The relation of the isoelectric point for the amino acid to solubility is

an amino acid is least soluble at its isoelectric point

The answer is option 3. an amino acid is least soluble at its isoelectric point.

The relation of the isoelectric point for the amino acid to solubility is that an amino acid is least soluble at its isoelectric point.

Isoelectric Point (pI): The isoelectric point of an amino acid is the pH at which it carries no net electrical charge. At this point, the amino acid exists as a zwitterion, with the amino group (NH2) being positively charged and the carboxyl group (COOH) being negatively charged. The pI is determined by the specific amino acid's chemical structure and the pKa values of its functional groups.

Solubility and pI: Amino acids are least soluble at their isoelectric points because this is the pH at which they are least ionized. In other words, at the pI, the amino acid's solubility in water decreases because it exists mostly in its non-ionized form. Above or below the pI, amino acids become more charged due to the ionization of their functional groups, which increases their solubility through electrostatic interactions with water molecules.

Summary:

Least Soluble at pI: Amino acids are least soluble at their isoelectric points because they exist primarily in their non-ionized form, reducing their interaction with water molecules.

Solubility and Charge: The solubility of amino acids is influenced by their overall charge, which varies with pH. Above or below the pI, amino acids are more charged and therefore more soluble due to electrostatic interactions with water molecules.

Relation between pI and Solubility: There is a clear relationship between the isoelectric point and solubility of amino acids, with solubility generally decreasing at the pI.

So, the correct statement is: an amino acid is least soluble at its isoelectric point.