Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T23:53:12.289Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Modelling Plant SignallingNetworks

Published online by Cambridge University Press:  10 July 2013

D. Muraro ,
H.M. Byrne ,
J.R. King  and
M.J. Bennett
D. Muraro*
Affiliation:
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham Sutton Bonington Campus, Loughborough LE12 5RD, UK Weatherall Institute of Molecular Medicine, University of Oxford, Oxford, OX3 9DS, UK
H.M. Byrne
Affiliation:
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham Sutton Bonington Campus, Loughborough LE12 5RD, UK Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, Oxford, OX1 3LB, UK School of Mathematical Sciences, University of Nottingham, University Park Nottingham NG7 2RD, UK
J.R. King
Affiliation:
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham Sutton Bonington Campus, Loughborough LE12 5RD, UK School of Mathematical Sciences, University of Nottingham, University Park Nottingham NG7 2RD, UK
M.J. Bennett
Affiliation:
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham Sutton Bonington Campus, Loughborough LE12 5RD, UK
*
⋆ Corresponding author. E-mail: daniele.muraro@ndm.ox.ac.uk
Get access

Abstract

During the last two decades, molecular genetic studies and the completion of thesequencing of the Arabidopsis thaliana genome have increased knowledge ofhormonal regulation in plants. These signal transduction pathways act in concert throughgene regulatory and signalling networks whose main components have begun to be elucidated.Our understanding of the resulting cellular processes is hindered by the complex, andsometimes counter-intuitive, dynamics of the networks, which may be interconnected throughfeedback controls and cross-regulation. Mathematical modelling provides a valuable tool toinvestigate such dynamics and to perform in silico experiments that may not be easilycarried out in a laboratory. In this article, we firstly review general methods formodelling gene and signalling networks and their application in plants. We then describespecific models of hormonal perception and cross-talk in plants. This mathematicalanalysis of sub-cellular molecular mechanisms paves the way for more comprehensivemodelling studies of hormonal transport and signalling in a multi-scale setting.

Keywords

Arabidopsis thalianasignalling networksmathematical modelling
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 4: Plant growth modelling , 2013 , pp. 5 - 24
Copyright
© EDP Sciences, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, R., Barabási, A.L.. Statistical mechanics of complex networks. Rev. Mod. Phys., 74 (2002), 47. CrossRefGoogle Scholar
U. Alon. An introduction to systems biology: design principles of biological circuits. Boca Raton: Chapman & Hall/CRC, 2007.
Alon, U.. Network motifs: theory and experimental approaches. Nat. Rev. Genet., 8 (2007), 450–461. CrossRefGoogle Scholar
Arkin, A., Ross, J., McAdams, H.H.. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics, 149 (1998), 4:1633–48. Google ScholarPubMed
L.R. Band, S. Ubeda-Tomas, R.J. Dyson, A.M. Middleton, T.C. Hodgman, M.R. Owen, O.E. Jensen, M.J. Bennett, J.R. King. Growth-induced hormone dilution can explain the dynamics of plant root cell elongation. Published online before print PNAS (2012), doi: 10.1073/pnas.1113632109.
Bansal, M., di Bernardo, D.. Inference of gene networks from temporal gene expression profiles. IET Syst. Biol., 1 (2007), (5), 306–312. CrossRefGoogle ScholarPubMed
Barabási, A.L., Bonabeau, E.. Scale-Free Networks. Scientific American 288 (2003), 60–69. CrossRefGoogle ScholarPubMed
Bartholomay, A.F.. Stochastic models for chemical reactions: I. Theory of the unimolecular reaction process. Bull. Math. Biophysics, 20 (1958), 175–90. CrossRefGoogle Scholar
Bartholomay, A.F.. Stochastic models for chemical reactions: II. The unimolecular rate constant. Bull. Math. Bio., 21 (1959), 4:363–373. CrossRefGoogle Scholar
Batt, G., Page, M., Cantone, I., Goessler, G., Monteiro, P., de Jong, H.. Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. Bioinformatics, 26 (2010), 18: i603–i610. CrossRefGoogle ScholarPubMed
Beal, M.J., Falciani, F., Ghahramani, Z., Rangel, C., Wild, D.L.. A Bayesian Approach to Reconstructing Genetic Regulatory Networks with Hidden Factors. Bioinformatics, 21 (2005), 349–356. CrossRefGoogle ScholarPubMed
Bleakley, K., Biau, G., Vert, J.P.. Supervised Reconstruction of Biological Networks with Local Models. Bioinformatics, 1 (2007), 23(13):i57–65. Google Scholar
Blilou, I., Xu, J., Wildwater, M., Willemsen, V., Paponov, I., Friml, J., Heidstra, R., Aida, M., Palme, K., Scheres, B.. The PIN auxin efflux facilitator controls growth and patterning in Arabidopsis roots. Nature, 433 (2005), 39–44. CrossRefGoogle ScholarPubMed
H.L.D. de Cavalcante, S., Gauthier, D.J., Socolar, J.E.S., Zhang, R.. On the origin of chaos in autonomous Boolean networks. Phil. Trans. R. Soc. A, 28 (2010), 368(1911):495–513. Google Scholar
V. Chandrasekaran, P.A. Parrilo, A.S. Willsky. Latent Variable Graphical Model Selection via Convex Optimization. to appear in The Annals of Statistics.
Cheng, J., Greiner, R., Kelly, J., Bell, D. A., Liu, W.. Learning Bayesian networks from data: an information-theory based approach. Artif. Intell., 137 (2002), 43–90. CrossRefGoogle Scholar
Chiquet, J., Grandvalet, Y., Ambroise, C.. Inferring multiple graphical structures. Stat. and Comput., 21 (2011), 4, 537–553. CrossRefGoogle Scholar
Chow, B., McCourt, P.. Plant hormone receptors: perception is everything. Genes Dev., 20 (2006), 1998–2008. CrossRefGoogle ScholarPubMed
Crick, F.. Diffusion in embryogenesis. Nature, 225 (1970), 420–422. CrossRefGoogle ScholarPubMed
Deamer, D.. On the origin of systems. Systems biology, synthetic biology and the origin of life. EMBO Rep., 10(S1) (2009), S1–S4. CrossRefGoogle ScholarPubMed
De Jong, H.. Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol., 9 (2002), 1, 67–103. CrossRefGoogle Scholar
Dello Ioio, R., Nakamura, K., Moubayidin, L., Perilli, S., Taniguchi, M., Morita, M.T., Aoyama, T., Costantino, P., Sabatini, S.. A Genetic Framework for the Control of Cell Division and Differentiation in the Root Meristem. Nature, 322 (2008), 1380–1384. Google ScholarPubMed
De Smet, I., Tetsumura, T., DeRybel, B., Frei dit Frey, N., Laplaze, L., Casimiro, I., Swarup, R., Naudts, M., Vanneste, S., Audenaert, D., Inzé, D., Bennett, M., Beeckman, T.. Auxin-dependent regulation of lateral root positioning in the basal meristem of Arabidopsis. Development, 134 (2007), 4:681. CrossRefGoogle ScholarPubMed
Dharmasiri, N., Dharmasiri, S., Estelle, M.. The F-box protein TIR1 is an auxin receptor. Nature, 435 (2005), 441–445. CrossRefGoogle ScholarPubMed
Díaz, J., Álvarez-Buylla, E.R.. A model of the ethylene signaling pathway and its gene response in Arabidopsis thaliana: Pathway cross-talk and noise-filtering properties. Chaos, 16 (2006), 023112. CrossRefGoogle ScholarPubMed
Dupuy, L., Vignes, M., McKenzie, B.M., White, P.J.. The dynamics of root meristem distribution in the soil. Plant Cell Environ., 33 (2010), 3:358–69. CrossRefGoogle Scholar
Edwards, R.. Analysis of continuous-time switching networks. Physica D, 146 (2000), 165–199. CrossRefGoogle Scholar
Elowitz, M.B., Leibler, S.. A synthetic oscillatory network of transcriptional regulators. Nature, 403 (2000), 335–338. CrossRefGoogle Scholar
Espinosa-Soto, C., Padilla-Longoria, P., Alvarez-Buylla, E.R.. 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 (2004), 11:2923–39. CrossRefGoogle Scholar
Ezura, H., Harberd, N.P.. Endogenous gibberellin levels influence in-vitro shoot regeneration in Arabidopsis thaliana (L.) Heynh. Planta, 197 (1995), 2:301–5. CrossRefGoogle Scholar
Friedman, N., Linial, M., Nachman, I., Pe’er, D.. Using Bayesian networks to analyze expression data. J. Comput. Biol., 7 (2000), 3-4:601–20. CrossRefGoogle ScholarPubMed
N. Friedman, K. Murphy, S. Russell. Learning the structure of dynamic probabilistic networks. UAI Proc. Morgan Kaufman, 1998.
Friedman, N., Vardi, S., Ronen, M., Alon, U., Stavans, J.. Precise temporal modulation in the response of the SOS DNA repair network in individual bacteria. PLoS Biol., 3 (2005), e238. CrossRefGoogle ScholarPubMed
Fujita, H., Toyokura, K., Okada, K., Kawaguchi, M.. Reaction-Diffusion Pattern in Shoot Apical Meristem of Plants. PLoS ONE, 6 (2011), 3: e18243. doi:10.1371/journal.pone.0018243. CrossRefGoogle Scholar
Gazzarrini, S., McCourt, P.. Cross-talk in plant hormone signalling: what Arabidopsis mutants are telling us. Ann. Bot., 91 (2003), 6:605–12. CrossRefGoogle ScholarPubMed
Genoud, T., Trevino Santa Cruz, M.B., Métraux, J.P.. Numeric Simulation of Plant Signaling Networks. Plant Physiol., 126 (2001), 4:1430–1437. CrossRefGoogle ScholarPubMed
Gillespie, D.T.. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81 (1977), 25, 2340–2361. CrossRefGoogle Scholar
Gillespie, D.T.. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem., 58 (2007), 35–55. CrossRefGoogle Scholar
Gillespie, D.T.. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys., 115 (2001), 1716–1733. CrossRefGoogle Scholar
Glass, L., Kauffman, S.. The logical analysis of continuous, non-linear biochemical control networks. J. Theor. Biol., 39 (1973), 103–129. CrossRefGoogle ScholarPubMed
Goodwin, B.C.. Oscillatory behaviour in enzymatic control processes. Adv. Enzyme Regul., 3 (1965), 425–428. CrossRefGoogle ScholarPubMed
Gordon, S.P., Chickarmane, V.S., Ohno, C., Meyerowitz, E.M.. Multiple feedback loops through cytokinin signaling control stem cell number within the Arabidopsis shoot meristem. PNAS, 106 (2009), 38:16529–16534. CrossRefGoogle ScholarPubMed
Grieneisen, V.A., Xu, J., Marée, A.F., Hogeweg, P., Scheres, B.. Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature, 449 (2007), 1008–1013. CrossRefGoogle ScholarPubMed
Griffith, J.S.. Mathematics of cellular control processes I. Negative feedback to one gene. J. Theor. Biol., 20 (1968), 2, 202–208. CrossRefGoogle ScholarPubMed
Grzegorczyk, M., Husmeier, D.. Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes. Bioinformatics, 27 (2011), 5:693–699. CrossRefGoogle ScholarPubMed
Guerriero, M.L., Pokhilko, A., Fernández, A.P., Halliday, K.J., Millar, A.J., Hillston, J.. Stochastic properties of the plant circadian clock. J. R. Soc. Interface, 9 (2011), 1–19. Google ScholarPubMed
Hagen, G., Guilfoyle, T.. Auxin-responsive gene expression: genes, promoters and regulatory factors. Plant Mol. Biol., 49 (2002), 373–385. CrossRefGoogle ScholarPubMed
Hill, A.V.. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol., 40 (Suppl): iv-vii. (1910-01-22), Retrieved 2009-03-18.
Huynh-Thu, V.A., Irrthum, A., Wehenkel, L., Geurts, P.. Inferring Regulatory Networks from Expression Data Using Tree-Based Methods. PLoS ONE, 5 (2010), 9: e12776. CrossRefGoogle ScholarPubMed
Johnson, A.D., Meyer, B.J., Ptashne, M.. Interactions between DNA-bound repressors govern regulation by the λ phage repressor. PNAS, 76 (1979), 5061–5065. CrossRefGoogle ScholarPubMed
Kang, Y.H., Kirik, V., Hulskamp, M., Nam, K.H., Hagely, K., Lee, M.M., Schiefelbein, J.. The MYB23 Gene Provides a Positive Feedback Loop for Cell Fate Specification in the Arabidopsis Root Epidermis. Plant Cell, 21 (2009), 1080–1094. CrossRefGoogle ScholarPubMed
Karlebach, G., Shamir, R.. Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol., 9 (2008), 10: 770–80. CrossRefGoogle ScholarPubMed
Kauffman, S.. Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets. J. Theor. Biol., 22 (1969), 437–467. CrossRefGoogle ScholarPubMed
Kauffman, S., Peterson, C., Samuelsson, B., Troein, C.. Random Boolean network models and the yeast transcriptional network. PNAS, 100 (2003), 25:14796–9. CrossRefGoogle ScholarPubMed
Kepinski, S., Leyser, O.. The arabidopsis f-box protein tir1 is an auxin receptor. Nature, 435 (2005), 436–437. CrossRefGoogle ScholarPubMed
Kholodenko, B.N., Kiyatkin, A., Bruggeman, F.J., Sontag, E., Westerhoff, H.V., Hoek, J.B.. Untangling the wires: a strategy to trace functional interactions in signaling and gene networks. PNAS, 99 (2002), 20:12841–12846. CrossRefGoogle ScholarPubMed
Kiehl, T.R., Mattheyses, R.M., Simmons, M.K.. Hybrid simulation of cellular behavior. Bioinformatics, 20 (2004):316–322. CrossRefGoogle Scholar
Kramer, E.M., Bennett, M.J.. Auxin transport: a field in flux. Trends Plant Sci., 11 (2006), 382–386. CrossRefGoogle ScholarPubMed
Yu.A. Kuznetsov Elements of Applied Bifurcation Theory. Springer, 3rd edition, 2004.
Lahav, G., Rosenfeld, N., Sigal, A., Geva-Zatorsky, N., Levine, A.J., Elowitz, M.B., Alon, U.. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature Genet., 36 (2004), 147–150. CrossRefGoogle ScholarPubMed
Laplaze, L., Benkova, E., Casimiro, I., Maes, L., Vanneste, S., Swarup, R., Weijers, D., Calvo, V., Parizot, B., Begoña Herrera-Rodriguez, M., Offringa, R., Graham, N., Doumas, P., Friml, J., Bogusz, D., Beeckman, T., Bennett, M.. Cytokinins Act Directly on Lateral Root Founder Cells to Inhibit Root Initiation. Plant Cell, 19 (2007), 3889–3900. CrossRefGoogle ScholarPubMed
Lèbre, S., Becq, J., Devaux, F., Stumpf, M.P.H., Lelandais, G.. Statistical inference of the time-varying structure of gene-regulation networks. BMC Syst. Biol., 4 (2010), 130. CrossRefGoogle ScholarPubMed
Lee, S.H., Reid, D.M.. The role of endogenous ethylene in the expansion of Helianthus annuus leaves. Can. J. Bot., 75 (1997), 3:501–8. CrossRefGoogle ScholarPubMed
Li, P., Zhang, C., Perkins, E.J., Gong, P., Deng, Y.. Comparison of probabilistic Boolean network and dynamic Bayesian approaches for inferring gene regulatory networks. BMC Bioinformatics, 8 (2007) Suppl 7: S13. CrossRefGoogle ScholarPubMed
Liang, S., Fuhrman, S., Somogyi, R.. REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. PSB, 3 (1998), 18–29. Google Scholar
Liu, J., Mehdi, S., Topping, J., Tarkowski, P., Lindsey, K.. Modelling and experimental analysis of hormonal crosstalk in Arabidopsis. Mol. Syst. Biol., 6 (2010), Article number: 373. CrossRefGoogle ScholarPubMed
Locke, J.C.W., Kozma-Bognár, L., Gould, P.D., Feheŕ, B., Kevei, E., Nagy, F., Turner, M.S., Hall, A., Millar, A.J.. Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol. Syst. Biol., 2 (2006), 59. CrossRefGoogle ScholarPubMed
Madar, A., Greenfield, A., Vanden-Eijnden, E., Bonneau, R.. DREAM3: Network Inference Using Dynamic Context Likelihood of Relatedness and the Inferelator. PLoS ONE, 5 (2010), 3. CrossRefGoogle ScholarPubMed
Marbach, D., Prill, R.J., Schaffter, T., Mattiussi, C., Floreano, D., Stolovitzky, G.. Revealing strengths and weaknesses of methods for gene network inference. PNAS, 107 (2010), 14 6286–6291. CrossRefGoogle Scholar
Marbach, D., Costello, J., K"uffner, R., Vega, N., Prill, R., Camacho, D., Allison, K., The DREAM5 Consortium, Kellis, M., Collins, J., Stolovitzky, G.. Wisdom of crowds for robust gene network inference. Nature Methods, 9 (2012), 8: 796–804. CrossRefGoogle ScholarPubMed
Margolin, A.A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Dalla Favera, R., Califano, A.. ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics, 20 (2006), 7 Suppl 1:S7. CrossRefGoogle Scholar
Meinhardt, H.. A model for pattern formation in insect embryogenesis. J. Cell Sci., 23 (1977), 117–139. Google ScholarPubMed
Middleton, A.M., King, J.R., Bennett, M.J., Owen, M.R.. Mathematical modelling of the Aux/IAA negative feedback loop. B. Math. Biol., 72 (2010), 1383–1407. CrossRefGoogle ScholarPubMed
A.M. Middleton, S. Úbeda-Tomás, J. Griffiths, T. Holman, P. Hedden, S.G. Thomas, A.L. Phillips, M.J. Holdsworth, M.J. Bennett, J.R. King, M.R. Owen. Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling. Published online before print PNAS, April 20, 2012, doi: 10.1073/pnas.1113666109.
Moreno-Risueno, M.A., Van Norman, J.M., Moreno, A., Zhang, J., Ahnert, S.E., Benfey, P.N.. Oscillating Gene Expression Determines Competence for Periodic Arabidopsis Root Branching. Science, 329 (2010), 1306. CrossRefGoogle ScholarPubMed
Moubayidin, L., Di Mambro, R., Sabatini, S.. Cytokinin-auxin crosstalk. Trends Plant Sci., 14 (2009), 10: 557–562. CrossRefGoogle ScholarPubMed
Moubayidin, L., Perilli, S., Dello Ioio, R., Di Mambro, R., Costantino, P., Sabatini, S.. The Rate of Cell Differentiation Controls the Arabidopsis Root Meristem Growth Phase. Curr. Biol., 20 (2010), 1138–1143. CrossRefGoogle ScholarPubMed
Muraro, D., Byrne, H., King, J., Voß, U., Kieber, J., Bennett, M.. The influence of cytokinin-auxin cross-regulation on cell-fate determination in Arabidopsis thaliana root development. J. Theor. Biol., 283 (2011), 152–167. CrossRefGoogle Scholar
K. Murphy, S. Mian. Modelling gene expression data using dynamic Bayesian networks. Technical Report, University of California, Berkeley, 1999.
Needham, C.J., Manfield, I.W., Bulpitt, A.J., Gilmartin, P.M., Westhead, D.R.. From gene expression to gene regulatory networks in Arabidopsis thaliana. BMC Syst. Biol., 3 (2009), 85. CrossRefGoogle ScholarPubMed
Passioura, J.B., Fry, S.C.. Turgor and Cell Expansion: Beyond the Lockhart Equation. Aust. J. Plant Physiol., 19 (1992), 5, 565–576. CrossRefGoogle Scholar
Paulsson, J.. Models of stochastic gene expression. Phys. Life Rev., 2 (2005), 157–175. CrossRefGoogle Scholar
Penfold, C.A., Wild, D.L.. How to infer gene networks from expression profiles, revisited. Interface Focus, 1 (2011), 1, 857–870. CrossRefGoogle Scholar
Rabitz, H., Kramer, M., Dacol, D.. Sensitivity analysis in chemical kinetics. Annu. Rev. Phys. Chem., 34 (1983), 419–461. CrossRefGoogle Scholar
Rau, A., Jaffrézic, F., Foulley, J.L., Doerge, R.W.. An empirical Bayesian method for estimating biological networks from temporal microarray data. Stat. Appl. Genet. Mol. Biol., 9 (2010), 1, Article 9. CrossRefGoogle Scholar
Rice, J., Tu, Y., Stolovitzky, G.. Reconstructing biological networks using conditional correlation analysis. Bioinformatics, 21 (2005), 6: 765–773. CrossRefGoogle Scholar
Rosenfeld, N., Elowitz, M.B., Alon, U.. Negative autoregulation speeds the response times of transcription networks. J. Mol. Biol., 323 (2002), 5:785–93. CrossRefGoogle Scholar
Ruzicka, K., Simaskova, M., Duclercq, J., Petrasek, J., Zazimalova, E., Simon, S., Friml, J., Van Montagu, M.C.E., Benkova, E.. Cytokinin regulates root meristem activity via modulation of the polar auxin transport. PNAS, 106 (2009), 11, 4284–4289. CrossRefGoogle Scholar
Saddic, L.A., Huvermann, B., Bezhani, S., Su, Y., Winter, C.M., Kwon, C.S., Collum, R.P., Wagner, D.. The LEAFY target LMI1 is a meristem identity regulator and acts together with LEAFY to regulate expression of CAULIFLOWER. Development, 133 (2006), 1673–1682. CrossRefGoogle Scholar
I. Shmulevich, E. R. Dougherty. Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks. SIAM Press, 2009.
Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.. Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics, 18 (2002), 261–274. CrossRefGoogle ScholarPubMed
Skoog, F., Miller, C.O.. Chemical regulation of growth and organ formation in plant tissues cultured in vitro. Syrup. Soc. Exp. Biol., 54 (1957), 118–130. Google Scholar
Stepanova, A.N., Yun, J., Likhacheva, A.V., Alonso, J.M.. Multilevel interactions between ethylene and auxin in Arabidopsis roots. Plant Cell., 7 (2007), 2169-85. Epub 2007 Jul 13. CrossRefGoogle Scholar
Sun, T.P., Gubler, F.. Molecular Mechanism of Gibberellin Signaling in Plants. Annu. Rev. Plant Biol., 55 (2004), 197–223. CrossRefGoogle Scholar
Swarup, R., Perry, P., Hagenbeek, D., Van Der Straeten, D., Beemster, G.T.S., Sandberg, G., Bhalerao, R., Ljung, K., Bennett, M.J.. Ethylene Upregulates Auxin Biosynthesis in Arabidopsis Seedlings to Enhance Inhibition of Root Cell Elongation. Plant Cell, 19 (2007), 2186–2196. CrossRefGoogle ScholarPubMed
L. Taiz, E. Zeiger. Plant Physiology, Fifth Edition. Sinauer Associates Inc., Publishers, Sunderland, Massachussets U.S.A., 2010.
Thomas, R.. Boolean formalization of genetic control circuits. J. Theor. Biol., 42 (1973), 563–585. CrossRefGoogle ScholarPubMed
R. Thomas, R. D’Ari. Biological Feedback. CRC-Press, Boca Raton, Florida, 1990.
Tian, Q., Uhlir, N.J., Reed, J.W.. Arabidopsis SHY2/IAA3 Inhibits Auxin-Regulated Gene Expression. Plant Cell, 14 (2002), 301–319. CrossRefGoogle ScholarPubMed
Tiwari, S.B., Hagan, G., Guilfoyle, T.. The roles of Auxin response factor domains in Auxin-responsive transcription. Plant Cell, 15 (2003), 533–543. CrossRefGoogle ScholarPubMed
Tsuda, K., Ito, Y., Sato, Y., Kurata, N.. Positive Autoregulation of a KNOX Gene Is Essential for Shoot Apical Meristem Maintenance in Rice. Plant Cell, 23 (2011): 4368–4381. CrossRefGoogle Scholar
Turing, A.M.. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London B, 237 (1952), 37–72. CrossRefGoogle Scholar
Tyson, J.J.. On the existence of oscillatory solutions in negative feedback cellular control processes. J. Math. Biol., 1 (1975), 4, 311–315. CrossRefGoogle Scholar
Úbeda-Tomás, S., Beemster, G., Bennett, M.. Hormonal regulation of root growth: integrating local activities into global behaviour. Trends Plant Sci., 17 (2012), 6, 326–331. CrossRefGoogle Scholar
Ueguchi-Tanaka, M., Ashikari, M., Nakajima, M., Itoh, H., Katoh, E., Kobayashi, M., Chow, T.Y., Hsing, Y.I., Kitano, H., Yamaguchi, I., Matsuoka, M.. GIBBERELLIN INSENSITIVE DWARF1 encodes a soluble receptor for gibberellin. Nature, 437 (2005), 693–698. CrossRefGoogle ScholarPubMed
Ueguchi-Tanaka, M., Nakajima, M., Katoh, E., Ohmiya, H., Asano, K., Saji, S., Hongyu, X., Ashikari, M., Kitano, H., Yamaguchi, I., Matsuoka, M.. Molecular interactions of a soluble gibberellin receptor, GID1, with a rice DELLA protein, SLR1, and gibberellin. Plant Cell, 19 (2007), 2140–2155. CrossRefGoogle ScholarPubMed
Ulmasov, T., Hagen, G., Guilfoyle, T.J.. Dimerization and DNA binding of auxin response factors. Plant J., 19 (1999), 309–319. CrossRefGoogle ScholarPubMed
Vignes, M., Vandel, J., Allouche, D., Ramadan-Alban, N., Cierco-Ayrolles, C., Schiex, T., Mangin, B., de-Givry, S.. Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis. PLoS ONE, 6 (2011), 12: e29165. CrossRefGoogle ScholarPubMed
Vogel, J.P., Woeste, K.E., Theologis, A., Kieber, J.J.. Recessive and dominant mutations in the ethylene biosynthetic gene ACS5 of Arabidopsis confer cytokinin insensitivity and ethylene overproduction, respectively. PNAS, 95 (1998), 8:4766–71. CrossRefGoogle ScholarPubMed
Watkinson, J., Liang, K., Wang, X., Zheng, T., Anastassiou, D.. Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information. Ann. N. Y. Acad. Sci., 1158 (2009), 302–13. CrossRefGoogle ScholarPubMed
Watts, D., Strogatz, S.. Collective dynamics of ‘small-world’ networks. Nature, 393 (1998), 6684: 440–442. CrossRefGoogle ScholarPubMed
Werhli, A.V., Grzegorczyk, M., Husmeier, D.. Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models and Bayesian networks. Bioinformatics, 22 (2006), 20: 2523–2531. CrossRefGoogle ScholarPubMed
Werhli, A.V., Husmeier, D.. Gene Regulatory Network Reconstruction by Bayesian Integration of Prior Knowledge and/or Different Experimental Conditions. J. Bioinform. Comput. Biol., 6 (2008), 3: 543–72. CrossRefGoogle ScholarPubMed
Wermuth, N., Lauritzen, S.. Graphical and recursive models for contingence tables. Biometrika, 72 (1983), 537–552. CrossRefGoogle Scholar
Willige, B.C., Ghosh, S., Nill, C., Zourelidou, M., Dohmann, E.M., Maier, A., Schwechheimer, C.. The DELLA domain of GA INSENSITIVE mediates the interaction with the GA INSENSITIVE DWARF1. A gibberellin receptor of Arabidopsis. Plant Cell, 19 (2007), 1209–1220. CrossRefGoogle Scholar
Wolpert, L.. Positional information and the spatial pattern of cellular differentiation. J. Theor. Biol., 25 (1999), 1–47. CrossRefGoogle Scholar
Yip, K.Y., Alexander, R.P., Yan, K.K., Gerstein, M.. Improved Reconstruction of In Silico Gene Regulatory Networks by Integrating Knockout and Perturbation Data. PLoS ONE, 5 (2010), 1. CrossRefGoogle ScholarPubMed
Vu, T.T., Vohradsky, J.. Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of Saccharomyces cerevisiae. Nucleic Acids Res., 35 (2006), 1, 279–287. CrossRefGoogle ScholarPubMed
Zou, M., Conzen, S.D.. A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics, 21 (2005), 1. CrossRefGoogle Scholar