8885dc06_190-2371/27/047:13 AM Page200mac76mac76:385 Chapter 6 Enzymes Reaction Ra overall catalytic mechanism. Once a substrate is bound enhancement to an enzyme, properly positioned catalytic functional groups aid in the cleavage and formation of bonds by a CHa-C-OR CHs variety of mechanisms, including general acid-base catalysis, covalent catalysis, and metal ion catalysis CHs-C These are distinct from mechanisms based on binding energy, because they generally involve transient cova- CH3-C-0- lent interaction with a substrate or group transfer to or from a substrate (b) C-OR General Acid-Base Catalysis Many biochemical reactions involve the formation of unstable charged intermedi k(s-1) ates that tend to break down rapidly to their con stituent reactant species, thus impeding the reaction (Fig. 6-8). Charged intermediates can often be stabi- lized by the transfer of protons to or from the substrate (c) or intermediate to form a species that breaks down -OR more readily to products. For nonenzymatic reactions k(s-1) 10M the proton transfers can involve either the constituents of water alone or other weak proton donors or accep- tors. Catalysis of this type that uses only the (HsO or OH ions present in water is referred to as FIGURE 6-7 Rate enhancement by entropy reduction Shown here specific acid-base catalysis. If protons are trans are reactions of an ester with a carboxylate group to form an anhy ferred between the intermediate and water faster than dride. The R group is the same in each case. (a) For this bimolecular the intermediate breaks down to reactants the inter- reaction, the rate constant k is second order, with units of m-Is mediate is effectively stabilized every time it forms. No (b)When the two reacting groups are in a single molecule, the reac. additional catalysis mediated by other proton accep- tion is much faster. For this unimolecular reaction k has units of tors or donors will occur. In many cases, however, Dividing the rate constant for (b) by the rate constant for (a) gives a water is not enough. The term general acid-base rate enhancement of about 105M. (The enhancement has units of mo. catalysis refers to proton transfers mediated by other larity because we are comparing a unimolecular and a bimolecular classes of molecules. For nonenzymatic reactions in reaction)Put another way, if the reactant in(b)were present at a con. aqueous solutions, this occurs only when the unstable centration of 1 M, the reacting groups would behave as though they reaction intermediate breaks down to reactants faste were present at a concentration of 10 M. Note that the reactant in(b) than protons can be transferred to or from water. Many has freedom of rotation about three bonds (shown with curved weak organic acids can supplement water as proton rows), but this still represents a substantial reduction of entropy over donors in this situation, or weak organic bases can (a). If the bonds that rotate in(b)are constrained as in(c), the en- serve as proton acceptors tropy is reduced further and the reaction exhibits a rate enhancement In the active site of an enzyme a number of amino of10° M relative to(a) acid side chains can similarly act as proton donors and acceptors(Fig. 6-9). These groups can be precisely po- sitioned in an enzyme active site to allow proton trans This is referred to as induced fit, a mechanism postu- fers, providing rate enhancements of the order of 10to lated by Daniel Koshland in 1958. Induced fit serves to 10. This type of catalysis occurs on th e vast majority bring specific functional groups on the enzyme into the of enzymes. In fact, proton transfers are the most com- proper position to catalyze the reaction. The conforma- mon biochemical reactions tional change also permits formation of additional weak bonding interactions in the transition state. In either case, Covalent Catalysis In covalent catalysis, a transient co- the new enzyme conformation has enhanced catalytic valent bond is formed between the enzyme and the sub- properties. As we have seen, induced fit is a common fea- strate. Consider the hydrolysis of a bond between ture of the reversible binding of ligands to proteins(Chap- groups A and B ter 5) Induced fit is also important in the interaction of almost every enzyme with its substrate. A-B a+B Specific Catalytic Groups Contribute to Catalysis In the presence of a covalent catalyst(an enzyme with a nucleophilic group X: the reaction becomes In most enzymes, the binding energy used to form the ES complex is just one of several contributors to the A-B+X A-X+B-A+X:+B
This is referred to as induced fit, a mechanism postulated by Daniel Koshland in 1958. 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. Specific Catalytic Groups Contribute to Catalysis In most enzymes, the binding energy used to form the ES complex 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. These are distinct from mechanisms 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 Many biochemical reactions involve the formation of unstable charged intermediates that tend to break down rapidly to their constituent reactant species, thus impeding the reaction (Fig. 6–8). Charged intermediates can often be stabilized by the transfer of protons to or from the substrate or intermediate to form a species that breaks down more readily to products. For nonenzymatic reactions, the proton transfers can involve either the constituents of water alone or other weak proton donors or acceptors. Catalysis of this type that uses only the H (H3O) or OH ions present in water is referred to as specific acid-base catalysis. If protons are transferred between the intermediate and water faster than the intermediate breaks down to reactants, the intermediate is effectively stabilized every time it forms. No additional catalysis mediated by other proton acceptors or donors will occur. In many cases, however, water is not enough. The term general acid-base catalysis refers to proton transfers mediated by other classes of molecules. For nonenzymatic reactions in aqueous solutions, this occurs only when the unstable reaction intermediate breaks down to reactants faster than protons can be transferred to or from water. Many weak organic acids can supplement water as proton donors in this situation, or weak organic bases can serve as proton acceptors. In the active site of an enzyme, a number of amino acid side chains can similarly act as 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. In fact, proton transfers are the most common biochemical reactions. 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: H2O AOB On A B In the presence of a covalent catalyst (an enzyme with a nucleophilic group X:) the reaction becomes H2O AOB X On AOX B On A X B 200 Chapter 6 Enzymes O CH3 C CH3 CH3 OR O CH3 C O k (M1 s1 ) OR C C O O O Reaction Rate enhancement (a) 1 k (s1 ) OR (b) O C C C C 105 M OR O O O O O k (s1 ) OR (c) 108 M C O O C O OR O C O C O O O 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 M1 s 1 . (b) When the two reacting groups are in a single molecule, the reaction is much faster. For this unimolecular reaction, k has units of s1 . 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 and a bimolecular reaction.) Put another way, if the reactant in (b) were present at a concentration of 1 M, 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). 8885d_c06_190-237 1/27/04 7:13 AM Page 200 mac76 mac76:385_reb:
8885dc06_190-2371/27/047:13 AM Page201mac76mac76:385 6.2 How Enzymes Work This alters the pathway of the reaction, and it results in reaction. A number of amino acid side chains, including catalysis only when the new pathway has a lower all those in Figure 6-9, and the functional groups of some activation energy than the uncatalyzed pathway. Both enzyme cofactors can serve as nucleophiles in the of the new steps must be faster than the uncatalyzed 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 H-C-OH Reactant substrate for further reaction in a manner that is usu- ally specific to the particular group or coenzyme. 二1 Metal lon Catalysis Metals, whether tightly bound to the enzyme or taken up from solution along with the sul strate, can participate in catalysis in several ways. Ionic interactions between an enzyme-bound metal and a sub- HC-0-C-0 strate can help orient the substrate for reaction or sta- R2 N-H bilize charged reaction transition states. This use of weak bonding interactions between metal and substrate B is similar to some of the uses of enzyme-substrate bind- HoH HA ing energy described earlier. Metals can also mediate oxidation-reduction reactions by reversible changes in the metal ions oxidation state. Nearly a third of all known enzymes require one or more metal ions for cat HOH HOHI alytic activity When proton transfer ton transfer to or from ho or from H2O is slower Most enzymes employ a combination of several cat than the rate of breakdown alytic strategies to bring about a rate enhancement. a rate of breakdown of intermediates, only a action of the intermediates good example of the use of both covalent catalysis and ormed are stabilized general acid-base catalysis is the reaction catalyzed by The presence of alternative chymotrypsin. The first step is cleavage of a peptide acceptors does not odors(HA)ol increase the rate of (B increases bond, which is accompanied by formation of a covalent the rate of the reaction linkage between a Ser residue on the enzyme and part R RS Amino acid General aci General base form (proton dor (proton acceptor GI R-COOH Lys, Arg R-tNH R-NH2 ys R-S R R-C=CH His HN、∠NH HH R R-OH R-0 GURE 6-8 How a catalyst circumvents unfavorable charge devel- opment during cleavage of an amide. The hydrolysis of an amide bond, 址m○m shown here, is the same reaction as that catalyzed by chymotrypsin and other proteases. Charge development is unfavorable and can be FIGURE 6-9 Amino acids in general acid-base catalysis. Many circumvented by donation of a proton by H3O(specific acid catal- organic reactions are promoted by proton donors (general acids)or ysis) or HA (general acid catalysis), where HA represents any acid. proton acceptors (general bases). The active sites of some enzymes Similarly, charge can be neutralized by proton abstraction by OH contain amino acid functional groups, such as those shown here, that (specific base catalysis)or B:(general base catalysis), where B: rep- can participate in the catalytic process as proton donors or proton resents any base
This alters the pathway of the reaction, and it results in catalysis 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. A number of 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. 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 employ a combination of several catalytic strategies to bring about a rate enhancement. A good example of the use of both covalent catalysis and general acid-base catalysis is the reaction catalyzed by chymotrypsin. The first step is cleavage of a peptide bond, which is accompanied by formation of a covalent linkage between a Ser residue on the enzyme and part 6.2 How Enzymes Work 201 O H C N R4 R1 R2 R3 C Products Without catalysis, unstable (charged) intermediate breaks down rapidly to form reactants. When proton transfer to or from H2O is faster than the rate of breakdown of intermediates, the presence of other proton donors or acceptors does not increase the rate of the reaction. H2OH OH B H C OH O N R4 R1 R2 R3 C H Reactant species H O H O H C N R4 R1 R2 R3 C H H O O A HA B H C R1 R2 R3 O O C HOH HOH N H R4 H H When proton transfer to or from H2O is slower than the rate of breakdown of intermediates, only a fraction of the intermediates formed are stabilized. The presence of alternative proton donors (HA) or acceptors (B ) increases the rate of the reaction. 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. Amino acid residues General acid form (proton donor) General base form (proton acceptor) Glu, Asp Lys, Arg Cys His Ser Tyr R COO H S R R COO R OH R OH O R O N H R R R NH2 H R SH H R C CH HN N C H NH R C CH HN C H FIGURE 6–9 Amino acids in general acid-base catalysis. Many organic reactions 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. 8885d_c06_190-237 1/27/04 7:13 AM Page 201 mac76 mac76:385_reb:
8885ac06_2022/2/042:50 PM Page202mac76mac76:385reb: Chapter 6 Enzymes a Additional catalytic mechanisms employed by Chymotrypsin enzymes include general acid-base catalysis covalent catalysis, and metal ion catalysis Catalysis often involves transient covalent interactions between the substrate and the enzyme, or group transfers to and from the enzyme, so as to provide a new, lower-energy FIGURE 6-10 Covalent and general acid-base catalysis. The first step 6.3 Enzyme Kinetics as an Approach the reaction catalyzed by chymotrypsin is the acylation step. The to Understanding Mechanism roxy group of Ser is the nucleophile in a reaction aided by gen eral base catalysis(the base is the side chain of His57). This provides Biochemists commonly use several approaches to study a new pathway for the hydrolytic cleavage of a peptide bond. Catal- the mechanism of action of purified enzymes. A knowl- ysis occurs only if each step in the new pathway is faster than the un. edge of the three-dimensional structure of the protein catalyzed reaction. The chymotrypsin reaction is described in more provides important information, and the value of struc- tural information is greatly enhanced by classical pro- tein chemistry and modern methods of site-directed of the substrate; the reaction is enhanced by general mutagenesis(changing the amino acid sequence of a base catalysis by other groups on the enzyme (Fig protein by genetic engineering; see Fig. 9-12). These 6-10). The chymotrypsin reaction is described in more technologies permit enzymologists to examine the role detail in section 6.4 of individual amino acids in enzyme structure and ac tion. However, the central approach to studying the SUMMARY 6.2 How Enzymes Work mechanism of an enzyme-catalyzed reaction is to de- termine the rate of the reaction and how it changes in response to changes in experimental parameters, a dis Enzymes are highly effective catalysts cipline known as enzyme kinetics. This is the oldest commonly enhancing reaction rates by a factor of105to1017 approach to understanding enzyme mechanisms and remains the most important. we provide here a basic a Enzyme-catalyzed reactions are characterized introduction to the kinetics of enzyme-catalyzed reac- y the formation of a complex between tions. more advanced treatments are available in the substrate and enzyme (an Es complex) sources cited at the end of the chapter. Substrate binding occurs in a pocket on the enzyme called the active site. Substrate Concentration Affects the Rate a The function of enzymes and other catalysts is of Enzyme-Catalyzed Reactions to lower the activation energy, AG, for a A key factor affecting the rate of a reaction catalyzed reaction and thereby enhance the reaction rate by an enzyme is the concentration of substrate, [ S The equilibrium of a reaction is unaffected by However, studying the effects of substrate concentra the enzyme tion is complicated by the fact that [ s changes during aA significant part of the energy used for the course of an in vitro reaction as substrate is con- enzymatic rate enhancements is derived from verted to product. One simplifying approach in kinetics weak interactions (hydrogen bonds and experiments is to measure the initial rate (or initial hydrophobic and ionic interactions) between velocity), designated Vo, when s] is much greater than substrate and enzyme. The enzyme active site e concentration of enzyme, E. In a typical reaction, is structured so that some of these weak the enzyme may be present in nanomolar quantities interactions occur preferentially in the reaction whereas [S may be five or six orders of magnitude transition state, thus stabilizing the transition higher. If only the beginning of the reaction is monitored state. The need for multiple interactions is one (often the first 60 seconds or less), changes in [ Scan reason for the large size of enzymes. The be limited to a few percent, and s can be regarded as binding energy, AGB, can be used to lower constant. Vo can then be explored as a function of s substrate entropy or to cause a conformational which is adjusted by the investigator. The effect on Vo change in the enzyme (induced fit). Binding of varying [S when the enzyme concentration is held energy also accounts for the exquisite constant is shown in Figure 6-11. At relatively low con- pecificity of enzymes for their substrates centrations of substrate, Vo increases almost linearly
of the substrate; the reaction is enhanced by general base catalysis by other groups on the enzyme (Fig. 6–10). The chymotrypsin reaction is described in more detail 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, G‡ , for a reaction and thereby enhance the reaction rate. The equilibrium of a reaction is unaffected by the enzyme. ■ A significant part of the energy used for enzymatic rate enhancements is derived from weak interactions (hydrogen bonds and hydrophobic and ionic interactions) between substrate and enzyme. The enzyme active site is structured so that some of these weak interactions occur preferentially in the reaction transition state, thus stabilizing the transition state. The need for multiple interactions is one reason for the large size of enzymes. The binding energy, GB, can be used to lower substrate entropy or to cause a conformational change in the enzyme (induced fit). Binding energy also accounts for the exquisite specificity of enzymes for their substrates. ■ Additional catalytic mechanisms employed by enzymes include general acid-base catalysis, covalent catalysis, and metal ion catalysis. Catalysis often involves transient covalent interactions between the substrate and the enzyme, or group transfers to and from the enzyme, so as to provide a new, lower-energy reaction path. 6.3 Enzyme Kinetics as an Approach to Understanding Mechanism Biochemists commonly use several approaches to study the mechanism of action of purified enzymes. A knowledge of the three-dimensional structure of the protein provides important information, and the value of structural information is greatly enhanced by classical protein chemistry and modern methods of site-directed mutagenesis (changing the amino acid sequence of a protein by genetic engineering; see Fig. 9–12). These technologies permit enzymologists to examine the role of individual amino acids in enzyme structure and action. However, the central approach to studying the mechanism of an enzyme-catalyzed reaction is to determine the rate of the reaction and how it changes in response to changes in experimental parameters, a discipline known as enzyme kinetics. This is the oldest approach to understanding enzyme mechanisms and remains the most important. We provide here a basic introduction to the kinetics of enzyme-catalyzed reactions. More advanced treatments are available in the sources cited at the end of the chapter. Substrate Concentration Affects the Rate of Enzyme-Catalyzed Reactions 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 in kinetics experiments is to measure the initial rate (or initial velocity), designated V0, when [S] is much greater than the concentration of enzyme, [E]. 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 (often the first 60 seconds or less), changes in [S] can be limited to a few percent, and [S] can be regarded as constant. V0 can then be explored as a function of [S], which is adjusted by the investigator. The effect on V0 of varying [S] when the enzyme concentration is held constant is shown in Figure 6–11. At relatively low concentrations of substrate, V0 increases almost linearly 202 Chapter 6 Enzymes NH C R1 R2 H N O H C R O 1 R2 O H Chymotrypsin Ser195 B Ser195 B O H FIGURE 6–10 Covalent and general acid-base catalysis. The first step in the reaction catalyzed by chymotrypsin is the acylation step. The hydroxyl group of Ser195 is the nucleophile in a reaction aided by general base catalysis (the base is the side chain of His57). This provides a new pathway for the hydrolytic cleavage of a peptide bond. Catalysis occurs only if each step in the new pathway is faster than the uncatalyzed reaction. The chymotrypsin reaction is described in more detail in Figure 6–21. 8885d_c06_202 2/2/04 2:50 PM Page 202 mac76 mac76:385_reb:
8885dc06_190-2371/27/047:13 AM Page203mac76mac76:385 6.3 Enzyme Kinetics as an Approach to Understanding Mechanism 203 its substrate to form an enzyme-substrate complex in a relatively fast reversible step E+s= ES The ES complex then breaks down in a slower second step to yield the free enzyme and the reaction product P 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 Substrate concentration, [)(mM) that reacts in the second step, that is, Es FIGURE 6-11 Effect of substrate concentration on the initial velo At any given instant in an enzyme-catalyzed reac ity of an enzyme-catalyzed reaction. Vmax is extrapolated from the tion, the enzyme exists in two forms, the free or un- plot, because Vo approaches but never quite reaches Vmax. The sub- combined form E and the combined form ES At low [SI strate concentration at which Vo is half maximal is Km, the Michaelis most of the enzyme is in the uncombined form E. Here, constant. The concentration of enzyme in an experiment such as this the rate is proportional to [S] because the equilibrium is generally so low that [SI>> E) even when (SI is described as low of Equation 6-7 is pushed toward formation of more ES or relatively low. The units shown are typical for enzyme-catalyzed as s] increases. The maximum initial rate of the cat reactions and are given only to help illustrate the meaning of Vo and alyzed reaction (vmax) is observed when virtually all the [].(Note that the curve describes part of a rectangular hyperbola, enzyme is present as the es complex and e is van with one asymptote at Vmax. If the curve were continued below [S] =0, shingly small. Under these conditions, the enzyme is it would approach a vertical asymptote at [S]=-Kmd) saturated" with its substrate so that further increases in S have no effect on rate. This condition exists when with an increase in [S]. At higher substrate concentra- S is sufficiently high that essentially all the free en- tions, Vo increases by smaller and smaller amounts in zyme has been converted to the es form. After the es sponse to increases in [ S]. Finally, a point is reached complex breaks down to yield the product P, the en- beyond which increases in Vo are vanishingly small as zyme is free to catalyze reaction of another molecule of S] increases. This plateau-like Vo region is close to the substrate. The saturation effect is a distinguishing char- maximum velocity, Vmax. acteristic of enzymatic catalysts and is responsible for The Es complex is the key to understanding th the plateau observed in Figure 6-ll. The pattern seen kinetic behavior, just as it was a starting point for our in Figure 6-ll is sometimes referred to as saturation discussion of catalysis. The kinetic pattern in Figure 6-11 kinetics led Victor Henri, following the lead of Wurtz, to propose When the enzyme is first mixed with a large excess in 1903 that the combination of an enzyme with its sub- of substrate, there is an initial period, the pre-steady strate molecule to form an Es complex is a necessary state, during which the concentration of Es builds up step in enzymatic catalysis. This idea was expanded into This period is usually too short to be easily observed a general theory of enzyme action, particularly by lasting just microseconds. The reaction quickly achieves Leonor Michaelis and Maud Menten in 1913. They pos- a steady state in which ES(and the concentrations tulated that the enzyme first combines reversibly with of any other intermediates) remains approximately con- stant over time. The concept of a steady state was in troduced by G. E. Briggs and Haldane in 1925. The measured Vo generally reflects the steady state, even though Vo is limited to the early part of the reaction, and analysis of these initial rates is referred to as teady-state kinetics The Relationship between Substrate Concentration and Reaction Rate Can Be Expressed Quantitatively The curve expressing the relationship between [S and Vo (Fig. 6-11) has the same general shape for most Leonor michaelis Maud Menten enzymes(it approaches a rectangular hyperbola), which 1875-1949 1879-1960 can be expressed algebraically by the Michaelis-Menten
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. 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 6–11 led Victor Henri, following the lead of Wurtz, 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: k1 E S ES (6–7) k1 The ES complex then breaks down in a slower second step to yield the free enzyme and the reaction product P: k2 ES E P (6–8) k2 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. At any given instant in an enzyme-catalyzed reaction, the enzyme exists in two forms, the free or uncombined form E and the combined form ES. 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. After the ES complex breaks down to yield the product P, the enzyme is free to catalyze reaction of another molecule of substrate. The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Figure 6–11. The pattern seen in Figure 6–11 is sometimes referred to as saturation kinetics. When the enzyme is first mixed with a large excess of substrate, there is an initial period, the pre–steady state, during which the concentration of ES builds up. This period is usually too short to be easily observed, lasting just microseconds. The reaction quickly achieves a steady state in which [ES] (and the concentrations of any other intermediates) remains approximately constant over time. The concept of a steady state was introduced by G. E. Briggs and Haldane in 1925. The measured V0 generally reflects the steady state, even though V0 is limited to the early part of the reaction, and analysis of these initial rates is referred to as steady-state kinetics. The Relationship between Substrate Concentration and Reaction Rate Can Be Expressed Quantitatively The curve expressing the relationship between [S] and V0 (Fig. 6–11) has the same general shape for most enzymes (it approaches a rectangular hyperbola), which can be expressed algebraically by the Michaelis-Menten yz yz 6.3 Enzyme Kinetics as an Approach to Understanding Mechanism 203 Initial velocity, V0 ( M/min) Substrate concentration, [S] (mM) Km Vmax 1 2 Vmax FIGURE 6–11 Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction. 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.) Leonor Michaelis, 1875–1949 Maud Menten, 1879–1960 8885d_c06_190-237 1/27/04 7:13 AM Page 203 mac76 mac76:385_reb:
8885dc06190-2371/27/047:13 AM Page204 6mac76:385 Chapter 6 Enzymes equation. Michaelis and Menten derived this equation k1(E]-[ES]S]=k-1ES]+k2ES](6-14) starting from their basic hypothesis that the rate- limiting step in enzymatic reactions is the breakdown Step 3 In a series of algebraic steps, we now solve of the ES complex to product and free enzyme. The Equation 6-14 for ES]. First, the left side is multiplied equation Is out and the right side simplified to give KIEJISJ-K1ESISI=(k-1+k2)ES (6-15) Adding the term k,esis to both sides of the equation The important terms are Sh, vo, Vmax, and a constan and simplifying gives called the Michaelis constant. K. All these terms are kIlEJISJ=(k,S]+k-1+ k2ES (6-16) readily measured experimentally We then solve this equation for Es: Here we develop the basic logic and the algebraic steps in a modern derivation of the Michaelis-Menten klEISI (6-17) equation, which includes the steady-state assumption introduced by Briggs and Haldane. The derivation starts with the two basic steps of the formation and break This can now be simplified further, combining the rate down of ES (Eqns 6-7 and 6-8). Early in the reaction, constants into one expression: the concentration of the product, [PI, is negligible, and ES=ES- (6-18) we make the simplifying assumption that the reverse S+(k2+k_lk action,P-S(described by k-2), can be ignored. This The term(k2+k_1Mk, is defined as the Michaelis assumption is not critical but it simplifies our task. The overall reaction then reduces to constant, Km. Substituting this into Equation 6-18 simplifies the expression to E+S÷Es→→E+P 6-10 ES (6-19) Vo is determined by the breakdown of Es to form prod- Step 4 We can now express Vo in terms of [ES]. Sub- uct, which is determined by Es stituting the right side of Equation 6-19 for ES] in Equa (6-11) tion 6-ll gives Because Es in Equation 6-11 is not easily measured (6-20) experimentally, we must begin by finding an alternative expression for this term. First, we introduce the term This equation can be further simplified. Because the Etl, representing the total enzyme concentration (the maximum velocity occurs when the enzyme is satu- sum of free and substrate-bound enzyme). Free or un- rated(that is, with ES]=[E, D Vmax can be defined as bound enzyme can then be represented by [Et] -[ES]. k2[E Substituting this in Equation 6-20 gives equa- Also, because s is ordinarily far greater than Et, the tion 6-9 amount of substrate bound by the enzyme at any given time is negligible compared with the total s]. with these Vo=Km +is] conditions in mind, the following steps lead us to an ex- pression for vo in terms of easily measurable parameters. This is the Michaelis-Menten equation, the rate equation for a one-substrate enzyme-catalyzed reac- Step I The rates of formation and breakdown of Es tion. It is a statement of the quantitative relationship are determined by the steps governed by the rate con- between the initial velocity Vo, the maximum velocity stants kI(formation) and k-1+ k2(breakdown), ac cording to the expressions Vmax and the initial substrate concentration S, all re- lated through the Michaelis constant Km. Note that K Rate of ES formation=K,(E,] (6-12) has units of concentration. Does the equation fit ex perimental observations? Yes; we can confirm this by Rate of ES breakdown=k_IlES+k2lES] (6-13) considering the limiting situations where [S is very high Step 2 We now make an important assumption: that or very low, as shown in Figure 6-12 the initial rate of reaction reflects a steady state in which An important numerical relationship emerges from ES] is constant-that is, the rate of formation of ES is the Michaelis-Menten equation in the special case when equal to the rate of its breakdown. This is called the Vo is exactly one-half Vmax(Fig. 6-12).Then steady-state assumption. The expressions in equa- tions 6-12 and 6-13 can be equated for the steady state (6-21) giving
equation. Michaelis and Menten derived this equation starting from their basic hypothesis that the ratelimiting step in enzymatic reactions is the breakdown of the ES complex to product and free enzyme. The equation is V0 K V m ma x [ [ S S ] ] (6–9) The important terms are [S], V0, Vmax, and a constant called the Michaelis constant, Km. All these terms 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 introduced by Briggs and Haldane. 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 n S (described by k2), can be ignored. This assumption is not critical but it simplifies our task. The overall reaction then reduces to k1 k2 E S ES On E P (6–10) k1 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 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 k1 k2 (breakdown), according to the expressions Rate of ES formation k1([Et] [ES])[S] (6–12) Rate of ES breakdown k1[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 yz k1([Et] [ES])[S] k1[ES] k2[ES] (6–14) Step 3 In a series of algebraic steps, we now solve Equation 6–14 for [ES]. First, the left side is multiplied out and the right side simplified to give k1[Et][S] k1[ES][S] (k1 k2)[ES] (6–15) Adding the term k1[ES][S] to both sides of the equation and simplifying gives k1[Et][S] (k1[S] k1 k2)[ES] (6–16) We then solve this equation for [ES]: [ES] k1[S k ] 1 [E k t] [S 1 ] k2 (6–17) This can now be simplified further, combining the rate constants into one expression: [ES] (6–18) The term (k2 k1)/k1 is defined as the Michaelis constant, Km. Substituting this into Equation 6–18 simplifies the expression to [ES] K [ m Et ][S [S ] ] (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 K k2 m [E t][ [ S S ] ] (6–20) This equation can be further simplified. Because the maximum velocity occurs when the enzyme is saturated (that is, with [ES] [Et]) Vmax can be defined as k2[Et]. Substituting this in Equation 6–20 gives Equation 6–9: V0 K V m ma x [ [ S S ] ] 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 the Michaelis constant Km. Note that Km has units of concentration. Does the equation fit experimental observations? Yes; we can confirm this by considering the limiting situations where [S] is very high or very low, as shown in Figure 6–12. An important numerical relationship emerges from the Michaelis-Menten equation in the special case when V0 is exactly one-half Vmax (Fig. 6–12). Then Vm 2 ax K V m ma x [ [ S S ] ] (6–21) [Et ][S] [S] (k2 k1)/k1 204 Chapter 6 Enzymes 8885d_c06_190-237 1/27/04 7:13 AM Page 204 mac76 mac76:385_reb: