Graph-Based Modeling of Biological Regulatory Networks: Introduction of Singular States

  • Adrien Richard
  • Jean-Paul Comet
  • Gilles Bernot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3082)


In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. R. Thomas and coworkers introduced a qualitative description of the dynamics of such regulatory networks, called the generalized logical analysis, and used the concept of circuit-characteristic states to identify all steady states and functional circuits. These characteristic states play an essential role on the dynamics of the system, but they are not represented in the state graph. In this paper we present an extension of this formalism in which all singular states including characteristic ones are represented. Consequently, the state graph contains all steady states. Model checking is then able to verify temporal properties concerning singular states. Finally, we prove that this new modeling is coherent with R. Thomas’ modeling since all paths of R. Thomas’ dynamics are represented in the new state graph, which in addition shows the influence of singular states on the dynamics.


Model Check State Graph Feedback Circuit Regular State Computation Tree Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Adrien Richard
    • 1
  • Jean-Paul Comet
    • 1
  • Gilles Bernot
    • 1
  1. 1.La.M.I UMR 8042, CNRS & Université d’ÉvryÉvryFrance

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