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

Annika Eichler, Gerwald Lichtenberg

2016

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 functions, which are known to be appropriate for genetic networks. This paper introduces a high performance algorithm, which solves the parameter identification problem by so called Zhegalkin identification and exploits the restriction to canalyzing functions resulting in reduced calculation time. The canalyzing constraint is formulated in terms of orthogonal ternary vector lists - which are intrinsically used in a Branch-and-Cut algorithm obeying this constraint. The algorithm is applied to mRNA micro array data from mice under different contaminant conditions and good correspondence to a known apoptotic pathway can be shown.

References

  1. Bochmann, D. and Steinbach, B. (1991). Logikentwurf mit XBOOLE. Verlag Technik.
  2. Breindl, C., Chaves, M., and Allgöwer, F. (2013). A linear reformulation of boolean optimization problems and structure identification of gene regulation networks. In Proc. 52nd IEEE Conf. Decision Control, pages 733- 738.
  3. Faisal, S. (2008). Discrete-Time Modelling of Gene Networks by Zhegalkin Polynomials. Ingenieurwissenschaften. Dr. Hut Verlag.
  4. Faisal, S., Lichtenberg, G., Trump, S., and Attinger, S. (2010). Structural properties of continuous representations of boolean functions for gene network modelling. Automatica, 46(12):2047-2052.
  5. Faisal, S., Lichtenberg, G., and Werner, H. (2005). A polynomial approach to structural gene dynamics modelling. In Proc. 16th IFAC World Congr., pages 2119- 2119.
  6. Faisal, S., Lichtenberg, G., and Werner, H. (2006). Canalizing Zhegalkin polynomials as models for gene expression time series data. In Proc. 1st Int. Cong. Eng. Intell. Syst.
  7. Jarrah, A. S., Raposa, B., and Laubenbacher, R. (2007). Nested canalyzing, unate cascade, and polynomial functions. PhysicaD: Nonlinear Phenomena, 233(2):167-174.
  8. Kanehisa, M. and Goto, S. (2000). KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Research, 28(1):27-30.
  9. Kauffman, S. (1993). The Origins of Order, Self Organization and Selection in Evolution. Oxford University Press.
  10. Kauffman, S. A., Petersen, C., Samuelsson, B., and Troein, C. (2003). Random boolean network models and the yeast transcriptional network. PNAS, 100(25):14796- 14799.
  11. Kolda, T. and Bader, B. (2009). Tensor Decompositions and Applications. SIAM Review, 51(3):455-500.
  12. Lichtenberg, G. and Eichler, A. (2011). Multilinear algebraic boolean modelling with tensor decompositions techniques. In Proc. 18th IFAC World Congr., pages 5603-5608.
  13. Lichtenberg, G., Faisal, S., and Werner, H. (2005). Ein Ansatz zur dynamischen Modellierung der Genexpression mit Shegalkin-Polynomen. Automatisierungstechnik, 53:589-596.
  14. Lin, P. and Khatri, S. (2013). Logic Synthesis for Genetic Diseases: Modeling Disease Behavior Using Boolean Networks. Springer.
  15. Veliz-Cuba, A., Jarrah, A. S., and Laubenbacher., R. (2010). Polynomial algebra of discrete models in systems biology. Bioinformatics, 26(13):1637-1643.
  16. Zhegalkin, I. (1928). Arithmetics of symbolic logic. Mat. Sb., 35(3-4):311-377.
Download


Paper Citation


in Harvard Style

Eichler A. and Lichtenberg G. (2016). Parameter Identification of Canalyzing Boolean Functions with Ternary Vectors for Gene Networks . In Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-199-1, pages 110-118. DOI: 10.5220/0005978701100118


in Bibtex Style

@conference{simultech16,
author={Annika Eichler and Gerwald Lichtenberg},
title={Parameter Identification of Canalyzing Boolean Functions with Ternary Vectors for Gene Networks},
booktitle={Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2016},
pages={110-118},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005978701100118},
isbn={978-989-758-199-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Parameter Identification of Canalyzing Boolean Functions with Ternary Vectors for Gene Networks
SN - 978-989-758-199-1
AU - Eichler A.
AU - Lichtenberg G.
PY - 2016
SP - 110
EP - 118
DO - 10.5220/0005978701100118