Question

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

Short answer

Answer: The isoelectric point (pI) of aspartic acid is 2.77, and for glutamic acid, it is 3.22.

Step-by-step solution

Find the pK values for COOH, NH3+, and the side chain carboxyl group

Aspartic acid has the following pK values: pK1 (COOH) = 1.88, pK2 (NH3+) = 9.60, and pK3 (side chain carboxyl group) = 3.65. Glutamic acid has the following pK values: pK1 (COOH) = 2.19, pK2 (NH3+) = 9.67, and pK3 (side chain carboxyl group) = 4.25.

Identify the pH range between which the net charge of amino acid is zero

At the isoelectric point, we are looking for the pH when the COOH group has a -1 charge and the NH3+ group has a +1 charge. Since the side chain carboxyl group has a lower pK value than the NH3+ group, we will consider the pH range between the COOH group's pK value and the side chain carboxyl group's pK value as the range in which the net charge of the amino acid is zero.

Calculate the isoelectric point (pI) as the average of the two relevant pK values

For aspartic acid, the pI will be the average of pK1 (COOH) and pK3 (side chain carboxyl group). The isoelectric point can be calculated as: $$\mathrm{pI} = \frac{pK_1 + pK_3}{2}$$ $$\mathrm{pI} = \frac{1.88 + 3.65}{2}$$ $$\mathrm{pI} = \frac{5.53}{2}$$ $$\mathrm{pI} = 2.77$$ For glutamic acid, we will average pK1 (COOH) and pK3 (side chain carboxyl group) values. The isoelectric point can be calculated as:$$\mathrm{pI} = \frac{pK_1 + pK_3}{2}$$ $$\mathrm{pI} = \frac{2.19 + 4.25}{2}$$ $$\mathrm{pI} = \frac{6.44}{2}$$ $$\mathrm{pI} = 3.22$$

State the results

The isoelectric point (pI) for aspartic acid is 2.77, and for glutamic acid, it is 3.22.

Key concepts

Amino Acids

Amino acids are fundamental units that build up proteins, which are crucial for numerous biological functions in living organisms. Each amino acid consists of a central carbon atom called the \( \alpha \-carbon \), attached to an amino group (\( -NH_3^+ \)), a carboxyl group (\( -COOH \)), a hydrogen atom, and a distinctive side chain, or R-group, that determines the properties and identity of the amino acid.

There are 20 standard amino acids, and among them, aspartic acid and glutamic acid are classified as acidic amino acids due to their additional carboxyl groups present in their side chains, which impart an acidic nature. These extra groups significantly contribute to the amino acid's behavior, especially when it comes to their isoelectric points—a concept intrinsic to understanding their biochemistry in aqueous solutions.

pK Values

The pK value is a critical concept in biochemistry that informs us about the acid dissociation constant of a group. It describes the pH at which a particular molecule or group, like an amino, carboxyl or side chain group, will exist half dissociated—meaning 50% will be in the protonated form and 50% in the deprotonated form.

For amino acids such as aspartic and glutamic acid, three important pK values are considered: the pK value for the \( \alpha \-COOH \) group (pK1), the pK value for the \( \alpha \-NH_3^+ \) group (pK2), and the pK value for the side chain carboxyl group (pK3). Knowing these values is essential for calculating the isoelectric point, which is the pH where the amino acid does not move in an electric field, commonly known as the point of zero net electric charge.

Biochemistry

Biochemistry is the study of chemical processes within and related to living organisms. It encompasses a vast array of chemical reactions, interactions, and signaling pathways that are foundational for life. A central topic of biochemistry is understanding how the structure of a molecule, such as an amino acid, relates to its function in the body.

Calculating the isoelectric point of amino acids is a biochemistry application that provides insight into how amino acids behave under varying pH conditions. This knowledge is crucial in areas such as protein purification, enzyme activity study, and understanding the physicochemical properties of proteins. It allows scientists and researchers to predict how amino acids and proteins will interact in different environments, affecting their biological roles and their interactions with other molecules.