The model imposes a specific DnaA-ATP threshold at the moment of initiation ( t = X ). A: The model with fixed parameters cannot explain an 'initiation threshold' since a different value of the ratio DnaA-ATP:genome length (r) is obtained at initiation (t = X) for each value of the cell doubling time, τ. B: We perform a mathematical transformation upon the model to impose a threshold for the ratio DnaA-ATP:genome length (r) at the moment of initiation (t = X) (in this specific example the threshold has been imposed by allowing the binding affinity of DnaA-ATP to its self repressor site to vary). In both panels A and B, the x-axis has been translated and normalized to denote fractions of cell cycles with the initiation time given by . C: In the case in which both autorepression and RIDA are included in the model there are two scenarios in which an 'initiation threshold' can be imposed upon the model. The first of these requires the binding affinity of DnaA-ATP to its self repressor sites to decrease with increasing cell doubling time. The second scenario requires that the RIDA rate increases with increasing cell doubling time. In all scenarios the value of k
increases with increasing growth rate.