In most of the signaling pathways the activated receptor when activates Protein Kinase through the action of secondary messenger, then these protein kinases almost always phosphorylate on the specific Serine, Threonine, or Tyrosine amino acid residues? what is the reason of phosphorylating specifically these amino acid residues. why not other than these amino acid residues are choosen for phosphorylation ?
Phosphorylation requires a nucleophile and hydroxyl oxygen acts like one. Serine, theronine and tyrosine get phosphorylated on the free OH group in their side chains.
Nitrogen, in some cases also can act as a nucleophile. In case of histidine, the imidazole nitrogen is phosphorylated during bacterial chemotaxis signaling. As far as I know eukaryotes do not have an enzyme for histidine phosphorylation.
Carboxylic groups in glutamate and aspartate can technically be phosphorylated as it happens in case of phosphoglycerate. Glutamate is phosphorylatyed by the enzyme glutamine synthase during the synthesis of glutamine. Same happens in the case of aspartate during aspargine synthesis. However, this is a reactive intermediate and the phosphorylation is not stable like that of hydroxyls.
Other amino acids do not have such nucleophilic groups to render an attack on the phosphorous atom in phosphate- so they are not phosphorylated.
This is mostly because of the nature of the amino acids. You need to have a Hydroxy-group in the sidechain of the amino acid which is the point where the phosphogroup is attached. Since this process needs to be reversible, this can only happen here. See the image below (from here) about the chemical structure:
In eukaryotes not only these three are phosphorylated, histidine phosphorylation also occurs (and happens more frequently than tyrosine phosphorylation, see this article:"Phosphorylation of basic amino acid residues in proteins: important but easily missed.").