Phosphorylates inhibitors of NF-kappa-B thus leading to the dissociation of the inhibitor/NF-kappa-B complex and ultimately the degradation of the inhibitor. Phosphorylates 'Ser-10' of histone H3 at NF-kappa-B-regulated promoters during inflammatory responses triggered by cytokines. ATP + L-seryl-[I-kappa-B protein] = ADP + H(+) + O-phospho-L-seryl-[I-kappa-B protein] Activated when phosphorylated and inactivated when dephosphorylated. Shuttles between the cytoplasm and the nucleus. Belongs to the protein kinase superfamily. Ser/Thr protein kinase family. I-kappa-B kinase subfamily.