Amino acid with dissociation constant closest to physiological pH is
To understand dissociation constant (pKa) of amino acids one must know the ionizable groups of amino acids.
Each amino acid has two ionizable groups (i) α-carboxyl group (-COOH), and (ii) α-amino group (-NH2).
Besides these two groups, some amino acids have special ionizable groups. e.g. -SH of cysteine, imidazole of histidine.
The dissociation constant (pKa) is the value of pH at which any ionizable group of the amino acid is in 50% ionized form and 50% non-ionized form.
Thus, each amino acid has two pKa values:-

pk1:- pH at which 50% of amino acid molecules have a-carboxyl group in the ionized form (COO-) and 50% molecules have it in unionized form (COOH).
pk2:- pH at which 50% of amino acid molecules have an a-amino group in the ionized form (NH3+) and 50% molecules have it in unionized form (NH2).

The value of pk-1 and pk-2 is different for different amino acids. But it ranges between 3.5-4.0 for pk-1 (i.e. pKa of α -carboxyl group is 3.5-4.0) and 8.0-9.0 for pk-2 (i.e. pKa of a-amino group is 8.0-9.0).

Beside a-carboxyl and a-amino group, some amino acids contain special ionizable group, which will provide one more pKa value (pk3). For example pKa of imidazole group of histidine ranges between 6.5-7.4. That means somewhere between pH 6.5-7.4, 50% of histidine molecules in a solution will have imidazole group in ionized form and 50% molecules will have in unionized form
Serine
Histidine
Threonine
Proline