Amino Acids and Their Properties

Amino acids are the building blocks of proteins. They have a central alpha ($\alpha$) carbon atom bonded to an amino group ($\text{-NH}_2$), a carboxyl group ($\text{-COOH}$), a hydrogen atom ($\text{-H}$), and a side chain ($\text{-R}$). The nature of the side chain determines the specific properties of each amino acid.

Let's analyze each statement provided in the options:

Amino Acids and α-helix Formation

The first statement says Proline has a high propensity to form α-helix in globular proteins. Proline is unique because its side chain is covalently bonded to the alpha-amino nitrogen, forming a cyclic structure. This structure imposes significant restrictions on the conformation of the polypeptide backbone. Specifically, the rotation around the $\text{N}-\text{C}_\alpha$ bond (the $\Phi$ dihedral angle) is constrained. Due to this restriction and the lack of a free hydrogen atom on the nitrogen (which is needed for hydrogen bonding in the α-helix), Proline cannot participate normally in the hydrogen bonding pattern of an α-helix. It often introduces a kink in the helix or is found at its termination. Therefore, Proline has a low propensity to form α-helix, not high.

Amino Acids and Diastereomers

The second statement says both isoleucine and threonine can exist as diastereomers. A molecule can exist as stereoisomers if it contains chiral centers. Stereoisomers are isomers that differ only in the spatial arrangement of their atoms. Diastereomers are stereoisomers that are not enantiomers. Enantiomers are non-superimposable mirror images of each other. A molecule with 'n' chiral centers can have up to $2^\text{n}$ stereoisomers.

• Threonine ($\text{CH}_3\text{CH(OH)CH(NH}_2)\text{COOH}$) has two chiral centers: the $\alpha$-carbon and the $\beta$-carbon (the one bonded to the -OH group).
• Isoleucine ($\text{CH}_3\text{CH}_2\text{CH(CH}_3)\text{CH(NH}_2)\text{COOH}$) also has two chiral centers: the $\alpha$-carbon and the $\beta$-carbon (the one bonded to the $-\text{CH}_3$ group).

Since both Isoleucine and Threonine have two chiral centers, they can exist as $2^2 = 4$ stereoisomers. These four stereoisomers will form two pairs of enantiomers. The relationship between stereoisomers that are not enantiomers is diastereomeric. Thus, both Isoleucine and Threonine can exist as diastereomers (e.g., L-Threonine and L-allo-Threonine are diastereomers). This statement is true.

Amino Acids Side Chain pKa

The third statement says the side chain pKa of aspartic acid is more than the side chain pKa of glutamic acid. Both Aspartic acid and Glutamic acid have an acidic side chain containing a carboxyl group ($\text{-COOH}$). Aspartic acid has a side chain $\text{-CH}_2\text{COOH}$, while Glutamic acid has a side chain $\text{-CH}_2\text{CH}_2\text{COOH}$. The side chain carboxyl group of Aspartic acid is closer to the $\alpha$-carbon and the main chain amino and carboxyl groups than that of Glutamic acid. The electronic effects from the main chain can influence the acidity of the side chain carboxyl group. Typically, the side chain carboxyl group of Aspartic acid is slightly more acidic (lower pKa) than that of Glutamic acid. Approximate side chain pKa values are ~3.9 for Aspartic acid and ~4.3 for Glutamic acid. Therefore, the side chain pKa of aspartic acid is less than the side chain pKa of glutamic acid, making this statement false.

Amino Acids Dihedral Angles

The fourth statement says the Ψ dihedral angle of proline is more restricted than the Φ dihedral angle. The $\Phi$ angle is rotation around the $\text{N}-\text{C}_\alpha$ bond, and the $\Psi$ angle is rotation around the $\text{C}_\alpha-\text{C}$ bond (where C is the carbonyl carbon). Due to Proline's cyclic structure, where the nitrogen is part of a ring involving the side chain, the rotation around the $\text{N}-\text{C}_\alpha$ bond (the $\Phi$ angle) is severely restricted to a narrow range of values, typically around $-60^\circ$ to $-75^\circ$. While the cyclic structure also restricts the possible values of the $\Psi$ angle compared to other amino acids, the restriction on the $\Phi$ angle is significantly greater because the N atom is part of the rigid ring structure. Therefore, the $\Phi$ dihedral angle of proline is more restricted than the $\Psi$ dihedral angle, making this statement false.

Based on the analysis of all statements, the only true statement is that both isoleucine and threonine can exist as diastereomers.