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Serine and threonine both have an extra OH functional group and hence they should be able to dissociate when the pH gets high enough. However multiple amino acid pH charts do not show the 3rd pKa of these 2 amino acids. Why is this so?

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Serine and threonine have extremely high 3rd pKa values

Serine and threonine have a stable OH group, making it unlikely to dissociate except at extremely high pH values. To put things in perspective, physiological pH (the standard pH of the body) is about 7.4. The C-terminus is generally deprotonated at a pH of 1-3, so it's always deprotonated in physiological conditions. The N-terminus is generally deprotonated at basic conditions of 9-11, so it's unlikely to be deprotonated in the body. However, the pkR (side chain pka) for serine is 13, which makes it physiologically irrelevant. Thus, it is not found on amino acid tables together with other pka values.

For more on pKa values of amino acids, see here.

What makes the pKa of serine/threonine so high?

Other amino acids, glutamic acid and aspartic acid specifically, also have side-chain OH groups. These are stabilized by resonance from the carbonyl carbon. When deprotonated, the negative charge spreads out uniformly over both oxygen atoms. The same holds true for the C-terminus of every amino acid. They are stable in anionic form at low pH because of their strong resonance. However, serine and threonine, which have no resonance, don't have stable conjugate anions at low pH and therefore have high pKa values.

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