Solubility
In short Solubility describes how readily a substance disperses in a solvent. For peptides it depends mainly on the side chains of the amino acids and on the pH.
Peptides with many charged side chains usually dissolve well in water. Peptides with many water-repelling side chains dissolve less readily and need an acidic or basic approach.
If some material remains undissolved after patient swirling, that points to a peptide with poor water solubility. Vigorous shaking does not help; it only puts the substance under additional strain.
The key is the net charge. A peptide dissolves least well where its positive and negative charges just balance out, at the isoelectric point. Shift the pH away from that point and the molecules repel one another and go into solution more easily.
This gives a simple rule: dissolve basic sequences in the acidic range and acidic sequences in the slightly basic range. For the first case dilute acetic acid is the usual route, and acetic acid is stocked as a laboratory reagent; organic solvents are the last resort and the worst choice when cysteine or methionine is in the sequence.
If a solution stays cloudy or shows strands, that is a reason to stop: undissolved material in suspension means that every withdrawal takes a different amount. The general procedure is described under reconstitution.