How do you determine the relative solubility of amino acids?

How is it possible to determine which amino acid ionization state of a particular amino acid is the least soluble in water. At different pHs arginine is ionized in a variety of ways. I understand that charged and polar particles are soluble in water. However, almost all of arginines ionization states are charge. Even the neutral form has positive and negative ends, despite the fact that they cancel out. So how do you distinguish between all these charged forms in determining which one is least soluble? Thanks in advance for any help