A dynamic model of the Escherichia coli phosphate-starvation response.

A mathematical model of the Escherichia coli Pho regulon was developed to study the induction of the phoA gene by starvation for inorganic phosphate. The model includes phosphate transport, detection of the phosphate concentration at the cell surface, and the signal transduction cascade ultimately leading to the induction of various Pho-controlled genes. Four parameters were manipulated to match the dynamic response of a culture growing with phosphate as the growth-limiting substrate to available experimental data for alkaline phosphatase production and internal phosphate concentration. Steady-state analysis demonstrates that the cascade design of this genetic control system gives rise to a harp transition between the uninduced and induced state for a small change in the external phosphate concentration. Parameter sensitivity indicates that the dissociation constant of the repression complex (which holds PhoR in the inactive form when phosphate is in excess), the rate constants for PhoB and PhoR phosphorylation, and the rate constant for induced transcription of Pho genes have the most influence over the expression of Pho-controlled genes. Changes in the repression complex dissociation constant and the PhoB/PhoR phosphorylation rates alter the sensitivity of the phosphate-starvation response to external phosphate concentration, whereas changes in the transcription rate constant affect the gain of the system. The model also predicts that additional Pho promoter (i.e., for the production of a heterologous protein from the phoA promoter on a plasmid) titrate activator protein PhoB A, such that a lower phosphate concentration is required to initiate expression from a high-copy plasmid than from a single-copy plasmid or the chromosome.