Journal of Mathematical Biology

, Volume 67, Issue 5, pp 1171–1197 | Cite as

Spatial aspects in the SMAD signaling pathway

  • J. Claus
  • E. Friedmann
  • U. Klingmüller
  • R. Rannacher
  • T. Szekeres


Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neglect spatial aspects. We present a model for the SMAD signaling pathway, which gives a temporal and spatial description on the basis of reaction diffusion equations to answer the question whether cell geometry plays a role in signaling. In this article we simulate the ordinary differential equations as well as partial differential equations of parabolic type with suile numerical methods, the latter on different cell geometries. In addition to manual construction of idealized cells, we also construct meshes from microscopy images of real cells. The main focus of the paper is to compare the results of the model without and with spatial aspects to answer the addressed question. The results show that diffusion in the model can lead to significant intracellular gradients of signaling molecules and changes the level of response to the signal transduced by the signaling pathway. In particular, the extent of these observations depends on the geometry of the cell.


Cell signaling Mixed differential equations Finite elements  Mesh generation 

Mathematics Subject Classification (2000)

34A34 34D05 34D20 35K57 65N30 65N50 



Special thanks to Dr. D. Jungblut, Goethe Center for Scientific Computing (G-CSC), University Frankfurt, Germany, for doing the 3D geometry reconstruction with his software developed in his PhD.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • J. Claus
    • 1
  • E. Friedmann
    • 2
  • U. Klingmüller
    • 3
  • R. Rannacher
    • 2
  • T. Szekeres
    • 3
  1. 1.Center for Modeling and Simulation in the Biosciences (BIOMS)Universität HeidelbergHeidelbergGermany
  2. 2.Department of Applied MathematicsHeidelbergGermany
  3. 3.Systems Biology of Signal TransductionGerman Cancer Research CenterHeidelbergGermany

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