Supplementary material and animated GIF’s for the paper of H

Pattern formation in E.coli: a model for the localization of the division site

by the pole-to-pole oscillations of Min proteins - an overview

Contents:

Formation of stable patterns by local autocatalysis and depletion of a long-ranging substrate

A minimum mechanism to generate oscillating polar patterns

Polar oscillating MinD patterns generated by traveling waves of MinE that remove MinD from the membrane

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

References

Time-lapse fluorescence micrographs

Back to main entrance page: Theoretical aspects of pattern formation and neuronal development

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?

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. In the bacterium, a protein called MinD 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, and so on. In this way, 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). In the analogy, the cow is anyway small and localized in relation to the strip. To achieve a similar localization of a biochemical reaction, a pattern forming reaction is required. By mathematical modelling, the type of interactions are explored that account for the observed dynamic behaviour of the substances involved.

More scientifically speaking, the preparation for division starts with the assembly of a polymeric ring of the tubulin-like GTPase FtsZ (Z-ring). In E.coli, this ring is localized to the center by the actions of the MinC, MinD, and MinE proteins. MinC inhibits the initiation of the Z-ring. MinC co-localizes with MinD. In wildtype cells (WT), MinC/D forms a polar pattern that oscillates between the poles, keeping the center free for initiation of cell division. Thus, virtually all of MinC/D dynamically assembles on the membrane in the shape of a test-tube covering the membrane from one pole up to approximately midcell (time-lapse fluorescence micrographs). Most of MinE accumulates at the rim of this tube, in the shape of a ring (the E-ring). The rim of the MinC/D tube and associated E-ring move from a central position to the cell pole until both the tube and ring vanish. Meanwhile, a new MinC/D tube and associated E-ring form in the opposite cell half and the process repeats, resulting in a pole-to-pole oscillation cycle of the division inhibitor. A full cycle takes about 50s. The panel below shows a schematic drawing of the MinC/D (green) and MinE (red) localization cycles. The animations show a typical computer simulation using our model to describe the dynamic behaviour of these proteins (Meinhardt and de Boer, 2001).

In the model, the signal for septum formation (the Z ring, blue) is generated by a pattern forming process which becomes localized to the membrane at the cell center due to the pole-to-pole oscillation of the inhibitor of Z-ring assembly (MinC/MinD, green). A local high concentration of a substance (MinE, red) at the membrane is generated by a pattern formation reaction which depends on membrane-bound MinD. Membrane-associated MinE displaces membrane-bound MinD. Since local MinE assembly depends on membrane-bound MinD, the removal of MinD causes the local high MinE concentration to destabilize itself and to shift into a neighboring position with higher MinD concentrations. This results in a traveling wave of MinE which 'peels' MinD off the membrane as it moves towards a cell pole. Meanwhile, MinD reassembles on the membrane in the opposite cell half. This attracts a new MinE activation which, somewhat later, leads to the wave-like removal of MinD from the membrane in that half of the cell as well. The result is a pole-to-pole oscillation of MinD and associated MinC. On time average, the MinC/MinD concentration is highest at the poles, forcing the FtsZ pattern to the center. The model accounts for the experimental observations on Min protein dynamics in live cells (Fu et al., 2001; Hale et al., 2001; Hu and Lutkenhaus, 1999; Raskin and de Boer, 1997; Raskin and de Boer, 1999a; Raskin and de Boer, 1999b; Rowland et al., 2000)

The following simulations illustrate the elementary steps: