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Parameter Identification of Canalyzing and Nested Canalyzing Boolean Functions with Ternary Vectors for Gene Networks

  • Annika Eichler
  • Gerwald Lichtenberg
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 676)

Abstract

In gene dynamics modeling, parameters of Boolean networks are identified from continuous data under various assumptions expressed by logical constraints. These constraints may restrict the dynamics of the network to the subclass of canalyzing or nested canalyzing functions, which are known to be appropriate for genetic networks. This paper introduces high performance algorithms, which solve the parameter identification problem by so called Zhegalkin identification and exploit the restriction to canalyzing or nested canalyzing functions resulting in reduced calculation time. The constraints are formulated in terms of orthogonal ternary vector lists, which offer an efficient representation for Boolean functions. The canalyzing constraints can be intrinsically incorporated in an existing Branch-and-Cut algorithm, which lead to a natural restriction of the search space and thus of the calculation time. For nested canalyzing constraints this is not possible. Instead, an identification algorithm based on enumeration is proposed. The algorithms are applied to mRNA micro array data from mice under different contaminant conditions and good correspondence to a known apoptotic pathway can be shown.

Keywords

Parameter identification Networks Gene dynamics Systems biology Boolean functions Ternary logic 

Notes

Acknowledgements

The authors would like to thank Saskia Trump and Sabine Attinger from Helmholtz Center for Environmental Research Leipzig for access to microarray data.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Automatic Control LaboratoryETH ZurichZurichSwitzerland
  2. 2.Faculty Life SciencesHamburg University of Applied SciencesHamburgGermany

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