ODE-Based Modeling of Complex Regulatory Circuits

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Plant Gene Regulatory Networks

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1629))

Abstract

Transcriptional regulatory circuits are often complex, consisting of many components and regulatory interactions. Mathematical modeling is an important tool for understanding the behavior of these circuits, and identifying gaps in our understanding of gene regulation. Ordinary differential equations (ODEs) are a commonly used formalism for constructing mathematical models of complex regulatory networks. Here, I outline the steps involved in develo**, parameterizing, and testing an ODE model of a gene regulatory network.

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References

  1. Dalchau N (2012) Understanding biological timing using mechanistic and black-box models. New Phytol 193(4):852–858. doi:10.1111/j.1469-8137.2011.04004.x

    Article  CAS  PubMed  Google Scholar 

  2. Chew YH, Smith RW, Jones HJ, Seaton DD, Grima R, Halliday KJ (2014) Mathematical models light up plant signaling. Plant Cell 26(1):5–20. doi:10.1105/tpc.113.120006

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Pokhilko A, Fernández AP, Edwards KD, Southern MM, Halliday KJ, Millar AJ (2012) The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops. Mol Syst Biol 8:574. doi:10.1038/msb.2012.6

    Article  PubMed  PubMed Central  Google Scholar 

  4. Seaton DD, Smith RW, Song YH, MacGregor DR, Stewart K, Steel G, Foreman J et al (2015) linked circadian outputs control elongation growth and flowering in response to photoperiod and temperature. Mol Syst Biol 11(1):776. doi:10.15252/msb.20145766

    Article  PubMed  PubMed Central  Google Scholar 

  5. Csikász-Nagy A, Battogtokh D, Chen KC, Novák B, Tyson JJ (2006) Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J 90(12):4361–4379. doi:10.1529/biophysj.106.081240

    Article  PubMed  PubMed Central  Google Scholar 

  6. Aldridge BB, Burke JM, Lauffenburger DA, Sorger PK (2006) Physicochemical modelling of cell signalling pathways. Nat Cell Biol 8(11):1195–1203. doi:10.1038/ncb1497

    Article  CAS  PubMed  Google Scholar 

  7. Buchler NE, Louis M (2008) Molecular titration and ultrasensitivity in regulatory networks. J Mol Biol 384(5):1106–1119. doi:10.1016/j.jmb.2008.09.079

    Article  CAS  PubMed  Google Scholar 

  8. Seaton DD, Krishnan J (2012) Effects of multiple enzyme-substrate interactions in basic units of cellular signal processing. Phys Biol 9(4):045009. doi:10.1088/1478-3975/9/4/045009

    Article  CAS  PubMed  Google Scholar 

  9. Tyson JJ, Albert R, Goldbeter A, Ruoff P, Sible J (2008) Biological switches and clocks. J R Soc Interface 1(August):S1–S8. doi:10.1098/rsif.2008.0179.focus

    Article  Google Scholar 

  10. Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI—a COmplex PAthway SImulator. Bioinformatics 22(24):3067–3074. doi:10.1093/bioinformatics/btl485

    Article  CAS  PubMed  Google Scholar 

  11. Locke JCW, Kozma-Bognár L, Gould PD, Fehér B, Kevei E, Nagy F, Turner MS, Hall A, Millar AJ (2006) Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol Syst Biol 2(1). doi:10.1038/msb4100102

  12. Locke JCW, Millar AJ, Turner MS (2005) Modelling genetic networks with noisy and varied experimental data: the circadian clock in Arabidopsis thaliana. J Theor Biol 234(3):383–393. doi:10.1016/j.jtbi.2004.11.038

  13. Salazar JD, Saithong T, Brown PE, Foreman J, Locke JC, Halliday KJ, Carré IA, Rand DA, Millar AJ (2009) Prediction of photoperiodic regulators from quantitative gene circuit models. Cell 139(6):1170–1179. doi:10.1016/j.cell.2009.11.029

    Article  CAS  PubMed  Google Scholar 

  14. Song YH, Smith RW, To BJ, Millar AJ, Imaizumi T (2012) FKF1 conveys timing information for CONSTANS stabilization in photoperiodic flowering. Science (New York, NY) 336(6084):1045–1049. doi:10.1126/science.1219644

    Article  CAS  Google Scholar 

  15. Toni T, Welch D, Strelkowa N, Ipsen A, MPH S (2009) Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface 6(31):187–202. doi:10.1098/rsif.2008.0172

    Article  PubMed  Google Scholar 

  16. Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, and the rest of the SBML Forum et al (2003) The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4):524–531. doi:10.1093/bioinformatics/btg015

    Article  Google Scholar 

  17. Novère L, Nicolas BB, Broicher A, Courtot M, Donizelli M, Dharuri H, Lu L et al (2006) BioModels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res 34(Database issue):D689–D691. doi:10.1093/nar/gkj092

    Article  PubMed  Google Scholar 

  18. Domijan M, Brown PE, Shulgin BV, Rand DA (2016) PeTTSy: a computational tool for perturbation analysis of complex systems biology models. BMC Bioinformatics 17:124. doi:10.1186/s12859-016-0972-2

    Article  PubMed  PubMed Central  Google Scholar 

  19. Rand DA (2008) Map** global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law. J R Soc Interface 5(Suppl 1):S59–S69. doi:10.1098/rsif.2008.0084.focus

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Seaton DD, Krishnan J (2016) Model-based analysis of cell cycle responses to dynamically changing environments. PLoS Comput Biol 12(1):e1004604

    Article  PubMed  PubMed Central  Google Scholar 

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Correspondence to Daniel D. Seaton .

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Seaton, D.D. (2017). ODE-Based Modeling of Complex Regulatory Circuits. In: Kaufmann, K., Mueller-Roeber, B. (eds) Plant Gene Regulatory Networks. Methods in Molecular Biology, vol 1629. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-7125-1_20

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  • DOI: https://doi.org/10.1007/978-1-4939-7125-1_20

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  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-7124-4

  • Online ISBN: 978-1-4939-7125-1

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