Question

$\mathrm{p}{K}_a$ 's in a protein. Suppose the protein in problem 1 has an aspartic acid residue and a lysine residue at its surface. In bulk water, the $\mathrm{p}{K}_a$ of the aspartic acid side group is $3.9$ and the $\mathrm{p}{K}_a$ of the lysine ${\mathrm{NH}}_2$ side group is $10.8$. What are the $\mathrm{p}{K}_a^{\prime }\mathrm{s}$ of these groups in a protein if it has a net charge of $+20$ e?

Short answer

The $\text{p}{K}_a$ of aspartic acid will decrease (below 3.9), and the $\text{p}{K}_a$ of lysine will increase (above 10.8).

Step-by-step solution

- Understand the pKa Values

The $\text{p}{K}_a$ values are a measure of the acidity of a functional group. Here, we have $\text{p}{K}_a=3.9$ for aspartic acid and $\text{p}{K}_a=10.8$ for lysine. In water, these values indicate their tendency to gain or lose protons.

- Analyze the Protein Environment

In a protein with a net charge of $+20e$, the environment around the residues is different compared to bulk water. This could influence the $\text{p}{K}_a$ values of the aspartic acid and lysine residues.

- Predict the Effect of the Net Charge

A highly positive environment (net charge of +20e) will tend to decrease the $\text{p}{K}_a$ of acidic residues (like aspartic acid) and increase the $\text{p}{K}_a$ of basic residues (like lysine). This is because such an environment stabilizes the deprotonated form of acidic groups and the protonated form of basic groups.

- Estimate the New pKa Values

Given the highly positive environment:For the aspartic acid residue, the $\text{p}{K}_a$ will likely decrease from 3.9 to a lower value.For the lysine residue, the $\text{p}{K}_a$ will likely increase from 10.8 to a higher value.Without exact values for these changes, we can only predict the direction of the shift.

Key concepts

Proteins Environment

The environment within a protein significantly impacts the behavior of its residues. This is because the protein’s internal conditions differ drastically from bulk water.
Proteins can create unique microenvironments around their residues, influenced by factors like charge, polarity, and hydrogen bonding. When a protein has a high net charge, such as +20e, it usually indicates a highly charged and perhaps polar environment.
Such an environment can affect the protonation state of acidic and basic residues, which in turn influences their pKa values.

Acidic and Basic Residues

Aspartic acid and lysine are two examples of acidic and basic residues, respectively.
Each of these amino acids has a side chain with a specific pKa, which describes the pH at which half of the side chain molecules are protonated.

• Aspartic acid has a carboxylate side chain with a pKa of 3.9 in water. It is acidic because its side chain tends to donate protons.
• Lysine has an amino side chain with a pKa of 10.8 in water. It is basic because its side chain readily accepts protons.

In different environments, the pKa of these side chains can change, altering their tendency to be protonated or deprotonated.

Protonation and Deprotonation

Protonation and deprotonation refer to the gain and loss of protons, respectively.
These processes are critical because they affect the charge and function of protein residues.

• When the pH of the environment is below the pKa, the residue is more likely to be protonated (gain a proton).
• When the pH is above the pKa, the residue is more likely to be deprotonated (lose a proton).

In the context of a protein with a +20e charge, acidic residues like aspartic acid are more likely to lose protons (deprotonated) because the environment favors stabilizing the negative charge. Conversely, basic residues like lysine are more likely to retain protons (protonated) due to the positively charged environment. This shifts the pKa values for these residues, usually decreasing for acidic residues and increasing for basic residues.