Pattern formation in E.coli: a model for the localization of the division site by the pole-to-pole oscillations of Min proteins

How a bacterium finds its center in order to localize the division machinery is a long-standing question. The center is millions of molecules away from the poles. Thus, what type of signalling system enables the position of the division apparatus? Crucial is a pol-to-pol oscillation of a molecules called MinD, which block,s together with another molecule (MinC) the initiation of cell division. Cell division becomes restricted to the centre where, on overage, the MinC/D concentration is lowest. The figure below shows snapshots of the MinD oscillation. The numbers are seconds. Each full cycle requires about 50 seconds [1,2].

(MinD oscillation in E.Coli, photograph kindly by P. De Boer, see [1])

What type of molecular interaction allows this pole-to-pole oscillation? Although more or less all molecules involved in this center-finding process were known for long, it remained an open problem of how these components work together. In a review Shapiro and Losick wrote in 2000 : "we are left with two topological mysteries: how does a bacterial cell knows where its middle is and what is the medial mark that triggers polymerisation" [3].

To facilitate an understanding of this highly complex process, first an analogy should be given (knowing that all analogies are a bit dangerous). Imagine a strip of very rapidly growing grass on which a cow is grazing. After eating up all grass in the immediate surrounding, the cow will start to move into a region in which more grass is available. In which direction to go first is more ore less random but it will continue in this direction since less grass is left behind. After reaching the end of the strip, the cow will move rapidly to the other side of the strip where still fresh grass is available. After reaching the other end, the process will start anew, assuming that the grass recovered meanwhile. Since the cow passes the centre twice as frequent as the poles, there will remain less grass in the centre,

In the bacterium, a protein called MinD would covers uniformly the membrane (the grass). According to our model, a local signal (MinE, the cow) needs MinD to bind to the membrane but removes thereby MinD from the membrane. Thus, the MinE signal will move into a region where more MinD is available. Thus, the minE signal sweeps over the field like a windshield wiper of a car. On time average, the MinD concentration is lowest in the center, allowing the initiation of the division apparatus (FtsZ-ring) (for more details clicke here): The analogy in not perfect in two aspects. The Min molecules but not the grass is recycled. Further, the cow is anyway a localized object. To achieve a similar localization of a the MinE distribution , a pattern forming reaction is required. The following simulation shows a typical computer simulation using our model (Meinhardt, H, de Boer, P.A.J., 2001) [PDF]

On the subsequent pages, the elements of this model are described in more detail

A minimum mechanism to generate oscillating polar patterns
Simulation of the actual MinD/MinE pattern
Oscillation in counter-phase and multiple division sites in long extended filaments
Some examples of the changing behavior after parameter changes
Simulation using a tube-like geometry
A more static mechanism for center detection: Insertion of new maxima at maximum distance from the poles
A short program that allows the simulation of the MinD/MinE waves

More details and time-lapse fluorescence micrographs

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For further details and references see Meinhardt, H, de Boer, P.A.J. (2001). Pattern formation in Escherichia coli: A model for the pole-to-pole oscillations of Min proteins and the localization of the division site. PNAS 98, 14202-14207 [PDF]. Around the same time, two alternative but somewhat related models were published [7,8].

References:

[1] Raskin, D. M., and de Boer, P. A. J. (1999b). Rapid pole-to-pole oscillation of a protein required for directing division to the middle of Escherichiacoli., PNAS 96, 4971-4976
[2] Hu, Z., and Lutkenhaus, J. (1999). Topological regulation of cell division in Escherichia coli involves rapid pole to pole oscillation of the division inhibitor MinC under the control of MinD and MinE., Mol Microbiol 34, 82-90.
[3] Shapiro, L. and Losick, R. (2000). Dynamic spatial regulation in the bacterial cell. Cell 100, 89-98.
[4] Fu, X., Shih, Y. L., Zhang, Y., and Rothfield, L. I. (2001). The MinE ring required for proper placement of the division site is a mobile structure that changes its cellular location during the Escherichiacoli division cycle., Proc Natl Acad Sci U S A 98, 980-985.
[5] Hale, C. A., Meinhardt, H., and de Boer, P. A. J. (2001). Dynamic localization cycle of the cell division regulator MinE in E.coli., EMBO J. 20, 1563-1572.
[6] Rowland, S. L., Fu, X., Sayed, M. A., Zhang, Y., Cook, W. R., and Rothfield, L. I. (2000). Membrane redistribution of the Escherichiacoli MinD protein induced by MinE., J Bacteriol 182, 613-619.
[7] Kruse, K. (2002). A dynamic model for determining the middle of Escherichia coli. Biophys. J. 82, 618-627.
[8] Howard, M., Rutenberg, A.D. and de Vet, S. (2001). Dynamic compartmentalization in bacteria: accurate division in E.coli. Phys.Rev. Letters 87, 278102-1-4.

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