Session #31: Homework Solution

Session #31: Homework Solution Problem #1 Rank the following amino acids in decreasing order of migration towards the cathode (negative electrode) when separated by electrophoresis in a solution of pH = 7.3. I. II. III. Lysine: pI = 9.87 Alanine: pI = 6.02 Aspartate: pI = 5.95 Solution I > II > III Problem #2 Define what is meant by isoelectric point (pI) and give an example. Solution Isoelectric point is the pH of an amino acid at which it has no net electric charge. For amino acids that have no ionizable side chain, the pI value is the average of its two pKa’s. If the amino acid has an ionizable side chain, the pI value is the average of the pKa’s of similarly ionizable groups. Ex: Alanine: pK a = 9.69 pI= Ex. Lysine: 2.34 + 9.69 = 6.02 2 Lysine: pI = 10.79 + 8.95 = 9.87 2 Problem #3 You are given a mixture that contains glutamic acid (pI = 3.2), arginine (pI = 10.8), and valine (pI = 6.0), and you subject the mixture to electrophoresis. (a) Which amino acids migrate towards the cathode when the electrophoresis is carried out at a pH of 7.1? (b) Which amino acids migrate toward the anode when the electrophoresis is carried out at a pH of 7.1? (c) Which amino acid migrates farthest toward the anode at a pH of 7.1? Solution a) b) c) arginine valine and glutamic acid glutamic acid Problem #4 Draw the dipeptide Val-Tyr at pH 7.0. Solution Problem #5 Draw the structure of the tetrapeptide Ser-Leu-Phe-Pro at pH 7.0. Solution Problem #6 The pKa values for the α-carboxylic acid and the α-amino acid groups is cysteine are 1.092 and 10.78, respectively. The pKa for the titratable −SH side chain in the amino acid is 8.33. Calculate the pI of cysteine. Solution The structure of cysteine at pH = 7 shows that the side group is protonated. So we must conclude that even though the pKa is 8.33, the sulfhydryl (−SH) is acting as an acid. The isoelectric point, pI, is the pH at which the zwitterion is the dominant species. Let’s start with extreme acid conditions, pH < 1.96. Under these circumstances according to the LeChatelier Principle the amino acid will be fully protonated in an effort to try to consumer the proton excess in solution. The resulting structure of the amino acid is , which is net positive (cationic). In slightly more alkaline solutions, 1.96 < pH < 8.33, the carboxylic acid sheds its proton in order to neutralize OH-. The resulting structure of the amino acid is , which is the zwitterion. Hence we calculate the value of pI to be the average of 1.06 and 8.33 = 5.14. Just to complete the analysis, consider still greater basicity, 8.33 < pH < 10.78. Over this range of composition the resulting structure of the amino acid is , which is net negative (anionic). Finally, at extreme alkaline conditions, pH > 10.78, everything is deprotonated in an effort to neutralize the rising OH- population. Over this range of composition the resulting structure of the amino acid is , which is net negative and doubly charged (anionic). Also worth mentioning, at neutral pH, reduced sulfhydryls on two different cysteine side groups can be oxidized to form disulfide linkages.