A stochastic model based on current concepts of the control of F plasmid replication by the titration of iterons by active repE protein has been formulated. One set of differential equations has been formulated that describes the age-dependent probability of finding a cell with a particular number of plasmids, given that those plasmids have not yet undergone replication since the last cell division. Another set of differential equations describes similar probabilities for cells whose plasmids have already completed replication. A constant plasmid production rate with age is assumed, and repE turnover is taken as proportional to its free concentration. Iterons are subdivided into two classes, those in the region of the replication origin and those more distant. Combinatorics have been developed describing the fraction of cells at any moment with a total number of plasmids n, j of which are bound; other combinatorics describe the fraction of cells at any moment whose origin iterons are saturated. Replication is modeled as occurring at a fairly rapid but constant rate only from those cells whose iterons are saturated. The model is completed by imposing periodic conditions at mitosis in which the plasmids in the mother cells are randomly redistributed to the daughter cells. Differential equations have been programmed and their solution has been shown to be numerically stable. The probability per unit time of plasmid replication has been found to increase monotonically, but linearly rather than as a high power of age as expected from previous experimental analyses. Sensitivity of this result to variation in input parameters and model structure is under investigation.
| Morrison, Paul F; Chattoraj, Dhruba K (2004) Replication of a unit-copy plasmid F in the bacterial cell cycle: a replication rate function analysis. Plasmid 52:13-30 |
