When cysteine is placed in the substrate binding site, the thiol no longer fits ideally in the binding pocket, but (with poor geometry) comes within about 2.5 Å of residues E279 and T380 (ideal contacts to a thiol would be closer to 3.0 Å). Moreover, it would not be expected to make as strong H-bonding interactions since the S-H bond is relatively non-polar.
When threonine is substituted, a bad contact arises between the gamma methyl group of the threonine and the carbonyl oxygen of residue 348 (about 2.2 Å).
Alanine and glycine both lose the interactions made by the serine hydroxyl group, thus losing whatever binding energy those two interactions contribute.