Robust control of initiation of prokaryotic chromosome replication: essential considerations for a minimal cell

A genomically and chemically detailed mathematical model of a "minimal cell" would be useful to understand better the "design logic" of cellular regulation. A "minimal cell" will be a prokaryote with the minimum number of genes necessary for growth and replication in an ideal environment (i.e., preformed precursors, constant temperature, etc.). The Cornell single-cell model of Escherichia coli serves as the basic framework upon which a minimal cell model can be constructed. A critical issue for any cell model is to describe a mechanism for control of initiation of chromosome replication. There is strong evidence that the essence of chromosome replication control is highly conserved in eubacteria and even extends to the archae. A generalized mechanism is possible based on binding of the protein DnaA-ATP to the origin of replication (oriC) as a primary control. Other features, such as regulatory inactivation of DnaA (RIDA) by conversion of DnaA-ATP to DnaA-ADP and titration of DnaA by binding to other DnaA boxes on the chromosome, have emerged as critical elements in obtaining a functional system to control initiation of chromosome synthesis. We describe a biologically realistic model of chromosome replication initiation control embedded in a complete whole-cell model that explicitly links the external environment to the mechanism of replication control. The base model is deterministic and then modified to include stochastic variation in the components for replication control. The stochastic model allows evaluation of the model's robustness, employing a low standard deviation of interinitiation time as a measure of robustness. Four factors were examined: DnaA synthesis rate; DnaA-ATP binding sites at oriC; the binding rate of DnaA-ATP to the nonfunctional DnaA boxes; and the effect of changing the number of nonfunctional binding sites. The observed DnaA synthesis rate (2000 molecules/cell) and the number of DnaA binding sites per origin (30) are close to the values predicted by the model to provide good control (low variance of interinitiation time), with a reasonable expenditure of cell resources. At relatively high binding rates for DnaA-ATP to the DnaA boxes (10(16) M(-1) s(-1)), increasing the number of DnaA binding sites to about 300, improved control (but little further improvement was seen by extension to 1000 boxes); however, at a low binding rate (10(10) M(-1) s(-1)), an increase in DnaA boxes had an adverse effect on control. The combination of all four factors is probably necessary to obtain a robust control system. Although this mechanism of replication initiation control is highly conserved, it is not clear if simpler control in a minimal cell might exist based on experimental observations with Mycoplasma. This issue is discussed in this investigation.