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.