The phosphorelay system was first discussed in detail in \cite{Hoch_1993}. The following quotes are from the linked article (emphasis mine).
"The major signal-transduction pathway for the initiation of sporulation is the phosphorelay, which responds to environmental, cell cycle, and metabolic signals, and phosphorylates the SpoOA transcription factor activating its function."
"in a normal culture grown in the laboratory, sporulation occurs during the stationary phase, and many of the processes, alternate pathways, and enzymes formed during the early part of stationary phase are controlled along with sporulation because the cell controls sporulation and many of the stationary-phase processes by a single transcription factor, SpoOA."