PS#2#Due#10/14/14#In#Class# # # Name:__________________________________#!Bi/Ch!110!Introduction!to!Biochemistry:!Problem!Set!2! Problem 1: Enzyme Kinetics (35 points) Enzymes that exhibit Michaelis-Menten characteristics have a characteristic KM value. These values vary substantially with different enzymes and substrates. We will explore what this KM value means and how it relates to the chemical kinetics. a. What is KM in terms of the rate constants for enzyme complex equilibrium and product formation? (k1, k2, k-1) (2 point) b. Pyruvate carboxylase has three substrates with which it exhibits Michaelis-Menten characteristics. What are they and what are the KM values associated? (5 point) c. Describe what the KM values say about the enzyme. Can you infer some things about the mechanism of how Pyruvate carboxylase works? Think about what KM units are and what they say about the system. (5 points) d. Consider this equation. What happens to the reaction rate when the substrate concentration is high relative to the dissociation constant? (4 points) Reaction Rate = Kcat [Eo] [S] K + [S] e. Consider the following equation. What happens when Kcat is significantly greater than K2? (4 points) Km = K2 + Kcat K1 f. Suppose that doing homework can be considered a reversible reaction described by the equilibrium constant keq. keq Hwo Hwf At MIT, biochemistry students are not very good with their homework so at equilibrium only 3 student in a class of 11 total students has converted their homework (Hwo) to a finished product (Hwf).At Caltech biochemistry students are sharper, so out of 11 students 9 have finished the homework and 2 have not. This finished homework is of a higher quality so it can be considered a distinct product from the Hwf you find at MIT. However in both cases the students’ homework must go through the same transition state. i. What is the ∆G for these two scenarios (in kJ/mol; 3 sig figs)? Comment on whether the reaction is spontaneous in each case. Assume the temperature is 25°C. (5 points) ii. Draw a (qualitative) free energy diagram comparing the energetics of the two reactions. Indicate which corresponds to which reaction, and in each case indicate the activation energy and ∆G. (5 points) iii. Caltech students are a keen bunch, and stir an enzyme called “Googlase” in with their homework in order to speed up the process of converting it to finished product. Indicate on your free energy diagram how Googlase will change the energetics of the reaction. (5 points) Problem 2: Allosteric Enzymes and Competition (39 points) a. Draw the Reaction velocity vs Substrate concentration graphs for Michaelis-Menten and Allosteric Enzymes. (4 points) b. Draw a Lineweaker-Burke plot depicting competitive, non-competitive and uncompetitive inhibition. Describe what is happening to Km and Vmax in each instance. (10 points) c. A competitive inhibitor, an uncompetitive inhibitor, and a noncompetitive inhibitor show different methods for decreasing enzyme activity. (2 points) i. Which of these would be used if the active site of the enzyme was known? ii. Which of these would be used if a site known to alter the shape of the enzyme was known? d. What is the difference between reversible and irreversible inhibition? (2 points) e. There are four types of reversible inhibitors. Identify them and describe their mechanisms of action. (4 points) f. Draw diagrams depicting the inhibitors in action. Include the inhibitor, enzyme, and substrate in these diagrams. (4 points)g. Can any of these inhibitors be overcome by adding more substrate? If so, identify which one(s). (2 point) h. The following kinetic data were obtained for the enzyme “Beaverase” with or without inhibitor. Generate a Lineweaver-Burk plot with the data and calculate Vmax and Km for Beaverase in the presence and absence of inhibitor. Show all work on calculations and include units. (10 points) Substrate concentration (mM) Rate with no inhibitor (mM/s) Rate with inhibitor (mM/s) 1.5 0.212 0.793 2 0.253 0.101 3 0.281 0.117 4 0.325 0.132 8 0.444 0.158 16 0.409 0.182 i. What type of inhibitor was used with Beaverase? (1 point) Problem 3: Enzyme-Substrate Interactions (16 points) a. Binding of a substrate by an enzyme results in a loss of entropy that must be compensated for complex formation to be a favorable reaction. How is this energy barrier overcome? Draw the binding pocket of an enzyme, illustrating potential interactions. (8 points) b. The enzyme aspartase catalyzes the hydrolysis of asparagine to aspartic acid, as follows: Experimental work has show that the enzyme requires a metal ion for its activity, as well as a functional group of pKa 5.0. Draw a mechanism for the reaction, illustrating how each of the components is involved. (8 points)Problem 4: Protein Folding (10 points) a. Observe the following Ramachandran plots for two different proteins. Which types of secondary structures are present in Protein A? In Protein B? Which protein would you expect to have more glycine residues? Explain. (10