Model checking liveness properties of genetic regulatory networks

  • Authors:

  • Grégory Batt;Calin Belta;Ron Weiss

  • Affiliations:

  • Center for Information and Systems Engineering and Center for BioDynamics, Boston University, Brookline, MA;Center for Information and Systems Engineering and Center for BioDynamics, Boston University, Brookline, MA;Department of Electrical Engineering and Department of Molecular Biology, Princeton University, Princeton, NJ

  • Venue:
  • TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
  • Year:
  • 2007

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Abstract

Recent studies have demonstrated the possibility to build genetic regulatory networks that confer a desired behavior to a living organism. However, the design of these networks is difficult, notably because of uncertainties on parameter values. In previous work, we proposed an approach to analyze genetic regulatory networks with parameter uncertainties. In this approach, the models are based on piecewise-multiaffine (PMA) differential equations, the specifications are expressed in temporal logic, and uncertain parameters are given by intervals. Abstractions are used to obtain finite discrete representations of the dynamics of the system, amenable to model checking. However, the abstraction process creates spurious behaviors along which time does not progress, called time-converging behaviors. Consequently, the verification of liveness properties, expressing that something will eventually happen, and implicitly assuming progress of time, often fails. In this work, we extend our previous approach to enforce progress of time. More precisely, we define transient regions as subsets of the state space left in finite time by every solution trajectory, show how they can be used to rule out time-converging behaviors, and provide sufficient conditions for their identification in PMA systems. This approach is implemented in RoVerGeNe and applied to the analysis of a network built in the bacterium E. coli.