Mathematical modelling of the sporulation-initiation network in Bacillus subtilis revealing the dual role of the putative quorum-sensing signal molecule PhrA

Bacillus subtilis cells may opt to forgo normal cell division and instead form spores if subjected to certain environmental stimuli, for example nutrient deficiency or extreme temperature. The resulting spores are extremely resilient and can survive for extensive periods of time, importantly under particularly harsh conditions such as those mentioned above. The sporulation process is highly time and energy consuming and essentially irreversible. The bacteria must therefore ensure that this route is only undertaken under appropriate circumstances. The gene regulation network governing sporulation initiation accordingly incorporates a variety of signals and is of significant complexity. We present a model of this network that includes four of these signals: nutrient levels, DNA damage, the products of the competence genes, and cell population size. Our results can be summarised as follows: (i) the model displays the correct phenotypic behaviour in response to these signals; (ii) a basal level of sda expression may prevent sporulation in the presence of nutrients; (iii) sporulation is more likely to occur in a large population of cells than in a small one; (iv) finally, and of most interest, PhrA can act simultaneously as a quorum-sensing signal and as a timing mechanism, delaying sporulation when the cell has damaged DNA, possibly thereby allowing the cell time to repair its DNA before forming a spore.