Question

For lysine and arginine, the isoelectric point, \(\mathrm{pI}\), occurs at a \(\mathrm{pH}\) where the net charge on the nitrogen-containing groups is \(+1\) and balances the charge of \(-1\) on the \(\alpha\)-carboxyl group. Calculate pI for these amino acids.

Short answer

Question: Calculate the isoelectric points (pI) for the amino acids lysine and arginine. Answer: The isoelectric points for lysine and arginine are 9.74 and 10.74, respectively.

Step-by-step solution

Identify the groups involved for each amino acid

For lysine and arginine, first identify the \(\mathrm{pK_a}\) values for the associated functional groups. Lysine has three ionizable groups: the \(\alpha\)-amino group, the \(\alpha\)-carboxyl group, and the side chain \(\epsilon\)-amino group. Arginine has similar groups: the \(\alpha\)-amino group, the \(\alpha\)-carboxyl group, and the side chain guanidinium group.

Find the pKa values for each group of amino acids

Now find the \(\mathrm{pK_a}\) values for each group present in these amino acids from a pKa table or a textbook. For lysine: \(\mathrm{pK_{a1}}\) for \(\alpha\)-carboxyl group: 2.18 \(\mathrm{pK_{a2}}\) for \(\alpha\)-amino group: 8.95 \(\mathrm{pK_{a3}}\) for side chain \(\epsilon\)-amino group: 10.53 For arginine: \(\mathrm{pK_{a1}}\) for \(\alpha\)-carboxyl group: 1.82 \(\mathrm{pK_{a2}}\) for \(\alpha\)-amino group: 8.99 \(\mathrm{pK_{a3}}\) for side chain guanidinium group: 12.48

Calculate the isoelectric point for each amino acid

According to the net charges on the amino acids, we need to find the average pKa values for the groups with the relevant charges. For both lysine and arginine, this is between the positive charge on the nitrogen-containing group and the negative charge on the α-carboxyl group. For lysine: \(\mathrm{pI} = \frac{\mathrm{pK_{a2}} + \mathrm{pK_{a3}}}{2} = \frac{8.95 + 10.53}{2}\) For arginine: \(\mathrm{pI} = \frac{\mathrm{pK_{a2}} + \mathrm{pK_{a3}}}{2} = \frac{8.99 + 12.48}{2}\)

Calculate the final pI value

Perform the calculation for each amino acid to calculate the final pI value. For lysine: \(\mathrm{pI} = \frac{8.95 + 10.53}{2} = 9.74\) For arginine: \(\mathrm{pI} = \frac{8.99 + 12.48}{2} = 10.74\) Thus, the isoelectric points for lysine and arginine are 9.74 and 10.74, respectively.