Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model

  • Ronojoy Ghosh
  • Claire J. Tomlin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2034)


Biological cell networks exhibit complex combinations of both discrete and continuous behaviors: indeed, the dynamics that govern the spatial and temporal increase or decrease of protein concentration inside a single cell are continuous differential equations, while the activation or deactivation of these continuous dynamics are triggered by discrete switches which encode protein concentrations reaching given thresholds. In this paper, we model as a hybrid system a striking example of this behavior in a biological mechanism called Delta-Notch signaling, which is thought to be the primary mechanism of cell differentiation in a variety of cell networks. We present results in both simulation and reachability analysis of this hybrid system.We emphasize how the hybrid system model is computationally superior (for both simulation and analysis) to other nonlinear models in the literature, without compromising faithful modeling of the biological phenomena.


Hybrid Model Phase Portrait Lateral Inhibition Ciliated Cell Transition Diagram 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ronojoy Ghosh
    • 1
  • Claire J. Tomlin
    • 1
  1. 1.Stanford UniversityStanfordUSA

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