A stochastic model of the control of F plasmid replication by the titration of iterons by active repE protein has been formulated. Stochastics is required by the small number of binding proteins and iterons per cell. 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 their 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. Computations are underway to assess whether the equations are numerically stable and, if so, whether the probability that a cell will replicate its plasmid increases strongly with cell age as observed experimentally in the baby cell experiments of Helmstetter. - replication, plasmids, stochastics, transition rates
| 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 |
