UBC Math Biology Seminar: Eldon Emberly

In many bacteria, the segregation of their DNA is actively transported by a two protein system. One of the proteins acts as a substrate and binds to DNA in an ATP bound form, while the other stimulates its phosphatase activity, causing it to unbind after conversion to an ADP bound form. The result is a burnt-bridges style locomotion where the activity of the proteins generates a spatial gradient of the substrate that can drive motion. When this machinery is segregating low-copy plasmids, experiments show that the plasmids oscillate along the cell length, eventually placing themselves regularly along the cell. However it is unclear whether these oscillations persist as plasmids continue to replicate, or if system moves to a stable fixed point? Here I will present a deterministic model for the spatial dynamics of plasmids under the control of this two protein system. We find that over the course of the cell cycle, through a competition between spatial confinement and fluctuations in the amount of free substrate protein, the system can transition from a stable point to oscillations, then back to a stable point again. The prediction is that the system measure's cell length via oscillations but eventually gets pushed into a fixed point that faithfully partitions the genetic information.