Predictions from a stochastic polymer model for the MinDE protein dynamics in Escherichia coli.
The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations--both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.
Borowski
Peter
P
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia, Canada. peterphysik@gmail.com
Cytrynbaum
Eric N
EN
D000251:Adenosine Triphosphatases / Q000737:chemistry / Q000378:metabolism*; D001704:Biopolymers / Q000737:chemistry / Q000378:metabolism*; D018797:Cell Cycle Proteins / Q000737:chemistry / Q000378:metabolism*; D004926:Escherichia coli; D029968:Escherichia coli Proteins / Q000737:chemistry / Q000378:metabolism*; D008958:Models, Molecular; D013269:Stochastic Processes
D001704:Biopolymers; D018797:Cell Cycle Proteins; D029968:Escherichia coli Proteins; C093548:MinE protein, E coli; D000251:Adenosine Triphosphatases; C072069:MinD protein, E coli