A mathematical model for timing the release from sequestration and the resultant Brownian migration of SeqA clusters in E. coli.

DNA replication in Escherichia coli is initiated by DnaA binding to oriC, the replication origin. During the process of assembly of the replication factory, the DnaA is released back into the cytoplasm, where it is competent to reinitiate replication. Premature reinitiation is prevented by binding SeqA to newly formed GATC sites near the replication origin. Resolution of the resulting SeqA cluster is one aspect of timing for reinitiation. A Markov model accounting for the competition between SeqA binding and methylation for one or several GATC sites relates the timing to reaction rates, and consequently to the concentrations of SeqA and methylase. A model is proposed for segregation, the motion of the two daughter DNAs into opposite poles of the cell before septation. This model assumes that the binding of SeqA and its subsequent clustering results in loops from both daughter nucleoids attached to the SeqA cluster at the GATC sites. As desequestration occurs, the cluster is divided in two, one associated with each daughter. As the loops of DNA uncoil, the two subclusters migrate apart due to the Brownian ratchet effect of the DNA loop.

Analyses of mechanisms for force generation during cell septation in Escherichia coli.

Escherichia coli is a rod-shaped bacterium that divides at its midplane, partitioning its cellular material into two roughly equal parts. At the appropriate time, a septum forms, creating the two daughter cells. Septum formation starts with the appearance of a ring of FtsZ proteins on the cell membrane at midplane. This Z-ring causes an invagination in the membrane, which is followed by growth of two new endcaps for the daughter cells. Invagination occurs against a cell overpressure of several atmospheres. A model is presented for the shape of the cell as determined by the tension in the Z-ring. This model allows the calculation of the force required for invagination. Then three possible models to generate the force necessary to achieve invagination are presented and analyzed. These models are based on converting GTP-bound FtsZ polymeric structures to GDP-bound FtsZ structures, which then leave the polymer. Each model is able to generate the force by relating the hydrolyzation to an irreversible molecular binding event, resulting in a net motion of putative anchors for the structures. All three models show that cross-linking the FtsZ protofilaments into a polymer structure allows the removal of GDP-FtsZ without interrupting the structure during force generation, as would happen for a simple polymeric chain.