Figure 2.

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), k_A (basal transcription rate of one dnaA gene), c₁, c₂ (binding constants), (number of pairs of replication forks), k_R (RIDA rate per replication fork), k_Λ (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.