Abstract
The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants and compared the results to the corresponding deterministic mean-field description. We found that wild-type (wt) and filamentous (ftsZ −) cells are well characterized by the mean-field model, but that a stochastic model is necessary to account for several of the characteristics of the spherical (rodA−) and phospathedylethanolamide-deficient (PE−) phenotypes. For spherical cells, the mean-field model is bistable, and the system can get trapped in a non-oscillatory state. However, when the intrinsic noise is considered, only the experimentally observed oscillatory behavior remains. The stochastic model also reproduces the change in oscillation directions observed in the spherical phenotype and the occasional gliding of the MinD region along the inner membrane. For the PE− mutant, the stochastic model explains the appearance of randomly localized and dense MinD clusters as a nucleation phenomenon, in which the stochastic kinetics at low copy number causes local discharges of the high MinDATP to MinDADP potential. We find that a simple five-reaction model of the Min system can explain all documented Min phenotypes, if stochastic kinetics and three-dimensional diffusion are accounted for. Our results emphasize that local copy number fluctuation may result in phenotypic differences although the total number of molecules of the relevant species is high.
Highlights
Quantitative modeling of biological processes is becoming increasingly important as the processes we seek to understand become more and more complicated
We model the stochastic reaction–diffusion kinetics of the Min systems using the framework provided by the reaction– diffusion master equation (RDME) [34,35,36,37]
We have developed computational methods that have made it possible to simulate a model of the Min system based on the reaction–diffusion master equation [34,36,37,46]
Summary
Quantitative modeling of biological processes is becoming increasingly important as the processes we seek to understand become more and more complicated. In this case, it is obvious that the cartoon representation of the possible reactions, e.g., that, does not give all the information about the system. The Min system, which directs E. coli cell division to the middle of the cell [1], is an extraordinary example of how quantitative modeling has helped to clarify spatiotemporal pattern formation of biological relevance [2]. Molecule discreteness and fluctuation in non-homogeneous systems has, for instance, been shown to create new steady states [3], drive spatial oscillations [4], cause spatial phase separation of a bistable system [5], or drive the irregular relocation dynamics of Soj protein in Bacillus subtilis [6]
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