Question

4. Papain is a protease with a pH optimum of approximately 6.5. The enzyme utilizes a catalytic triad to break peptide bonds. The nucleophile within this triad is a cysteine (Cys25) having a perturbed pKa value of 3.3. Write the Henderson-Hasselbalch equation. Using this equation, calculate the percent deprotonated of papain’s Cys25 side chain at pH 3.7. Why will the enzyme not function maximally at this pH? There will be no partial credit for the calculation, but your work must be shown to receive credit. 


Answer 1

Ans. Given, position of cysteine residue in protein = Cys²⁵

The NH2- and COOH terminal of all non-terminal residues is involved in peptide bond formation. So, the only portion of amino acid that undergoes protonation or deprotonation in such residues is the side chain.

The pKc of side chain of Cys residue is 8.14.

In catalytic triad, the thiol group (-SH) of cysteine acts as weak acid and donates a proton as follow-

            -SH -----------> -S^- + H⁺

The resultant negatively charged sulfide ion acts as nucleophile.

# Henderson- Hasselbalch equation-

            pH = pKa + log ([A^-] / [AH])                    - equation 1

            where, [A^-] = [-S^-] – conjugate base

[AH] = [HS] – weak acid

Putting the values in equation 1-

            3.7 = 3.3 + log [-S^-] / [-SH]

            Or, 3.7 – 3.3 = log [-S^-] / [-SH]

            Or, [-S^-] / [-SH] = antilog 0.4

            Or, [-S^-] = 2.51 [-SH]                      - equation 1

# Total concertation of both chemical species = [-S^-] + [-SH]

                                                                        = 2.51 [-SH] + [-SH]

                                                                        = 3.51 [-SH]

Now,

% deprotonated form (% -S^-) = { [-S^-] / ([-S^-] + [-SH]) } x 100

                                                = (2.51 [-SH] / 3.51 [-SH]) x 100

                                                = 71.51 %

# Note that only the negatively charged deprotonated form (-S^-) acts as nucleophile.

So, the enzyme is expected to exhibit only 71.51% of its maximal catalysis.

The remaining 28.5 % of the catalytic triad is still in protonated form at pH 3.7. Or, 28.5% of the catalytic triad in NOT able to catalyze the reaction.

Therefore, the catalytic triad does NOT function maximally at pH 3.7.