Abstract
Motivation: A novel mixed-integer optimization framework is proposed for the design and analysis of regulatory networks. The model combines gene expression data and prior biological knowledge regarding the potential for regulatory interactions between genes and their corresponding transcription factors. The formalism provides significant advantages over available modeling methodologies in that the complexity of the regulatory network can be explicitly taken into account, multiple alternative structures can be systematically generated and finally robust and biological significant regulators can be rigorously identified. The original non-convex mixed integer reformulation is appropriately linearized and the resulting MILP is effectively optimized using standard solvers. The versatility is demonstrated using gene expression and binding data from an E. coli case study during transition from glucose to acetate as the sole carbon source.
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Alter, O., Golub, G.H.: Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. Proc. Natl. Acad. Sci. U.S.A. 101(47), 16577–16582 (2004)
Biegler, L.T., Grossmann, I.E. et al.: Systematic Methods of Chemical Process Design. Prentice Hall (1997)
Boulesteix, A.L., Strimmer, K.: Predicting transcription factor activities from combined analysis of microarray and ChIP data: a partial least squares approach. Theor. Biol. Med. Model. 2, 23 (2005)
Brooke, A., Kendrick, D. et al.: GAMS A user’s guide. GAMS Development Corporation (2004)
Bussemaker, H.J., Li, H. et al.: Regulatory element detection using correlation with expression. Nat. Genet. 27(2), 167–171 (2001)
Calvo, J.M., Matthews, R.G.: The leucine-responsive regulatory protein, a global regulator of metabolism in Escherichia coli. Microbiol. Rev. 58(3), 466–490 (1994)
Chapuy-Regaud, S., Ogunniyi, A.D. et al.: RegR, a global LacI/GalR family regulator, modulates virulence and competence in Streptococcus pneumoniae. Infect. Immun. 71(5), 2615–2625 (2003)
Chen, C.C., Wu, H.Y.: LeuO protein delimits the transcriptionally active and repressive domains on the bacterial chromosome. J. Biol. Chem. 280(15), 15111–15121 (2005)
Chen, K.C., Wang, T.Y. et al.: A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae. Bioinformatics 21(12), 2883–2890 (2005)
Covert, M.W., Knight, E.M. et al.: Integrating high-throughput and computational data elucidates bacterial networks. Nature 429(6987), 92–96 (2004)
DiRusso, C.C., Heimert, T.L. et al.: Characterization of FadR, a global transcriptional regulator of fatty acid metabolism in Escherichia coli. Interaction with the fadB promoter is prevented by long chain fatty acyl coenzyme A. J. Biol. Chem. 267(12), 8685–8691 (1992)
Drazinic, C.M., Smerage, J.B. et al.: Activation mechanism of the multifunctional transcription factor repressor-activator protein 1 (Rap1p). Mol. Cell. Biol. 16(6), 3187–3196 (1996)
Gao, F., Foat, B.C. et al.: Defining transcriptional networks through integrative modeling of mRNA expression and transcription factor binding data. BMC Bioinformatics 5, 31 (2004)
Gervais, F.G., Phoenix, P. et al.: The rcsB gene, a positive regulator of colanic acid biosynthesis in Escherichia coli, is also an activator of ftsZ expression. J. Bacteriol. 174(12), 3964–3971 (1992)
Harbison, C.T., Gordon, D.B. et al.: Transcriptional regulatory code of a eukaryotic genome. Nature 431(7004), 99–104 (2004)
Iyer, V.R., Horak, C.E. et al.: Genomic binding sites of the yeast cell-cycle transcription factors SBF and MBF. Nature 409(6819), 533–538 (2001)
Kakeda, M., Ueguchi, C. et al.: An Escherichia coli curved DNA-binding protein whose expression is affected by the stationary phase-specific sigma factor sigma S. Mol. Gen. Genet. 248(5), 629–634 (1995)
Kao, K.C., Yang, Y.L. et al.: Transcriptome-based determination of multiple transcription regulator activities in Escherichia coli by using network component analysis. Proc. Natl. Acad. Sci. U.S.A. 101(2), 641–646 (2004)
Kao, K.C., Tran, L.M. et al.: A global regulatory role of gluconeogenic genes in Escherichia coli revealed by transcriptome network analysis. J. Biol. Chem. 280(43), 36079–36087 (2005)
Kato, M., Hata, N. et al.: Identifying combinatorial regulation of transcription factors and binding motifs. Genome Biol. 5(8), R56 (2004)
Landini, P., Hajec, L.I. et al.: Structure and transcriptional regulation of the Escherichia coli adaptive response gene aidB. J. Bacteriol. 176(21), 6583–6589 (1994)
Lawley, B., Pittard, A.J.: Regulation of aroL expression by TyrR protein and Trp repressor in Escherichia coli K-12. J. Bacteriol. 176(22), 6921–6930 (1994)
Lawley, B., Fujita, N. et al.: The TyrR protein of Escherichia coli is a class I transcription activator. J. Bacteriol. 177(1), 238–241 (1995)
Lee, T.I., Rinaldi, N.J. et al.: Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298(5594), 799–804 (2002)
Maxson, M.E., Darwin, A.J.: Multiple promoters control expression of the Yersinia enterocolitica phage-shock-protein A (pspA) operon. Microbiology 152(Pt 4), 1001–1010 (2006)
Ng, A., Bursteinas, B. et al.: pSTIING: a ‘systems’ approach towards integrating signalling pathways, interaction and transcriptional regulatory networks in inflammation and cancer. Nucleic Acids Res. 34(Database issue), D527–D534 (2006)
Oh, M.K., Rohlin, L. et al.: Global expression profiling of acetate-grown Escherichia coli. J. Biol. Chem. 277(15), 13175–13183 (2002)
Pournara, I., Wernisch, L.: Factor analysis for gene regulatory networks and transcription factor activity profiles. BMC Bioinformatics 8, 61 (2007)
Rolfes, R.J., Zalkin, H.: Escherichia coli gene purR encoding a repressor protein for purine nucleotide synthesis. Cloning, nucleotide sequence, and interaction with the purF operator. J. Biol. Chem. 263(36), 19653–19661 (1988)
Salgado, H., Santos-Zavaleta, A. et al.: RegulonDB (version 3.2): transcriptional regulation and operon organization in Escherichia coli K-12. Nucleic Acids Res. 29(1), 72–74 (2001)
Savageau, M.A.: Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology. Addison-Weslet, Reading (1976)
Stormo, G.D., Fields, D.S.: Specificity, free energy and information content in protein-DNA interactions. Trends Biochem. Sci. 23(3), 109–113 (1998)
Sun, N., Carroll, R.J. et al.: Bayesian error analysis model for reconstructing transcriptional regulatory networks. Proc. Natl. Acad. Sci. U.S.A. 103(21), 7988–7993 (2006)
Thomas, R., Mehrotra, S. et al.: A model-based optimization framework for the inference on gene regulatory networks from DNA array data. Bioinformatics 20(17), 3221–3235 (2004)
Tran, L.M., Brynildsen, M.P. et al.: gNCA: A framework for determining transcription factor activity based on transcriptome: identifiability and numerical implementation. Metab. Eng. 7(2), 128–141 (2005)
van Steensel, B., Delrow, J. et al.: Genomewide analysis of Drosophila GAGA factor target genes reveals context-dependent DNA binding. Proc. Natl. Acad. Sci. U.S.A. 100(5), 2580–2585 (2003)
Wagner, A., Wright, J.: Alternative routes and mutational robustness in complex regulatory networks. Biosystems 88(1–2), 163–172 (2007)
Wang, X.D., de Boer, P.A. et al.: A factor that positively regulates cell division by activating transcription of the major cluster of essential cell division genes of Escherichia coli. Embo. J. 10(11), 3363–3372 (1991)
Wang, W., Cherry, J.M. et al.: A systematic approach to reconstructing transcription networks in Saccharomyces cerevisiae. Proc. Natl. Acad. Sci. U.S.A. 99(26), 16893–16898 (2002)
Yeung, M.K., Tegner, J. et al.: Reverse engineering gene networks using singular value decomposition and robust regression. Proc. Natl. Acad. Sci. U.S.A. 99(9), 6163–6168 (2002)
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Foteinou, P.T., Yang, E., Saharidis, G.K. et al. A mixed-integer optimization framework for the synthesis and analysis of regulatory networks. J Glob Optim 43, 263–276 (2009). https://doi.org/10.1007/s10898-007-9266-6
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DOI: https://doi.org/10.1007/s10898-007-9266-6