A mathematical model for lambda dv plasmid replication: analysis of wild-type plasmid.

A mathematical model for lambda dv plasmid replication in a growing single cell of Escherichia coli has been formulated and solved numerically. Quantitative description of the molecular control mechanism for initiation of lambda dv replication presumes regulatory functions of repressor and initiator proteins and transcriptional activation of the origin region. Random selection of a single plasmid for activation and replication is assumed, as is regular plasmid segregation to daughter cells. The model is capable of simulating the periodic changes in each regulatory element and the plasmid copy number during the cell cycle. The calculated average copy number, repressor concentration, and timing of plasmid replication agree well with experimental data. The simulated lambda dv plasmid replication rate is controlled primarily by transcription frequency. Initiation of plasmid replication is not related to variations in the levels of repressor or initiator proteins during the cell cycle. Simulation studies of perturbations in plasmid and repressor segregation indicate that replication regulation of the lambda dv plasmid compensates to readjust copy number to normal values in a few generations. Implications of these studies relative to the molecular mechanisms of replication control are discussed.