Plays a key role in the control of the eukaryotic cell cycle. It is required in higher cells for entry into S-phase and mitosis. p34 is a component of the kinase complex that phosphorylates the repetitive C-terminus of RNA polymerase II. ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] [DNA-directed RNA polymerase] + ATP = ADP + H(+) + phospho-[DNA-directed RNA polymerase] Phosphorylation at Thr-20 or Tyr-21 inactivates the enzyme, while phosphorylation at Thr-162 activates it. Forms a stable but non-covalent complex with a regulatory subunit and with a cyclin. Belongs to the protein kinase superfamily. CMGC Ser/Thr protein kinase family. CDC2/CDKX subfamily.