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 (By similarity). 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 both activates and inactivates the enzyme depending on the site of phosphorylation. Forms a stable but non-covalent complex with a regulatory subunit and with a cyclin. Interacts with cks-1. Belongs to the protein kinase superfamily. CMGC Ser/Thr protein kinase family. CDC2/CDKX subfamily.