ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] Undergoes autophosphorylation in the catalytic domain. Belongs to the protein kinase superfamily. STE Ser/Thr protein kinase family. STE20 subfamily.