Sporulation in Bacillus subtilis serves as a model for the development of two different cell types from a single cell. Although much information has been accumulated about the mechanisms that initiate the developmental programmes, important questions remain that can be answered only by quantitative analysis. Here we develop, with the help of existing and new experimental results, a mathematical model that reproduces published in vitro experiments and explains how the activation of the key transcription factor is regulated. The model identifies the difference in volume between the two cell types as the primary trigger for determining cell fate. It shows that this effect depends on the allosteric behaviour of a key protein kinase and on a low rate of dephosphorylation by the corresponding phosphatase; both predicted effects are confirmed experimentally.

No abstract

No abstract

Sporulation in Bacillus subtilis provides a valuable model system for studying differential gene expression. The anti-sigma factor SpoIIAB is a bifunctional protein, responsible for regulating the activity of the first sporulation-specific sigma factor, sigma(F). SpoIIAB can either bind to (and thus inhibit) sigma(F) or phosphorylate the anti-anti-sigma factor SpoIIAA. The phosphorylation reaction follows an unusual time course in which a pre-steady-state phase is succeeded by a slower steady-state phase. Previous experiments have shown that in the steady-state phase SpoIIAB is unable to inhibit sigma(F). A fluorescent derivative of SpoIIAB (AB-F97W) was made that was indistinguishable from the wild type in its interactions with SpoIIAA and sigma(F). AB-F97W exhibited distinctive changes in its fluorescence intensity when bound to ATP, ADP, or SpoIIAA. By following changes in the fluorescence properties of AB-F97W during the phosphorylation reaction, we confirmed a previous hypothesis that during the steady-state phase the predominant species are SpoIIAA.SpoIIAB.ADP complexes. The formation of these complexes is responsible for the slowing of the reaction, an important feature during sporulation since it reduces the loss of ATP in the nutrient-deprived cell. We also show that, to form a complex with SpoIIAA and ADP during the reaction, SpoIIAB must undergo a change in state which increases its affinity for ADP, and that this change in state is stimulated by its interaction with SpoIIAA. We derive a model of the reaction using previously determined kinetic and binding constants, and relate these findings to the known structure of SpoIIAB.