Deciphering environmental signal integration in σ54-dependent promoters with a simple mathematical model

A mathematical model was developed to describe the physiological co-regulation of two Pseudomonas σ54-dependent promoter/regulator systems, Pu/XylR and Po/DmpR of Pseudomonas strains mt2 and CF600, respectively. Five ordinary differential equations and six algebraic equations were developed to describe the following processes of transcription initiation: binding of the activator protein to the upstream activating sequence, union of the sigma factor with the core polymerase, formation of the open complex, and escape of the transcription machinery from the promoter region. In addition, growth-phase control of the integration host factor (IHF), sigma-70 regulation during stationary phase, and the contribution of (p)ppGpp to both sigma factor selectivity and promoter escape were hypothesized. By including any three of these four effects, the model predicted that expression from both promoters is repressed during exponential growth and sharply increases as the cells enter stationary phase. The difference in behavior of the two systems during overexpression of either σ54 or (p)ppGpp could be explained by different values of two model parameters. To accurately represent the behavior of both promoters in (p)ppGpp null strains, an additional parameter must be varied. Although numerical data available for this system is scarce, the model has proved useful for helping to interpret the experimental observations and to evaluate four hypotheses that have been proposed to explain the phenomenon of exponential silencing.