A polymerization-depolymerization model that accurately generates the self-sustained oscillatory system involved in bacterial division site placement

Abstract

Determination of the proper site for division in Escherichia coli and other bacteria involves a unique spatial oscillatory system in which membrane-associated structures composed of the MinC, MinD and MinE proteins oscillate rapidly between the two cell poles. In vitro evidence indicates that this involves ordered cycles of assembly and disassembly of MinD polymers. We propose a mathematical model to explain this behavior. Unlike previous attempts, the present approach is based on the expected behavior of polymerization-depolymerization systems and incorporates current knowledge of the biochemical properties of MinD and MinE. Simulations based on the model reproduce all of the known topological and temporal characteristics of the in vivo oscillatory system.Min ͉ cell division ͉ cytoskeleton M ost bacteria divide by forming a division septum at the midpoint of the cell. Accurate placement of the division site is required to permit the equidistribution of genetic and cytoplasmic components between daughter cells. In Escherichia coli and related organisms, placement of the septum is regulated by a system of negative control, mediated by the three proteins of the MinCDE system (reviewed in ref. 1). The Min system prevents septation at potential division sites near cell poles without blocking septum formation at the desired midcell location. The MinC protein is responsible for the septation block. MinD and MinE prevent MinC from blocking division at the desired midcell site while permitting it to act at other potential division sites, thereby giving topological specificity to the division inhibitor. This process involves a unique oscillatory system in which membrane-associated MinC, -D, and -E oscillate rapidly from pole to pole.The oscillation process is initiated by assembly of a membraneassociated polar zone consisting of MinC, MinD, and MinE (2-5), which first appears near a cell pole and grows toward midcell (Fig. 1). As the growing polar zone approaches midcell, MinE forms an annular structure (the E-ring) at its leading edge. The polar zone then disassembles, retracting from midcell back to the original pole. The E-ring remains associated with the medial edge of the zone during the disassembly stage (6, 7).As the polar zone retracts from one pole, a new cycle of assembly and disassembly is initiated at the opposite end of the cell. In this way, MinC, -D, and -E oscillate from pole-to-pole with a periodicity of Ϸ1 min (2, 4-7). As a result, the timeaveraged concentration of the MinC division inhibitor is kept low at midcell, thereby permitting assembly of the new septum at this site. Although MinC normally accompanies MinD throughout the oscillation cycle, MinC is not required for the oscillation phenomenon, which requires only MinD and MinE (2, 3).In vitro, MinD binds to phospholipid vesicles in the presence of ATP (8). MinE destabilizes the phospholipid-MinD-ATP interaction by binding to the vesicle-bound MinD; this activates the MinD ATPase (9), leading to release of MinD-ADP and MinE from the vesicles.MinD ...

Phosphatidic Acid and N-Acylphosphatidylethanolamine Form Membrane Domains in Escherichia coli Mutant Lacking Cardiolipin and Phosphatidylglycerol

“…On the other hand, MinD preference for anionic phospholipids might play a role at the step of the nucleation of the MinD polymers at the cell pole (35) where anionic phospholipid domains appear to exist. The assumption for a nucleation site for MinD polymerization was formulated previously in our hypothesis (36) and was suggested in the "Min proteins polymerization-depolymerization model" by (37). The multistranded MinDE polymerization model (38) also supports this assumption.…”

Quantitative analysis of time-series fluorescence microscopy using a spot tracking method: application to Min protein dynamics

“…Computationally, several studies have been carried out with different reaction-diffusion 28 S. Unai et al models to explain these oscillations (Howard et al 2001;Kruse 2002;Howard & Rutenberg 2003;Huang et al 2003;Modchang et al 2005). It has also recently emerged that MinD forms helical filaments in living cells (Shih et al 2003) and recent mathematical models (Drew et al 2005, Pavin et al 2006) have attempted to include this feature. The model by Drew et al (2005) includes polymer growth from nucleation sites at the ends of the cell.…”

“…It has also recently emerged that MinD forms helical filaments in living cells (Shih et al 2003) and recent mathematical models (Drew et al 2005, Pavin et al 2006) have attempted to include this feature. The model by Drew et al (2005) includes polymer growth from nucleation sites at the ends of the cell. Both of these models use continuous partial differential equations.…”

Multiple modes of interconverting dynamic pattern formation by bacterial cell division proteins

“…This necessitated the exercise be limited to simpler sce-narios involving as small a number of distinct molecular states as feasible, for example, typically dividing the protein molecules into only two molecular states, membrane-bound molecules and those free in the cytosol, with an assumption that all MinD molecules in the system are in the state of competence for membrane binding. Some models also explored the possibility of protein polymerization on the membrane surface (26), which would be more readily handled by stochastic approaches (27). Other models attempted to incorporate reaction steps related to the ATPase cycle, thus introducing a MinD state not competent for membrane binding (23).…”