Mitogen-activated protein kinase involved in a signal transduction pathway that is activated by changes in the osmolarity of the extracellular environment. Controls osmotic regulation of transcription of target genes. ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] Activated by tyrosine and threonine phosphorylation. In contrast to other yeasts, the nuclear translocation is delayed under severe osmotic conditions although it is activated rapidly. The TXY motif contains the threonine and tyrosine residues whose phosphorylation activates the MAP kinases. Dually phosphorylated on Thr-174 and Tyr-176, which activates the enzyme (By similarity). Phosphorylated in response of osmotic stress, oxidative stress and UV stress, but not heat stress. Belongs to the protein kinase superfamily. Ser/Thr protein kinase family. MAP kinase subfamily. HOG1 sub-subfamily.