A model for the initiation of replication in Escherichia coli

The role of the protein DnaA as the principal control of replication initiation is investigated by a mathematical model. Data showing that DnaA is growth rate regulated suggest that its concentration alone is not the only factor determining the timing of initiation. A mathematical model with stochastic and deterministic components is constructed from known experimental evidence and subdivides the total pool of DnaA protein into four forms. The active form, DnaA.ATP, can be bound to the origin of replication, oriC, where it is assumed that a critical level of these bound molecules is needed to initiate replication. The active form can also exist in a reserve pool bound to the chromosome or a free pool in the cytoplasm. Finally, a large inactive pool of DnaA protein completes the state variables and provides an explanation for how the DnaA.ATP form could be the principal controlling element in the timing of initiation. The fact that DnaA protein is an autorepressor is used to derive its synthesis rate. The model studies a single exponentially growing cell through a series of cell divisions. Computer simulations are performed, and the results compare favorably to data for different cell cycle times. The model shows synchrony of initiation events in agreement with experimental results.