4. What is the general expression Keq (the equilibrium constant) in terms of product and reactant concentration? tell us about the enzyme.

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1 Section 8 Enzyme Kinetics Pre-Activity Assignment 1. Produce a reading log for the sections in your text that discuss the Michaelis-Menten equation and including kcat. 2. Focus on the derivation of the Michaelis-Menten equation. List and explain the assumptions underlying the Michalis-Menten equation. Provide definitions for each term. 3. What is equal at equilibrium? 4. What is the general expression Keq (the equilibrium constant) in terms of product and reactant concentration? Why Enzymes catalyze most reactions that occur in biological systems and thus control the rates of these reactions. Examining the kinetics of an enzyme catalyzed reaction helps us learn about how enzymes function. In this activity, you will learn about the kinetic parameters that biochemists use to characterize enzymes and the graphical methods that allow biochemists to obtain kinetic parameters from experimental data. Outcomes 1. Be able to articulate and apply what the enzyme parameters of K M, V max, k cat and k cat /K M tell us about the enzyme. 2. Know the Michaelis-Menten rate equation and be able to utilize the rearranged versions of the Michaelis- Menten equation to determine the values for K M and V max. Plan 1. Form enzyme teams. Assign roles of manager, reflector, recorder, spokesperson. 2. Answer the Critical Thinking Questions and solve the Critical Analysis Problem. 3. Pose two questions that your group needs answered concerning the kinetics of enzyme catalyzed reactions. Equation 1 Equation 2 1 V o = k E + S 1 K m V max [S] + 1 V max k 1 ES k 2 E + P Graph 1 Velocity, mm product/min [S]. mm 17

2 Critical Thinking Questions 1. Recall your study of equilibria and kinetics from general chemistry. You used equations with upper case K and lower case k during the study of equilibria and kinetics respectively. What do the upper and lower case letters refer to? 2. Compare your answers from your assignment and take only two minutes. Discuss the assumptions made during the derivation of the Michaelis-Menten equation. Be sure to consider assumptions pertaining to [ES], rate of product formation, [S], and number of substrates per reaction. 3. Solve the Michaelis-Menten equation for K M when V 0 = V max /2. What does this tell you about the relationship between [substrate] and enzymes with high K M values? With low K M values? Make a generalization. 4. What is the K M value as you can estimate it off Graph 1? 5. When k 2 is very small compared to k 1 the K M becomes a K d (or in some textbooks this is called a K S ) for the ES complex. A K d is really an equilibrium constant (K eq ) for a dissociation reaction in which the products are the dissociated form of the reactants. Write the reaction for which this K d equals the K eq for your reaction. Make a generalization about the relationship between K M and enzyme-substrate binding affinity. 18 Foundations of Biochemistry (Selected Activities)

3 6. When k 2 is very small compared to k 1 and k 1, what process is rate determining? 7. Many enzyme-catalyzed processes are multi-step reactions. (a) In a multi-step reaction, what step determines the overall reaction rate? (b) What step in M-M kinetics determines overall reaction rate? (c) The k cat is the overall rate constant for multi-step reactions. Discuss why it makes sense that k cat = k 2 in simple Michaelis-Menten reactions. 8. In simple M-M kinetics, the units of k cat are s 1. Discuss how the units are consistent with the name turnover number. If k cat is large, what does that imply about the enzyme? Section 8 Enzyme Kinetics 19

4 9. Discuss the term catalytic efficiency; what does it mean for an enzyme to be efficient? 10. How is your answer to 9 above consistent with the term for catalytic efficiency (k cat /K m )? Discuss the contribution of the terms k cat and K M to the overall term of catalytic efficiency. 11. Discuss the meaning of enzyme reaction mechanism in the context of catalysis. How does the study of enzyme kinetics relate to reaction mechanism? 12. Review the PLAN outlined previously. Consider the enzymes in the table below and answer the following questions. Answers should be brief (1-3 sentences). Enzyme K M (M) k cat (s -1 ) A B C Which enzyme has the highest affinity for substrate? How do you know? 20 Foundations of Biochemistry (Selected Activities)

5 2. Which enzyme converts the most substrate to product in a given period of time? How do you know? 3. Which enzyme has the highest catalytic efficiency? How do you know? Ser 195 catalytic triad Gly 193 R N H O H O N H C N H N H Cα Cβ N R His 57 O O C Asp 102 A diagram of the enzyme active site for chymotrypsin is shown. The amino acids Gly 193, Ser 195, His 57 and Asp 102 form part of the active site. A portion of a natural peptide substrate from R to R is depicted with the residue phenylalanine occupying the hydrophobic pocket of the enzyme. C 4. Chymotrypsin is a serine protease enzyme. The K M for the reaction of chymotrypsin with N-acetylvaline ethyl ester is M, and the K M for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is M. a) Which substrate has a higher apparent affinity for the enzyme? b) Propose a reason for the difference in affinity based on the shape of each of the substrates (see active site figure, chymotrypsin cleaves on the C-side of aromatic residues). Section 8 Enzyme Kinetics 21

6 c) Which of the substrates is likely to have a higher V max? 22 Foundations of Biochemistry (Selected Activities)