URDME simulating Turing patterns



The above animation displays the dynamics until approximate equilibirum of the Schnakenberg model, a model which develops Turing patterns. Here spots of the morphogen are seen to be developed; in the formulation above the reaction-diffusion system is interpreted in a stochastic sense and the noise is seen to cause the pattern to fluctuate somewhat at the end of the simulation.

References

  • 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).
  • The Schnakenberg and other models were implemented and solved in URDME in Y. Saygun: Computational Stochastic Morphogenesis, Master's thesis, 2015.
    • Stefan Engblom
    Last modified: Thu March 16 16:53:56 MEST 2017