Biomolecules Set-1

Q1. Calculate the isoelectric point ($pI$) of an amino acid whose carboxyl group has $pK_a=2.34$ and amino group has $pK_a=9.60$. (For a neutral amino acid $pI=\dfrac{pK_a(\text{COOH})+pK_a(\text{NH}_3^+)}{2}$.)

Q2. An enzyme follows Michaelis–Menten kinetics with $V_{\max}=120\ \mu\text{mol min}^{-1}$ and $K_m=8\ \text{mM}$. Calculate the initial rate $v$ when $[S]=2\ \text{mM}$ using $v=\dfrac{V_{\max}[S]}{K_m+[S]}$.

Q3. Consider the dipeptide Gly–Glu at pH $7.0$. Using $pK_a(\text{C-terminal COOH})=2.35$, $pK_a(\text{side-chain COOH of Glu})=4.25$ and $pK_a(\text{N-terminal NH}_3^+)=9.60$, what is the net charge on Gly–Glu at pH $7.0$?

Q4. A sample of D-glucose in water shows an observed optical rotation $[\alpha]_{\text{obs}}=+42.3^\circ$. Given $[\alpha]_\alpha=+112.2^\circ$ for pure $\alpha$-D-glucopyranose and $[\alpha]_\beta=+18.7^\circ$ for pure $\beta$-D-glucopyranose, calculate the percentage of the $\alpha$-anomer in the equilibrium mixture. (Use $[\alpha]_{\text{obs}}=x_\alpha[\alpha]_\alpha+x_\beta[\alpha]_\beta$ with $x_\alpha+x_\beta=1$.)

Q5. One gram each of sucrose and maltose are completely hydrolysed to their monosaccharide units. Which sample produces the greater number of reducing sugar molecules (free reducing ends)? (Note: both disaccharides have formula $C_{12}H_{22}O_{11}$.)

Q6. Given the $pK_a$ values for alanine: $pK_{a1}$ (–COOH) = 2.35 and $pK_{a2}$ (–NH$_3^+$) = 9.87, calculate its isoelectric point $pI$ (use $pI=\dfrac{pK_{a1}+pK_{a2}}{2}$).

Q7. Consider the tripeptide Ala–Lys–Glu (N‑ to C‑terminus). Given $pK_a$(N‑terminal NH$_3^+$) = 9.5, $pK_a$(C‑terminal COOH) = 2.0, $pK_a$(Lys side chain) = 10.5 and $pK_a$(Glu side chain) = 4.1, what is the net formal charge of the peptide at pH 7.0?

Q8. An enzyme follows Michaelis–Menten kinetics with $K_m=20\ \mathrm{mM}$. At what substrate concentration $[S]$ will the initial rate equal $75\%$ of $V_{max}$? (Use $v=\dfrac{V_{max}[S]}{K_m+[S]}$.)

Q9. Assertion (A): Histidine residues frequently participate in proton transfer in enzyme active sites at physiological pH. Reason (R): The imidazole side chain of histidine has $pK_a\approx6.0$, so near physiological pH ($\sim7.4$) it exists substantially in both protonated and unprotonated forms.

Q10. Histone proteins bind DNA via Lys side chains (side chain $pK_a=10.5$). Using the Henderson–Hasselbalch expression for the fraction protonated

by approximately what factor does the fraction of protonated Lys side chains decrease when pH is raised from $8.0$ to $10.5$?