Understanding Enzymes: Essential Catalysts of Life

1. Chap. 6A Enzymes • Introduction to Enzymes • How Enzymes Work • Enzyme Kinetics as an Approach to Understanding Mechanism • Examples of Enzymatic Reactions • Regulatory Enzymes Fig. 6-22. The chymotrypsin enzyme-substrate complex.

2. Intro. to Enzymes All living organisms must be able to self-replicate and catalyze chemical reactions efficiently and selectively. Enzymes (from the Greek enzymos, “leavened”) are the chemical catalysts of biological systems. Enzymes have extraordinary catalytic power, often far greater than that of synthetic or inorganic catalysts. They have a high degree of specificity for their substrates and they accelerate chemical reactions tremendously. They function in aqueous solutions under very mild conditions of temperature and pH, unlike many catalysts used in organic chemistry. Enzymes are central to every biochemical process. They catalyze the hundreds of stepwise reactions of metabolism, conserve and transform chemical energy, and make biological macromolecules from simple precursors. In many diseases, the activity of one or more enzymes is abnormal. Many drugs act via binding to enzymes.

3. Chemical Features of Enzymes (I) With the exception of a small group of catalytically active RNA molecules (Chap. 26), all enzymes are proteins. Their catalytic activity depends on the integrity of their native protein conformation. Some enzymes require no chemical groups for activity other than their amino acid residues. Others require an additional chemical component called a cofactor. Cofactors can be inorganic ions (Table 6-1), or complex organic or metalloorganic molecules called coenzymes (Table 6-2, next slide).

4. Chemical Features of Enzymes (II) Coenzymes usually act as transient carriers of specific functional groups (Table 6-2). Most are derived from vitamins, which are organic nutrients that are required in small amounts in the diet. 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 an enzyme protein is called a prosthetic group. A complete, catalytically active enzyme together with its bound coenzyme and/or metal ion is called a holoenzyme. The protein part of such an enzyme is called the apoenzyme or apoprotein. Many enzymes are modified by phosphorylation or other processes. Modifications often are used to regulate enzyme activity.

5. Enzyme Classification 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. Biochemists by international agreement have adopted a system for naming and classifying enzymes 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. For example the enzyme know commonly as hexokinase is formally ATP:glucose phosphotransferase. Its Enzyme Commission number is 2.7.1.1, in which the first number (2) denotes the class name (transferase); the second number (7), denotes 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.

6. Enzyme Active Sites Under biologically relevant conditions, uncatalyzed reactions tend to be slow because most biological molecules are quite stable in the neutral-pH, mild-temperature, aqueous environment inside cells. Enzymes greatly increase the rates of biological reactions by providing a specific environment within which a reaction can occur more rapidly. Enzyme-catalyzed reactions take place within the confines of a pocket on the enzyme called the active site. The reactant molecule is referred to as the substrate. The surface of the active site is lined with amino acid residues with substituent groups that bind to the substrate and catalyze its chemical transformation. Often, the active site encloses the substrate, sequestering it from solution. The active site of the enzyme chymotrypsin is highlighted in Fig. 6-1.

7. Enzymes Affect Rxn Rates, Not Equilibria (I) Any reaction, such as S  P, can be described by a reaction coordinate diagram, in which the free energy change during the reaction is plotted as a function of the progress of the reaction (Fig. 6-2). The free energy change (∆G’0) (and equilibrium position) of the reaction is determined by the difference in ground state free energies of S and P. The rate of the reaction is dependent on the height of the free energy barrier between S and P. At the top of this hump is the transition state. The transition state is not a chemical species with any significant stability, and should not be confused with a reaction intermediate. Rather it is a fleeting molecular moment in which events such as bond breakage, bond formation, and charge development have proceeded to the point at which decay to either substrate or product is equally likely. The difference between the energy levels of the ground state and the transition state is the activation energy, ∆G‡. The rate of the reaction is inversely and exponentially proportional to the value of ∆G‡.

8. Enzymes Affect Rxn Rates, Not Equilibria (II) Like other catalysts, enzymes enhance reaction rates by lowering activation energies (Fig. 6-3). They have no effect on the position of reaction equilibria. The example shown is for an enzyme which follows the simple enzymatic steps of E + S ⇄ ES ⇄ EP ⇄ E + P. (E-enzyme; S-substrate; P-product; ES-transient complex between the enzyme and substrate; EP-transient complex between the enzyme and product). In the presence of the enzyme, three peaks occur in the reaction coordinate diagram. Whichever peak is the highest signifies the rate-limiting step of the overall reaction. As discussed below, binding energy provided by the interaction of the enzyme with the transition state contributes strongly to lowering the activation energy of the reaction, and accelerating its rate.

9. Relationship Between K’eq and ∆G’0 To describe the free energy changes for reactions, chemists define a standard set of conditions (temperature 298˚K; partial pressure of each gas = 1 atm; concentration of each solute 1 M) and express the free energy change for a reacting system under these conditions as ∆G0, the standard free energy change. Because biochemical systems commonly have H+ concentrations far below 1 M, biochemists define a biochemical standard free energy change, ∆G’0, the standard free energy change at pH 7.0. The equilibrium constant for a reaction (K’eq) under standard biochemical conditions is mathematically linked to the standard free energy change for a reaction, ∆G’0, via the equation ∆G’0 = -2.303 RT log K’eq. In this equation, R is the gas constant, 8.315 J/mol.K, and T is the absolute temperature, 298˚K (25˚C). The numerical values for ∆G’0 as a function of K’eq are tabulated in Table 6-4. Note that a large negative value of ∆G’0 reflects a favorable equilibrium in which the ratio of products to reactants is much greater than 1/1.

10. Relationship Between ∆G‡ and Rxn Rate The rate of a chemical reaction is determined by the concentration of the reactant(s) 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 time--is expressed by a rate equation, V = k[S]. In this reaction, the rate depends only on the concentration of S. This is a first-order reaction. The factor k is a proportionality constant that reflects the probability of a reaction under a given set of conditions (pH, temperature, etc.). Here, k is a first-order rate constant and has the units of reciprocal time (s-1). If a reaction rate depends on the concentration of two different compounds, or if the reaction is between two molecules of the same compound, then 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]. From physical chemistry, it can be derived that the magnitude of a rate constant is inversely and exponentially related to the activation energy, ∆G‡. Thus, a lower activation energy means a faster reaction rate.

11. Catalytic Power and Specificity of Enzymes Enzymes commonly bring about enhancements in reaction rates 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. The rate enhancements observed for enzymes come from two distinct but interwoven parts. First, catalytic functional groups on an enzyme react with a substrate and lower the activation energy barrier for the reactions by providing an alternative, lower-energy reaction path. Second, noncovalent binding interactions between the substrate and enzyme release a small amount of free energy with each interaction that helps lower the energy of the transition state. The energy derived from enzyme-substrate interaction is called the binding energy, ∆GB.

12. Complementary Shapes of Enzymes and Substrates The active site of an enzyme has a surface contour that is complementary in shape to its substrate (and products). This is illustrated for the two substrates of the enzyme dihydrofolate reductase in Fig. 6-4. Structural complementarity is responsible for the high specificity of enzyme reactions. The idea that the enzyme and substrate are complementary to one another was first proposed by the organic chemist, Emil Fisher, in 1894. He stated that the two components fit together like a lock and key. This proposal has greatly influenced the development of biochemistry. However, it is slightly misleading in that precise complementarity between an enzyme and its substrate would be counterproductive to efficient catalysis. Later day biochemical researchers instead realized that the enzyme must be more complementary to the reaction transition state than to the substrate per se for efficient catalysis to occur (next slide).

13. Transition State Complementarity Explains Rate Enhancement (I) The importance of transition state complementarity to rate enhancement can be illustrated using an example of a hypothetical “stickase” which catalyses the breakage of a metal stick, and binds to the sick via magnetic interactions (Fig. 6-5). In the uncatalyzed reaction, (Part a), the stick must first be bent to a transition state structure before being broken. Due to the high activation energy barrier of the bent stick transition state, the overall reaction (which has a negative free energy change) is relatively slow. If the stickase were precisely complementary to the metal bar (Part b), the rate of the reaction would not be improved as the enzyme actually would stabilize the structure of the stick. Under these conditions, the ES complex corresponds to a trough in the reaction coordinate diagram from which the substrate would have difficulty escaping. (Continued on the next slide).

14. Transition State Complementarity Explains Rate Enhancement (II) However, if the stickase were more complementary to the transition state of the reaction (Part c), then the increase in free energy required to draw the stick into a bent and partially broken conformation would be offset, or paid for, by the magnetic interactions (binding energy) between the enzyme and the substrate in its transition state. This energy payment translates into a lower net activation energy and a faster reaction rate.

15. Transition State Complementarity Explains Rate Enhancement (III) Real enzymes work on an analogous principle. Some weak interactions are formed in the ES complex, but the full complement of such interactions between the 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 ∆G‡ and the favorable (negative) binding 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 is a brief point in time that the substrate spends atop an energy hill. The enzyme-catalyzed reaction is much faster than the uncatalyzed process because the hill is much smaller. The important point is that weak binding interactions between the enzyme and the substrate provide a substantial driving force for enzymatic catalysis.

16. Contributions of Binding Energy to Reaction Specificity and Catalysis (I) For a reaction to take place, significant physical and thermodynamic factors contributing to ∆G‡ must be overcome. These include 1) the entropy (freedom of motion) of molecules in solution, which reduces the possibility that they will react together, 2) the solvation shell of hydrogen-bonded water molecules that surrounds and helps to stabilize most biomolecules in 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. All of these factors can be overcome due to the binding energy released on interaction of the enzyme with the transition state, as explained in the next slide. Binding energy also gives an enzyme its specificity, which is the ability of an enzyme to discriminate between its substrate and a competing molecule with a similar structure.

17. Contributions of Binding Energy to Reaction Specificity and Catalysis (II) The mechanism by which binding energy compensates for physical and thermodynamic factors that impede reaction rates are as follows. 1) Entropy reduction: The restriction in the motions of two substrates that are about to react is one benefit of binding them to an enzyme. Binding energy holds the substrates in the proper orientation to react--a substantial contribution to catalysis, because productive collisions between molecules in solution can be exceedingly rare. Studies have shown that constraining the motion of two reactants can produce rate enhancements of many orders of magnitude (Fig. 6-7). 2) Desolvation: Formation of weak bonds between the enzyme and substrate results in the desolvation of the substrate. The removal of bound water molecules from the substrate removes water molecules which otherwise might impede the reaction.

18. Contributions of Binding Energy to Reaction Specificity and Catalysis (III) 3) Substrate distortion: Binding energy involving weak interactions formed only in the reaction transition state helps to compensate thermodynamically for any distortion, primarily electronic redistribution, that the substrate must undergo to react. 4) Catalytic group alignment: Enzymes typically undergo changes in conformation when the substrate binds that are induced by multiple weak interactions with the substrate. The alignment of catalytic functional groups is referred to as induced fit, and it serves to bring specific functional groups on the enzyme into the proper position to catalyze the reaction.

19. Other Contributions to Enzyme Catalysis: 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 slowing 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. Catalysis, such as in organic chemistry reactions, that uses only the H+ or OH- ions present in solution is referred to a specific acid-base catalysis. Proton transfers mediated by weak acids and bases other than water, such as the functional groups in the side-chains of amino acids, is referred to as general-acid base catalysis. Amino acid side-chains that are commonly involved in general acid-base catalysis are listed in Fig. 6-9.

20. Other Contributions to Enzyme Catalysis: 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 the nucleophilic group X:) the reaction becomes 1) A-B + X:  A-X + B 2) A-X + H2O  A + X: This alters the pathway of the reaction, and it results in catalysis if 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 of those in Fig. 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.

21. Other Contributions to Enzyme Catalysis: 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 binding 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 enzymes require one or more metal ions for catalytic activity.

22. Intro to Enzyme Kinetics The oldest approach to understanding enzyme mechanisms, and the one that remains the most important, is to determine the rate of a reaction and how it changes in response to changes in experimental parameters. This is the discipline known as enzyme kinetics. A key factor affecting the rate of a reaction catalyzed by an enzyme is the concentration of substrate, [S]. 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 kinetic experiments is to measure the initial rate (initial velocity), designated V0 (Fig. 6-10). 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] therefore can be limited to a few percent, and [S] can be regarded as constant. V0 then can be examined as a function of [S] which is adjusted using several reactions.

23. Effect of Substrate Concentration on Reaction Rate The effect on V0 of varying [S] when the enzyme concentration is held constant is shown in Fig. 6-11. This is the appearance of a V0 vs [S] kinetic plot for a typical enzyme. 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.

24. The Role of the ES Complex (I) The ES complex is the key to understanding the kinetic behavior of an enzyme. In 1913, Leonor Michaelis and Maud Menten, developed a kinetic equation to explain the behavior of many simple enzymes. Key to the development of their equation, is the assumption that the enzyme first combines with its substrate to form an enzyme-substrate complex in a relatively fast reversible step: k1 E + S ⇄ ES k-1 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 k-2 If the slower second reaction limits the rate of the overall reaction, the overall rate must be proportional to the concentration of the species that reacts in the second step, i.e., 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 E form. Here, the rate is proportional to [S] because the direction of the first equation above is pushed toward formation of more ES as [S] increases. (Continued on the next slide).

25. The Role of the ES Complex (II) The maximum initial rate of the catalyzed reaction (Vmax) is observed when virtually all of the enzyme is present in 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. The saturation effect is a distinguishing characteristic of enzymatic catalysts and is responsible for the plateau observed in Fig. 6-11. The pattern seen in that figure 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, and is not evident in Fig. 6-10. The reaction quickly achieves a steady state in which [ES] remains approximately constant over time. The measured V0 generally reflects the steady state, even though V0 is limited to the early part of the reaction. The analysis of these initial rates is referred to as steady-state kinetics.

26. Derivation of the MM Equation (I) The kinetic curves expressing the relationship between V0 and [S] have the same general shape (a rectangular hyperbola) for most enzymes, which can be expressed algebraically by the MM 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 MM equation is V0 = Vmax[S]/(Km + [S]). All these terms, [S], V0, Vmax, as well as the constant called the Michaelis constant, Km, can be readily measured experimentally. The derivation of the MM equation starts with the two basic steps of the formation and breakdown of ES. Early in the reaction, the concentration of the product [P] is negligible, and a simplifying assumption is made that the reaction P  S (described by k-2) can be ignored. The overall reaction then reduces to k1k2 E + S ⇄ ES  E + P. k-1

27. Derivation of the MM Equation (II) V0 is determined by the breakdown of ES to form product, which is determined by [ES] through the equation V0 = k2[ES]. Because [ES] in the above equation is not easily measured experimentally, an alternative expression for this term must be found. First, the term [Et], representing the total enzyme concentration (the sum of free and substrate-bound enzyme) is introduced. 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 to an expression for V0 in terms of easily measurable parameters.

28. Derivation of the MM Equation (III)

29. Derivation of the MM Equation (IV)

30. Derivation of the MM Equation (V) The MM equation describes the kinetic behavior of a great many enzymes, and all enzymes that exhibit a hyperbolic dependence of V0 on [S] are said to follow Michaelis-Menten kinetics. However the MM equation does not depend on the relatively simple two-step reaction mechanism discussed above. Many enzymes that follow MM kinetics have quite different mechanisms, and enzymes that catalyze reactions with six or eight identifiable steps often exhibit the same steady-state kinetic behavior. Even though the MM equation holds true for many enzymes, both the magnitude and the real meaning of Vmax and Km can differ from one enzyme to another. This is an important limitation of the steady-state approach to enzyme kinetics.

31. Validation of the MM Equation The MM equation can be shown to correctly explain the V0 vs [S] curves of many enzymes by considering limiting situations where [S] is very high or very low (Fig. 6-12). At low [S], Km >> [S] and the [S] term in the denominator of the MM equation becomes insignificant. The equation simplifies to V0 = Vmax[S]/Km and V0 exhibits a linear dependence on [S], as is observed at the left side of V0 vs [S] graphs. At high [S], where [S] >> Km, the Km term in the denominator of the MM equation becomes insignificant and the equation simplifies to V0 = Vmax. This is consistent with the plateau in V0 observed at high [S] in kinetic graphs. An important numerical relationship emerges from the MM equation in the special case when V0 is exactly one-half Vmax. Here Vmax/2 = Vmax[S]/(Km + [S]). On dividing by Vmax, the equation is 1/2 = [S]/(Km + [S]). After solving for Km, we get Km + [S] = 2[S], or Km = [S]. This is a very useful, practical definition of Km. Km is equivalent to the substrate concentration at which V0 is one-half Vmax.

32. Double-reciprocal Plots Because the plot of V0 vs [S] for an enzyme-catalyzed reaction asymptotically approaches the value of Vmax at high [S], it is difficult to accurately determine Vmax (and thereby, Km) from such graphs. The problem is readily solved by converting the Michaelis-Menten kinetic equation to the so-called double-reciprocal equation (Lineweaver-Burk equation) which describes a linear plot from which Vmax and Km can be easily obtained (Box 6-1, Fig. 1). The Lineweaver-Burk equation is derived by first taking the reciprocal of both sides of the Michaelis-Menten equation 1/V0 = (Km + [S])/Vmax[S] Separating the components of the numerator on the right side of the equation gives 1/V0 = Km/Vmax[S] + [S]/Vmax[S] Which simplifies to 1/V0 = Km/Vmax[S] + 1/Vmax. The plot of 1/V0 vs 1/[S] gives a straight line, the y-intercept of which is 1/Vmax and the x-intercept of which is -1/Km.

33. The Meaning of the Km The Km can vary greatly from enzyme to enzyme, and even for different substrates of the same enzyme (Table 6-6). The Km is sometimes used (often inappropriately) as an indicator of the affinity of an enzyme for its substrate. The actual meaning of the Km depends on specific aspects of the reaction mechanism such as the number and relative rates of the individual steps. For example, for a reaction with two steps, Km = (k2 + k-1)/k1. If k2 is actually rate-limiting, then k2 << k-1, and Km reduces to k-1/k1, which is 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. However this scenario often doesn’t apply for an enzyme due to variances in the contributions of individual rate constants to the overall reaction rate. Thus Km cannot always be considered a simple measure of the affinity of an enzyme for its substrate.

34. Information Derived from Vmax The meaning of the quantity Vmax also varies greatly from one enzyme to the next. If an enzyme reacts via the two-step MM mechanism, then Vmax = k2[Et]. However, the number of reaction steps and the identity of the rate-limiting step can vary from enzyme to enzyme. Therefore, it is useful to define a more general rate constant, kcat, to describe the rate constant of the rate limiting step(s) of any enzyme-catalyzed reaction at saturation. With the modification that Vmax = kcat[Et], the MM equation becomes V0 = kcat[Et][S]/(Km + [S]). The constant kcat is a first-order rate constant and hence has the units of reciprocal time (s-1). It is also called the turnover number for the enzyme-catalyzed reaction. 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 listed in Table 6-7.

35. The Specificity Constant (kcat/Km) Together, the parameters kcat and Km can be used to evaluate the catalytic efficiency of an enzyme. The best way to determine the catalytic efficiency of an enzyme is to determine the ratio of kcat/Km for its reaction. This parameter, sometimes called the specificity constant, is the rate constant for the conversion of E + S to E + P. When [S] << Km, the previous MM equation form converts to V0 = (kcat/Km)([Et][S]). V0 in this case depends on the concentration of two reactants, [Et] and [S]. Therefore, this is a second-order rate equation and the constant kcat/Km is a second-order rate constant with the units 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.

36. Bisubstrate Reactions In most enzymatic reactions, two or more different substrate molecules bind to an enzyme and participate in the reaction. The rates of such bisubstrate reactions can also be analyzed by the MM approach (Fig. 6-14, not covered). Reactions with two substrates usually involve transfer of an atom or a functional group from one substrate to the other. These reactions can proceed by several different 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. 6-13a). As noted in the figure, the substrates can bind in a random sequence or in a specific order. 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. 6-13b). In these reactions, a functional group often is transferred from the first substrate to the second.

37. Intro. to Enzyme Inhibition Enzyme inhibitors are molecules that interfere with catalysis, slowing or halting enzymatic reactions. 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 cause pain. The study of enzyme inhibitors also has provided valuable information about enzyme mechanisms and has helped define metabolic pathways. There are two broad classes of enzyme inhibitors: reversible and irreversible inhibitors.

38. Competitive Inhibition (I) One example of reversible enzyme inhibition will be covered: competitive inhibition (Fig. 6-15a). A competitive inhibitor (I) competes with the substrate for binding to the active site of an enzyme. While the inhibitor occupies the active site, it prevents the binding of the substrate to the enzyme and blocks the reaction. Many competitive inhibitors are structurally similar to the substrate and combine with the enzyme to form an EI complex, but without leading to catalysis. Competitive inhibition can be analyzed quantitatively by steady-state kinetics. In the presence of a competitive inhibitor, the MM equation becomes V0 = Vmax[S]/(Km + [S]) Where  = 1 + [I]/KI and KI = [E][I]/[EI]. The experimentally determined variable Km, the Km observed in the presence of the competitive inhibitor, is often called the “apparent” Km.

39. Competitive Inhibition (II) Because a competitive inhibitor binds reversibly to an enzyme, the competition can be biased to favor the substrate simply by adding more substrate to the reaction. When [S] far exceeds [I], the probability that an inhibitor will bind to the enzyme is minimized and the reaction exhibits a normal Vmax. However, the [S] at which V0 = 1/2 Vmax, the apparent Km, increases in the presence of inhibitor by the factor . This affect 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 kinetic plot (Box 6-2. Fig. 1). The equilibrium constant for inhibitor binding, KI, can also be obtained from these plots. Many drugs act by competitively inhibiting enzymes (e.g., ibuprofen and the cyclooxygenase enzymes, COX 1 & 2).

40. Irreversible Inhibition Irreversible inhibitors bind covalently to or destroy a functional group on an enzyme that is essential for the enzyme’s activity. They also can inhibit an enzyme by forming a particularly stable noncovalent association with the enzyme. An example of a irreversible covalent inhibitor of the protease, chymotrypsin, is shown in Fig. 6-16. As we will discuss in the next lecture slide file, chymotrypsin contains a reactive serine residue in its active site that is intimately involved in catalysis of peptide bond cleavage. This serine will react with the inhibitor diisopropylfluorophosphate (DIFP) which modifies the serine residue irreversibly, and thereby inhibits the proteolytic activity of the enzyme. In contrast to ibuprofen, aspirin is a covalent irreversible inhibitor of COX enzymes.

41. Mechanism-based Inactivators A special class of irreversible inhibitors are the mechanism-based (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 into a very reactive compound that combines irreversibly with the enzyme. These inhibitors earn their name because they hijack the normal enzyme reaction mechanism to inactivate the enzyme. Because drugs that serve as mechanism-based inactivators are highly specific for their target enzymes, they often have the advantage of few side effects. An example of a mechanism-based inhibitor that is used in the treatment of the disease, trypanosomiasis, is presented in Box 6-3 (not covered).

42. Transition-state Analogs An irreversible enzyme inhibitor need not bind covalently to an enzyme if noncovalent binding is so tight that the inhibitor dissociates only rarely. Such inhibitors commonly resemble the predicted transition state structure of the reaction and are called transition-state analogs. These compounds bind more tightly to an enzyme than the substrate because they fit into the active site better. For example, transition state analogs designed to inhibit the glycolytic enzyme aldolase bind to that enzyme more than four order of magnitude more tightly than its actual substrates (Fig. 6-17). Observations that such molecules are effectively irreversible inhibitors of enzymes, support the concept that enzyme active sites are most complementary to that of the transition state of the reaction. Lastly, anti-HIV drugs that inhibit the required protease function of the virus are actually transition-state analogs.

43. Enzyme pH-activity Profiles Enzymes have an optimum pH at which their activity is maximal. At higher or lower pH values, their activity declines (Fig. 6-18). This is because ionizable amino acid side-chains that are important for catalysis of the reaction, or maintain the structure of the enzyme, must maintain a certain state of ionization to function properly. The pH range over which an enzyme undergoes changes in activity can provide a clue as to the type of amino acid residue involved in catalysis. A change in activity near pH 7.0, for example, often reflects titration of a His residue. However, the effects of pH on activity must be interpreted cautiously, as in the closely packed environment of a protein, the pKa of an amino acid side-chain can vary significantly from the pKa of the free amino acid in solution. The pH optimum for the activity of an enzyme generally is close to that of the pH of the environment in which the enzyme normally functions. For example, the pH optimum of pepsin, a gastric digestive enzyme, is about 1.6. The pH optimum of the cytoplasmic enzyme, glucose 6-phosphatase, of hepatocytes is about 7.8.