Polynomial algebra of discrete models in systems biology

Bioinformatics

Volumn 26, Issue 13, 2010, Pages 1637-1643

  Veliz Cuba, Alan ^a   Jarrah, Abdul Salam ^a,b   Laubenbacher, Reinhard ^a  

^a VIRGINIA BIOINFORMATICS INSTITUTE   (United States)

^b AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; STATISTICAL MODEL; SYSTEMS BIOLOGY;

ALGORITHMS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; SYSTEMS BIOLOGY;

EID: 77954191450     PISSN: 13674803     EISSN: 14602059     Source Type: Journal    
DOI: 10.1093/bioinformatics/btq240     Document Type: Article

References (34)

1. Albert,R. and Othmer,H. (2003) The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Bio., 223,1-18.
2. Barrett,C. et al. (2005) The global transcriptional regulatory network for metabolism in Escherichia coli exhibits few dominant functional states. Proc. Natl Acad. Sci. USA, 102,19103-19108.
3. Chaouiya,C. et al. (2004) Qualitative modelling of genetic networks: from logical regulatory graphs to standard Petri nets. In ICATPN'04, Springer, Berlin, Germany, pp. 137-156.
4. Chaouiya,C. et al. (2008) Petri net modelling of biological regulatory networks. J. Discrete Algorithms, 6, 165-177.
5. Comet,J.-P. et al. (2005) Modeling multi-valued genetic regulatory networks using highlevel Petri nets. In Ciardo,G. and Darondeau,P. (eds) Proceedings of the International Conference on the Application and Theory of Petri Nets, Springer, Berlin, Germany, pp. 208-227.
6. Davidich,M. and Bornholdt,S. (2007) Boolean network model predicts cell cycle sequence of fission yeast. PLoS One, 3, e1672.
7. Elspas,B. (1959) The theory of autonomous linear sequential networks. IRE Trans. Circuit Theory, CT-6, 45-60.
8. Egri-Nagy,A. and Nehaniv,C. (2008) Algebraic properties of automata associated to Petri nets and applications to computation in biological systems. Biosystems, 94, 297-307.
9. Espinosa-Soto,C. et al. (2004) A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell, 16, 2923-2939.
10. Faure,A. et al. (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics, 22, 124-131.
11. Formanowicz,D. et al. (2007) Petri net based model of the body iron homeostasis. J. Biomed. Inform., 40, 476-485.
12. Grunwald,S. et al. (2008) Petri net modelling of gene regulation of the duchenne muscular dystrophy. Biosystems, 92, 189-205.
13. Hernández-Toledo,A. (2005) Linear finite dynamical systems. Communications in Algebra, 33, 2977-2989.
14. Jarrah,A. et al. (2010) The Dynamics of Conjunctive and Disjunctive Boolean Network Models. Bull. Math. Bio., [Epub ahead of print, doi: 10.1007/s11538-010-9501-z, January 20, 2010].
15. Jarrah,A. et al. (2007) Nested canalyzing, unate cascade, and polynomial functions. Physica D, 233, 167-174.
16. Kielbassa,J. et al. (2009) Modeling the U1 snRNP assembly pathway in alternative splicing in human cells using Petri nets. Comput. Biol. Chem., 33, 46-61.
17. Klamt,S. et al. (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics, 7, 56.
18. Laubenbacher,R. and Stigler,B. (2004)Acomputational algebra approach to the reverseengineering of gene regulatory networks. J. Theor. Biol., 229, 523-537.
19. Li,F. et al. (2004) The yeast cell-cycle network is robustly designed. Proc. Natl Acad. Sci. USA, 101, 4781-4786.
20. Mendoza,L. (2006) A network model for the control of the differentiation process in Th cells. Biosystems, 84, 101-114.
21. Mendoza,L. and Xenarios,I. (2006) A method for the generation of standardized qualitative dynamical systems of regulatory networks. Theor. Biol. Med. Model., 3, Article no. 13.
22. Mendoza,L. et al. (1999) Genetic control of flower morphogenesis in arabidopsis thaliana: a logical analysis. Bioinformatics, 15, 593-606.
23. Naldi,A. et al. (2007) Decision diagrams for the representation and analysis of logical models of genetic networks. InCMSB'07,Vol. 4695 of LNCS/LNBI, Springer, Berlin, Germany, pp. 233-247.
24. Peleg,M. et al. (2005) Using Petri net tools to study properties and dynamics of biological systems. J. Am. Med. Informatics Assoc., 12, 181-199.
25. Remy,E. et al. (2006) From logical regulatory graphs to standard Petri nets: dynamical roles and functionality of feedback circuits. In Transactions on Computation Systems Biology VII (TCSB), Springer, Berlin, Germany, pp. 55-72.
26. Saez-Rodriguez,J. et al. (2009) Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction. Mol. Syst. Biol., 5, 331.
27. Samal,A. and Jain,S. (2008) The regulatory network of E. coli metabolism as a Boolean dynamical system exhibits both homeostasis and flexibility of response. BMC Syst. Biol., 2, Article 21.
28. Simao,E. et al. (2005) Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. coli. Bioinformatics, 21, 190-196.
29. Steggles,L. et al. (2007) Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach. Bioinformatics, 23, 336-343.
30. Steggles,L. et al. (2006) Modelling and analysing genetic networks: From Boolean networks to Petri nets. In Computational Methods in Systems Biology. International Conference, Springer, Berlin, Germany, pp. 127-141.
31. Thomas,R. (1973) Boolean formalisation of genetic control circuits. J. Theor. Biol., 42, 565-583.
32. Thomas,R. and D'Ari,R. (1989) Biological Feedback. CRC Press, Boca Raton, FL.
33. Warren,P. et al. (2009) Flux networks in metabolic graphs. Phys. Biol., 6, 46006.
34. Zhao,Q. (2005) A remark on " Scalar Equations for Synchronous Boolean Networks with Biological Applications" by C. Farrow, J. Heidel, J. Maloney, and J. Rogers. IEEE Trans. Neural Netw., 16, 1715-1716.