Assignments 3 Problem 1 Below is the protein melting data for a pair of wild-type and mutant proteins. WT: Temp: deg C Fluorescence Int. 5 1.71 10 1.73 15 1.77 20 1.84 25 1.96 30 2.14 35 2.32 40 2.49 45 2.61 50 2.69 55 2.74 60 2.76 65 2.78 70 2.78 75 2.79 80 2.79 85 2.79 90 2.80 95 2.80 Mutant: Temp: deg C Fluorescence Int. 5 1.77 10 1.78 15 1.82 20 1.88 25 1.96 30 2.08 35 2.21 40 2.33 45 2.42 50 2.49 55 2.53 60 2.56 65 2.57 70 2.58 75 2.59 80 2.59 85 2.59 90 2.60 95 2.60Determine the following pieces of information. Note: While you are doing the plots and the calculations, make sure that you convert the temperatures from Celsius to Kelvin. a) Plot the melting curves (Fluorescence intensity vs. temp) for both the mutant and the wild-type protein. b) Determine your signal for the fully folded and the fully unfolded form (both mutant and WT). c) Plot the melting curves as the fraction of folded protein vs. temp. d) What are the melting temperatures for the two proteins? e) Pick the appropriate plots to determine ΔH and ΔS of unfolding for both proteins. f) What is the ΔΔG between the two proteins at 25 deg C. g) What fraction of the molecules of the mutant is folded at 20 deg C. h) If you want exactly 0.1 % of the wild-type protein to be folded, what temperature do you have to choose? Problem 2 Your lab is investigating a receptor molecule and wants to use your new physical chemistry skills to answer some new questions. Here is the state of the project when you come in: - The lab has designed a mutant of the receptor, which converts an Asp in a flexible, solvent-exposed loop on the protein surface into a Phe. - They determined the structures of both the mutant and the wild-type protein and except for the side-chain change the two structures look identical. - Protein stability experiments on the wild-type protein gave: ΔHunfold=32kcal ΔSunfold=90cal You get the following data from a protein melting experiment of the mutant Temp in deg C rel. fluorescence intensity 25 0.5 40 0.61 55 1.15 70 1.80 85 2.0a) Determine the Tm, ΔHunfold, ΔSunfold, ΔGunfold (at 20 deg.C) of the mutant and the ΔΔHunfold, ΔΔSunfold, ΔΔGunfold (at 20 deg C) relative to the wild-type protein. b) Somebody in your lab wonders if the unfolded form of the mutant protein may be populated enough to play a biological role in the signaling reaction. To help out, calculate the fraction of unfolded molecules at 20 degrees C. Why would it be hard to measure the fraction of unfolded mutant protein at 20 deg. C experimentally? c) Now it is head scratching time! Do the results from the mutant surprise you? What effect, if any, would you have expected to see for the mutation? How could you rationalize the result? Two hints: i) remember that ΔG is defined by two states of the protein. Which of the two states may be responsible for the effect of the mutant. ii) Remember what you learned about the molecular nature of the hydrophobic effect? Problem 3 Below is the picture of a section through a protein interior that contains two methionine residues. (The rest of the protein is shown as a solid mass. Assume that this interior is entirely hydrophobic). You want to use this protein to test how much energy it costs form a salt bridge in the interior of a protein. a) Which two amino acids would be best suited to substitute for the two methionines for your mutants and why? b) Calculate the expected energetic cost of burying this salt-bridge. (You did this in your previous assignments)c) Assume your wild-type protein has a ΔH of 52kcal and ΔS 160 cal. What would be the Tm of the wild-type protein and what would be the Tm of your mutant. d) Given what you learned in class, what should you do besides measuring ΔΔG of the mutant, to convince yourself that your experiment is really working? What sort of things could go “wrong” with your design? Problem 4 You are working on a protein-engineering project. Your goal is to generate a more stable version of protein X. You finally expressed and purified both the wild-type form of X and the mutant you designed. Now want to know if the mutant is indeed more stable than the wild-type protein. To answer this question, you do two experiments: 1st you use fluorescence spectroscopy to measure the fraction of unfolded protein at 37 deg. C. Second you use CD spectroscopy to determine the unfolding temperature. You are a bit puzzled by your results: At 37 deg. C the wild-type sample contains less unfolded protein than the sample of the mutant (i.e. wt is more stable). However, in your second experiment the mutant has the higher temperature of unfolding (i.e. mutant is more stable). First you think that either the CD or the Fluorescence spectrometer may be broken, or that you switched your samples, but after checking everything twice you are sure that your instruments seems to be working fine. So finally you go back and measure complete melting curves for both wild-type and mutant protein. Here is the data: Wild-type Mutant deg. C signal deg. C signal 10 0.50177714 10 0.50690435 20 0.50703773 20 0.51772131 30 0.52477872 30 0.54148579 40 0.5745794 40 0.58688752 50 0.67674709 50 0.6584774 60 0.80715497 60 0.74699714 70 0.9067036 70 0.83146568 80 0.95924841 80 0.89600718 90 0.98254687 90 0.93834395Assume that a fully unfolded protein would give you a signal of 1 and a fully folded protein gives you a signal of 0.5. a) Determine ΔHunfold and ΔSunfold for both the mutant and the wild-type protein. b) Do the values you get for ΔHunfold and ΔSunfold explain your previous observations? Calculate the fraction of unfolded protein at 37 deg. C for both the wt and the mutant protein. Also calculate the melting temperature (Tm) for both proteins. c) Based on these results, does it really make sense to talk about one protein being more stable than another one? Please