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Vladimir Krstic
University of Zagreb

Min-protein Oscillations in E. Coli: 3D Off-lattice Stochastic Reaction-Diffusion Model

Division site in the rod-shaped bacterium E. coli is partially regulated by pole-to-pole oscillations of the Min-family proteins: MinC, MinD, and MinE. Only MinD and MinE proteins are required to obtain oscillations. MinC proteins are recruited to the membrane by MinD, and hence follow the same oscillatory pattern. MinC when attached to the membrane (in the form of MinD-MinC complex) inhibits septum formation. As time-averaged distributions of the membrane associated MinD/MinE/MinC proteins have minimum in the central region of the cell, this region is strongly favored division site. We introduce 3D off-lattice stochastic reaction-diffusion model to describe MinD/MinE dynamical structures. The model simulates: (1) MinD/MinE diffusion (2) MinD - membrane interaction (3) MinD - MinE interaction (4) MinE driven ATP hydrolysis (5) transformation of MinD:ADP into MinD:ATP by nucleotide exchange. In addition, we assume that each membrane associated MinD protein can form up to three bonds with adjacent membrane associated MinD molecules and that MinE induced hydrolysis strongly depends on the number of bonds MinD has established.

Each of approximately 5000 molecules are explicitly tracked within our 3D simulation. This is extremely time consuming job. We have speeded up our simulation by using adaptive time steps: in our stochastic system one can use much longer time steps when the molecule tracked is in the region far from the membrane then when the molecule is in the region near the membrane. Our model reproduces many different experimentally observed phenomena using a small number of "free" parameters (many analytical models can do the same), but we think our model is step forward because it enables one to attack the problem of Min-oscillations from the microscopic point of view.

[1] K.C. Huang, Y.Meir, and  N.S. Wingreen, Dynamic structures in Escherichia coli: Spontaneous formation of MinE  rings and MinD polar zones, Proc. Natl. Acad. Sci. USA 100, 12724 (2003).

[2] S.S. Andrews and D. Bray, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail Phys. Biol. 1, 137 (2004).

[3] N. Pavin, H. Cipcic Paljetak, V. Krstic, Min Oscillations in Escherichia coli with Spontaneous Formation of  Two-Stranded Filaments in 3D Stochastic Reaction-Diffusion Model, http://arxiv.org/abs/q-bio.SC/0505051 (submitted to PRL).

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