Understanding the Isoelectric Point (pI) of Lysine

The isoelectric point (pI) of an amino acid is the pH at which the molecule carries no net electrical charge. For amino acids with only two ionizable groups (like alanine or glycine), the pI is simply the average of the two pKa values. However, amino acids like lysine have an ionizable side chain, meaning they have three or more pKa values.

Lysine is a basic amino acid because its side chain contains an amino group which can be protonated and carry a positive charge. The question provides the pKa values for the three ionizable groups in lysine:

To find the pI for an amino acid with an ionizable side chain, we need to identify the two pKa values that surround the pH range where the molecule has a net charge of zero (the zwitterionic form). For a basic amino acid like lysine, the zwitterionic form exists between the deprotonation of the alpha-amino group and the deprotonation of the side chain epsilon-amino group.

Let's consider the charges of lysine at different pH ranges based on the given pKa values:

• At very low pH (below pKa 1 = 2.16): The alpha-carboxyl group is protonated (neutral), the alpha-amino group is protonated (charge +1), and the epsilon-amino group is protonated (charge +1). The net charge is +2.
• At pH between pKa 1 (2.16) and pKa 2 (9.06): The alpha-carboxyl group is deprotonated (charge -1), the alpha-amino group is protonated (charge +1), and the epsilon-amino group is protonated (charge +1). The net charge is -1 + 1 + 1 = +1.
• At pH between pKa 2 (9.06) and pKa 3 (10.54): The alpha-carboxyl group is deprotonated (charge -1), the alpha-amino group is deprotonated (charge 0), and the epsilon-amino group is protonated (charge +1). The net charge is -1 + 0 + 1 = 0. This is the zwitterionic state.
• At very high pH (above pKa 3 = 10.54): The alpha-carboxyl group is deprotonated (charge -1), the alpha-amino group is deprotonated (charge 0), and the epsilon-amino group is deprotonated (charge 0). The net charge is -1.

The zwitterionic form (net charge 0) exists in the pH range between pKa 2 (9.06) and pKa 3 (10.54). Therefore, the pI is calculated as the average of these two pKa values:

\begin{equation*} \text{pI} = \frac{\text{pKa}_2 (\alpha\text{-amino}) + \text{pKa}_3 (\epsilon\text{-amino})}{2} \end{equation*}

Plugging in the values:

\begin{equation*} \text{pI} = \frac{9.06 + 10.54}{2} \end{equation*}

\begin{equation*} \text{pI} = \frac{19.60}{2} \end{equation*}

\begin{equation*} \text{pI} = 9.80 \end{equation*}

The calculated pI for lysine is 9.80.

This calculation uses the two pKa values associated with the groups that are positively charged at low pH and become neutral as the pH increases through the zwitterionic point. For a basic amino acid like lysine, these are the pKa values of the alpha-amino and epsilon-amino groups.

Comparing this value to the given options:

1. 7.25
2. 5.61
3. 6.35
4. 9.8

The calculated pI of 9.80 matches option 4 (9.8).

Revision Table: Key Concepts for Lysine pI

Additional Information on Amino Acid Charge and pI

Amino acids exist as different ionic species depending on the pH of their environment. At very low pH, all ionizable groups are typically protonated. As pH increases, groups deprotonate in order of their pKa values, from the lowest pKa to the highest pKa.

• The alpha-carboxylic acid group is the most acidic (lowest pKa, around 2-3) and deprotonates first ($\text{-COOH} \rightarrow \text{-COO}^-$).
• The alpha-amino group is less acidic (pKa around 9-10) and deprotonates next ($\text{-NH}_3^+ \rightarrow \text{-NH}_2$).
• Ionizable side chains have varying pKa values. For basic amino acids like lysine (epsilon-amino, pKa ~10.5) and arginine (guanidino, pKa ~12.5), the side chain is typically protonated at neutral pH and deprotonates at higher pH. For acidic amino acids like aspartic acid and glutamic acid (carboxyl group, pKa ~3.9 and ~4.3 respectively), the side chain is typically deprotonated at neutral pH.

The pI is found between the two pKa values that bracket the species with a net charge of zero. For acidic amino acids, this is typically the average of the alpha-carboxyl pKa and the side chain carboxyl pKa. For basic amino acids, it is the average of the alpha-amino pKa and the basic side chain pKa.

Knowing the pI is important in techniques like electrophoresis or ion-exchange chromatography, where the net charge of a molecule is used for separation.