1 Chemistry 4011/8011 Monday, December 18, 2006 (Final) Exam 3 Please do not open or sign this packet until you are instructed to do so. Please write all of your answers for this exam in this exam packet. Although you may use as many blue books for scratch work as you would like, the blue books will not be collected at the end of the exam or graded. Answer each question in the space provided if you can, but feel free to continue your answer on the back of the page if you need more room. (Please write a note by your answer pointing us to the continuation if you do this.) You will be given 2 hours total to finish the exam. This exam contains two problems, which are split into parts. Do not get stuck on one part and then assume that you will be unable to answer the rest of the question—move on. In addition, partial credit will be given for incorrect but plausible or consistent answers, so guess on problems you cannot answer perfectly. At the end of the 2-hour exam period you will be asked to return your exam to the proctor. (You may, of course, also turn the packet in earlier if you choose.) This exam is open-resource—you may use any books, notes, calculator, etc. you have brought with you to the exam. However, you are not allowed to communicate with anyone during the exam, or to bring any materials in or out of the room while you are taking the exam. You are also not allowed to use any devices that could be used to communicate with anyone (laptop computers, cellphones, etc.). Please do not take any part of the exam packet with you when you are done; everything will be returned to you after the exams are graded. This packet should contain 11 pages, including this one. Please check to make sure that your packet contains 11 pages before beginning your exam. Name: __________________________________________________ Signature: __________________________________________________ Helpful constants to know for this exam: Boltzmann’s constant: kB = 2.94 × 10-24 cal K-1 = 1.38 × 10-23 J K-1 Gas constant: R = 1.99 cal K-1 mol-1 = 8.314 J K-1 mol-1 Planck’s constant: h = 1.58 × 10-34 cal s = 6.626 × 10-34 J s e = 2.718 1 J = 1 N⋅m = 1 kg m2 s-22 1. (60 pts total) Chorismate mutase is an enzyme that catalyzes the transformation of chorismate (1) to prephenate (2). CO2-OHO CO2--O2COHOCO2-chorismatemutase12 The concerted mechanism shown above occurs only when the substituents of 1 are in a “diaxial” conformation.1 Computational studies predict that this is not the ground-state conformation of 1, and that flipping the ring substituents from 1dieq to 1diax costs 6 kcal/mol. HHOHOHHHOO-O2CCO2--O2CCO2-1dieq(diequatorial)1diax(diaxial)HHOHO-O2CCO2-‡chairtransitionstate2ΔGeq =6 kcal/molTS‡ Although this is definitely the mechanism of the uncatalyzed reaction, it is not clear whether the enzyme-catalyzed reaction occurs by this same mechanism, or if it does, whether the enzyme specifically stabilizes the transition state (TS‡) more than it stabilizes 1diax. An X-ray crystal structure of the chorismate mutase enzyme bound to inhibitor 3 (structurally similar to 1diax and TS‡)2 shows a number of specific H-bonding and electrostatic interactions, illustrated in the diagram on the right. The crystal structure also makes it clear that the diequatorial conformation 1dieq would not be able to fit in the enzyme active site. Given this information, this problem explores the catalytic mechanism of chorismate mutase. 1 Copley, S. D.; Knowles, J. R. J. Am. Chem. Soc. 1985, 107, 5306. 2 From B. subtilis. Chook, Y. M.; Ke, H.; Lipscomb, W. N. Proc. Natl. Acad. Sci USA 1993, 90, 8600. 3HHOOCO2-HOONH2NH2HNH2NNH2HNOOHArg7Arg90Glu78from crystal structure,chorismate mutase3 a. (15 pts) For parts (a-c) of this problem, assume that chorismate mutase catalyzes the same concerted reaction mechanism observed in the uncatalyzed reaction, and that the enzyme binds 1diax and TS‡ with the same affinity (ΔG). Draw a potential energy diagram that illustrates • The energy profile of the uncatalyzed reaction; • The overall activation energy of the uncatalyzed reaction (ΔG‡overall,uncat); • The energy profile of the enzyme-catalyzed reaction; • The overall activation energy of the enzyme-catalyzed reaction (ΔG‡overall,cat). . Label each ground state in your diagram with an abbreviation that describes its chemical state. (E.g., “E•1diax” would be the complex of the enzyme with 1diax.) Also label the rate-determining transition states for the uncatalyzed (TS‡) and catalyzed (E•TS‡) reactions. E reaction coordinate4 b. (5 pts) In the scenario you drew on the previous page, what is the maximum value of koverall,cat/koverall,uncat? Assume T = 298 K. Calculations (for partial credit if answer above is incorrect): c. (5 pts) Given the reaction profiles you drew in part (a), what would be the effect of the enzyme on ΔH‡ and ΔS‡ for the overall reaction? ΔH‡overall,cat - ΔH‡overall,uncat 0 >, < or = ΔS‡overall,cat - ΔS‡overall,uncat 0 >, < or = (koverall,cat/koverall,uncat)max =5 Hilvert and coworkers have demonstrated that amino acid 90 in chorismate mutase (shown in the diagram on page 2) must be a cationic residue; enzymes that have lysine instead of arginine at this position are still active, but other amino acids at this position give inactive enzyme, even when they are H-bond donors.3 This observation suggests an alternative, two-step mechanism for the enzyme-catalyzed reaction in which C-O bond-breaking (to form a cation-stabilized enolate) and C-C bond-making occur in separate steps: HHOO-O2CCO2-OONH2NH2HNH2NNH2HNArg7Arg90Glu78H1diaxHHOO-O2CCO2-OONH2NH2HNH2NNH2HNArg7Arg90Glu78HINT2 To test this hypothesis (and others), the Hilvert group measured kinetic isotope effects for a number of heavy atoms in 1.4 77kk-O18-O16 11kk-C13-C12 99-C13-C12kk enzyme-catalyzed 1.045 1.0043 1.0129 uncatalyzed 1.0482 1.0118 1.0154 d. (15 pts) Clearly, the largest isotope effect the group observed was k16O/k18O at oxygen 7. What is the largest value of k16O/k18O one would expect to see for this substitution? In your calculation, use νstretch(12C – 16O) = 1000 cm-1. Assume T = 298 K. Answer on the next page. 3 Kast, P.; Grisostomi, C.; Chen, I. A.; Li, S.; Krengel, U.; Xue, Y.; Hilvert, D. J. Biol. Chem. 2000, 275, 36832. 4 Wright, S. K.; DeClue, M. S.; Mandal, A.; Lee,