Chapter 13 Enzyme Kinetics

1. Chapter 13Enzyme Kinetics

2. Outline • What characteristic features define enzymes? • Can the rate of an enzyme-catalyzed reaction be defined in a mathematical way? • What equations define the kinetics of enzyme-catalyzed reactions? • What can be learned from the inhibition of enzyme activity? • What is the kinetic behavior of enzymes catalyzing bimolecular reactions? • How can enzymes be so specific? • Are all enzymes proteins? • Is it possible to design an enzyme to catalyze any desired reaction?

3. Virtually All Reactions in Cells Are Mediated by Enzymes • Enzymes catalyze thermodynamically favorable reactions, causing them to proceed at extraordinarily rapid rates • Enzymes provide cells with the ability to exert kinetic control over thermodynamic potentiality • Living systems use enzymes to accelerate and control the rates of vitally important biochemical reactions • Enzymes are the agents of metabolic function

4. 13.1 What Characteristic Features Define Enzymes? • Catalytic power is defined as the ratio of the enzyme-catalyzed rate of a reaction to the uncatalyzed rate • Specificity is the term used to define the selectivity of enzymes for their substrates • Regulation of enzyme activity ensures that the rate of metabolic reactions is appropriate to cellular requirements • Enzyme nomenclature provides a systematic way of naming metabolic reactions • Coenzymes and cofactors are nonprotein components essential to enzyme activity.

5. 13.1 What Characteristic Features Define Enzymes? • Enzymes can accelerate reactions as much as 1021 over uncatalyzed rates • Urease is a good example: • Catalyzed rate: 3x104/sec • Uncatalyzed rate: 3x10 -10/sec • Ratio (catalytic power) is 1x1014

6. Specificity • Enzymes selectively recognize proper substrates over other molecules • Enzymes produce products in very high yields - often much greater than 95% • Specificity is controlled by structure - the unique fit of substrate with enzyme controls the selectivity for substrate and the product that’s formed.

7. 90% yield in each step; 35% over 10 steps

8. Enzyme Nomenclature Provides a Systematic Way of Naming Metabolic Reactions

9. 13.2 Can the Rate of an Enzyme-Catalyzed Reaction Be Defined in a Mathematical Way? • Kinetics is the branch of science concerned with the rates of reactions • Enzyme kinetics seeks to determine the maximum reaction velocity that enzymes can attain and the binding affinities for substrates and inhibitors • Analysis of enzyme rates yields insights into enzyme mechanisms and metabolic pathways • This information can be exploited to control and manipulate the course of metabolic events

10. Several Kinetics Terms to Understand • rate or velocity • rate constant • rate law • order of a reaction • molecularity of a reaction

11. Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics • Consider a reaction of overall stoichiometry as shown: • The rate is proportional to the concentration of A

12. Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics • The simple elementary reaction of A→P is a first-order reaction • Figure 13.4 shows the course of a first-order reaction as a function of time • This is a unimolecular reaction • For a bimolecular reaction, the rate law is: v = k[A][B] • Kinetics cannot prove a reaction mechanism • Kinetics can only rule out various alternative hypotheses because they don’t fit the data

13. The Time-Course of a First-Order Reaction Figure 13.4 Plot of the course of a first-order reaction. The half-time, t1/2 is the time for one-half of the starting amount of A to disappear.

14. Catalysts Lower the Free Energy of Activation for a Reaction • A typical enzyme-catalyzed reaction must pass through a transition state • The transition state sits at the apex of the energy profile in the energy diagram • The reaction rate is proportional to the concentration of reactant molecules with the transition-state energy • This energy barrier is known as the free energy of activation • Decreasing ΔG‡ increases the reaction rate • The activation energy is related to the rate constant by:

15. Catalysts Lower the Free Energy of Activation for a Reaction Energy diagram for a chemical reaction (A→P) and the effects of (a) raising the temperature from T1 to T2, or (b) adding a catalyst.

16. The Transition State Understand the difference between DG and DG‡ • The overall free energy change for a reaction, DG,is related to the equilibrium constant • The free energy of activation for a reaction, DG‡, is related to the rate constant • It is extremely important to appreciate this distinction

17. 13.3 What Equations Define the Kinetics of Enzyme-Catalyzed Reactions? • Simple first-order reactions display a plot of the reaction rate as a function of reactant concentration that is a straight line • Enzyme-catalyzed reactions are more complicated • At low concentrations of the enzyme substrate, the rate is proportional to S, as in a first-order reaction • At higher concentrations of substrate, the enzyme reaction approaches zero-order kinetics • This behavior is a saturation effect

18. As [S] increases, kinetic behavior changes from 1st order to zero-order kinetics Figure 13.7 Substrate saturation curve for an enzyme-catalyzed reaction.

19. The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics Louis Michaelis and Maud Menten's theory • assumes the formation of an enzyme-substrate complex • assumes that the ES complex is in rapid equilibrium with free enzyme • assumes that the breakdown of ES to form products is slower than 1) formation of ES and 2) breakdown of ES to re-form E and S

20. Michaelis-Menten Equation • Derive Michaelis-Menten Equation

21. The Michaelis-Menten equation where and

22. Understanding Km The "kinetic activator constant" • Km is a constant • Km is a constant derived from rate constants • Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S • Small Km means tight binding; high Km means weak binding

23. Understanding Vmax The theoretical maximal velocity • Vmax is a constant • Vmax is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality • To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate • Vmax is asymptotically approached as substrate is increased

24. The dual nature of the Michaelis-Menten equation Combination of 0-order and 1st-order kinetics • When S is low, the equation for rate is 1st order in S • When S is high, the equation for rate is 0-order in S • The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S

25. Table 13.3 gives the Km values for some enzymes and their substrates

26. The Turnover Number Defines the Activity of One Enzyme Molecule A measure of catalytic activity • kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate. • If the M-M model fits, k2 = kcat = Vmax/Et • Values of kcat range from less than 1/sec to many millions per sec

27. The Turnover Number Defines the Activity of One Enzyme Molecule

28. The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme The catalytic efficiency: kcat/KmAn estimate of "how perfect" the enzyme is • kcat/Km is an apparent second-order rate constant • It measures how well the enzyme performs when S is low • The upper limit for kcat/Km is the diffusion limit - the rate at which E and S diffuse together

29. The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme

30. Linear Plots Can Be Derived from the Michaelis-Menten Equation Be able to derive these equations • Lineweaver-Burk: • Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides • Rearrange to obtain the Lineweaver-Burk equation: • A plot of 1/v versus 1/[S] should yield a straight line

31. Linear Plots Can Be Derived from the Michaelis-Menten Equation

32. Linear Plots Can Be Derived from the Michaelis-Menten Equation • Hanes-Woolf: • Begin with Lineweaver-Burk and multiply both sides by [S] to obtain: • Hanes-Woolf is best - why? • Because Hanes-Woolf has smaller and more consistent errors across the plot

33. Linear Plots Can Be Derived from the Michaelis-Menten Equation

34. Enzymatic Activity is Strongly Influenced by pH • Enzyme-substrate recognition and catalysis are greatly dependent on pH • Enzymes have a variety of ionizable side chains that determine its secondary and tertiary structure and also affect events in the active site • The substrate may also have ionizable groups • Enzymes are usually active only over a limited range of pH • The effects of pH may be due to effects on Km or Vmax or both

35. Enzymatic Activity is Strongly Influenced by pH The pH activity profiles of four different enzymes.

36. The Response of Enzymatic Activity to Temperature is Complex • Rates of enzyme-catalyzed reactions generally increase with increasing temperature • However, at temperatures above 50°to 60°C, enzymes typically show a decline in activity • Two effects here: • Enzyme rate typically doubles in rate for ever 10º C as long as the enzyme is stable and active • At higher temperatures, the protein becomes unstable and denaturation occurs

37. The Response of Enzymatic Activity to Temperature is Complex The effect of temperature on enzyme activity.

38. 13.4 What Can Be Learned from the Inhibition of Enzyme Activity? • Enzymes may be inhibited reversibly or irreversibly • Reversible inhibitors may bind at the active site or at some other site • Enzymes may also be inhibited in an irreversible manner • Penicillin is an irreversible suicide inhibitor

39. Reversible Inhibitors May Bind at the Active Site or at Some Other Site

40. Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].

41. Pure Noncompetitive Inhibition – where S and I bind to different sites on the enzyme Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax.

42. Mixed Noncompetitive Inhibition: binding of I by E influences binding of S by E Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I.

43. Uncompetitive Inhibition, where I combines only with E, but not with ES Lineweaver-Burk plot of uncompetitive inhibition. Note that both intercepts change but the slope (Km/Vmax) remains constant in the presence of I.

44. Enzymes Can Be Inhibited Irreversibly Penicillin is an irreversible inhibitor of the enzyme glycoprotein peptidease, which catalyzes an essential step in bacterial cell all synthesis.

45. 13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions? • Enzymes often catalyze reactions involving two (or more) substrates • Bisubstrate reactions may be sequential or single-displacement reactions or double-displacement (ping-pong) reactions • Single-displacement reactions can be of two distinct classes: 1. Random, where either substrate may bind first, followed by the other substrate 2. Ordered, where a leading substrate binds first, followed by the other substrate

46. Conversion of AEB to PEQ is the Rate-Limiting Step in Random, Single-Displacement Reactions In this type of sequential reaction, all possible binary enzyme-substrate and enzyme-product complexes are formed rapidly and reversibly when enzyme is added to a reaction mixture containing A, B, P, and Q.

47. In an Ordered, Single-Displacement Reaction, the Leading Substrate Must Bind First The leading substrate (A) binds first, followed by B. Reaction between A and B occurs in the ternary complex and is usually followed by an ordered release of the products, P and Q.

48. An Alternative way of Portraying the Ordered, Single-Displacement Reaction

49. 13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions? Single-deplacement bisubstrate mechanism.

50. The Double Displacement (Ping-Pong) Reaction Double-Displacement (Ping-Pong) reactions proceed via formation of a covalently modified enzyme intermediate. Reactions conforming to this kinetic pattern are characterized by the fact that the product of the enzyme’s reaction with A (called P in the above scheme) is released prior to reaction of the enzyme with the second substrate, B.