Question

The substituents \(\mathbf{R}_{1}\) and \(\mathbf{R}_{2}\) for nine peptides are listed in the table given below. How many of these peptides are positively charged at \(\mathrm{pH}=7.0\) ? $$ \begin{array}{|c|c|c|} \hline \text { Peptide } & \mathbf{R}_{1} & \mathbf{R}_{\mathbf{2}} \\ \hline \mathrm{I} & \mathrm{H} & \mathrm{H} \\ \hline \mathrm{II} & \mathrm{H} & \mathrm{CH}_{3} \\ \hline \mathrm{III} & \mathrm{CH}_{2} \mathrm{COOH} & \mathrm{H} \\ \hline \mathrm{IV} & \mathrm{CH}_{2} \mathrm{CONH}_{2} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\ \hline \mathrm{V} & \mathrm{CH}_{2} \mathrm{CONH}_{2} & \mathrm{CH}_{2} \mathrm{CONH}_{2} \\ \hline \mathrm{VI} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\ \hline \mathrm{VII} & \mathrm{CH}_{2} \mathrm{COOH} & \mathrm{CH}_{2} \mathrm{CONH}_{2} \\ \hline \mathrm{VIII} & \mathrm{CH}_{2} \mathrm{OH} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} \\ \hline \mathrm{X} & \left(\mathrm{CH}_{2}\right)_{4} \mathrm{NH}_{2} & \mathrm{CH}_{3} \\ \hline \end{array} $$

Short answer

Peptides IV, VI, VIII, and X are positively charged at pH 7.0, for a total of 4 peptides.

Step-by-step solution

Understanding the Basic Concept

To determine whether a peptide is positively charged at a specific pH, we must know the pKa values of its ionizable groups. At pH 7.0, groups with pKa values lower than 7 will be in their deprotonated form, and groups with pKa values higher than 7 will be in their protonated form. For peptides, the ionizable groups are typically the N-terminal amino group, the C-terminal carboxyl group, and any ionizable side chains. A positive charge is generally carried by amino groups that are protonated.

Identifying Positively Charged Side Chains

Review each peptide and look for side chains that will carry a positive charge at pH 7.0. Basic amino acid side chains, such as those containing ammonium or amino groups (H_{2}N)), typically carry a positive charge at this pH since their pKa values are above 7. In contrast, acidic side chains like carboxyl groups (COOH) will not be positively charged at pH 7.0 since their pKa values are below 7.

Evaluate Each Peptide

Evaluate the R1 and R2 side chains of each peptide to determine the overall charge at pH 7.0. Peptides I and II have side chains without any charge. Peptide III has one acidic side chain, which is deprotonated and will not contribute to a positive charge. Peptides IV, VI, VIII, and X each have amino groups in their side chains which will carry a positive charge at pH 7.0. Peptides V and VII have an acidic and an amide side chain but no amino side chain, so they will not carry a positive charge.

Key concepts

pKa Values of Amino Acids

The pKa value of an amino acid represents the pH at which half of the molecule's population is deprotonated (i.e., has lost a hydrogen ion). This property is crucial when predicting the charge of an amino acid or peptide at a given pH. In the context of peptides, each amino acid's side chain can affect the overall pKa and thereby the charge of the peptide.

At a neutral pH, typically pH 7.0, amino acids with acidic side chains (like aspartic acid and glutamic acid) have pKa values less than 7, which means they will be deprotonated and carry a negative charge. On the other hand, amino acids with basic side chains (like lysine, arginine, and histidine) have pKa values above 7, remaining protonated and positively charged.

It’s important to understand that a peptide can have multiple ionizable groups, each with its own pKa value. The peptide’s net charge is the sum of the charges of these ionizable groups. Knowing the pKa values helps us predict this net charge at any given pH.

Amino Acid Side Chains

Amino acids, the building blocks of peptides, have various side chains that contribute to their individual characteristics, including their charges. The side chain of an amino acid is commonly known as the 'R' group and can range from a simple hydrogen atom to more complex ring structures or chains of atoms.

For instance, some amino acids have side chains with additional amino groups (like lysine) that can accept protons and hence possess a positive charge under certain pH conditions. Others have side chains with carboxyl groups (like aspartic acid) that can lose protons and carry a negative charge. Amino acids like alanine, with non-ionizable side chains, generally do not affect the charge of the peptide at physiological pH.

In determining a peptide's charge, we consider the cumulative effect of each amino acid's side chain, especially those that are capable of gaining or losing protons.

Ionizable Groups in Peptides

Peptides, being polymers of amino acids, contain distinct ionizable groups that influence their overall charge. The key ionizable groups in peptides are the amino (–NH3+) and carboxyl (–COOH) groups present at the ends of the peptide chain. Additionally, the side chains of certain amino acids also have ionizable groups.

For peptides, the N-terminal amino group has a pKa value near 9, which means it can accept a proton and be positively charged at pH 7.0. The C-terminal carboxyl group, which has a pKa around 2, will be deprotonated and negatively charged at this pH. Any ionizable side chains must also be accounted for, as they can significantly alter the charge state of a peptide.

When calculating the charge of a peptide at pH 7.0, one must consider all ionizable groups. A peptide is positively charged if the sum of the charges of all ionizable groups is positive, neutral if the sum is zero, and negatively charged if the sum is negative. In the exercise, we identify which peptides have side chains that can carry a positive charge at pH 7.0, particularly looking for basic side chains with pKa values higher than 7.