Negative regulator of sigma-B activity. Phosphorylates and inactivates its specific antagonist protein, RsbV. Upon phosphorylation of RsbV, RsbW is released and binds to sigma-B, thereby blocking its ability to form an RNA polymerase holoenzyme (E-sigma-B). ATP + L-seryl-[protein] = ADP + H(+) + O-phospho-L-seryl-[protein] ATP + L-threonyl-[protein] = ADP + H(+) + O-phospho-L-threonyl-[protein] The higher affinity of RsbW for RsbV than for sigma-B, rather than a difference in the concentrations of RsbV and sigma-B, is the driving force that is responsible for the switch of RsbW to non-phosphorylated RsbV. The kinase activity of RsbW is directly regulated by changes in the ATP/ADP ratio. Homodimer. In stressed cells, forms a complex with RsbV. The predominant form of this complex has a stoichiometry of 2:2 (one dimer of RsbW is bound by two monomers of RsbV). In unstressed cells, forms a 2:1 complex with sigma-B. By heat shock, salt stress, oxidative stress, glucose limitation and oxygen limitation. Belongs to the anti-sigma-factor family.