Ingredients of the model. A: illustration of 1) the autorepression of the dnaA gene 2) the growth of the chromosome by the DNA replication process 3) RIDA taking place at the replication forks. B: The key equations of the model, with the terms colour coded to match the ingredients shown in panel A. The parameters in the model are: A- (number of DnaA-ATP molecules), A+ (number of DnaA-ADP molecules), Λ (total genome length), P (number of RNA polymerase molecules), Θ (number of dnaA genes), kA (basal transcription rate of one dnaA gene), c1, c2 (binding constants), (number of pairs of replication forks), kR (RIDA rate per replication fork), kΛ (growth rate of the chromosome per replication fork). The first equation represents the change in the number of DnaA-ATP molecules, with a source term due to the dnaA promoter (as all newly synthesised DnaA is assumed to bind to ATP due to the relative abundance of ATP in the cell), and a sink term due to the conversion of DnaA-ATP to DnaA-ADP in RIDA. The second equation represents the growth of the genome in the cell. The third equation represents the change in the number of DnaA-ADP molecules. The only source term is the same as the sink term in the DnaA-ATP equation since it is assumed DnaA-ADP is only created from DnaA-ATP during RIDA.
Grant et al. BMC Systems Biology 2011 5:201 doi:10.1186/1752-0509-5-201