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# I need help with these questions! BIOL/CHEM 3361 Biochemistry I (and BIOL 6352)PROBLEM SET 1

Spring 2016

Due: Mon., Feb. 2 at 5:00 pm in the collection box in the hall outside FO 3.606 (No late Problem Sets will be accepted.)
(To void last minute difficulties, you may turn them in early -- at lecture or dropped in the collection box.)

There are 31 lettered subparts to the questions below. Each will be graded on a 5 point scale, and then the summed score will be converted to a percentage of the total points.

For full credit, all steps to the solutions of the following problems must be shown. You may work together on the problems, but you may not copy or plagiarize. Your answers must be written, must show your own math steps, and must be in your own words.

Round your answers as appropriate, but in no case to no more than three significant figures.

For problems 1 and 2, assume an activity coefficient of 1 for all substances and no effect of ionic strength. Eliminate terms in quadratic solutions for [H+] only if the weak acid is dissociated < 5%. Reported pKa values can vary depending on the conditions under which they were measured; therefore, in solving the following problems use the pKa values given with the problems.

1. a. What mM concentration of HBr gives a pH of 1.3? What is the pH of 10 mM NaOH? At equilibrium 0.1 M nitrous acid (HNO2) produces 7.4 mM NO2-. Calculate the pKa of HNO2. b. What is the pH of 0.5 M benzoic acid? Benzoic acid Ka = 6.46 x 10-5 M
c. What is the pH of 45 mM H3PO4? For c-f: Phosphoric acid (H3PO4) is a triprotic acid; pKa1 = 2.12, pKa2 = 7.21, pKa3 = 12.32 Acetic acid pKa = 4.75
d. What is the ratio of H2PO4- to H3PO4 at a pH of 3?
e. If 2 volumes of 18 mM KOH are mixed with 1 volume of 22.5 mM H3PO4, what will be the pH of the final mixture?
f. If 15 μmoles of acetic acid is generated in a 1.0 ml enzymatic reaction buffered by 50 mM Na- phosphate (pH 7.0), what will be the final pH of the reaction mixture? Would the change in pH be smaller or larger if the reaction were buffered by 50 mM Na phosphate (pH 6.0)? Explain you answer; no calculations required.
2. a. Parietal cells control the concentration of HCl in the stomach by secreting H+ and Cl-. While fasting, they maintain stomach pH at 3.0. After a meal, they decrease stomach pH to 1.4. What is the fold-change in [H+] from fasting to after a meal? b. For every H+ ion secreted into the stomach, parietal cells also secrete a HCO3- ion into blood plasma. HCO3- plays an important role in maintaining the pH of blood plasma (see textbook page 45 for equations). Patients with achlorhydria have impaired HCl secretion and thus have a loss of HCO3- in the blood. What will be the blood pH of a achlorhydria patient with half the normal concentration of HCO3- in the blood? Assume a constant CO2(d) of 1.2 mM and a normal HCO3- of 24 mM.

c. The pH of the stomach can influence the ionization of drugs such as Aspirin (aka acetylsalicylic acid or HAsp). Given that at equilibrium the pH of a 0.1 M Aspirin is 2.24, what is the pKa of Aspirin?

d. Using the pKa from c., what is the ratio of Asp- to HAsp in the stomach of the patient after a meal?

Would the ratio of Asp to HAsp increase, decrease or stay the same if the patient had fasted?

1. Two amino acids can join together via a peptide bond to make a dipeptide. Below is an example of such a reaction. glutamate + cysteine  γ-glutamylcysteine
ΔG°’ at 25°C for this reaction is 10 KJ/mol; assume 25°C in answering the following.
1. Does the ΔG°’ indicate that formation of γ-glutamylcysteine is favored? Explain your answer; no calculations required.
2. What is Keq’ for this reaction?
3. In certain conditions, the formation of γ-glutamylcysteine can be coupled to ATP hydrolysis. ATP  ADP + Pi (ΔG°’=-30.5 kJ/mol). What is the overall ΔG°’ for the coupled reaction? Is the formation of γ-glutamylcysteine favored?
4. What is Keq’ for the coupled reaction?
5. If glutamate, ATP, ADP, Pi are present at 20 mM, 1 mM, 0.2 mM and 3 mM, what is the equilibrium ratio of γ-glutamylcysteine to cysteine?
6. If γ-glutamylcysteine is removed such that the ratio decreases 10-fold and then 100-fold, what will be the resulting change in ΔG° (Δ ΔG°)?
2. Table 3.1 of your G&G text gives some thermodynamic values for the denaturation of several proteins, i.e., unfolding of the polypeptides, under various conditions, e.g. moderately high or low pH. Among the proteins are myoglobin and RNase. Later in your text, Fig. 6.30 shows the fractional unfolding of RNase A and B as a function of temperature. Figure 6-30 p168

a. Use the temperatures in Fig. 6.30 at which RNase A is 25, 50, and 75% unfolded to make a van’t Hoff plot. Use Excel to tabulate your data and make the plot. Include a trendline and its equation.

b. From the plot determine H ́ and S ́ for the denaturation reaction. What are the corresponding values for RNase A folding?

c. What is ΔG° ́ for RNase A folding at 30? In making this calculation, assume H ́ and S ́ are constant with respect to temperature.

1. Is the RNase folding driven by entropy or enthalpy? State the basis for your answer.
2. How do the thermodynamic values you calculated compare to those for myoglobin and RNase in Table 3.1? What could explain any differences?

5. Ser, Thr, and Tyr are well known targets for post-translational phosphorylation. A lesser known target is His [Kee and Muir, ACS Chem. Biol., 2012, 7 (1), pp 44–51], which can be phosphorylated at either the N-1 or N-3 positions of the imidazole group. One hindrance in studying this phosphorylation is its chemical lability, especially at low pH. Nevertheless, His phosphorylation is now recognized as an important signaling mechanism in prokaryotes and lower eukaryotes, and is being associated with mammalian cellular processes, cancer, and inflammation.

In E. coli the RcsD protein is part of a phosphorelay signal transduction system that accepts phosphate from RcsC, becoming phosphorylated on the His residue in the target sequence SDFAALAQTAHRLKGVFAMLN. Assume you have synthesized this sequence and achieved in vitro phosphorylation of the His by transfer from RcsC. Chemical characterization of the oligopeptide reveals the following pKas:

N- and C-terminal, 9.5 and 4.5, respectively; Asp side chain 4.3; Lys side chain 10.1; Arg side chain 12.0; and His side chain 5.5. Upon phosphorylation, the His imidazole pKa shifts to 6.5; the phospho group has pKas of 2.0 and 6.8.

1. Write the single letter sequences of the His- and pHis-oligopeptides and indicate above the sequence the charges the residues will carry at pH 7.0. Indicate partial charges (i.e., 10% - 90% charged) with δ+ and δ-.
2. Calculate the pI of each oligopeptide.
3. If a mixture of the His- and pHis-oligopeptides were passed through a column containing DEAE-matrix at pH 7.0, how would they behave? Explain why.
4. If a mixture of the two oligopeptides were reacted with cyanogen bromide followed by V8 protease digestion, could the His and pHis-containing peptides be separated by DEAE chromatography at pH 7.0? Explain why.

6. Assume you are given a mixture of proteins that you analyze by standard 2-D electrophoresis, with the following results for isoelectric points and apparent molecular weights: protein A (Mr 45,140; pI 7.52), protein B (Mr 74,400; pI 5.21), and protein C (Mr 108,370; pI 6.26).

1. In the SDS-PAGE step, in what order did the proteins band, starting nearest the anode and going toward the cathode? Explain why.
2. Which protein would be considered the most basic? Explain why.
3. If you subject the mixture of proteins A, B and C to gel filtration on a 100 ml Sephadex G200 column and find that C elutes at 40 ml and A at 80 ml, at what volume will protein B elute?
4. If protein D (Mr 91,385; pI 6.66) were added to the mixture of proteins A, B and C and the new mix subjected to SDS-PAGE, at what position would D be found in the gel relative to proteins B and C? Express you answer as the fractional distance between proteins C and B at which D bands, i.e., CD distance/CB distance.
5. If the mixture of A, B, and C is subjected to salting out with ammonium sulfate at pH 6.5, in what order would the proteins precipitate? Explain why.

f. If the mixture of A, B, and C is subjected to P-cellulose (pKa1 3, pKa2 6) chromatography, what optimal pH range should you use for the buffer and in what order will the proteins emerge from the column? Explain why.

1 Attachment
BIOL/CHEM 3361 Biochemistry I Due: Mon., Feb. 2 at 5:00 pm in the collection (and BIOL 6352) box in the hall outside FO 3.606 Spring 2016 ( No late Problem Sets will be accepted.) (To void last minute difficulties, you may turn them in early -- at lecture or dropped in the collection box.) PROBLEM SET 1 There are 31 lettered subparts to the questions below. Each will be graded on a 5 point scale, and then the summed score will be converted to a percentage of the total points. For full credit, all steps to the solutions of the following problems must be shown. You may work together on the problems, but you may not copy or plagiarize. Your answers must be written, must show your own math steps, and must be in your own words. Round your answers as appropriate, but in no case to no more than three significant figures. For problems 1 and 2, assume an activity coefficient of 1 for all substances and no effect of ionic strength. Eliminate terms in quadratic solutions for [H + ] only if the weak acid is dissociated < 5%. Reported pKa values can vary depending on the conditions under which they were measured; therefore, in solving the following problems use the pKa values given with the problems. 1. a. What mM concentration of HBr gives a pH of 1.3? What is the pH of 10 mM NaOH? At equilibrium 0.1 M nitrous acid (HNO 2 ) produces 7.4 mM NO 2 - . Calculate the pKa of HNO 2 . b. What is the pH of 0.5 M benzoic acid? Benzoic acid Ka = 6.46 x 10 -5 M c. What is the pH of 45 mM H 3 PO 4 ? For c-f: Phosphoric acid (H 3 PO 4 ) is a triprotic acid; pKa 1 = 2.12, pKa 2 = 7.21, pKa 3 = 12.32 Acetic acid pKa = 4.75 d. What is the ratio of H 2 PO 4 - to H 3 PO 4 at a pH of 3? e. If 2 volumes of 18 mM KOH are mixed with 1 volume of 22.5 mM H 3 PO 4 , what will be the pH of the final mixture? f. If 15 μmoles of acetic acid is generated in a 1.0 ml enzymatic reaction buffered by 50 mM Na- phosphate (pH 7.0), what will be the final pH of the reaction mixture? Would the change in pH be smaller or larger if the reaction were buffered by 50 mM Na phosphate (pH 6.0)? Explain you answer; no calculations required. 2. a. Parietal cells control the concentration of HCl in the stomach by secreting H+ and Cl-. While fasting, they maintain stomach pH at 3.0. After a meal, they decrease stomach pH to 1.4. What is the fold-change in [H+] from fasting to after a meal? b. For every H+ ion secreted into the stomach, parietal cells also secrete a HCO 3 - ion into blood plasma. HCO 3 - plays an important role in maintaining the pH of blood plasma (see textbook page 45 for equations). Patients with achlorhydria have impaired HCl secretion and thus have a loss of HCO 3 - in the blood. What will be the blood pH of a achlorhydria patient with half the normal concentration of HCO 3 - in the blood? Assume a constant CO 2 (d) of 1.2 mM and a normal HCO 3 - of 24 mM.
c. The pH of the stomach can influence the ionization of drugs such as Aspirin (aka acetylsalicylic acid or HAsp). Given that at equilibrium the pH of a 0.1 M Aspirin is 2.24, what is the pKa of Aspirin? d. Using the pKa from c., what is the ratio of Asp - to HAsp in the stomach of the patient after a meal? Would the ratio of Asp to HAsp increase, decrease or stay the same if the patient had fasted? 3. Two amino acids can join together via a peptide bond to make a dipeptide. Below is an example of such a reaction. glutamate + cysteine γ-glutamylcysteine ΔG°’ at 25°C for this reaction is 10 KJ/mol; assume 25°C in answering the following. a. Does the ΔG°’ indicate that formation of γ-glutamylcysteine is favored? Explain your answer; no calculations required. b. What is Keq’ for this reaction? c. In certain conditions, the formation of γ-glutamylcysteine can be coupled to ATP hydrolysis. ATP ADP + P i (ΔG°’=-30.5 kJ/mol). What is the overall ΔG°’ for the coupled reaction? Is the formation of γ-glutamylcysteine favored? d. What is Keq’ for the coupled reaction? e. If glutamate, ATP, ADP, P i are present at 20 mM, 1 mM, 0.2 mM and 3 mM, what is the equilibrium ratio of γ-glutamylcysteine to cysteine? f. If γ-glutamylcysteine is removed such that the ratio decreases 10-fold and then 100-fold, what will be the resulting change in ΔG° (Δ ΔG°)? 4. Table 3.1 of your G&G text gives some thermodynamic values for the denaturation of several proteins, i.e., unfolding of the polypeptides, under various conditions, e.g. moderately high or low pH. Among the proteins are myoglobin and RNase. Later in your text, Fig. 6.30 shows the fractional unfolding of RNase A and B as a function of temperature. Figure 6-30 p168

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