Bulletin of Mathematical Biology

, Volume 75, Issue 6, pp 920–938 | Cite as

Analysis and Characterization of Asynchronous State Transition Graphs Using Extremal States

  • Therese Lorenz
  • Heike Siebert
  • Alexander Bockmayr
Original Article


Logical modeling of biological regulatory networks gives rise to a representation of the system’s dynamics as a so-called state transition graph. Analysis of such a graph in its entirety allows for a comprehensive understanding of the functionalities and behavior of the modeled system. However, the size of the vertex set of the graph is exponential in the number of the network components making analysis costly, motivating development of reduction methods. In this paper, we present results allowing for a complete description of an asynchronous state transition graph of a Thomas network solely based on the analysis of the subgraph induced by certain extremal states. Utilizing this notion, we compare the behavior of a simple multivalued network and a corresponding Boolean network and analyze the conservation of dynamical properties between them. Understanding the relation between such coarser and finer models is a necessary step toward meaningful network reduction as well as model refinement methods.


Regulatory networks Logical modeling Thomas formalism Model reduction Finite dynamical systems Systems biology 


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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Therese Lorenz
    • 1
  • Heike Siebert
    • 1
  • Alexander Bockmayr
    • 1
  1. 1.DFG Research Center MatheonFreie Universität BerlinBerlinGermany

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