Step 1: Definition of isoelectric point.
The isoelectric point (pI) is the pH at which an amino acid or peptide has no net charge. For amino acids with more than one dissociable group, pI is the average of the two pK\(_a\) values corresponding to the ionizable groups that contribute to the net charge.
Step 2: Formula for pI.
For lysine, the isoelectric point can be calculated as:
\[
\text{pI} = \frac{\text{pK}_a1 + \text{pK}_a2}{2}
\]
Using the given pK\(_a\) values for lysine (pK\(_a1\) = 2.2 and pK\(_a2\) = 9.1), the average is:
\[
\text{pI} = \frac{2.2 + 9.1}{2} = 6.7
\]
Step 3: Conclusion.
Thus, the isoelectric point of lysine is 6.7.