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Comparison of Gene Regulatory Networks via Steady-State Trajectories

Abstract

The modeling of genetic regulatory networks is becoming increasingly widespread in the study of biological systems. In the abstract, one would prefer quantitatively comprehensive models, such as a differential-equation model, to coarse models; however, in practice, detailed models require more accurate measurements for inference and more computational power to analyze than coarse-scale models. It is crucial to address the issue of model complexity in the framework of a basic scientific paradigm: the model should be of minimal complexity to provide the necessary predictive power. Addressing this issue requires a metric by which to compare networks. This paper proposes the use of a classical measure of difference between amplitude distributions for periodic signals to compare two networks according to the differences of their trajectories in the steady state. The metric is applicable to networks with both continuous and discrete values for both time and state, and it possesses the critical property that it allows the comparison of networks of different natures. We demonstrate application of the metric by comparing a continuous-valued reference network against simplified versions obtained via quantization.

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References

  1. De Jong H: Modeling and simulation of genetic regulatory systems: a literature review. Journal of Computational Biology 2002, 9(1):67-103. 10.1089/10665270252833208

    Article  Google Scholar 

  2. Srivastava R, You L, Summers J, Yin J: Stochastic vs. deterministic modeling of intracellular viral kinetics. Journal of Theoretical Biology 2002, 218(3):309-321. 10.1006/jtbi.2002.3078

    Article  MathSciNet  Google Scholar 

  3. Albert R, Barabási A-L: Statistical mechanics of complex networks. Reviews of Modern Physics 2002, 74(1):47-97. 10.1103/RevModPhys.74.47

    Article  MathSciNet  MATH  Google Scholar 

  4. Kim S, Li H, Dougherty ER, et al.: Can Markov chain models mimic biological regulation? Journal of Biological Systems 2002, 10(4):337-357. 10.1142/S0218339002000676

    Article  MATH  Google Scholar 

  5. Albert R, Othmer HG: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster . Journal of Theoretical Biology 2003, 223(1):1-18. 10.1016/S0022-5193(03)00035-3

    Article  MathSciNet  Google Scholar 

  6. Aburatani S, Tashiro K, Savoie CJ, et al.: Discovery of novel transcription control relationships with gene regulatory networks generated from multiple-disruption full genome expression libraries. DNA Research 2003, 10(1):1-8. 10.1093/dnares/10.1.1

    Article  Google Scholar 

  7. Goutsias J, Kim S: A nonlinear discrete dynamical model for transcriptional regulation: construction and properties. Biophysical Journal 2004, 86(4):1922-1945. 10.1016/S0006-3495(04)74257-5

    Article  Google Scholar 

  8. Li H, Zhan M: Systematic intervention of transcription for identifying network response to disease and cellular phenotypes. Bioinformatics 2006, 22(1):96-102. 10.1093/bioinformatics/bti752

    Article  Google Scholar 

  9. Datta A, Choudhary A, Bittner ML, Dougherty ER: External control in Markovian genetic regulatory networks. Machine Learning 2003, 52(1-2):169-191.

    Article  MATH  Google Scholar 

  10. Choudhary A, Datta A, Bittner ML, Dougherty ER: Control in a family of boolean networks. IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS '06), College Station, Tex, USA, May 2006

    Google Scholar 

  11. Devroye L, Györffi L, Lugosi G: A Probabilistic Theory of Pattern Recognition. Springer, New York, NY, USA; 1996.

    Book  MATH  Google Scholar 

  12. Ivanov I, Dougherty ER: Modeling genetic regulatory networks: continuous or discrete? Journal of Biological Systems 2006, 14(2):219-229. 10.1142/S0218339006001763

    Article  MATH  Google Scholar 

  13. Ivanov I, Dougherty ER: Reduction mappings between probabilistic boolean networks. EURASIP Journal on Applied Signal Processing 2004, 2004(1):125-131. 10.1155/S1110865704309182

    Article  MATH  Google Scholar 

  14. Ott S, Imoto S, Miyano S: Finding optimal models for small gene networks. Proceedings of the Pacific Symposium on Biocomputing (PSB '04), Big Island, Hawaii, USA, January 2004 557-567.

    Google Scholar 

  15. Wessels LF, van Someren EP, Reinders MJ: A comparison of genetic network models. Proceedings of the Pacific Symposium on Biocomputing (PSB '01), Lihue, Hawaii, USA, January 2001 508-519.

    Google Scholar 

  16. Elowitz MB, Levine AJ, Siggia ED, Swain PS: Stochastic gene expression in a single cell. Science 2002, 297(5584):1183-1186. 10.1126/science.1070919

    Article  Google Scholar 

  17. Kauffman SA: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, New York, NY, USA; 1993.

    Google Scholar 

  18. Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P: Molecular Biology of the Cell. 4th edition. Garland Science, New York, NY, USA; 2002.

    Google Scholar 

  19. Kauffman SA: Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology 1969, 22(3):437-467. 10.1016/0022-5193(69)90015-0

    Article  Google Scholar 

  20. Lynn PA: An Introduction to the Analysis and Processing of Signals. John Wiley & Sons, New York, NY, USA; 1973.

    Google Scholar 

  21. Arkin A, Ross J, McAdams HH: Stochastic kinetic analysis of developmental pathway bifurcation in phage -infected Escherichia coli cells. Genetics 1998, 149(4):1633-1648.

    Google Scholar 

  22. Iyer V, Struhl K: Absolute mRNA levels and transcriptional initiation rates in Saccharomyces cerevisiae . Proceedings of the National Academy of Sciences of the United States of America 1996, 93(11):5208-5212. 10.1073/pnas.93.11.5208

    Article  Google Scholar 

  23. Lorsch JR, Herschlag D: Kinetic dissection of fundamental processes of eukaryotic translation initiation in vitro. EMBO Journal 1999, 18(23):6705-6717. 10.1093/emboj/18.23.6705

    Article  Google Scholar 

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Correspondence to Marcel Brun.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Brun, M., Kim, S., Choi, W. et al. Comparison of Gene Regulatory Networks via Steady-State Trajectories. J Bioinform Sys Biology 2007, 82702 (2007). https://doi.org/10.1155/2007/82702

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  • DOI: https://doi.org/10.1155/2007/82702

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