As a rule amino acids have both a carboxyl group and an amine group coming off the alpha carbon. Some amino acids are dicarboxylated, some have more than one amine group, and others have -SH or -OH moieties. Below is pictured a generalized amino acid which identifies the alpha carbon.

The drawing represents an amino acid that is acidified. This amino acid can deprotonate by losing protons at the COOH and the NH₃⁺ locations. The pK_a for the COOH off the alpha carbon is low (around 2) and the pKa for the alpha NH₃⁺group is basic. If an amino acid is titrated it will follow the pattern for a polyprotic acid. The one pictured is diprotic. The pK_a values of the alpha COOH and alpha NH₃⁺ are largely separated indicating that each moiety can be considered a separate titration. Below is pictured the changes which would occur during the addition of NaOH.

The middle species is a zwitterion (bipolar ion). The pH which zwitterions reach maximum concentration is the pI. The pI is equal to (pK_a1 + pK_a2)/2. To learn more detail about amino acids behaving as polyprotic acids, visit the excellent site for titration of amino acids.