was the first to be isolated and remains one of the most effective, but it is degraded by stomach acid and must be administered by injection. Penicillin V is nearly as effective and is acid stable, so it can be administered orally. Amoxicillin has a broad range of effectiveness, is readily administered orally, and thus is the most widely prescribed β -lactam antibiotic. (b) Attack on the amide moiety of the β -lactam ring by a transpeptidase active-site Ser results in a covalent acyl-enzyme product. This is hydrolyzed so slowly that adduct formation is practically irreversible, and the transpeptidase is inactivated. Human use of penicillin and its derivatives has led to the evolution of strains of pathogenic bacteria that express β - lactamases (Fig. 6-34a), enzymes that cleave β -lactam antibiotics, rendering them inactive. The bacteria thereby become resistant to the antibiotics. The genes for these enzymes have spread rapidly through bacterial populations under the selective pressure imposed by the use (and oen overuse) of β - lactam antibiotics. Human medicine responded with the development of compounds such as clavulanic acid, a suicide inactivator, which irreversibly inactivates the β -lactamases (Fig. 6-34b). Clavulanic acid mimics the structure of a β -lactam antibiotic and forms a covalent adduct with a Ser in the β - lactamase active site. This leads to a rearrangement that creates a much more reactive derivative, which is subsequently attacked by another nucleophile in the active site to irreversibly acylate the enzyme and inactivate it. Amoxicillin and clavulanic acid are combined in a widely used pharmaceutical formulation with the trade name Augmentin. The cycle of chemical warfare between humans and bacteria continues unabated. Strains of disease- causing bacteria that are resistant to both amoxicillin and clavulanic acid have been discovered. Mutations in β -lactamase within these strains render it unreactive to clavulanic acid. The development of new antibiotics promises to be a growth industry for the foreseeable future. FIGURE 6-34 β -Lactamases and β -lactamase inhibition. (a) β -Lactamases promote cleavage of the β -lactam ring in β -lactam antibiotics, thus inactivating them. (b) Clavulanic acid is a suicide inhibitor, making use of the normal chemical mechanism of β -lactamases to create a reactive species at the active site. This reactive species is attacked by a nucleophilic group (Nu:) in the active site to irreversibly acylate the enzyme. SUMMARY 6.4 Examples of Enzymatic Reactions Chymotrypsin is a serine protease with a well-understood mechanism, featuring general acid-base catalysis, covalent catalysis, and transition-state stabilization. Hexokinase provides an excellent example of induced fit as a means of using substrate binding energy. The enolase reaction proceeds via metal ion catalysis. Understanding enzyme mechanism allows for the development of drugs to inhibit enzyme action. 6.5 Regulatory Enzymes In cellular metabolism, groups of enzymes work together in sequential pathways to carry out a given metabolic process, such as the multireaction breakdown of glucose to lactate or the multireaction synthesis of an amino acid from simpler precursors. Each separate reaction is catalyzed by a different enzyme. In such enzyme systems, the reaction product of one enzyme becomes the substrate of the next. This functional compartmentalization of cellular chemistry does more than accelerate individual reactions; it provides opportunities for the exquisitely precise regulation of all cellular processes. Most of the enzymes in each metabolic pathway follow the kinetic patterns we have already described. Each pathway, however, includes one or more enzymes that have a greater effect on the rate of the overall sequence. The catalytic activity of these regulatory enzymes increases or decreases in response to certain signals. Adjustments in the rate of reactions catalyzed by regulatory enzymes, and therefore in the rate of entire metabolic sequences, allow the cell to meet changing needs for energy and for biomolecules required in growth and repair. The activities of regulatory enzymes are modulated in a variety of ways. Allosteric enzymes function through reversible, noncovalent binding of regulatory compounds called allosteric modulators or allosteric effectors, which are generally small metabolites or cofactors. Other enzymes are regulated by reversible covalent modification. Both classes of regulatory enzymes tend to be multisubunit proteins, and in some cases the regulatory site(s) and the active site are on separate subunits. Metabolic systems have at least two other mechanisms of enzyme regulation. Some enzymes are stimulated or inhibited when they are bound by separate regulatory proteins. Others are activated when peptide segments are removed by proteolytic cleavage; unlike effector-mediated regulation, regulation by proteolytic cleavage is irreversible. Important examples of both mechanisms are found in physiological processes such as digestion, blood clotting, hormone action, and vision. Cell growth and survival depend on efficient use of resources, and this efficiency is made possible by regulatory enzymes. No single rule governs which of the various types of regulation occur in different systems. Several types of regulation may occur in a single regulatory enzyme. The remainder of this chapter is devoted to a discussion of these major mechanisms of enzyme regulation. Allosteric Enzymes Undergo Conformational Changes in Response to Modulator Binding As we saw in Chapter 5, allosteric proteins are those having “other shapes” or conformations induced by the binding of modulators. The same concept applies to certain regulatory enzymes, as conformational changes induced by one or more modulators interconvert more-active and less-active forms of the enzyme. The modulators for allosteric enzymes may be inhibitory or stimulatory. The modulator can be the substrate itself; regulation in which substrate and modulator are identical is referred to as homotropic. The effect is similar to that of O2 binding to hemoglobin (Chapter 5): binding of the ligand — or substrate, in the case of enzymes — causes conformational changes that affect the subsequent activity of other sites on the protein. In most cases, the conformational change converts a relatively inactive conformation (oen referred to as a T state — a convention based on the early hemoglobin literature) to a more active conformation (an R state). When the modulator is a molecule other than the substrate, the enzyme is said to be heterotropic. Note that heterotropic modulators should not be confused with uncompetitive and mixed inhibitors. Although the latter bind at a second site on the enzyme, they do not necessarily mediate conformational changes between active and inactive forms, and the kinetic effects are distinct. The properties of allosteric enzymes are significantly different from those of simple nonregulatory enzymes. Some of the differences are structural. In addition to active sites, allosteric enzymes oen have one or more regulatory, or allosteric, sites for binding to each heterotropic modulator (Fig. 6-35). Just as an enzyme’s active site is specific for its substrate, each regulatory site is specific for its modulator. Enzymes with several modulators generally have different specific binding sites for each. In homotropic enzymes, the active site and regulatory site are the same. FIGURE 6-35 Subunit interactions in an allosteric enzyme, and interactions with inhibitors and activators. In many allosteric enzymes, the substrate-binding site and the modulator-binding site(s) are on different subunits: the catalytic (C) and regulatory (R) subunits, respectively. Binding of the positive (stimulatory) modulator (M) to its specific site on the regulatory subunit is communicated to the catalytic subunit through a conformational change. This change renders the catalytic subunit active and capable of binding the substrate (S) with higher affinity. Upon dissociation of the modulator from the regulatory subunit, the enzyme reverts to its inactive or less-active form. Allosteric enzymes are typically larger and more complex than nonallosteric enzymes, with two or more subunits. A classic example is aspartate transcarbamoylase (oen abbreviated ATCase), which catalyzes an early step in the biosynthesis of pyrimidine nucleotides, the reaction of carbamoyl phosphate and aspartate to form carbamoyl aspartate: ATCase has 12 polypeptide chains organized into 6 catalytic subunits (organized as 2 trimeric complexes) and 6 regulatory subunits (organized as 3 dimeric complexes). Figure 6-36 shows the quaternary structure of this enzyme, deduced from x-ray analysis. The enzyme exhibits allosteric behavior as detailed below, as the catalytic subunits function cooperatively. The regulatory subunits have binding sites for ATP and CTP, which function as positive and negative regulators, respectively. CTP is one of the end products of the pathway, and negative regulation by CTP serves to limit ATCase action under conditions when CTP is abundant. On the other hand, high concentrations of ATP indicate that cellular metabolism is robust, that the cell is growing, and that additional pyrimidine nucleotides may be needed to support RNA transcription and DNA replication. FIGURE 6-36 The regulatory enzyme aspartate transcarbamoylase. (a) The inactive T state and (b) the active R state of the enzyme are shown. This allosteric regulatory enzyme has two stacked catalytic clusters, each with three catalytic polypeptide chains (in shades of blue and purple), and three regulatory clusters, each with two regulatory polypeptide chains (in beige and yellow). The regulatory clusters form the points of a triangle (not evident in this side view) surrounding the catalytic subunits. Binding sites for allosteric modulators (including CTP) are on the regulatory subunits. Modulator binding produces large changes in enzyme conformation and activity. The role of this enzyme in nucleotide synthesis, and details of its regulation, are discussed in Chapter 22. [Data from (a) PDB ID 1RAB, R. P. Kosman et al., Proteins 15:147, 1993; (b) PDB ID 1F1B, L. Jin et al., Biochemistry 39:8058, 2000.] The Kinetic Properties of Allosteric Enzymes Diverge from Michaelis- Menten Behavior Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for allosteric enzymes, plots of V0 versus [S] (Fig. 6-37) usually produce a sigmoid saturation curve, rather than the hyperbolic curve typical of nonregulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis-Menten relationship. Instead, the symbol [S]0.5 or K0.5 is oen used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6-37).

FIGURE 6-37 Substrate-activity curves for representative allosteric enzymes. Three examples of complex responses of allosteric enzymes to their modulators. (a) The sigmoid curve of a homotropic enzyme, in which the substrate also serves as a positive (stimulatory) modulator, or activator. Notice the resemblance to the oxygen-saturation curve of hemoglobin (see Fig. 5-12). The sigmoid curve is a hybrid curve in which the enzyme is present primarily in the relatively inactive T state at low substrate concentration, and primarily in the more active R state at high substrate concentration. The curves for the pure T and R states are plotted separately in color. ATCase exhibits a kinetic pattern similar to this. (b) The effects of several different concentrations of a positive modulator (+) or a negative modulator (−) on an allosteric enzyme in which K0.5 is altered without a change in Vmax. The central curve shows the substrate-activity relationship without a modulator. For ATCase, CTP is a negative modulator and ATP is a positive modulator. (c) A less common type of modulation, in which Vmax is altered and K0.5 is nearly constant. Sigmoid kinetic behavior reflects cooperative interactions between multiple protein subunits. In other words, changes in the structure of one subunit are translated into structural changes in adjacent subunits, an effect mediated by noncovalent interactions at the interface between subunits. Sigmoid kinetic behavior for enzymes is well explained by the concerted and sequential models for subunit interactions we previously encountered when considering O2 binding to hemoglobin (see Fig. 5-14). ATCase effectively illustrates both homotropic and heterotropic allosteric kinetic behavior. Binding of the substrates, aspartate and carbamoyl phosphate, to the enzyme gradually brings about a transition from the relatively inactive T state to the more active R state. This accounts for the sigmoid rather than hyperbolic change in V0 with increasing [S]. One characteristic of sigmoid kinetics is that small changes in the concentration of a modulator can be associated with large changes in activity. As exemplified in Figure 6-37a, a relatively small increase in [S] in the steep part of the curve causes a comparatively large increase in V0. The heterotropic allosteric regulation of ATCase is brought about by its interactions with ATP and CTP. For heterotropic allosteric enzymes, an activator may cause the curve to become more nearly hyperbolic, with a decrease in K0.5 but no change in Vmax, resulting in an increased reaction velocity at a fixed substrate concentration. For ATCase, the interaction with ATP brings this about, and the enzyme exhibits a V0 versus [S] curve that is characteristic of the active R state at sufficiently high ATP concentrations (V0 is higher for any value of [S]; Fig. 6-37b). A negative modulator (an inhibitor) may produce a more sigmoid substrate-saturation curve, with an increase in K0.5, as illustrated by the effects of CTP on ATCase kinetics (see curves for a negative modulator in Fig. 6-37b). Other heterotropic allosteric enzymes respond to an activator by an increase in Vmax with little change in K0.5 (Fig. 6-37c). Heterotropic allosteric enzymes therefore show different kinds of responses in their substrate-activity curves, because some have inhibitory modulators, some have activating modulators, and some (like ATCase) have both. Some Enzymes Are Regulated by Reversible Covalent Modification In another important class of regulatory enzymes, activity is modulated by covalent modification of one or more of the amino acid residues in the enzyme molecule. Over 500 different types of covalent modification have been found in proteins. Common modifying groups include phosphoryl, acetyl, adenylyl, uridylyl, methyl, amide, carboxyl, myristoyl, palmitoyl, prenyl, hydroxyl, sulfate, and adenosine diphosphate ribosyl groups (Fig. 6-38). There are even entire proteins that function as specialized modifying groups. These include ubiquitin and SUMO (small ubiquitin-like modifier), which are attached and detached from other proteins to regulate their activity in some way. All of these groups, small and large, are linked to and removed from a regulated enzyme by separate enzymes. When an amino acid residue in an enzyme is modified, a novel amino acid with altered properties has effectively been introduced into the enzyme. Introduction of a charge can alter the local properties of the enzyme and induce a change in conformation. Introduction of a hydrophobic group can trigger association with a membrane. The changes are oen substantial and can be critical to the function of the altered enzyme.

FIGURE 6-38 Some enzyme modification reactions. Although there are too many examples of covalent modification of proteins to cover in detail, a few examples are instructive. One enzyme that is regulated by methylation is the methyl-accepting chemotaxis protein of bacteria. This protein is part of a system that permits a bacterium to swim toward an attractant (such as a sugar) in solution and away from repellent chemicals. The methylating agent is S-adenosylmethionine (adoMet) (see Fig. 18- 18). Acetylation is another common modification, with approximately 80% of the soluble proteins in eukaryotes, including many enzymes, acetylated at their amino terminus. Ubiquitin is added to proteins as a tag that destines them for proteolytic degradation (see Fig. 27-47). Ubiquitination can also have a regulatory function. SUMO is found attached to many eukaryotic nuclear proteins and has roles in the regulation of transcription, chromatin structure, and DNA repair. ADP-ribosylation is an especially interesting reaction; the ADP- ribose is derived from nicotinamide adenine dinucleotide (NAD) (see Fig. 8-41). This type of modification occurs for the bacterial enzyme dinitrogenase reductase, resulting in regulation of the important process of biological nitrogen fixation. Diphtheria toxin and cholera toxin are enzymes that catalyze the ADP- ribosylation (and inactivation) of key cellular enzymes or other proteins. By far the most common type of regulatory modification is phosphorylation. About one-third of all proteins in a eukaryotic cell are phosphorylated, and one or (oen) many phosphorylation events are part of virtually every regulatory process. Some proteins have only one phosphorylated residue, others have several, and a few have dozens of sites for phosphorylation. This mode of covalent modification is central to a large number of regulatory pathways. We discuss it in some detail here, and again in Chapter 12. We will encounter all of these types of enzyme modification again in later chapters. Phosphoryl Groups Affect the Structure and Catalytic Activity of Enzymes The attachment of phosphoryl groups to specific amino acid residues of a protein is catalyzed by protein kinases. More than 500 genes encoding these critical enzymes are found in the human genome. In the reactions they catalyze, the γ -phosphoryl group derived from a nucleoside triphosphate (usually ATP) is transferred to a particular Ser, Thr, or Tyr residue (occasionally His as well) on the target protein. This introduces a bulky, charged group into a region of the target protein that was only moderately polar prior to modification. The oxygen atoms of a phosphoryl group can hydrogen-bond with one or several groups in a protein, commonly the amide groups of the peptide backbone at the start of an α helix or the charged guanidinium group of an Arg residue. The two negative charges on a phosphorylated side chain can also repel neighboring negatively charged (Asp or Glu) residues. When the modified side chain is located in a region of an enzyme critical to its three-dimensional structure, phosphorylation can have dramatic effects on enzyme conformation and thus on substrate binding and catalysis. Removal of phosphoryl groups from these same target proteins is catalyzed by phosphoprotein phosphatases, also called simply protein phosphatases. An important example of enzyme regulation by phosphorylation is the case of glycogen phosphorylase (M r 94,500) of muscle and liver (Chapter 15), which catalyzes the reaction (Glucose)nGlycogen + Pi→ (glucose)n−1Shortened glycogen chain + glucose 1-phosphate The glucose 1-phosphate so formed can be used for ATP synthesis in muscle or converted to free glucose in the liver. Note that glycogen phosphorylase, though it adds a phosphate to a substrate, is not itself a kinase, because it does not utilize ATP or any other nucleotide triphosphate as a phosphoryl donor in its catalyzed reaction. It is, however, the substrate for a protein kinase that phosphorylates it. In the discussion below, the phosphoryl groups we are concerned with are those involved in regulation of the enzyme, as distinguished from its catalytic function. Glycogen phosphorylase occurs in two forms: the more active phosphorylase a and the less active phosphorylase b (Fig. 6-39). Phosphorylase a has two subunits, each with a specific Ser residue (Ser14) that is phosphorylated at its hydroxyl group. Phosphorylase b is covalently transformed into active phosphorylase a by another enzyme, phosphorylase kinase, which catalyzes the transfer of phosphoryl groups from ATP to the hydroxyl groups of the two specific Ser residues in phosphorylase b: 2AT P + phosphorylase b →  2 (less active) AD P + phosphorylase a (more active) To serve as an effective regulatory mechanism, phosphorylation must be reversible. In general, phosphoryl groups are added and removed by different enzymes, and the processes can therefore be separately regulated. The phosphoryl groups of phosphorylase a are hydrolytically removed by a separate enzyme called phosphoprotein phosphatase 1 (PP1): Phosphorylase a (more active)  + 2H2O → phosphorylase b (less active)  + 2Pi These phosphoserine residues are required for maximal activity of the enzyme. FIGURE 6-39 Regulation of muscle glycogen phosphorylase activity by phosphorylation. In the more-active form of the enzyme, phosphorylase a, specific Ser residues, one on each subunit, are phosphorylated. Phosphorylase a is converted to the less active phosphorylase b by enzymatic loss of these phosphoryl groups, promoted by phosphoprotein phosphatase 1 (PP1). Phosphorylase b can be reconverted (reactivated) to phosphorylase a by the action of phosphorylase kinase. In this reaction, phosphorylase a is converted to phosphorylase b by the cleavage of two phosphoserine covalent bonds, one on each subunit of glycogen phosphorylase. The regulation of glycogen phosphorylase by phosphorylation illustrates the effects on both structure and catalytic activity of adding a phosphoryl group (Fig. 6-40). In the unphosphorylated state (phosphorylase b), each subunit of this enzyme is folded so as to bring the 20 residues at its amino terminus, including some basic residues, into a region containing several acidic amino acids; this produces an electrostatic interaction that stabilizes the conformation. Phosphorylation of Ser14 interferes with this interaction, forcing the amino-terminal domain out of the acidic environment and into a conformation that allows interaction between the –Ser and several Arg side chains (phosphorylase a). In this conformation, the enzyme is much more active. FIGURE 6-40 The conformation change brought about by phosphorylation in glycogen phosphorylase from rabbit muscle. Twenty amino acid residues at the amino terminus of each subunit are shown in red, including the residue phosphorylated in phosphorylase a (Ser14). This peptide segment interacts with different parts of the protein depending upon the phosphorylation state of Ser14, stabilizing the different conformations that characterize phosphorylase a and b. [Data from (a) PDB ID 8GPB, (b) PDB ID 1GPA, D. Barford et al., J. Mol. Biol. 218:233, 1991.] As we shall see in Chapter 15, phosphorylation is just one of the regulatory mechanisms by which the activity of glycogen phosphorylase is controlled. Allosteric regulation and additional hormonal responses also contribute to the overall precision of control needed to meet moment-to-moment cellular demands for glucose and ATP. Multiple Phosphorylations Allow Exquisite Regulatory Control The Ser, Thr, or Tyr residues that are typically phosphorylated in regulated proteins occur within common structural motifs, called consensus sequences, that are recognized by specific protein kinases (Table 6-10). Some kinases are basophilic, preferentially phosphorylating a residue that has basic neighbors; others have different substrate preferences, such as for a residue near a Pro residue. However, amino acid sequence is not the only important factor in determining whether a given residue will be phosphorylated. Protein folding brings together residues that are distant in the primary sequence; the resulting three-dimensional structure can determine whether a protein kinase has access to a given residue and can recognize it as a substrate. TABLE 6-10 Consensus Recognition Sequences for a Few Protein Kinases Protein kinase Consensus sequence and phosphorylated residue Protein kinase A -x-R-[RK]-x-[ST]-B- Protein kinase G -x-R-[RK]-x-[ST]-X- Protein kinase C -[RK](2)-x-[ST]-B-[RK](2)- Protein kinase B R-x-x-R-x-[ST]-x-ψ - Ca2+/calmodulin kinase I -B-x-R-x(2)-[ST]-x(3)-B- Ca2+/calmodulin kinase II -B-x-[RK]-x(2)-[ST]-x(2)- Myosin light chain kinase (smooth muscle) -K(2)-R-x(2)-S-x-B(2)- Phosphorylase b kinase -K-R-K-Q-I-S-V-R- Extracellular signal-regulated kinase (ERK) -P-x-[ST]-P(2)- Cyclin-dependent protein kinase (cdc2) -x-[ST]-P-x-[KR]- Casein kinase I -[SpTp]-x(2)-[ST]-B Casein kinase II -x-[ST]-x(2)-[ED]-x- β -Adrenergic receptor kinase -[DE](n)-[ST]-x(3) Rhodopsin kinase -x(2)-[ST]-E(n)-vABL-[YLV]-Y-X1-3-[PF]- Epidermal growth factor (EGF) receptor kinase -E(4)-Y-F-E-L-V- Information from L. A. Pinna and M. H. Ruzzene, Biochim. Biophys. Acta 1314:191, 1996; B. E. Kemp and R. B. Pearson, Trends Biochem. Sci. 15:342, 1990; P. J. Kennelly and E. G. Krebs, J. Biol. Chem. 266:15,555, 1991; T. P. Cujec, P. F. Madeiros, P. Hammond, C. Rise, and B. L. Kreider, Chem. Biol. 9:253, 2002. Note: Shown here are deduced consensus sequences (in roman type) and actual sequences from known substrates (italic). The Ser (S), Thr (T), or Tyr (Y) residue that undergoes phosphorylation is in bold; all amino acid residues are shown as their one- letter abbreviations (see Table 3-1). An x represents any amino acid; B, any hydrophobic amino acid; Sp and Tp are Ser and Thr residues that must already be phosphorylated for the kinase to recognize the site. ψ denotes any amino acid with a bulky hydrophobic side chain. a b a The best target site has two amino acid residues separating the phosphorylated and target Ser/Thr residues; target sites with one or three intervening residues function at a reduced level. Regulation by phosphorylation is oen complicated. Some proteins have consensus sequences recognized by several different protein kinases, each of which can phosphorylate the protein and alter its enzymatic activity. In some cases, phosphorylation is hierarchical: a certain residue can be phosphorylated only if a neighboring residue has already been phosphorylated. For example, glycogen synthase, the enzyme that catalyzes the condensation of glucose monomers to form glycogen (Chapter 15), is inactivated by phosphorylation of specific Ser residues and is also modulated by at least four other protein kinases that phosphorylate four other sites in the enzyme (Fig. 6-41). The enzyme does not become a substrate for glycogen synthase kinase 3 until one site has been phosphorylated by casein kinase II. Some phosphorylations inhibit glycogen synthase more than others, and some combinations of phosphorylations are cumulative. These multiple regulatory phosphorylations provide the potential for extremely subtle modulation of enzyme activity. b FIGURE 6-41 Multiple regulatory phosphorylations. The enzyme glycogen synthase has at least nine separate sites in five designated regions that are susceptible to phosphorylation by one of the cellular protein kinases. Thus, regulation of this enzyme is a matter not of binary (on/off) switching but of finely tuned modulation of activity over a wide range in response to a variety of signals. As is the case for kinases, there are many different enzymes that remove phosphoryl groups from proteins. Cells contain a family of phosphoprotein phosphatases that each hydrolyze specific –Ser, –Thr, and –Tyr esters, releasing Pi. The phosphoprotein phosphatases generally act on only a subset of phosphorylated proteins, but they show less substrate specificity than protein kinases. Some Enzymes and Other Proteins Are Regulated by Proteolytic Cleavage of an Enzyme Precursor For some enzymes, an inactive precursor called a zymogen is cleaved to form the active enzyme. Many proteolytic enzymes (proteases) of the stomach and pancreas are regulated in this way. Chymotrypsin and trypsin are initially synthesized as chymotrypsinogen and trypsinogen (Fig. 6-42). Specific cleavage causes conformational changes that expose the enzyme active site. This type of activation is irreversible, and additional regulation requires a different mechanism. When necessary, a previously activated protease is inactivated by inhibitor proteins that bind very tightly to the enzyme active site. For example, pancreatic trypsin inhibitor (M r 6,000) binds to and inhibits trypsin. α1-Antiproteinase (M r 53,000) primarily inhibits neutrophil elastase (neutrophils are a type of leukocyte, or white blood cell; elastase is a protease that acts on elastin, a component of some connective tissues). An insufficiency of α1- antiproteinase, which can be caused by exposure to cigarette smoke, has been associated with lung damage, including emphysema. FIGURE 6-42 Activation of zymogens by proteolytic cleavage. Shown here is the formation of active chymotrypsin (formally, α -chymotrypsin) and trypsin from their zymogens, chymotrypsinogen and trypsinogen. The π- chymotrypsin intermediate generated by trypsin cleavage has a somewhat altered specificity relative to the mature α -chymotrypsin. The bars represent the amino acid sequences of the polypeptide chains, with numbers indicating the positions of the residues (the amino-terminal residue is number 1). Residues at the termini of the polypeptide fragments generated by cleavage are indicated below the bars. Note that in the final active forms, some numbered residues are missing. Recall that the three polypeptide chains (A, B, and C) of chymotrypsin are linked by disulfide bonds (see Fig. 6-24). Proteases are not the only proteins activated by proteolysis. In other cases, however, the precursors are called not zymogens but, more generally, proproteins or proenzymes, as appropriate. For example, the connective tissue protein collagen is initially synthesized as the soluble precursor procollagen. A Cascade of Proteolytically Activated Zymogens Leads to Blood Coagulation The formation of a blood clot provides a well-studied example of a regulatory cascade, a mechanism that allows a very sensitive response to — and amplification of — a molecular signal. The blood coagulation pathways also bring together several other types of regulation, including proteolytic activation and regulatory proteins. We have not yet encountered the latter type of regulation. It employs proteins whose only function is to regulate the activity of other proteins by interacting with them noncovalently. In a regulatory cascade, a signal leads to the activation of protein X. Protein X catalyzes the activation of protein Y. Protein Y catalyzes the activation of protein Z, and so on. Since proteins X, Y, and Z are catalysts and activate multiple copies of the next protein in the chain, the signal is amplified in each step. In some cases, the activation steps involve proteolytic cleavage and are thus effectively irreversible. In other cases, activation entails readily reversible protein modification steps such as phosphorylation. Regulatory cascades govern a wide range of biological processes, including, besides blood coagulation, some aspects of cell fate determination during development, the detection of light by retinal rods, and programmed cell death (apoptosis). A regulatory cascade is also one of the strategies governing the overall activity of glycogen phosphorylase (see Fig. 15-13). A blood clot is an aggregate of specialized cell fragments that lack nuclei, called platelets. They are cross-linked and stabilized by proteinaceous fibers consisting mainly of the protein fibrin (Fig. 6-43a). Fibrin is derived from a soluble zymogen called fibrinogen. Aer albumins and globulins, fibrinogen is usually the third most abundant type of protein in blood plasma. Blood clotting begins with the activation of circulating platelets at the site of a wound. Tissue damage causes collagen molecules present beneath the epithelial cell layer that lines each blood vessel to become exposed to the blood. Platelet activation is primarily triggered by interaction with this collagen. Activation leads to the presentation of anionic phospholipids on the surface of each platelet and the release of signaling molecules such as thromboxanes (p. 355) that help stimulate the activation of additional platelets. The activated platelets aggregate at the site of a wound, forming a loose clot. Stabilization of the clot requires fibrin, generated by fibrinogen cleavage as the endpoint of regulatory cascades. FIGURE 6-43 The function of fibrin in blood clots. (a) A blood clot consists of aggregated platelets (small, light-colored cells) tied together with strands of cross-linked fibrin. Erythrocytes (red in this colorized scanning electron micrograph) are also trapped in the matrix. (b) The soluble plasma protein fibrinogen consists of two complexes of α , β , and γ subunits (α2β2γ2). The removal of amino-terminal peptides from the α and β subunits (not shown) leads to the formation of higher-order complexes and eventual covalent cross-linking that results in the formation of fibrin fibers. The “knobs” are globular domains at the ends of the proteolyzed subunits. Fibrinogen is a dimer of heterotrimers (Aα2Bβ2γ2) with three different but evolutionarily related types of subunits (Fig. 6-43b). Fibrinogen is converted to fibrin (α2β2γ2), and thereby activated for blood clotting, by the proteolytic removal of 16 amino acid residues from the amino-terminal end (the A peptide) of each α subunit and 14 amino acid residues from the amino-terminal end (the B peptide) of each β subunit. Peptide removal is catalyzed by the serine protease thrombin. The newly exposed amino termini of the α and β subunits fit neatly into binding sites in the carboxyl-terminal globular portions of the γ and β subunits, respectively, of another fibrin protein. Fibrin thus polymerizes into a gel-like matrix to generate a so clot. Covalent cross-links between the associated fibrins are generated by the condensation of particular Lys residues in one fibrin heterotrimer with Gln residues in another, catalyzed by a transglutaminase, factor XIIIa. The covalent cross-links convert the so clot into a hard clot. Fibrinogen activation to produce fibrin is the end point of not one but two parallel but intertwined regulatory cascades (Fig. 6-44). One of these is referred to as the contact activation pathway (“contact” refers to interaction of key components of this system with anionic phospholipids presented on the surface of platelets at the site of a wound). As all components of this pathway are found in the blood plasma, it is also called the intrinsic pathway. The second path is the tissue factor or extrinsic pathway. A major component of this pathway, the protein tissue factor (TF), is not present in the blood. Most of the protein factors in both pathways are designated by roman numerals. Many of these factors are either chymotrypsin-like serine proteases or regulatory proteins, most with zymogen precursors that are synthesized in the liver and exported to the blood. For those with both inactive and active forms, the roman numeral designates the inactive zymogen (VII, X, for example). An “a” is added to designate the cleaved and active form (VIIa, Xa). The regulatory proteins bind to particular serine proteases and help to activate them. FIGURE 6-44 The coagulation cascades. The interlinked intrinsic and extrinsic pathways leading to the cleavage of fibrinogen to form active fibrin are shown. Active serine proteases in the pathways are shown in blue. Green arrows denote activating steps, and red arrows indicate inhibitory processes. The extrinsic pathway comes into play first. Tissue damage exposes the blood plasma to TF embedded largely in the membranes of fibroblasts and smooth muscle cells beneath the endothelial layer. An initiating complex is formed between TF and factor VII, present in the blood plasma. Factor VII is a zymogen of a serine protease, and TF is a regulatory protein required for its function. Factor VII is converted to its active form, factor VIIa, by proteolytic cleavage catalyzed by factor Xa (another serine protease). The TF-VIIa complex then cleaves factor X, creating the active form, factor Xa. If TF-VIIa is needed to cleave X, and Xa is needed to cleave TF-VII, how does the process ever get started? A very small amount of factor VIIa is present in the blood at all times, enough to form a small amount of the active TF-VIIa complex immediately aer tissue is damaged. This allows formation of factor Xa and establishes the initiating feedback loop. Once levels of factor Xa begin to build up, Xa (in a complex with another regulatory protein, factor Va) cleaves prothrombin to form active thrombin, and thrombin cleaves fibrinogen. The extrinsic pathway thus provides a burst of thrombin. However, the TF-VIIa complex is quickly shut down by the protein tissue factor pathway inhibitor (TFPI). Clot formation is sustained by the activation of components of the second cascade, the intrinsic pathway. Factor IX is converted to the active serine protease factor IXa by the TF-VIIa protease during initiation of the clotting sequence. Factor IXa, in a complex with the regulatory protein VIIIa, is relatively stable and provides an alternative enzyme for the proteolytic conversion of factor X to Xa. Activated IXa can also be produced by the serine protease factor XIa. Most of the XIa is generated by cleavage of factor XI zymogen by thrombin in a feedback loop. Le uncontrolled, blood coagulation could eventually lead to blockage of blood vessels, causing heart attacks or strokes. More regulation is thus needed. As a hard clot forms, regulatory pathways are already acting to limit the time during which the coagulation cascade is active. In addition to cleaving fibrinogen, thrombin forms a complex with a protein embedded in the vascular surface of endothelial cells, thrombomodulin. The thrombin-thrombomodulin complex cleaves the serine protease zymogen protein C. Activated protein C, in a complex with the regulatory protein S, cleaves and inactivates factors Va and VIIIa, leading to suppression of the overall cascade. Another protein, antithrombin III (ATIII), is a serine protease inhibitor. ATIII makes a covalent 1:1 complex between an Arg residue on ATIII and the active-site Ser residue of serine proteases, particularly thrombin and factor Xa. These two regulatory systems, in concert with TFPI, help to establish a threshold or level of exposure to TF that is needed to activate the coagulation cascade. Individuals with genetic defects that eliminate or decrease levels of protein C or ATIII in the blood have a greatly elevated risk of thrombosis (inappropriate formation of blood clots). The control of blood coagulation has important roles in medicine, particularly in the prevention of blood clotting during surgery and in patients at risk for heart attacks or strokes. Several different medical approaches to anticoagulation are available. The first takes advantage of another feature of several proteins in the coagulation cascade that we have not yet considered. The factors VII, IX, X, and prothrombin, along with proteins C and S, have calcium-binding sites that are critical to their function. In each case, the calcium-binding sites are formed by modification of multiple Glu residues near the amino terminus of each protein to γ -carboxyglutamate residues (abbreviated Gla; p. 76). The Glu-to-Gla modifications are carried out by enzymes that depend on the function of the fat-soluble vitamin K (p. 359). Bound calcium functions to adhere these proteins to the anionic phospholipids that appear on the surface of activated platelets, effectively localizing the coagulation factors to the area where the clot is to form. Vitamin K antagonists such as warfarin (Coumadin) have proven highly effective as anticoagulants. A second approach to anticoagulation is the administration of heparins. Heparins are highly sulfated polysaccharides (see Fig. 7-19). They act as anticoagulants by increasing the affinity of ATIII for factor Xa and thrombin, thus facilitating the inactivation of key cascade elements (see Figs 7-23 and 7-24). Finally, aspirin (acetylsalicylate; Fig. 21-15b) is effective as an anticoagulant. Aspirin inhibits the enzyme cyclooxygenase, required for the production of thromboxanes. As aspirin reduces thromboxane release from platelets, the capacity of the platelets to aggregate declines. Humans born with a deficiency in any one of most components of the clotting cascade have an increased tendency to bleed that varies from mild to essentially uncontrollable, a fatal condition. Genetic defects in the genes encoding the proteins required for blood clotting result in diseases referred to as hemophilias. Hemophilia B is a sex-linked trait resulting from a deficiency in factor IX. This type of hemophilia affects about one in 25,000 males worldwide. The most famous example of the inheritance of hemophilia B occurred among European royalty. Queen Victoria (1819–1901) was evidently a carrier. Prince Leopold, her eighth child, suffered from hemophilia B and died at the age of 31 aer a minor fall. At least two of her daughters were carriers and passed the defective gene to other royal families of Europe (Fig. 6-45). FIGURE 6-45 The royal families of Europe, and inheritance of hemophilia B. Males are indicated by squares and females by circles. Males who suffered from hemophilia are represented by red squares, presumed female carriers by half-red circles. Some Regulatory Enzymes Use Several Regulatory Mechanisms Glycogen phosphorylase and the blood clotting cascade are not the only examples of complex regulatory patterns. Additional examples of regulatory complexity are found at key metabolic crossroads. Bacterial glutamine synthetase, which catalyzes a reaction that introduces reduced nitrogen into cellular metabolism (Chapter 22), is among the most complex regulatory enzymes known. It is regulated allosterically, with at least eight different modulators; by reversible covalent modification; and by the association of other regulatory proteins, a mechanism examined in detail when we consider the regulation of specific metabolic pathways in Part II of this book. What is the advantage of such complexity in the regulation of enzymatic activity? We began this chapter by stressing the central importance of catalysis to the existence of life. The control of catalysis is also critical to life. If all possible reactions in a cell were catalyzed simultaneously, macromolecules and metabolites would quickly be broken down to much simpler chemical forms. Instead, cells catalyze only the reactions they need at a given moment. When chemical resources are plentiful, cells synthesize and store glucose and other metabolites. When chemical resources are scarce, cells use these stores to fuel cellular metabolism. Chemical energy is used economically, parceled out to various metabolic pathways as cellular needs dictate. The availability of powerful catalysts, each specific for a given reaction, makes the regulation of these reactions possible. This, in turn, gives rise to the complex, highly regulated symphony we call life. SUMMARY 6.5 Regulatory Enzymes The activities of metabolic pathways in cells are regulated by control of the activities of certain enzymes. The activity of an allosteric enzyme is adjusted by reversible binding of a specific modulator to a regulatory site. A modulator may be the substrate itself or some other metabolite, and the effect of the modulator may be inhibitory or stimulatory. The kinetic behavior of allosteric enzymes reflects cooperative interactions among enzyme subunits. Other regulatory enzymes are modulated by covalent modification of a specific functional group necessary for activity. The phosphorylation of specific amino acid residues is a particularly common way to regulate enzyme activity. Many proteolytic enzymes are synthesized as inactive precursors called zymogens, which are activated by cleavage to release small peptide fragments. Blood clotting is mediated by two interlinked regulatory cascades of proteolytically activated zymogens. Enzymes at important metabolic intersections may be regulated by complex combinations of effectors, allowing coordination of the activities of interconnected pathways. Chapter Review KEY TERMS Terms in bold are defined in the glossary. enzyme cofactor coenzyme prosthetic group holoenzyme apoenzyme apoprotein active site substrate ground state standard free-energy change, ΔG∘ biochemical standard free-energy change, ΔG′° transition state activation energy (ΔG‡) reaction intermediate rate-limiting step equilibrium constant (Keq) rate constant binding energy (ΔGB) specificity desolvation induced fit specific acid-base catalysis general acid-base catalysis covalent catalysis enzyme kinetics pre–steady state steady state steady-state kinetics V0 Vmax Michaelis-Menten equation steady-state assumption Michaelis constant (Km) Lineweaver-Burk equation Michaelis-Menten kinetics dissociation constant (Kd) kcat turnover number Cleland nomenclature reversible inhibition competitive inhibition uncompetitive inhibition mixed inhibition noncompetitive inhibition irreversible inhibitors suicide inactivator transition-state analog serine proteases retrovirus regulatory enzyme allosteric enzyme allosteric modulator (allosteric effector) regulatory protein homotropic heterotropic protein kinases protein phosphatases zymogen proproteins (proenzymes) regulatory cascade platelets fibrin fibrinogen thromboxane thrombin intrinsic pathway extrinsic pathway PROBLEMS 1. Keeping the Sweet Taste of Corn The sweet taste of freshly picked corn (maize) is due to the high level of sugar in the kernels. Store-bought corn (several days aer picking) is not as sweet, because about 50% of the free sugar is converted to starch within one day of picking. To preserve the sweetness of fresh corn, the husked ears can be immersed in boiling water for a few minutes (“blanched”), then cooled in cold water. Corn processed in this way and stored in a freezer maintains its sweetness. What is the biochemical basis for this procedure? 2. Intracellular Concentration of Enzymes To approximate the concentration of enzymes in a bacterial cell, assume that the cell contains equal concentrations of 1,000 different enzymes in solution in the cytosol and that each protein has a molecular weight of 100,000. Assume also that the bacterial cell is a cylinder (diameter 1.0 μ m, height 2.0 μ m), that the cytosol (specific gravity 1.20) is 20% soluble protein by weight, and that the soluble protein consists entirely of enzymes. Calculate the average molar concentration of each enzyme in this hypothetical cell. 3. Rate Enhancement by Urease The enzyme urease enhances the rate of urea hydrolysis at pH 8.0 and 20 ∘C by a factor of 1014. Suppose that a given quantity of urease can completely hydrolyze a given quantity of urea in 5.0 min at 20 ∘C and pH 8.0. How long would it take for this amount of urea to be hydrolyzed under the same conditions in the absence of urease? Assume that both reactions take place in sterile systems so that bacteria cannot attack the urea. 4. Protection of an Enzyme against Denaturation by Heat When enzyme solutions are heated, there is a progressive loss of catalytic activity over time due to denaturation of the enzyme. A solution of the enzyme hexokinase incubated at 45 ∘C lost 50% of its activity in 12 min, but when incubated at 45 ∘C in the presence of a very large concentration of one of its substrates, it lost only 3% of its activity in 12 min. Suggest why thermal denaturation of hexokinase was retarded in the presence of one of its substrates. 5. Quantitative Assay for Lactate Dehydrogenase The muscle enzyme lactate dehydrogenase catalyzes the reaction NADH and NAD + are the reduced and oxidized forms, respectively, of the coenzyme NAD. Solutions of NADH, but not NAD +, absorb light at 340 nm. This property is used to determine the concentration of NADH in solution by measuring spectrophotometrically the amount of light absorbed at 340 nm (A340) by the solution. Explain how these properties of NADH can be used to design a quantitative assay for lactate dehydrogenase. 6. Effect of Enzymes on Reactions Consider this simple reaction: S k1 ⇌k2 P where K′eq = [P] [S] Which of the listed effects would be brought about by an enzyme catalyzing the simple reaction? a. increased k1 b. increased K′eq c. decreased ΔG‡ d. more negative ΔG′° e. increased k2 7. Relation between Reaction Velocity and Substrate Concentration: Michaelis-Menten Equation The Km of an enzyme is 5.0 mM. a. Calculate the substrate concentration when this enzyme operates at one-quarter of its maximum rate. b. Determine the fraction of Vmax that would be obtained when the substrate concentration, [S], is 0.5 Km, 2 Km, and 10 Km. c. An enzyme that catalyzes the reaction X⇌ Y is isolated from two bacterial species. The enzymes have the same Vmax but different Km values for the substrate X. Enzyme A has a Km of 2.0 μ M, and enzyme B has a Km of 0.5 μ M. Kinetic experiments used the same concentration of each enzyme and 1 μ M substrate X. The graph plots the concentration of product Y formed over time. Which curve corresponds to which enzyme? 8. Applying the Michaelis-Menten Equation I An enzyme has a Vmax of 1.2 μM  s−1. The Km for its substrate is 10 μ M. Calculate the initial velocity of the reaction, V0, when the substrate concentration is a. 2 μ M b. 10 μ M c. 30 μ M. 9. Applying the Michaelis-Menten Equation II An enzyme is present at a concentration of 1 nM and has a Vmax of 2 μM  s−1. The Km for its primary substrate is 4 μ M. a. Calculate kcat. b. Calculate the apparent (measured) Vmax and apparent (measured) Km of this enzyme in the presence of sufficient amounts of an uncompetitive inhibitor to generate an α′ of 2. Assume that the enzyme concentration remains at 1 nM. 10. Applying the Michaelis-Menten Equation III A research group discovers a new version of happyase, which they call happyase*, that catalyzes the chemical reaction HAPPY ⇌  SAD . The researchers begin to characterize the enzyme. a. In the first experiment, with [Et] at 4 nM, they find that the Vmax is 1.6 μM  s−1. Based on this experiment, what is the kcat for happyase*? (Include appropriate units.) b. In the second experiment, with [Et] at 1 nM and [HAPPY] at 30 μ M, the researchers find that V0= 300 nM  s−1. What is the measured Km of happyase* for its substrate HAPPY? (Include appropriate units.) c. Further research shows that the purified happyase* used in the first two experiments was actually contaminated with a reversible inhibitor called ANGER. When ANGER is carefully removed from the happyase* preparation and the two experiments are repeated, the measured Vmax in (a) is increased to 4.8 μM  s−1, and the measured Km in (b) is now 15 μ M. Calculate the values of α and α′ for ANGER. d. Based on the information given, what type of inhibitor is ANGER? 11. Applying the Michaelis-Menten Equation IV Researchers discover an enzyme that catalyzes the reaction X ⇌  Y. They find that the Km for the substrate X is 4 μ M, and the kcat is 20 min−1. a. In an experiment, [X]= 6 mM , and V0= 480 nM  min−1. What was the [Et] used in the experiment? b. In another experiment, [Et]= 0.5 μM , and the measured V0= 5 μM  min−1. What was the [X] used in the experiment? c. The researchers discover that compound Z is a very strong competitive inhibitor of the enzyme. In an experiment with the same [Et] as in (a), but a different [X], they add an amount of Z that produces an α of 10 and reduces V0 to 240 nM  min−1. What is the [X] in this experiment? d. Based on the kinetic parameters given, has this enzyme evolved to achieve catalytic perfection? Explain your answer briefly, using the kinetic parameter(s) that define catalytic perfection. 12. Estimation of Vmax and Km by Inspection Graphical methods are available for accurate determination of the Vmax and Km of an enzyme-catalyzed reaction. However, these quantities can sometimes be estimated by inspecting values of V0 at increasing [S]. Estimate the Vmax and Km of the enzyme-catalyzed reaction for which the data in the table were obtained. [S] () V0(μM /min) 2.5× 10−6 28 4.0× 10−6 40 1× 10−5 70 2× 10−5 95 4× 10−5 112 1× 10−4 128 2× 10−3 139 1× 10−2 140 13. Properties of an Enzyme of Prostaglandin Synthesis Prostaglandins are one class of the fatty acid derivatives called eicosanoids. Prostaglandins produce fever and inflammation, as well as the pain associated with inflammation. The enzyme prostaglandin endoperoxide synthase, a cyclooxygenase, uses oxygen to convert arachidonic acid to PGG2, the immediate precursor of many different prostaglandins (prostaglandin synthesis is described in Chapter 21). Ibuprofen inhibits prostaglandin endoperoxide synthase, thereby reducing inflammation and pain. The kinetic data given in the table are for the reaction catalyzed by prostaglandin endoperoxide synthase in the absence and presence of ibuprofen. a. Based on the data, determine the Vmax and Km of the enzyme. [Arachidonic acid] (m) Rate of formation of PGG2 (mM   min−1) Rate of formation of PGG2 with 10 mg/mL ibuprofen (mM   min−1) 0.5 23.5 16.67 1.0 32.2 25.25 1.5 36.9 30.49 2.5 41.8 37.04 3.5 44.0 38.91 b. Based on the data, determine the type of inhibition that ibuprofen exerts on prostaglandin endoperoxide synthase. 14. Graphical Analysis of Vmax and Km A kinetic study of an intestinal peptidase using glycylglycine as the substrate produced the experimental data shown in the table. The peptidase catalyzes this reaction: Glycylglycine +  H2O →  2 glycine [S] (m) Product formed (μ mol/min) 1.5 0.21 2.0 0.24 3.0 0.28 4.0 0.33 8.0 0.40 16.0 0.45 Use the Lineweaver-Burk equation to determine the Vmax and Km for this enzyme preparation and substrate. 15. The Eadie-Hofstee Equation There are several ways to transform the Michaelis-Menten equation so as to plot data and derive kinetic parameters, each with different advantages depending on the data set being analyzed. One transformation of the Michaelis-Menten equation is the Lineweaver-Burk, or double-reciprocal, equation. Multiplying both sides of the Lineweaver-Burk equation by Vmax and rearranging gives the Eadie-Hofstee equation: V0= (−Km) + Vmax Consider the plot of V0 versus V0/[S] for an enzyme-catalyzed reaction. The slope of the line is −Km. The x intercept is Vmax/Km. The control reactions (the blue line in the plot) did not contain any inhibitor. a. Which of the other lines (A, B, or C) depicts this enzyme’s activity in the presence of a competitive inhibitor? Hint: See Equation 6-33. b. Which line (A, B, or C) depicts this enzyme’s activity in the presence of an uncompetitive inhibitor? V0 [S] 16. The Turnover Number of Carbonic Anhydrase Carbonic anhydrase of erythrocytes (Mr 30,000) has one of the highest turnover numbers known. It catalyzes the reversible hydration of CO2: H2O + CO2 ⇌  H2CO3 This is an important process in the transport of CO2 from the tissues to the lungs. If 10.0 μg of pure carbonic anhydrase catalyzes the hydration of 0.30 g of CO2 in 1 min at 37 ∘C at Vmax, what is the turnover number (kcat) of carbonic anhydrase (in units of min−1)? 17. Describing Reactions with the Cleland Shorthand The chymotrypsin-catalyzed reaction is diagrammed using the Cleland shorthand. Match the letters in the drawing with each description: a. The product that includes the amino group from the cleaved peptide bond b. The product that includes the carbonyl group from the cleaved peptide bond c. Free chymotrypsin (nothing bound to it) d. Water e. The peptide substrate f. The acyl-enzyme intermediate 18. Kinetic Inhibition Patterns Indicate how the observed Km of an enzyme would change in the presence of inhibitors having the given effect on α and α′: a. α> α′; α′= 1.0 b. α′> α c. α= α′; α′> 1.0 d. α= α′; α′= 1.0 19. Deriving a Rate Equation for Competitive Inhibition The Michaelis-Menten rate equation for an enzyme subject to competitive inhibition is V0= Beginning with a new definition of total enzyme as [Et]= [E]+ [ES]+ [EI] and the definitions of α and KI provided in the text, derive the first rate equation. Use the derivation of the Michaelis- Menten equation as a guide. 20. Irreversible Inhibition of an Enzyme Many enzymes are inhibited irreversibly by heavy metal ions such as Hg2+, Cu2+, or Ag+, which can react with essential sulfhydryl groups to form mercaptides: Enz-SH + Ag+ →  Enz–S–Ag+ H+ The affinity of Ag+ for sulfhydryl groups is so great that Ag+ can be used to titrate —SH groups quantitatively. An investigator added just enough AgNO3 to completely inactivate a 10.0 mL solution containing 1.0 mg/mL enzyme. A total of 0.342 μ mol of AgNO3 was required. Calculate the minimum molecular weight of the enzyme. Why does the Vmax[S] αKm +   [S] value obtained in this way give only the minimum molecular weight? 21. Clinical Application of Differential Enzyme Inhibition Human blood serum contains a class of enzymes known as acid phosphatases, which hydrolyze biological phosphate esters under slightly acidic conditions (pH 5.0): Acid phosphatases are produced by erythrocytes and by the liver, kidney, spleen, and prostate gland. The enzyme of the prostate gland is clinically important, because its increased activity in the blood can be an indication of prostate cancer. The phosphatase from the prostate gland is strongly inhibited by tartrate ion, but acid phosphatases from other tissues are not. How can this information be used to develop a specific procedure for measuring the activity of prostatic acid phosphatase in human blood serum? 22. Inhibition of Carbonic Anhydrase by Acetazolamide Carbonic anhydrase is strongly inhibited by the drug acetazolamide, which is used as a diuretic (i.e., to increase the production of urine) and to lower excessively high pressure in the eye (due to accumulation of intraocular fluid) in glaucoma. Carbonic anhydrase plays an important role in these and other secretory processes because it participates in regulating the pH and bicarbonate content of several body fluids. Carbonic anhydrase activity can be analyzed using the initial reaction velocity (as percentage of Vmax) versus [S]. The black curve of the graph shows the uninhibited activity; the blue curve shows activity in the presence of acetazolamide. Based on the data provided, determine the nature of the inhibition by acetazolamide. Explain your reasoning. 23. The Effects of Reversible Inhibitors The Michaelis- Menten rate equation for reversible mixed inhibition is written as V0= Vmax[S] αKm + α′[S] Apparent, or observed, Km is equivalent to the [S] at which V0= Derive an expression for the effect of a reversible inhibitor on apparent Km from the previous equation. 24. Perturbed pKa Values in Enzyme Active Sites Alanine racemase is a bacterial enzyme that converts L-alanine to D- alanine, which is needed in small amounts to synthesize the bacterial cell wall. The active site of alanine racemase includes a Tyr residue with a pKa value of 7.2. The pKa of free tyrosine is 10. The altered pKa of this residue is due largely to the presence of a nearby charged amino acid residue. Which amino acid(s) could lower the pKa of the neighboring Tyr residue? Explain your reasoning. 25. pH Optimum of Lysozyme The enzyme lysozyme hydrolyzes glycosidic bonds in peptidoglycan, an oligosaccharide found in bacterial cell walls. The active site of lysozyme contains two amino acid residues essential for catalysis: Glu35 and Asp52. The pKa values of the carboxyl side chains of these residues are 5.9 and 4.5, respectively. What is the ionization state (protonated or deprotonated) of each residue at pH 5.2, the pH optimum of lysozyme? How can the ionization states of these residues explain the pH- activity profile of lysozyme shown? Vmax 2α′ DATA ANALYSIS PROBLEM 26. Mirror-Image Enzymes As noted in Chapter 3, “The amino acid residues in protein molecules are almost all L stereoisomers.” It is not clear whether this selectivity is necessary for proper protein function or is an accident of evolution. To explore this question, Milton and colleagues (1992) studied an enzyme made entirely of D stereoisomers. The enzyme they chose was HIV protease, the proteolytic enzyme made by HIV that converts inactive viral pre- proteins to their active forms as described earlier in Figure 6- 28. Previously, Wlodawer and coworkers (1989) had reported the complete chemical synthesis of HIV protease from L-amino acids (the L-enzyme), using the process shown in Figure 3-30. Normal HIV protease contains two Cys residues at positions 67 and 95. Because chemical synthesis of proteins containing Cys is technically difficult, Wlodawer and colleagues substituted the synthetic amino acid L-α -amino-n-butyric acid (Aba) for the two Cys residues in the protein. They did this to “reduce synthetic difficulties associated with Cys deprotection and ease product handling.” a. The structure of Aba is shown below. Why was this a suitable substitution for a Cys residue? In their study, Milton and coworkers synthesized HIV protease from D-amino acids, using the same protocol as the earlier study (Wlodawer et al.). Formally, there are three possible outcomes for the folding of the D- protease: (1) the same shape as the L-protease; (2) the mirror image of the L-protease, or (3) something else, possibly inactive. b. For each possibility, decide whether or not it is a likely outcome and defend your position. In fact, the D-protease was active: it cleaved a particular synthetic substrate and was inhibited by specific inhibitors. To examine the structure of the D- and L-enzymes, Milton and coworkers tested both forms for activity with D and L forms of a chiral peptide substrate and for inhibition by D and L forms of a chiral peptide-analog inhibitor. Both forms were also tested for inhibition by the achiral inhibitor Evans blue. The findings are given in the table. Inhibition Substrate hydrolysis Peptide inhibitor HIV protease form form form form form − + − + form + − + − c. Which of the three models proposed above is supported by these data? Explain your reasoning. d. Would you expect chymotrypsin to digest the D- protease? Explain your reasoning. e. Would you expect total synthesis from D-amino acids followed by renaturation to yield active enzyme for any enzyme? Explain your reasoning. References Milton, R.C., Milton, S.C., and Kent, S.B. 1992. Total chemical synthesis of a D-enzyme: the enantiomers of HIV-1 protease show demonstration of reciprocal chiral substrate specificity. Science 256, 1445–1448. Wlodawer, A., Miller, M., Jaskólski, M., Sathyanarayana, B.K., Baldwin, E., Weber, I.T., Selk, L.M., Clawson, L., Schneider, J., and Kent, S.B. 1989. Conserved folding in retroviral proteases: crystal structure of a synthetic HIV-1 protease. Science 245, 616–621.