Question

REFLECT AND APPLY If you were to have a mythical amino acid based on glutamic acid, but one in which the hydrogen that is attached to the \(\gamma\) -carbon were replaced by another amino group, what would be the predominant form of this amino acid at \(\mathrm{pH} 4\) \(7,\) and \(10,\) if the \(p K_{a}\) value were 10 for the unique amino group?

Short answer

At pH 4, the amino acid is \( -NH_{3}^{+}, \text{-COO}^{-}, -NH_{3}^{+}, \text{-COO}^{-} \. At pH 7, the form is \( -NH_{3}^{+}, \text{-COO}^{-}, -NH_{3}^{+}, \text{-COO}^{-}\. At pH 10, the form is 50% \( -NH_{2}, \text{-COO}^{-}-NH_{3}^{+}, \text{-COO}^{-}\.

Step-by-step solution

Identify the structure of the new amino acid

First, understand that the new amino acid is similar to glutamic acid, but has an additional amino group attached to the \(\text{γ}\text{-carbon}\). This structure will influence its ionization states.

Determine pKa values for relevant groups

The amino acid has the following pKa values: approximately 2 for the \( \text{carboxyl group} \), 4.3 for the side chain carboxyl group of glutamic acid, 9 for the \( \text{amino group} \), and 10 for the unique amino group attached to \(\text{γ}\text{-carbon}\).

Form at pH 4

At \( \text{pH 4} \), which is below the pKa of all groups except the carboxyl groups, both carboxyl groups will be deprotonated (\(\text{-COO}^{-}\)) and both amino groups will be protonated (\(\text{-NH}_{3}^{+}\)).

Form at pH 7

At \( \text{pH 7} \), the normal amino group (pKa = 9) and the unique amino group (pKa = 10) will be protonated. The \( \text{side chain carboxyl group} \) will be deprotonated (\(\text{-COO}^{-}\)), and the main chain \( \text{carboxyl group} \) will be deprotonated (\(\text{-COO}^{-}\)).

Form at pH 10

At \( \text{pH 10} \), the pH is equal to the pKa of the unique amino group. Therefore, the unique amino group will be 50% protonated (\(\text{-NH}_{2}\)) and 50% deprotonated (\(\text{-NH}_{3}^{+}\)). The other amino group (pKa = 9) will be mostly deprotonated (\(\text{NH}_{2}\)), while both carboxyl groups will remain deprotonated.

Key concepts

glutamic acid structure

Glutamic acid is an amino acid with a standard structure that consists of a central carbon (also called the alpha-carbon), to which an amino group, a carboxyl group, a hydrogen atom, and a side chain are attached. The side chain of glutamic acid has an additional carboxyl group, which gives it the ability to participate in various biochemical reactions. When you modify glutamic acid by replacing the hydrogen attached to the gamma-carbon (the third carbon in the side chain) with an additional amino group, the new structure greatly influences its ionization states. This modified amino acid has a total of four ionizable groups: two carboxyl groups and two amino groups.

pKa values

pKa values are essential in understanding how an amino acid will ionize in a given environment. The pKa value of a group is the pH at which half of the molecules of that group are deprotonated. In the context of amino acids, each ionizable group (carboxyl and amino) has its own pKa value. For the modified glutamic acid in question, the pKa values are as follows:

• 2 for the carboxyl group attached to the alpha-carbon.
• 4.3 for the side chain carboxyl group.
• 9 for the normal amino group attached to the alpha-carbon.
• 10 for the unique amino group attached to the gamma-carbon.

Understanding these pKa values helps predict the ionization state of the amino acid at different pH levels.

pH and ionization

The ionization state of an amino acid changes depending on the pH of its environment. At different pH levels, the ionizable groups can either gain or lose protons (H+ ions), affecting the overall charge of the molecule. Here’s how the modified glutamic acid behaves at different pH levels:

• **At pH 4**: Both carboxyl groups (pKa 2 and 4.3) are deprotonated, meaning they lose their H+ ions and carry a negative charge (-COO^-). Both amino groups (pKa 9 and 10) are protonated, meaning they retain their H+ ions and carry a positive charge (-NH₃⁺).
• **At pH 7**: The side chain and main chain carboxyl groups remain deprotonated, generating negative charges (-COO^-). The normal amino group (pKa 9) and the unique amino group (pKa 10) are still protonated, each bearing a positive charge (-NH₃⁺).
• **At pH 10**: The pH is equal to the pKa of the unique amino group, so it will be in equilibrium, 50% protonated (-NH₃⁺) and 50% deprotonated (-NH₂). The normal amino group (pKa 9) is mostly deprotonated, leading to a neutral charge (-NH₂). Both carboxyl groups remain deprotonated (-COO^-).

amino group ionization

The amino groups in amino acids can exist in different ionization states depending on the pH. The normal amino group connected to the alpha-carbon of the amino acid generally has a pKa value of around 9. This means that at pH values below 9, the amino group is often protonated (-NH₃⁺), while above pH 9, it is typically deprotonated (-NH₂).
In the case of our modified glutamic acid, the unique amino group attached to the gamma-carbon has a pKa value of 10. Therefore, this amino group will behave similarly but will remain protonated up to a higher pH value than the normal amino group. At pH 7, both the normal and the unique amino group are protonated. However, at pH 10, the unique amino group becomes half protonated and half deprotonated, reflecting its pKa value.