《生物化学原理》（英文版）（二）chapter 6 ENZYMES

8885dc061952/2/042:50 PM Page195mac76mac76:385reb 6.2 How Enzymes Work erate the reactions, they organize and control them so action rates are linked to the activation energy, AG.A that much of the energy released is recovered in other basic introduction to these thermodynamic relationships chemical forms and made available to the cell for other is the next step in understanding how enzymes work tasks. The reaction pathway by which sucrose(and other An equilibrium such as S P is described by sugars) is broken down is the primary energy-yieldin equilibrium constant, Keg, or simply K (p. 26).Un pathway for cells, and the enzymes of this pathway al- der the standard conditions used to compare biochem low the reaction sequence to proceed on a biologically ical processes, an equilibrium constant is denoted Ke useful time scale (or k) Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates. A reaction intermediate is From thermodynamics, the relationship between Ke any species on the reaction pathway that has a finite and AG can be described by the expression chemical lifetime (longer than a molecular vibration 10-3 seconds). When the S P reaction is catalyzed △G"°=- RT In k y an enzyme, the Es and EP complexes can be con- where R is the gas constant, 8. 315 J/mol- K, and T'is sidered intermediates, even though S and P are stable the absolute temperature, 298 K(25C) Equation 6-3 chemical species (Eqn 6-1); the Es and EP complexes is developed and discussed in more detail in Chapter 13 occupy valleys in the reaction coordinate diagram(Fig. The important point here is that the equilibrium con 6-3). Additional, less stable chemical intermediates of- stant is directly related to the overall standard free- ten exist in the course of an enzyme-catalyzed reaction. energy change for the reaction ( Table 6-4). A large The interconversion of two sequential reaction inter- negative value for AG reflects a favorable reaction mediates thus constitutes a reaction step. When several equilibrium-but as already noted this does not mear steps occur in a reaction, the overall rate is determined the reaction will proceed at a rapid rate by the step (or steps )with the hignea. In a simple case, centration of the reactant(or reactants)and by a rate The rate of any reaction is determined by the con- the rate-limiting step is the highest-energy point in constant, usually denoted by k. For the unimolecular the diagram for interconversion of S and P In practice, reaction S-P, the rate (or velocity) of the reaction, and for many enzymes several steps may have similar time-is expressed by a rate equation, cts per unit the rate-limiting step can vary with reaction conditions, V--representing the amount of s that activation energies, which means they are all partially (6-4) Activation energies are energy barriers to chemical In this reaction, the rate depends only on the concen- reactions. These barriers are crucial to life itself. The rate tration of s. This is called a first-order reaction. The at which a molecule undergoes a particular reaction factor k is a proportionality constant that reflects the decreases as the activation barrier for that reaction in- probability of reaction under a given set of conditions molecules would revert spontaneously to much simpler rate constant and has units of reciprocal time, such ass y w creases. Without such energy barriers, complex macro- (pH, temperature, and so forth). Here, k is a first-ordo molecular forms, and the complex and highly ordered If a first-order reaction has a rate constant k of 0.03s- structures and metabolic processes of cells could not ex- ist. Over the course of evolution, enzymes have devel- oped lower activation energies selectively for reactions TABLE 6-4 Relationship between Keg and AG that are needed for cell survival Reaction Rates and Equilibria Have Precise 一6 Thermodynamic Definitions 28.5 Reaction equilibria are inextricably linked to the stan- 10 228 dard free-energy change for the reaction, AG, and re- 11.4 *In this chapter, step and intermediate refer to chemical species in 0.0 the reaction pathway of a single enzyme-catalyzed reaction. In the 5.7 context of metabolic pathways involving many enzymes(discussed in 11.4 Part ID), these terms are used somewhat differently. An entire enzy. 10 1 Latic reaction is often 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 an"intermediat ote: The relationship is calculated from AG=-RI In Keg(Eqn 6-3)

erate 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 al￾low the reaction sequence to proceed on a biologically useful 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 seconds). When the S P reaction is catalyzed by an enzyme, the ES and EP complexes can be con￾sidered 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 of￾ten exist in the course of an enzyme-catalyzed reaction. The interconversion of two sequential reaction inter￾mediates 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. Activation energies are energy barriers to chemical reactions. These barriers are crucial to life itself. The rate at which a molecule undergoes a particular reaction decreases as the activation barrier for that reaction in￾creases. Without such energy barriers, complex macro￾molecules would revert spontaneously to much simpler molecular forms, and the complex and highly ordered structures and metabolic processes of cells could not ex￾ist. Over the course of evolution, enzymes have devel￾oped lower activation energies selectively for reactions that are needed for cell survival. Reaction Rates and Equilibria Have Precise Thermodynamic Definitions Reaction equilibria are inextricably linked to the stan￾dard free-energy change for the reaction, G, and re￾zy action rates are linked to the activation energy, G‡ . 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. 26). Un￾der the standard conditions used to compare biochem￾ical processes, an equilibrium constant is denoted K eq (or K): K eq =  [ [ P S] ]  (6–2) From thermodynamics, the relationship between Keq and G can be described by the expression G 
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 con￾stant is directly related to the overall standard free￾energy change for the reaction (Table 6–4). A large negative value for G reflects a favorable reaction equilibrium—but as already noted, this does not mean the reaction will proceed at a rapid rate. The rate of any reaction is determined by the con￾centration of the reactant (or reactants) and by a rate constant, usually denoted by k. For the unimolecular reaction S n P, the rate (or velocity) of the reaction, V—representing the amount of S that reacts per unit time—is expressed by a rate equation: V  k[S] (6–4) In this reaction, the rate depends only on the concen￾tration 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 , zy 6.2 How Enzymes Work 195 *In this chapter, step and intermediate refer to 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 enzy￾matic reaction is often 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 an “intermediate.” K eq G (kJ/mol) 10
6 34.2 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 TABLE 6–4 Note: The relationship is calculated from G 
RT ln K eq (Eqn 6–3). Relationship between K eq and G 8885d_c06_195 2/2/04 2:50 PM Page 195 mac76 mac76:385_reb:

8885dc061962/2/042:50 PM Page196mac76mac76:385reb Chapter 6 Enzymes this may be interpreted(qualitatively) to mean that 3% amino acid side chains, metal ions, and coenzymes). Cat of the available S will be converted to P in I s. A reac- alytic functional groups on an enzyme may form a tran tion with a rate constant of 2.000s will be over in a sient covalent bond with a substrate and activate it for small fraction of a second. If a reaction rate depends reaction, or a group may be transiently transferred from on the concentration of two different compounds, or the substrate to the enzyme. In many cases, these re- if the reaction is between two molecules of the same actions occur only in the enzyme active site. covalent compound, the reaction is second order and k is a interactions between enzymes and substrates lower the second-order rate constant, with units of M s. The activation energy (and thereby accelerate the reaction) rate equation then becomes by providing an alternative, lower-energy reaction path. V=kSS The specific types of rearrangements that occur are de- scribed in section 6.4 From transition-state theory we can derive an expres The second part of the explanation lies in the non- sion that relates the magnitude of a rate constant to the covalent interactions between enzyme and substrate Much of the energy required to lower activation ener gies is derived from weak, noncovalent interactions be- kT -AG+/RT tween substrate and enzyme. What really sets enzymes apart from most other catalysts is the formation of a where k is the Boltzmann constant and h is Planck's specific ES complex. The interaction between substrate constant. The important point here is that the relation- and enzyme in this complex is mediated by the same ship between the rate constant k and the activation en- forces that stabilize protein structure, including hydro- ergy AGt is inverse and exponential In simplified terms gen bonds and hydrophobic and ionic interactions this is the basis for the statement that a lower activa-(Chapter 4). Formation of each weak interaction in the tion energy means a faster reaction rate ES complex is accompanied by release of a small amount Now we turn from what enzymes do te ey of free energy that provides a degree of stability to the interaction. The energy derived from enzyme-substrate interaction is called binding energy, AGB. Its signifi A Few Principles Explain the Catalytic Power cance extends beyond a simple stabilization of the and Specificity of Enzyme enzyme-substrate interaction. Binding energy is a major source of free energy used by enzymes to lower Enzymes are extraordinary catalysts. The rate en- the activation energies of reactions hancements they bring about are in the range of 5 to 17 Two fundamental and interrelated principles pro orders of magnitude(Table 6-5). Enzymes are also very vide a general explanation for how enzymes use nonce- specific, readily discriminating between substrates with valent binding energy quite similar structures. How can these enormous and highly selective rate enhancements be explained? What 1. Much of the catalytic power of enzymes ultimately derived from the free energy released the activation energies for specific reactions? in forming many weak bonds and interactions The answer to these questions has two distinct but between an enzyme and its substrate. This binding interwoven parts. The first lies in the rearrangements energy contributes to specificity as well as to of covalent bonds during an enzyme-catalyzed reaction. catalysis Chemical reactions of many types take place between substrates and enzymes functional groups (specific Weak interactions are optimized in the reaction transition state; enzyme active sites are complementary not to the substrates per se but to TABLE 6-5 Some Rate Enhancements the transition states through which substrates pass Produced by Enzymes as they are converted to products during an enzymatic reaction. Cyclophilin Carbonic anhydrase These themes are critical to an understanding of en- Triose phosphate isomerase zymes, and they now become our primary focus Carboxypeptidase A 10 Phosphoglucomutase 1012 Weak Interactions between Enzyme and Substrate Succinyl-CoA transferase Are Optimized in the Transition State ease How does an enzyme use binding energy to lower the Orotidine monophosphate decarboxylase activation energy for a reaction? Formation of the es complex is not the explanation in itself, although some

this may be interpreted (qualitatively) to mean that 3% of the available S will be converted to P in 1 s. A reac￾tion 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
1 s
1 . The rate equation then becomes V k[S1][S2] (6–5) From transition-state theory we can derive an expres￾sion that relates the magnitude of a rate constant to the activation energy: k k h T e
G‡/RT (6–6) where k is the Boltzmann constant and h is Planck’s constant. The important point here is that the relation￾ship between the rate constant k and the activation en￾ergy G‡ is inverse and exponential. In simplified terms, this is the basis for the statement that a lower activa￾tion energy means a faster reaction rate. 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 en￾hancements 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? The answer to these questions has two distinct but interwoven parts. The first lies in the rearrangements of covalent bonds during an enzyme-catalyzed reaction. Chemical reactions of many types take place between substrates and enzymes’ functional groups (specific amino acid side chains, metal ions, and coenzymes). Cat￾alytic functional groups on an enzyme may form a tran￾sient 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 re￾actions 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. The specific types of rearrangements that occur are de￾scribed in Section 6.4. The second part of the explanation lies in the non￾covalent interactions between enzyme and substrate. Much of the energy required to lower activation ener￾gies is derived from weak, noncovalent interactions be￾tween substrate and enzyme. 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 hydro￾gen bonds and hydrophobic and ionic interactions (Chapter 4). Formation of each weak interaction in the ES complex is accompanied by release of a small amount of free energy that provides a degree of stability to the interaction. The energy derived from enzyme-substrate interaction is called binding energy,
GB. Its signifi￾cance extends beyond a simple stabilization of the enzyme-substrate interaction. Binding energy is a major source of free energy used by enzymes to lower the activation energies of reactions. Two fundamental and interrelated principles pro￾vide a general explanation for how enzymes use nonco￾valent binding energy: 1. Much of the catalytic power of enzymes is ultimately derived from the free energy released in forming many weak bonds and interactions between an enzyme and its substrate. This binding energy contributes to specificity as well as to catalysis. 2. Weak interactions are optimized in the reaction transition state; enzyme active sites are complementary not to the substrates per se but to the transition states through which substrates pass as they are converted to products during an enzymatic reaction. These themes are critical to an understanding of en￾zymes, and they now become our primary focus. Weak Interactions between Enzyme and Substrate Are Optimized in the Transition State How does an enzyme use binding energy to lower the activation energy for a reaction? Formation of the ES complex is not the explanation in itself, although some 196 Chapter 6 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 TABLE 6–5 Some Rate Enhancements Produced by Enzymes 8885d_c06_196 2/2/04 2:50 PM Page 196 mac76 mac76:385_reb:

8885dc06_190-2371/27/047:13 AM Page197mac76mac76:385 6.2 How Enzymes Work 197 of the earliest considerations of enzyme mechanisms be- Consider an imaginary reaction, the breaking of a gan with this idea. Studies on enzyme specificity car- magnetized metal stick. The uncatalyzed reaction is ried out by Emil Fischer led him to propose, in 1894, shown in Figure 6-5a. Let's examine two imaginary that enzymes were structurally complementary to their enzymes--two"stickases-that could catalyze this re- substrates, so that they fit together like a lock and key action, both of which employ magnetic forces as a par (Fig. 6-4). This elegant idea, that a specific(exclusive) adigm for the binding energy used by real enzymes. We interaction between two biological molecules is medi- first design an enzyme perfectly complementary to the ated by molecular surfaces with complementary shapes, substrate (Fig. 6-5b). The active site of this stickase is has greatly influenced the development of biochemistry, a pocket lined with magnets. To react(break), the stick and such interactions lie at the heart of many bio- must reach the transition state of the reaction, but the chemical processes. However, the " lock and key" hy- stick fits so tightly in the active site that it cannot bend pothesis can be misleading when applied to enzymatic because bending would eliminate some of the magnetic atalysis. An enzyme completely complementary to its interactions between stick and enzyme. Such an enzyme substrate would be a very poor enzyme, as we can impedes the reaction, stabilizing the substrate instead emonstrate 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 escap- ing. Such an enzyme would be useless The modern notion of enzymatic catalysis, first pro posed by Michael Polanyi(1921) and Haldane(1930) was elaborated by Linus Pauling in 1946: in order to cat- alyze 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 subset of the possible magnetic in- teractions are used rming the Es complex. The bound substrate must still undergo the increase in free energy needed to reach the transition state. Now, how- ever, 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(bind- ing energy) that form between the enzyme and sub- strate 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 en ergy 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 FIGURE 6-4 Complementary shapes of a substrate and its binding the transition state. The free energy(binding energy) site on an enzyme The enzyme dihydrofolate reductase with its sub- released by the formation of these interactions partially rate NADP+(red), unbound (top) and bound (bottom). Another bound offsets the energy required to reach the top of the en- bstrate te ahydrofolate(yellow), is also visible (PDB ID 1RA2) The ergy hill. The summation of the unfavorable (positive) NADP+binds to a pocket that is complementary to it in shape and activation energy AG and the favorable(negative)bind- onic properties. In reality, the complementarity between protein and ing energy AGB results in a lower net activation energy ligand (in this case substrate) is rarely perfect, as we saw in Chapter (Fig. 6-6). Even on the enzyme, the transition state 5. The interaction of a protein with a ligand often involves changes in is not a stable species but a brief point in time that the conformation of one or both molecules, a process called induced the substrate spends atop an energy hill. The enzyme- fit. This lack of perfect complementarity between enzyme and sub- catalyzed reaction is much faster than the uncatalyzed strate(not evident in this figure)is important to enzymatic catalysis. process, however, because the hill is much smaller. The

of the earliest considerations of enzyme mechanisms be￾gan with this idea. Studies on enzyme specificity car￾ried 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 medi￾ated by molecular surfaces with complementary shapes, has greatly influenced the development of biochemistry, and such interactions lie at the heart of many bio￾chemical processes. However, the “lock and key” hy￾pothesis 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. 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 re￾action, both of which employ magnetic forces as a par￾adigm 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 transition state of the reaction, but the stick fits so tightly in the active site that it cannot bend, because bending would eliminate some of the magnetic interactions between stick and enzyme. 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 escap￾ing. Such an enzyme would be useless. The modern notion of enzymatic catalysis, first pro￾posed by Michael Polanyi (1921) and Haldane (1930), was elaborated by Linus Pauling in 1946: in order to cat￾alyze 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 subset of the possible magnetic in￾teractions 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, how￾ever, 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 (bind￾ing energy) that form between the enzyme and sub￾strate 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 en￾ergy 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 en￾ergy hill. The summation of the unfavorable (positive) activation energy G‡ and the favorable (negative) bind￾ing energy GB 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. The enzyme￾catalyzed reaction is much faster than the uncatalyzed process, however, because the hill is much smaller. The 6.2 How Enzymes Work 197 FIGURE 6–4 Complementary shapes of a substrate and its binding site on an enzyme. The enzyme dihydrofolate reductase with its sub￾strate NADP
(red), unbound (top) and bound (bottom). Another bound substrate, tetrahydrofolate (yellow), is also visible (PDB ID 1RA2). The NADP
binds to a pocket that is complementary to it in shape and ionic properties. In reality, the complementarity between protein and ligand (in this case substrate) is rarely perfect, as we saw in Chapter 5. The interaction of a protein with a ligand often involves changes in the conformation of one or both molecules, a process called induced fit. This lack of perfect complementarity between enzyme and sub￾strate (not evident in this figure) is important to enzymatic catalysis. 8885d_c06_190-237 1/27/04 7:13 AM Page 197 mac76 mac76:385_reb:

8885dc06190-2371/27/047:13 AM Page198mac76mac76:385 Chapter 6 Enzymes (a)No enzyme Substrate Transition state Products (metal stick) (bent stick) broken stick) (b) Enzyme complementary to substrate Magnets (c) Enzyme complementary to transition state 的- E Reaction coordinate FIGURE 6-5 An imaginary enzyme (stickase) designed to catalyze tions compensates for the increase in free energy required to bend the breakage of a metal stick. (a)Before the stick is broken, it must fir: stick. Reaction coordinate diagrams (right) show the energy conse- be bent(the transition state). In both stickase examples, magnetic in- quences of complementarity to substrate versus complementarity to teractions take the place of weak bonding interactions between transition state(EP complexes are omitted). AGM, the difference be. enzyme and substrate. (b) A stickase with a magnet-lined pocket com- tween the transition-state energies of the uncatalyzed and catalyzed plementary in structure to the stick ( the substrate) stabilizes the reactions, is contributed by the magnetic interactions between the stick lbstrate. Bending is impeded by the magnetic attraction between stick and stickase. When the enzyme is complementary to the substrate(b), and stickase. (c) An enzyme with a pocket complementary to the re. the ES complex is more stable and has less free energy in the ground action transition state helps to destabilize the stick, contributing to state than substrate alone. The result is an increase in the activation atalysis of the reaction. The binding energy of the magnetic interac- ene important principle is that weak binding interactions reflects the need for superstructure to keep interacting between the enzyme and the substrate provide a sub- groups properly positioned and to keep the cavity from stantial driving force for enzymatic catalysis. The collapsing groups on the substrate that are involved in these weak interactions can be at some distance from the bonds that Binding Energy Contributes to Reaction Specificity are broken or changed. The weak interactions formed only in the transition state are those that make the pri and Catalysis mary contribution to catalysis Can we demonstrate quantitatively that binding energy The requirement for multiple weak interactions to accounts for the huge rate accelerations brought about drive catalysis is one reason why enzymes (and some by enzymes? Yes. As a point of reference, Equation 6-6 coenzymes)are so large. An enzyme must provide func- allows us to calculate that AG must be lowered by about tional groups for ionic, hydrogen-bond, and other inter- 5.7 kJ/mol to accelerate a first-order reaction by a fac actions, and also must precisely position these groups tor of ten, under conditions commonly found in cells so that binding energy is optimized in the transition The energy available from formation of a single weak in- state. Adequate binding is accomplished most readily by teraction is generally estimated to be 4 to 30 kJ/mol positioning a substrate in a cavity(the active site) where The overall energy available from a number of such in- it is effectively removed from water. The size of proteins teractions is therefore sufficient to lower activation en-

important principle is that weak binding interactions between the enzyme and the substrate provide a sub￾stantial 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 pri￾mary contribution to catalysis. The requirement for multiple weak interactions to drive catalysis is one reason why enzymes (and some coenzymes) are so large. An enzyme must provide func￾tional groups for ionic, hydrogen-bond, and other inter￾actions, 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. Binding Energy Contributes to Reaction Specificity and Catalysis 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 G‡ must be lowered by about 5.7 kJ/mol to accelerate a first-order reaction by a fac￾tor of ten, under conditions commonly found in cells. The energy available from formation of a single weak in￾teraction is generally estimated to be 4 to 30 kJ/mol. The overall energy available from a number of such in￾teractions is therefore sufficient to lower activation en- 198 Chapter 6 Enzymes Free energy, G ∆G‡ Free energy, G ∆GM ‡ S P ‡ S P ES Free energy, G Reaction coordinate ∆G‡ uncat ∆G‡ cat ∆GM ‡ S P ES ‡ ∆G‡ uncat ∆G‡ cat (a) No enzyme Substrate (metal stick) Transition state (bent stick) Products (broken stick) (b) Enzyme complementary to substrate Magnets (c) Enzyme complementary to transition state + ES ES ‡ E P 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 in￾teractions take the place of weak bonding interactions between enzyme and substrate. (b) A stickase with a magnet-lined pocket com￾plementary 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 re￾action transition state helps to destabilize the stick, contributing to catalysis of the reaction. The binding energy of the magnetic interac￾tions compensates for the increase in free energy required to bend the stick. Reaction coordinate diagrams (right) show the energy conse￾quences of complementarity to substrate versus complementarity to transition state (EP complexes are omitted). GM, the difference be￾tween 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. 8885d_c06_190-237 1/27/04 7:13 AM Page 198 mac76 mac76:385_reb:

8885dc06190-2371/27/047:13 AM Page199mac76mac76:385 6.2 How Enzymes Work 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 uncat enzyme-substrate interactions involving the phosphate group on carbon 3 of the substrate. This was determined by a careful comparison of the enzyme-catalyzed reactions with glyceraldehyde 3-phosphate and with glyceraldehyde(no phosphate group at position 3)as substrate Reaction coordinate The general principles outlined above can be illus- trated by a variety of recognized catalytic mechanisms FIGURE 6-6 Role of binding energy in catalysis. To lower the acti. These mechanisms are not mutually exclusive, and a ation energy for a reaction, the system must acquire an amount of given enzyme might incorporate several types in its energy equivalent to the amount by which AG is lowered. Much of overall mechanism of action. For most enzymes, it is dif- this energy comes from binding energy (ACB)contributed by forma- ficult to quantify the contribution of any one catalytic tion of weak noncovalent interactions between substrate and enzyme mechanism to the rate and/or specificity of a particular in the transition state. The role of AGg is analogous to that of AGm in enzyme-catalyzed reaction Figure 6-5 As we have noted, binding energy makes an impor tant and sometimes the dominant contribution to catal- rsis. Consider what needs to occur for a reaction to take ergies by the 60 to 100 kJ/mol required to explain the place. Prominent physical and thermodynamic factors large rate enhancements observed for many enzymes. contributing to AG, the barrier to reaction, might in- The same binding energy that provides energy for clude (1)a reduction in entropy, in the form of de catalysis also gives an enzyme its specificity, the abil- creased freedom of motion of two molecules in solution ity to discriminate between a substrate and a competing (2) the solvation shell of hydrogen-bonded water that molecule. Conceptually, specificity is easy to distinguish surrounds and helps to stabilize most biomolecules in from catalysis, but this distinction is much more difficult aqueous solution; ( 3) the distortion of substrates that to make experimentally, because catalysis and specificity must occur in many reactions; and(4) the need for arise from the same phenomenon. If an enzyme active proper alignment of catalytic functional groups on the site has functional groups arranged optimally to form a enzyme. Binding energy can be used to overcome all variety of weak interactions with a particular substrate these barriers in the transition state, the enzyme will not be able to in- First, a large restriction in the relative motions of teract to the same degree with any other molecule. For wo substrates that are to react, or entropy reduction, example, if the substrate has a hydroxyl group that forms is one obvious benefit of binding them to an enzyme. a hydrogen bond with a specific Glu residue on the en- Binding energy holds the substrates in the proper ori zyme, any molecule lacking a hydroxyl group at that par- entation to react-a substantial contribution to cataly- ticular position will be a poorer substrate for the enzyme. sis, because productive collisions between molecules il ddition, any molecule with an extra functional group solution can be exceedingly rare. Substrates can be pre- for which the enzyme has no pocket or binding site is cisely aligned on the enzyme, with many weak interac likely to be excluded from the enzyme. In general, spec tions between each substrate and strategically located ficity is derived from the formation of many weak in- groups on the enzyme clamping the substrate molecules teractions between the enzyme and its specific substrate into the proper positions. Studies have shown that con molecule straining the motion of two reactants can produce rate The importance of binding energy to catalysis can enhancements of many orders of magnitude(Fig. 6-7 e readily demonstrated. For example, the glycolyti Second formation of weak bonds between substrate enzyme triose phosphate isomerase catalyzes the inter- and enzyme also results in desolvation of the substrate conversion of glyceraldehyde 3-phosphate and dihy Enzyme-substrate interactions replace most or all of the dioxyacetone phosphate hydrogen bonds between the substrate and water Third, binding energy involving weak interactions formed only in the reaction transition state helps to HC-OH compensate thermodynamically for any distortion, pri- HC-OH trios marily electron redistribution, that the substrate must CH2OPo3- phosphate CH,OPo32 undergo to react Finally, the enzyme itself usually undergoes a hange in conformation when the substrate binds, in- duced by multiple weak interactions with the substrate

ergies 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 abil￾ity 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 in￾teract 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 en￾zyme, any molecule lacking a hydroxyl group at that par￾ticular position will be a poorer substrate for the enzyme. In addition, any molecule with an extra functional group for which the enzyme has no pocket or binding site is likely to be excluded from the enzyme. In general, speci￾ficity is derived from the formation of many weak in￾teractions 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 inter￾conversion of glyceraldehyde 3-phosphate and dihy￾droxyacetone 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 a careful comparison of 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 illus￾trated by a variety of recognized catalytic mechanisms. These mechanisms are not mutually exclusive, and a given enzyme might incorporate several types in its overall mechanism of action. For most enzymes, it is dif￾ficult to quantify the contribution of any one catalytic mechanism to the rate and/or specificity of a particular enzyme-catalyzed reaction. As we have noted, binding energy makes an impor￾tant, and sometimes the dominant, contribution to catal￾ysis. Consider what needs to occur for a reaction to take place. Prominent physical and thermodynamic factors contributing to G‡ , the barrier to reaction, might in￾clude (1) a reduction in entropy, in the form of de￾creased freedom of motion of two molecules in solution; (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 holds the substrates in the proper ori￾entation to react—a substantial contribution to cataly￾sis, because productive collisions between molecules in solution can be exceedingly rare. Substrates can be pre￾cisely aligned on the enzyme, with many weak interac￾tions between each substrate and strategically located groups on the enzyme clamping the substrate molecules into the proper positions. Studies have shown that con￾straining the motion of two reactants can produce rate enhancements of many orders of magnitude (Fig. 6–7). Second, formation of weak bonds between substrate and enzyme also results in desolvation of the substrate. Enzyme-substrate interactions replace most or all of the hydrogen bonds between the substrate and water. Third, binding energy involving weak interactions formed only in the reaction transition state helps to compensate thermodynamically for any distortion, pri￾marily electron redistribution, that the substrate must undergo to react. Finally, the enzyme itself usually undergoes a change in conformation when the substrate binds, in￾duced by multiple weak interactions with the substrate. 6.2 How Enzymes Work 199 ‡ Reaction coordinate S P G‡ uncat G‡ cat ‡ ES EP GB Free energy, G FIGURE 6–6 Role of binding energy in catalysis. To lower the acti￾vation energy for a reaction, the system must acquire an amount of energy equivalent to the amount by which G‡ is lowered. Much of this energy comes from binding energy (GB) contributed by forma￾tion of weak noncovalent interactions between substrate and enzyme in the transition state. The role of GB is analogous to that of GM in Figure 6–5. triose phosphate isomerase Glyceraldehyde 3-phosphate HC CH2OPO3 2 CH2OPO3 2 H2C C 1 HC OH 2 3 O Dihydroxyacetone phosphate OH O 8885d_c06_190-237 1/27/04 7:13 AM Page 199 mac76 mac76:385_reb: