Calculating $pI$ Difference: Lysine and Glutamic Acid

The isoelectric point ($pI$) is the pH at which an amino acid has no net electrical charge. It's calculated differently for standard, acidic, and basic amino acids based on their ionizable groups.

Calculating $pI$ for Glutamic Acid (Glu)

Glutamic acid is an acidic amino acid due to its side chain carboxyl group. The $pI$ is the average of the $pK_a$ values of the alpha-carboxyl group and the side chain carboxyl group.

• $pK_a$ of alpha-carboxyl group = 2.2
• $pK_a$ of side chain carboxyl group = 4.2

Calculation:

$pI_{Glu} = \frac{pK_{a(\text{alpha-COOH})} + pK_{a(\text{side-chain COOH})}}{2}$

$pI_{Glu} = \frac{2.2 + 4.2}{2} = \frac{6.4}{2} = 3.2$

Calculating $pI$ for Lysine (Lys)

Lysine is a basic amino acid due to its side chain amino group. The $pI$ is the average of the $pK_a$ values of the alpha-amino group and the side chain amino group.

• $pK_a$ of alpha-amino group = 9.2
• $pK_a$ of side chain amino group = 10.2

Calculation:

$pI_{Lys} = \frac{pK_{a(\text{alpha-NH}_3^+)} + pK_{a(\text{side-chain NH}_3^+)}}{2}$

$pI_{Lys} = \frac{9.2 + 10.2}{2} = \frac{19.4}{2} = 9.7$

Determining the $pI$ Difference

The difference between the isoelectric points of lysine and glutamic acid is calculated as follows:

Difference = $|pI_{Lys} - pI_{Glu}| = |9.7 - 3.2| = 6.5$

The difference in the isoelectric point ($pI$) of lysine and glutamic acid is 6.5.