Pattern formation by the Min system of Escherichia coli

Abstract

What is the Min System? Min proteins are a class of proteins that is widely conserved among bacteria. They are involved in locating the cell division machinery of the bacterium to the cell middle and form a part of the bacterial cytoskeleton. In the rod-shaped bacterium Escherichia coli, there are three Min proteins, namely MinC, MinD and MinE. These proteins form spatiotemporal patterns in the E. coli cell which are characterized by concentration maxima that oscillate from one cell pole to the other. Such Min oscillations prohibit the localization of the division plane to the cell poles and prevent in this way the formation of anucleate daughter cells - so-called mini cells. Our objective. There are strong indications that the pattern produced by the Min system in Escherichia coli is self-organized. In fact, MinD and MinE self-organize into traveling waves and spirals in vitro on a planar membrane. In this work, we want to understand by which mechanism the dynamic instability is generated in the Min system: Using the framework of a mean-field description, we ask which terms in the equations are essential to reproduce the qualitative behavior of the Min system. In order to test predictions of theoretical descriptions, we want to examine the Min system further experimentally. Our results. In this thesis, we use both theoretical and experimental tools to characterize the Min system. We consider two mean field models of the Min system that emphasize different aspects of Min protein interactions that can cause a dynamic instability. The first assumes that MinD proteins feel mutual interactions in the membrane-bound state leading to an aggregating current that results in the formation of concentration maxima. In the second model, MinD and MinE bind to the membrane in a self-enhanced manner thereby inducing a dynamic instability in the system. We study the solutions of the associated dynamical systems and compare them with the patterns observed in living E. coli and in vitro. We find that both models are able to generate patterns similar to those observed in wild type E. coli. Oscillations in filamentous E. coli mutants and the stochastic switching in very short, newborn cells are described more accurately by the first model whereas in vitro patterning of the Min system is more aptly captured by the second description. Applying fluorescence correlation spectroscopy to the Min system in living E. coli cells, we obtain characteristic time constants of the Min system. In particular, we estimate the mobility of MinD and MinE in the cytoplasm of the bacterium. Furthermore, we experimentally study the pattern formation of the Min system in short, newborn cells. We find that these show stochastic switching of Min concentration maxima instead of periodic switching as usually reported. During cell growth the switching becomes less stochastic and merges into oscillations at a critical cell length.

Min-Proteine sind ein Teil des bakteriellen Zytoskeletts. Im stäbchenförmigen Bakterium Escherichia coli bilden Min-Proteine raumzeitliche Muster. In dieser Doktorarbeit benutzen wir sowohl theoretische als auch experimentelle Methoden, um das Min-System zu charakterisieren. Im theoretischen Teil der Arbeit betrachten wir zwei verschiedene, grobkörnige Modelle des Min-Systems, die exemplarisch verschiedene Annahmen über die Erzeugung der dynamischen Instabilität machen. Das erste Modell geht davon aus, dass MinD-Proteine im membran-gebundenen Zustand miteinander wechselwirken, so dass ein aggregierender Strom entsteht, der zu einer Bildung von Konzentrationsmaxima führt. Das zweite Modell nimmt an, dass MinD und MinE selbstverstärkend an die Membran binden und so eine dynamische Instabilität im System erzeugen. Lösungen der zugehörigen dynamischen Systeme werden untersucht und mit den Mustern des Min-Systems in E.coli und in vitro verglichen. Durch Anwenden von Fluoreszenz-Korellations-Spektroskopie auf Min-Proteine in vivo konnten wir charakteristische Zeitskalen des Min-Systems bestimmen. Zusätzlich zeigen wir experimentell, dass in sehr kurzen E. coli Min-Konzentrationsmaxima stochastisch zwischen den Zellpolen hin- und herwechseln.