Lecture 7: Enzyme Kinetics PDF

BioC 3021 Notes Robert Roon Lecture 7: Enzyme Kinetics Slide 1. Enzyme Kinetics Today we will study enzyme kinetics. We will examine a variety of reaction schemes and mathematical equations to investigate the mechanisms that enzymes use to increase the ra...

BioC 3021 Notes Robert Roon Lecture 7: Enzyme Kinetics Slide 1. Enzyme Kinetics Today we will study enzyme kinetics. We will examine a variety of reaction schemes and mathematical equations to investigate the mechanisms that enzymes use to increase the rates of biochemical reactions. Slide 2. Pathway of an Enzyme Catalyzed Reaction Here we take another look at the figure showing the simplest formulation of enzyme kinetics. We see that an enzyme (E) binds its substrate (S), S being the reacting molecule or reactant, to form an enzyme-substrate complex (ES). A biochemical reaction then takes place in the enzyme-substrate complex. The product (P) is then released, and the enzyme is free to participate in another round of catalysis. Note again that the E at the left and the E at the right of the reaction are identical molecules. Be aware that if this were a real enzyme reaction, there would also be one or more transition states and an enzyme product complex between E + S and E + P. This simplified mechanism is useful in deriving the most basic equation for describing the kinetics of an enzymatic reaction. Slide 3. Enzyme Catalyzed Reaction with Rate Constants This is the same reaction scheme from the previous slide with the addition of rate constants for the four reactions. The reaction of substrate (S) and enzyme (E) to form an ES complex has the rate constant k1. The back reaction for the reversion of ES to E and S has the rate constant k-1. These reactions are generally relatively fast, and the constants are correspondingly large. The breakdown of the ES complex to form E and P has the rate constant k2, and the back reaction of E and P to form ES has the rate constant k-2. 1 BioC 3021 Notes Robert Roon These reactions are generally slower and the constants are relatively small. Slide 4. Initial Rates of Reaction at Various Substrate Concentrations On this figure, we see plots of the concentration of product (P) as a function of the time of an enzyme reaction. The four red lines represent four increasing levels of initial substrate concentration. These lines demonstrate that the rates of product formation increase as the initial substrate concentration is raised. The highest substrate level is demonstrated with the line labeled [S]4. When biologists measure enzyme reactions, they try to determine the rate data shown on the dashed line labeled V0. These data correspond to the initial rate of enzyme activity (V0) for substrate level [S]4. In this experiment, the investigators would determine the value of (V0) with all four substrate concentrations. Slide 5. Plot of Initial Reaction Velocity vs. Substrate Concentration When those initial rates of the enzyme reaction [V0] are plotted against the substrate concentration [S], a hyperbolic plot is obtained. This type of hyperbolic enzymatic response is described by the Michaelis-Menten equation. Slide 6. Leonor Michaelis and Maud Menten Drs. Michaelis and Menten developed a mathematical equation for describing enzyme reactions. Generations of biochemistry students have reveled in the opportunity to learn and apply this fascinating equation. Although these photographs look very very old, you might be interested to know that both of these esteemed researchers were still alive when I was a young man. How time flies! 2 BioC 3021 Notes Robert Roon Slide 7. The Michaelis-Menten Equation The slide shows a kinetic plot for a generic enzyme reaction involving one substrate. The equation corresponding to this plot was derived many years ago by Drs. Michaelis and Menten. The equation tells us that the velocity of an enzyme reaction (V) is equal to the maximum reaction velocity (Vmax) times the substrate concentration (S) divided by the substrate concentration (S) plus the Michaelis Constant (Km). Let us define the terms in this equation a bit more precisely: -V is the observable velocity of the reaction, which tells us how rapidly product (P) is being formed by the reaction. The V is sometimes expressed as ΔP/Δt (change in product concentration per unit time). -Vmax is the fastest reaction rate possible under the given assay conditions (of enzyme concentration, temperature, etc). Like V, Vmax also has the dimensions of change in product concentration per unit time. (If one knows the actual concentration of enzyme present in the experiment, the Vmax can be related to the Turnover Number, which has the units of molar change in product concentration per unit time per mole of enzyme.) -S is the substrate concentration (note that the same S term appears twice in the equation). -Km is the Michaelis Constant, which has the units of concentration. Now let us look at the kinetic plot corresponding to the M-M equation. V is plotted on the ordinate and (S) is plotted on the abscissa. This type of response is referred to as a rectangular hyperbola. 3 BioC 3021 Notes Robert Roon -At low (S), the plot is linear because the M-M equation reduces to V = K (S), which is the equation for a straight line. -At intermediate (S), the plot is curved, and one needs to use the whole M-M equation to describe the rate of reaction. -When (S) = Km, the M-M equation reduces to V = ½ Vmax. We will discuss the relationship between Km and enzyme efficiency below. -At high (S), the M-M equation flattens out and reduces to V = Vmax. When S levels are high, the M-M plot actually approaches a limiting value of Vmax. At high (S), where V approximates Vmax, virtually all of the enzyme active sites are occupied by substrate. The addition of more S would not significantly increase the rate of reaction, because the rate of reaction is limited by the total active sites available; once all the sites are filled, the reaction can go no faster. Slide 8. The Michaelis Constant We are not going to derive the Michaelis-Menten equation, but if we did that, we would find that the Michaelis constant is formed as a composite of three kinetic constants: k1, k-1, and k2. If you are interested in the derivation of the M-M equation, check out your textbook. It turns out that there is a much more concrete meaning for the Michaelis constant. That is, when S = Km, an enzyme reaction is proceeding at 1/2 Vmax. We will confirm this in a few minutes. It also happens that enzymes having a low Km are very efficient at low substrate concentrations, whereas enzymes with a high Km are inefficient at low substrate concentration. The Km values for enzymes can vary from about 10-7 M, which would indicate an 4 BioC 3021 Notes Robert Roon enzyme that was very efficient at low substrate levels, to 10-1 M for an enzyme that was inefficient at low substrate levels. (This is a sort of reversal from the usual pattern of “higher is better or faster” in that the higher the Km value, the less efficient the enzyme is at low substrate levels.) Slide 9. Enzyme Rates at Low Substrate Concentrations At low (S), the M-M plot is linear because the M-M equation reduces to V = K (S), which is the equation for a straight line. (This new equation tells us that the reaction velocity equals some constant times the concentration of S.) The M-M equation reduces to a straight line at low S because, when Km is much greater than (S), the (S) term can be dropped from the denominator of the equation. Therefore, at low S, V = Vmax (S)/Km = K (S). (The new K term is a combination of two constants, Vmax and Km.) Slide 10. Enzyme Rates at High Substrate Concentrations At high (S), the M-M equation simplifies to V = Vmax. The plot approaches the value of Vmax as an asymptote. That is, V would reach Vmax only at infinity, but it comes very close at high (S). For practical purposes, it can be seen that there is virtually no change in the reaction rate once (S) is ten times greater than Km. The M-M equation simplifies to the new equation because, when (S) is much greater than Km, the Km term can be dropped from the equation, and then V = Vmax (S)/(S) = Vmax. At high (S), where V approximates Vmax, virtually all of the enzyme active sites are occupied by substrate. Under those conditions, we say that the enzyme active sites are “saturated” with substrate. Slide 11. Enzyme Rates when Substrate Concentration Equals the Km When (S) = Km, the equation reduces to V = ½ Vmax. If (S) = Km, you can substitute (S) for Km in the denominator of the M-M 5 BioC 3021 Notes Robert Roon equation. Then, V = Vmax (S)/(S) + (S) = Vmax (S)/2(S) = Vmax/2. The Km term gives an indication of how efficient an enzyme is at low [S]. The plot of V0 vs S shows us that an enzyme with a low Km exhibits fast reaction rates at low S concentrations. An enzyme with a high Km has lower reactions rates at low S concentrations, and will only exhibit fast reaction rates at a higher S concentration. Slide 12. Michaelis Constant Values for Some Enzymes Michaelis constants generally vary considerably. Most enzymes exhibit Km values between 1 mM and 1 µM, but some Km’s are as high as 1M. (This latter value is for the enzyme catalase. Generally that would indicate a very inefficient enzyme. However, catalase has a turnover number of 40,000,000, so it can still function efficiently with a poor Km.) Slide 13. Values for Enzyme Turnover Number (Kcat) The turnover number (Kcat) of a reaction is given by the formula Kcat = Vmax/[Et]. The turnover number gives the number of molecules of substrate that can be converted per second per molecule of enzyme (or per enzyme active site for a multi-subunit enzyme). Turnover numbers relate to the molecules of a specific enzyme (not the total protein in a preparation). Unlike specific activity, which increases as an enzyme is purified, the turnover number of an enzyme is an intrinsic property that does not change with purification. Turnover numbers range from a miniscule 0.5 to a whopping 40,000,000. That’s forty million molecules of substrate reacting per second per enzyme active site. Wow! 6 BioC 3021 Notes Robert Roon Slide 14. The Lineweaver-Burk Plot The Lineweaver-Burk plot is an alternative method of plotting kinetic data. The L-B equation can be derived by inverting the M- M equation. That inversion gives the equation: 1/V = 1/Vmax + Km/Vmax[S] (When you use the L-B equation, instead of plotting V vs. S, you would plot 1/V vs. 1/S.) Slide 15. Utility of the Lineweaver-Burk Plot The Lineweaver-Burk plot is shown on this slide. (Remember that we are essentially dealing with the M-M equation turned on its head.) The beauty of this manipulation is that when you now plot 1/V vs. 1/S, you get the equation for a straight line. That is useful experimentally because the data points from an enzyme activity experiment should all fall on that straight line, and it is easy to extrapolate beyond the experimental data by simply placing a straight-edge ruler over the data points and extending the line until it intersects with the 1/(S) axis. We will not burden you with the mathematics, but it is relatively simple to show that the 1/V intercept is equal to 1/Vmax, the 1/(S) intercept is equal to -1/Km, and the slope of the straight line equals Km/Vmax. Slide 16. Inhibitors of Enzyme Activity Inhibitors interfere with enzyme activity. On the surface, it would seem that the world might be better off without enzyme inhibitors. That might be true in certain select circumstances. However, it turns out that there are many beneficial functions of enzyme inhibitors. For example, enzyme inhibitors are useful tools for experimental biologists, since inhibitors function as antibiotics and drugs, and also serve to protect many organisms from predators or 7 BioC 3021 Notes Robert Roon parasites. Enzyme inhibitors have various modes of action that can give us information about how enzymes function. Inhibitors are sometimes classified as reversible or irreversible. The effects of reversible inhibitors can be overcome by various methods, such as removing the inhibitor from the environment or interfering with the inhibition using some chemical agent. On the other hand, once an enzyme is inactivated by an irreversible inhibitor, the enzyme activity cannot be regained even if all of the inhibitor is removed. There are two common classes of reversible inhibitors. Competitive inhibitors generally bind to the active site of an enzyme and compete with the substrate for occupancy of the active site. In contrast, non-competitive inhibitors bind to an enzyme at some place other than the active site, and inhibit by causing the enzyme’s active site to change. Slide 17. Competitive vs. Non-Competitive Inhibition This slide differentiates between two types of reversible inhibitors. In the left panel, we see a normal catalytic interaction between substrate and the complimentary active site on the enzyme. The middle panel illustrates competitive reversible inhibition. The inhibitor molecule has some structural similarities with the substrate, and can bind to the enzyme’s active site. When the inhibitor is bound to the active site, the substrate cannot bind, and the catalytic activity of the enzyme is reduced. However, if the inhibitor leaves the active site, then the substrate can occupy the site and catalysis occurs. If the substrate concentration is raised to higher and higher levels, there is an increased probability that substrate will out compete the inhibitor for occupancy of the active site. At very high substrate levels, the effect of inhibitor can be almost totally overcome. Conversely, raising the inhibitor concentration to higher and higher levels decreases the probability 8 BioC 3021 Notes Robert Roon that substrate will bind, and at very high inhibitor levels, there is almost no observable enzyme activity. So with competitive inhibition, the ratio of inhibitor concentration to substrate concentration determines the degree of enzyme activity. The panel on the right illustrates the function of a reversible non- competitive inhibitor. The inhibitor site is spatially removed from the active site, and inhibitory effects are transmitted through the protein complex from the inhibitor site to the catalytic site. An effect like this, which is transmitted through a protein from one site to another, is referred to as an allosteric effect. The net result is a change in the geometry of the active site, which results in a loss of activity. Because the inhibitor and substrate need not resemble each other and they bind to different sites on the enzyme, there is no direct competition for binding. So, raising the substrate concentration does not decrease the probability that inhibitor will bind. Slide 18. Substrate Binding to an Active Site There is a geometric and chemical complimentarity between an enzyme and its substrate. Slide 19. A Competitive Inhibitor Binds to an Active Site Competitive inhibitors often look like an enzyme’s substrate (or one of its transition state intermediates), and they inhibit the enzyme by competing for occupancy of the active site. Slide 20. Competitive Inhibitors Vie with the Substrate for Occupancy of the Active Site With competitive inhibition, the substrate and the inhibitor bind reversibly to the same active site. The relative occupancy of the site depends on the concentration of substrate and inhibitor, and on the relative affinities of the two compounds for the active site. 9 BioC 3021 Notes Robert Roon Slide 21. Basis for Competitive inhibition Competitive inhibitors slow reaction rates by occupying the active site of an enzyme and preventing the substrate from binding. When present in high concentrations, the substrate always is the first to occupy a vacant active site, and the competitive inhibitor never gets a chance to bind. Thus, the effect of the competitive inhibitor is overcome, and maximum expression of enzyme activity occurs. That means the Vmax will be unchanged in the presence of a competitive inhibitor, but it will take higher levels of substrate to approach Vmax. Slide 22. Competitive Inhibitor Example Methotrexate is a competitive inhibitor that resembles the cofactor dihydrofolate, and it inhibits enzymes that use dihydrofolate as a cofactor. Methotrexate is used in chemotherapy treatment of a number of types of cancer. Slide 23. Michaelis-Menten Kinetics for Competitive Inhibition Competitive inhibitors bind reversibly to the active site of an enzyme, and they can be displaced by the substrate. Thus, competitive inhibition can be completely overcome by increasing the substrate concentration to high levels. The Michaelis-Menten plots of increasing inhibitor levels suggest that at high substrate levels, the inhibited reactions will eventually reach the same Vmax as the uninhibited reaction. Slide 24. Lineweaver-Burk Plots in the Absence and Presence of a Competitive Inhibitor Competitive inhibitors raise the apparent Km but do not affect the Vmax. This is demonstrated when Lineweaver-Burk plots are determined in the absence and presence of a competitive inhibitor. The 1/V intercept remains the same in the absence or presence of the inhibitor, indicating that the Vmax does not change. The 1/[S] 10 BioC 3021 Notes Robert Roon intercept (which gives -1/Km) becomes less negative, indicating that the apparent Km increases in the presence of a competitive inhibitor. (NB. Remember that this is a double reciprocal plot, so the inhibited reaction plot is higher than the uninhibited reaction plot. You might have to know that on an exam.) Slide 25. Lineweaver-Burk Plots with Two Different Concentrations of a Competitive Inhibitor Here, we see that the uninhibited reaction plot and the reaction plots for two levels of inhibitor all intersect the X-axis at the same place, indicating that 1/Vmax (and thus Vmax) remains constant. In contrast, the minus 1/Km intercept gets smaller with increasing competitive inhibitor levels, indicating that the Km is getting larger. Slide 26. A Noncompetitive Inhibitor Binds Away from the Active Site Noncompetitive inhibitors do not look like the substrate and generally bind to an enzyme away from the active site. Noncompetitive inhibitors cause an allosteric effect that is transmitted through the protein structure, changing the active site so that the substrate does not fit and/or does not react. Slide 27. Michaelis-Menten Kinetics with a Noncompetitive Inhibitor With noncompetitive inhibition, the substrate can still bind, but the ESI complex does not proceed to form the product. A Mayo Clinic 6/6/11 4:50 PM noncompetitive inhibitor does not compete with substrate for the Comment: Is this supposed to be E-S complex? same binding site, and thus is not displaced by the substrate. Because of this, non-competitive inhibition is not overcome by increasing the substrate concentration to high levels. The Michaelis-Menten plots of increasing inhibitor levels show that at high substrate levels, the inhibited reactions will never reach the same Vmax as the uninhibited reaction. 11 BioC 3021 Notes Robert Roon Slide 28. Lineweaver-Burk Plots in the Absence and Presence of a Noncompetitive Inhibitor Noncompetitive inhibitors do not change the apparent Km, but they do decrease the Vmax. This is demonstrated when Lineweaver- Burk plots are determined in the absence and presence of a competitive inhibitor. The 1/V intercept (equal to 1/Vmax) is increased in the presence of the inhibitor, indicating that the Vmax is lower. The 1/[S] intercept (which gives -1/Km) is unchanged, indicating that the apparent Km is not altered in the presence of a noncompetitive inhibitor. (NB. Again, remember that this is a double reciprocal plot, so the inhibited reaction plot is higher than the uninhibited reaction plot. You might have to know that on an exam.) Slide 29. Lineweaver-Burk Plots with Two Different Concentrations of a Noncompetitive Inhibitor Here, we see the uninhibited reaction plot and the reaction plots for two levels of noncompetitive inhibitor. Each plot intersects the X- axis at a different place, indicating that 1/Vmax (and thus Vmax) is changed in the presence of the inhibitor. The fact that the 1/Vmax value increases with increasing inhibitor concentration indicates that the Vmax is decreasing. In contrast, the minus 1/Km intercept does not change with increasing noncompetitive inhibitor levels, indicating that the Km is constant. Slide 30. Review of Reversible Inhibition Kinetics A competitive inhibitor: -binds to the active site of the enzyme -competes with the substrate for binding to E -raises the apparent Km -does not affect the Vmax A noncompetitive inhibitor -does not bind to the active site of the enzyme -does not compete directly with the substrate for binding to E 12 BioC 3021 Notes Robert Roon -does not raise the apparent Km -does lower the Vmax Slide 31. Irreversible Inhibitors Irreversible inhibitors covalently modify a protein in such a way that the inhibition cannot be easily reversed. These inhibitors contain reactive functional groups that react with protein R-groups to form covalent products. The R-groups that are modified frequently contain nucleophilic elements such as hydroxyl or sulfhydryl groups. The inhibitors are generally specific for one class of enzyme and do not inactivate all proteins. The inhibitors often modify R-groups in the active site of enzymes. Slide 32. The Irreversible Inhibitor TPCK Reacts with the Active Site of Chymotrypsin Irreversible inhibitors generally stick to an enzyme covalently and cannot be easily removed from the enzyme by mild techniques such as dialysis. The irreversible inhibitor, TPCK, is an analog of the natural substrates for the enzyme chymotrypsin. Slide 33. TPCK is an Affinity Labeling Reagent TPCK is an example of an irreversible inhibitor that is also an affinity label (reactive substrate analog). It binds at the active site of chymotrypsin and then reacts irreversibly with a histidine residue in the active site of the enzyme. Slide 34. The Irreversible Inhibitor DIFP Reacts with the Active Site of Chymotrypsin and Acetylcholinesterase DIFP is a group specific irreversible inhibitor. It specifically modifies unusually active serine residues in the active sites of serine proteases such as chymotrypsin, and it also modifies the active site serine residue of acetylcholinesterase. Slide 35. The Irreversible Inhibitor Iodoacetamide Reacts with the Active Site of Cysteine Proteases 13 BioC 3021 Notes Robert Roon The irreversible inhibitor, iodoacetamide, exhibits a similar ability to react with activated cysteine residues in the active sites of various enzymes. The acetamide portion of the inhibitor molecule forms a covalent bond with the sulfur atom in the active site of these enzymes. 14