Acta Informatica

, Volume 54, Issue 6, pp 589–623 | Cite as

Precise parameter synthesis for stochastic biochemical systems

  • Milan Češka
  • Frits Dannenberg
  • Nicola PaolettiEmail author
  • Marta Kwiatkowska
  • Luboš Brim
Original Article


We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability analysis of molecular computation by a DNA walker; and bistability in the gene regulation of the mammalian cell cycle.



We thank David Šafránek for useful discussions about the stochastic models of gene regulation of mammalian cell cycle and Nicolas Basset for helping with the termination of the threshold synthesis algorithm. We also thank Andrej Tokarčík and Petr Pilař for implementing the prototype version of the synthesis algorithms. We finally thank the anonymous reviewers for their insightful feedback.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Milan Češka
    • 2
    • 3
  • Frits Dannenberg
    • 3
  • Nicola Paoletti
    • 3
    Email author
  • Marta Kwiatkowska
    • 3
  • Luboš Brim
    • 1
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Faculty of Information TechnologyBrno University of TechnologyBrnoCzech Republic
  3. 3.Department of Computer ScienceUniversity of OxfordOxfordUK

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