1. For the following reaction, at equilibrium [S] = 5 mm, [P] = 0.5 mm, and k f = 10 s -1. k f

Transcription

1 1. For the following reaction, at equilibrium [S] = 5 mm, [P] = 0.5 mm, and k f = 10 s -1. S k f k r P a) Calculate K eq (the equilibrium constant) and k r. b) A catalyst increases k f by a factor of Calculate K eq and k r for these conditions. c) Draw a reaction coordinate diagram that includes both the uncatalyzed and catalyzed reactions. 2. Shown below is the Michealis-Menton plot for the reaction of 0.1 nm enzyme with its substrate. Use this plot to determine numerical values (with units) for k cat and K M. k cat = 3. Schistosomiasis is second only to malaria in a ranking of the most socio-economically devastating parasistic diseases. You are studying the parasite that causes schistosomiasis. In particular you are studying an enzyme within this parasite with the long term goal of designing inhibitors against it. a) Describe the series of experiments you will perform to determine the values for the Michaelis- Menton parameters for this enzyme. b) You have determined that the value for an observed rate constant increases with decreasing ph. What hypothesis could you formulate based on this result? Explain.

2 4. We have discussed a number of strategies enzymes may use to catalyze reactions. The following questions refer to these different strategies. (a) In the chemical formation of anhydrides, (shown in equations 1 & 2, below), the rate constant for the second reaction (eq. 2) is 3 x 10 7 fold faster than that for the first reaction (eq. 1). Describe in detail how enzymes might use a similar effect or strategy to catalyze reactions. reaction relative rate Eq. 1 1 Eq. 2 3 x 10 7 Eq. 3 b) As shown below, chymotrypsin catalyzes the hydrolysis of specific substrates (eq. 3) significantly faster than nonspecific substrates (eq. 4). This increase is not seen as tighter binding of the specific substrates. Explain in detail. reaction relative rate uncat. cat Eq

3 5. Consider the following mechanism: k 1 k 2 k 3 E + S ES EP E + P k -1 where all steps are accurately depicted as reversible or irreversible. Imagine that substrate (S) is colorless and product (P) is yellow whether or not it is bound to the enzyme. You properly set up an experiment in which you can monitor the formation of P over time under multiple turnover conditions by quantitatively measuring the increase in yellow color. Some of your data are shown below. a) Explain why this result is unlikely to be due to product inhibition. b) Provide and defend an alternate explanation for the two phases that you observe in the time course for the formation of P. % of total P A 0.5 time 6. The ribozyme from the hepatitis delta virus (HDV) is a self-cleaving RNA molecule. Due to the nature of this ribozyme, you can physically only perform single turnover reactions. Why is this true? 7. Sometimes my kids and I do "science" experiments in the kitchen. Our longtime favorite is the addition of vinegar (acetic acid) to baking soda (sodium biocarbonate). The solution gets very fizzy as the acid reacts with the bicarbonate to produce carbon dioxide and water. If my kids would only put their minds to it, I'm sure they could figure out how to measure the rate for the conversion of the bicarbonate to CO 2 and H 2 O in solution. We could then compare this rate to the rate for the same chemical conversion as catalyzed by the enzyme carbonic anhydrase in muscle tissues throughout our bodies. Based on the theory that describes an increase in "effective concentration" in an enzyme active site, would you predict the enzymatic rate to be equal to, faster than, or slower than the corresponding rate of reaction in solution.

4 8. Cellular trna molecules are initially transcribed as longer, precursor molecules that contain extra nucleotides at their 5' end. The enzyme RNase P catalyzes the production of mature trna molecules from these precursor-trna molecules through the hydrolysis of a specific phosphodiester bond, as shown in the following sketch. trna + E trna + + E (pre-trna) (maturetrna) (leader sequence) The biological substrate for RNase P (pre-trna) has many (>30) nucleotides in the leader sequence. However, artificial substrates with as few as 1 nucleotide in the leader (1-tRNA) are cleaved by RNase P in vitro. You are able to do binding experiments in which you watch substrate binding to RNase P in the absence of product formation. So, just observing E + S ES, you obtain the following data. substrate name leader length K D, nm pre-trna tRNA tRNA trna (product) Discuss these data in terms of general theories of enzyme catalysis. For example, consider any suggestions you can make about the catalytic strategies used by RNase P. Keep in mind that all nucleotides present in 1-tRNA are also present in substrates with longer leader sequences. 9. One day you stumble across the following information on the CDC website: "Dracunculiasis, more commonly known as Guinea worm disease (GWD), is a preventable infection caused by the parasite Dracunculus medinensis. The disease causes preventable suffering for infected persons and is a heavy economic and social burden for affected communities." You immediately start considering how you can contribute to alleviating the problem of Guinea worm disease in the world. Doing some research, you identify an enzyme that occurs in the causative parasite that does not exist in humans. It occurs to you that this enzyme would be a good target for inhibition. To inhibit the enzyme, you want to develop a molecule that will bind in the active site and therefore prevent the actual substrate from binding. Given a choice between inhibitors that resembled the substrate, transition state, or product of this enzymatic reaction, which would you choose? In your answer, carefully explain your reasoning as it pertains to each possible choice. (Tell me why you chose one type of inhibitor and why you did not choose the other two types).

5 10. Shown below is the Michealis-Menton plot for the reaction of 5 nm enzyme with substrate A. Imagine that K M is a true K D for the reaction of this enzyme with any substrate. Add a second Michaelis-Menton curve to this figure to represent the reaction of the same enzyme with a substrate for which it has greater specificity (call this substrate B). Explain the choices you made. v [S] 11. (This question is not based on a real enzyme). Structure relevant to this question are the following: ATP CTP Enzyme Madeitup functions in vivo to transfer a phosphate group from CTP to a particular protein. Upon substitution of CTP with ATP in vitro, ATP can act as the phosphate donor for this enzymatic reaction. Provide a well-reasoned hypothesis about the relative specificity of the enzyme for CTP versus ATP. Your answer should make it clear that you understand the concept of substrate specificity as it applies to enzymatic reactions.

6 12. This question concerns the hydrolysis of substrate catalyzed by the enzyme chymotrypsin, as accurately modeled below. a) The derived steady-state equation for this enzymatic reaction is shown below. Provide the work that leads to this equation, assuming the reaction occurs under steady-state conditions; that is, the steady-state assumption applies to all enzyme-bound species. (Feel free to use the abbreviations S and P in place of the molecules written above.) Rate = k -1 + k 2 k 3 k 1 k 2 k 3 [E T ] [S] + k 3 + k 2 [S] k 2 b) The substrates for this reaction are variants of N-acetyl-L-tryptophan-X, where X is further specified in this table: -X k cat, s -1 - OCH 2 CH OCH Use information from the steady-state rate equation to explain the fact that although the three esters shown in the table above have vastly different chemical hydrolysis rate constants (k 2 ), their values for k cat are quite similar.

7 13. a) Sketch the transition state and intermediate that occur during the hydrolysis of an amide bond, using the starting materials shown below. b) Provide three explanations for the observation that amide bond hydrolysis is slow at ph 7. c) Identify two chemical mechanisms that could catalyze this reaction. Explain how catalysis would be achieved in each mechanism. 14. You are studying the substrate specificity of enzyme E. You have done steady-state kinetics with six substrates and classified them into two groups, class 1 and 2. Your preliminary data are shown below. Substrate k cat (sec -1 ) K M (nm) Class 1: A B C Class 2: X Y Z a) For the following two questions: Either answer the question and explain your answer or explain why you cannot answer it based on the data you have collected thus far. For which class of substrate is the enzyme more specific? What is the origin of substrate specificity: reactivity, substrate binding affinity, or both? b) What type of experiment will you do next and why?

8 15. The reactions of enzyme Imaginase with two different substrates, A and B, have been studied in steady-state experiments. Substrate k cat (min -1 ) K M (mm) A B a) In the series of steady-state (Michealis-Menton) experiments that were performed to obtain that parameters shown above for the B substrate, what concentration of Imaginase would have been appropriate to use: 0.1mM, 5mM, or 100mM? Circle and briefly explain your choice. b) Using your above answer, you are set up experiments to compare the reaction of Imaginase with 500 mm A to the reaction of Imaginase with 500 mm B. Show your calculations for the % of product formed, with each substrate, at a 1 minute time point here. On this plot, show the time course data you would expect to get for each of these reactions. (Add numbers to the x-axis) % product time (min) c) You are now comparing the reaction of Imaginase and 0.1 mm A to the reaction of Imaginase with 0.1 mm B. In each reaction you have the same concentration of Imaginase. If you stop the reaction after three minutes, do you expect to see: more product in the A reaction (compared to the B reaction) less product in the A reaction (compared to the B reaction) the same amount of product in each reaction Check the box corresponding to your answer and briefly explain your reasoning.

9 16. Here are two reactions describing the chemical formation of anhydrides. (The negatively charged oxygen attacks a carbonyl ) reaction Rxn. 1 Rxn. 2 In your research lab you have used in vitro evolution to develop two RNA enzymes that each function to catalyze one of the above reactions. Enzyme 1 catalyzes Rxn 1 and Enzyme 2 catalyzes Rxn 2. Which enzyme will cause a greater rate enhancement for its reaction? In your answer, include a numerical estimate of the rate enhancement you expect to see in this enzyme. Explain your answer thoroughly with valid reasoning. 17. An enzyme reacts with three different substrates (A, B, and C), under multiple turnover conditions, with the following Michaelis-Menton parameters: Substrate A Substrate B Substrate C kcat (min -1 ) K M (µm) Answer the following questions OR briefly explain why the question is unanswerable: a) What is the rate of the reaction of 5 nm enzyme with 200 µm substrate B? b) For which substrate is the enzyme least specific? Explain. c) Which substrate binds with tightest affinity to the enzyme? d) How much product has been formed if 0.01 µm enzyme and 3 µm substrate C have reacted for 20 seconds?

10 18. The material in this question is taken from a paper entitled "Energetic contribution of non-essential 5' sequence to catalysis in a hepatitis delta virus ribozyme" (EMBO (2001) 20, 4884). The figures from this paper that are referred to in this question follow the entire question. a) Based on the data in Figure 2: sketch, on ONE free energy plot, the reaction progress for a substrate with 1 nucleotide in the 5' sequence (S1) and the reaction progress for a substrate with 2 nucleotides in the 5' sequence (S2). Explain your choices. Free energy diagram: Explanation: b) Define the concept of intrinsic binding energy. c) In light of the data in Figure 2, what is the energetic contribution of the 5' sequence to catalysis in this HDV ribozyme? Provide one hypothesis for the physical mechanism by which this 5' sequence might fulfill this function. Here are the relevant two figures: Figure 1 (left): The hepatitis delta virus (HDV) ribozyme nucleotides are shown as outlined letters. Substrate nucleotides are shown as bold letters, in the box. The ribozyme cleaves the substrate at the position indicated by the arrow. Nucleotides below that arrow are referred to as the 5' sequence.

11 Figure 2 (above): Change in the cleavage rate (k 2 ) and dissociation equilibrium constants (K d ) with increasing length of the 5' sequence. k 2 and K d were determined for wild-type substrates with length 5' to the cleavage site varying from 1 to 8 nt. Both k 2 (circles) and K d (squares) were plotted against the number of nucleotides in their 5' sequence. 19. For the following enzymatic reaction E + S k 1 ES k 2 EP k 3 E + P k-1 k-2 k-3 your friend has derived the following equation to describe the steady-state rate of this reaction: Based on this equation she claims that the release of product from the EP complex is the rate limiting step for this reaction. Confirm or refute your friend's claim. Back up your answer with as much specific detail as possible.

12 20. The following plots are multiple copies of the time course for the appearance of product for the reaction of 5nM enzyme with 50 nm substrate. This enzyme substrate reaction has a K M of 10nM. a) To this plot, add a line showing the time course for product formation for the reaction of 10 nm enzyme and 50 nm substrate. Explain briefly. 16 % product formation time (min) b) To this plot, add a line showing the time course for product formation for the reaction of 5 nm enzyme and 100 nm substrate. Explain briefly. 16 % product formation time (min)