URDME simulating stochastic spatial kinetics

In E. Coli, the Min family of proteins are believed to play a key role in the regulation of symmetric cell division. In a mechanism thought to be self-organized and to function in a manner similar to the formation of Turing-patterns, the MinD protein oscillates from pole to pole with a period close to 40 seconds. Another Min protein, MinC, co-localizes with MinD and acts as a repressor for the formation of the cell division site by destabilizing a polymerization. On average, MinD (and hence MinC) will spend less time near the center of the cell, allowing the division ring to assemble there.

In the simulation animated above a uniform random initial distribution of protein was used. After some time regular oscillations were obtained. In the figure below a series of simulations on bacteria of increasing length have been performed. It can clearly be seen that the oscillations stop abruptly at a certain length. If oscillations should be sustained, some additional effect or term should therefore enter in the model.


  • The numerical method employed in the simulation was described in S. Engblom, L. Ferm, A. Hellander, Lötstedt: Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes , in SIAM J. Sci. Comput. 31(3):1774--1797, 2009: (doi).
  • The URDME software was further discussed in B. Drawert, S. Engblom, and A. Hellander: URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries in BMC Syst. Biol. 6(76):1--17, 2012: (doi).

  • Stefan Engblom
    Last modified: Thu March 16 16:53:56 MEST 2017