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Quantifying transcriptional regulatory networks by integrating sequence features and microarray data


Genome-wide transcriptional regulatory networks (TRNs) specify the interactions between transcription factors (TFs) and their target genes. Many methods have been proposed to reconstruct regulatory networks from gene expression datasets and/or genome sequences, but most of them can only infer qualitative regulation relationships. Thus, developing a quantitative model that can estimate the kinetic parameters of transcriptional regulatory functions is an urgent and important task. In this paper I propose REMBE, a regulatory model based on binding energy, to quantify transcriptional regulatory networks. My model combines multiple kinetic quantities, including binding strength, TF-DNA’s binding energy, transcription productivity with respect to each binding state, and hidden TFs' concentration, into a general learning model. Experimental results show that my model can effectively learn these kinetic parameters and TFs’ concentration from genome sequences and gene expression data. Moreover, these learned parameters and TFs' concentration provide more informative biological senses than merely qualitative regulatory relationships can do.

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  1. 1.



TF concentration

γ :

Binding strength

α :

Transcriptional productivity

λ :

Indicator of interaction among TFs

s :

Binding state

β :

Maximal transcription rate

t :

Time point

j :


i :

Transcription factor

B ij :

Binding site of TF i on the promoter of gene j

E ij :

Average binding energy between TF i and gene j

b j :

Background expression level of gene j

c ij :

Indicator of regulation type

μ :

Regulation function


  1. 1.

    AdrianoV, Dirk H (2007) Reconstructing gene regulatory networks with Bayesian networks by combining expression data with multiple sources of prior knowledge. Stat Appl Genet Mol Biol 6, article 15

  2. 2.

    Bailey T, Elkan C (1994) Fitting a mixture model by expectation maximization to discover motifs in biopolymers. In: Proceedings of the second international conference on intelligent systems for molecular biology 18:28–36

  3. 3.

    Benos P, Martha L, Bulyk M, Stormo G (2002) Additivity in protein–DNA interactions: how good an approximation is it? Nucleic Acids Res 30:4442–4451

  4. 4.

    Berg J, Willmann S, Lassig M (2004) Adaptive evolution of transcription factor binding sites. BMC Evol Biol 4:42

  5. 5.

    Bulyk M, Johnson P, Church G (2002) Nucleotides of transcription factor binding sites exert interdependent effects on the binding affinities of transcription factors. Nucleic Acids Res 30:1255–1261

  6. 6.

    Davidich M, Bornholdt S (2008) Boolean network model predicts cell cycle sequence of fission yeast. PLoS ONE 3:e1672

  7. 7.

    Devlin C, Tice-Baldwin K, Shore D, Arndt K (1991) RAP1 is required for BAS1/BAS2- and GCN4-dependent transcription of the yeast HIS4 gene. Mol Cell Biol 11:3642–3651

  8. 8.

    Foat B, Morozov A, Bussemaker H (2006) Statistical mechanical modeling of genome-wide transcription factor occupancy data by MatrixREDUCE. Bioinformatics 22:e141–e149

  9. 9.

    Harbison C, Gordon D, Lee T et al (2004) Transcriptional regulatory code of a eukaryotic genome. Nature 431:99–104

  10. 10.

    Holter N, Mitra M, Maritan A (2000) Fundamental patterns underlying gene expression profiles: simplicity from complexity. Proc Natl Acad Sci USA 97:8409–8414

  11. 11.

    Hu Z, Killion P, Iyer V (2007) Genetic reconstruction of a functional transcriptional regulatory network. Nat Genet 39:683–687

  12. 12.

    Hughes J, Estep P et al (2000) Computational identification of cis-regulatory elements associated with groups of functionally related genes in Saccharomyces cerevisiae. J Mol Biol 296:1205–1214

  13. 13.

    Imoto S, Goto T, Miyano S (2002) Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. Proc Pac Symp Biocomput 7:175–186

  14. 14.

    Imoto S, Kim S, Goto T et al (2003) Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network. J Bioinformatics Comput Biol 1:231–252

  15. 15.

    Imoto S, Higuchi T, Goto T et al. (2003b) Combining microarrays and biological knowledge for estimating gene networks via Bayesian networks. In: Proceedings of the computational systems bioinformatics, pp 104–113

  16. 16.

    Kim HD, Shea EK (2008) A quantitative model of transcription factor activated gene expression. Nat Struct Mol Biol 15:1192–1198

  17. 17.

    Kirimasthong K, Manorat A et al (2007) Inference of gene regulatory network by Bayesian network using Metropolis-Hastings Algorithm. ICDM pp 276–286

  18. 18.

    Kuchin S, Vyas VK, Carlson M et al (2002) Snf1 protein kinase and the repressors Nrg1 and Nrg2 regulate FLO11, haploid invasive growth, and diploid pseudohyphal differentiation. Mol Cell Biol 1:3994–4000

  19. 19.

    Lahdesmaki H, Shmulevich I, Yli-Harja O (2004) On learning gene regulatory networks under the Boolean network model. Mach Learn 52:147–167

  20. 20.

    Lee TI, Rinaldi NJ, Robert F et al (2002) Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298:799–804

  21. 21.

    Liao JC, Boscolo R, Yang YL (2003) Network component analysis: reconstruction of regulatory signals in biological systems. Proc Natl Acad Sci USA 100:15522–15527

  22. 22.

    Liebermeister W (2002) Linear modes of gene expression determined by independent component analysis. Bioinformatics 18:51–60

  23. 23.

    Luscombe NM, Babu MM, Yu H (2004) Genomic analysis of regulatory network dynamics reveals large topological changes. Science 431:308–312

  24. 24.

    Maerkl SJ, Quake SR (2007) A systems approach to measuring the binding energy landscapes of transcription factors. Science 315:233–237

  25. 25.

    Man T, Stormo GD (2001) Non-independence of Mnt repressor–operator interaction determined by a new quantitative multiple fluorescence relative affinity (QuMFRA) assay. Nucleic Acids Res 29:2471–2478

  26. 26.

    Nachman I, Regev A, Friedman N (2004) Inferring quantitative models of regulatory networks from expression data. Bioinformatics 20:i248–i256

  27. 27.

    Pan Y, Durfee T, Bockhorst J, Craven M (2007) Connecting quantitative regulatory-network models to the genome. Bioinformatics 23:i367–i376

  28. 28.

    Park SH, Koh SS, Chun JH et al (1999) Nrg1 is a transcriptional repressor for glucose repression of STA1 gene expression in Saccharomyces cerevisiae. Mol Cell Biol 19:2044–2050

  29. 29.

    Pournara I, Wernisch L (2007) Factor analysis for gene regulatory networks and transcription factor activity profiles. BMC Bioinformatics 8:61

  30. 30.

    Raychaudhuri S, Stuart JM, Altman RB (2000) Principal components analysis to summarize microarray experiments: application to sporulation time series. Pac Symp Biocomput 45:2–463

  31. 31.

    Roider HG, Kanhere A, Manke T, Vingron M (2006) Predicting transcription factor affinities to DNA from a biophysical model. Bioinformatics 23:134–141

  32. 32.

    Sakamoto E (2001) Inferring a system of differential equations for a gene regulatory network by using genetic programming. In: Proc. congress on evolutionary computation, pp 720–726

  33. 33.

    Sanguinetti G, Rattray M, Lawrence ND (2006) A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription. Bioinformatics 22:1753–1759

  34. 34.

    Segal E, Barash Y, Simon I, Friedman N, Koller D (2002) From promoter sequence to expression: a probabilistic framework. RECOMB, pp 263–272

  35. 35.

    Segal E, Taskar B, Gasch A, Friedman N, Koller D (2003) Rich probabilistic models for gene expression. Bioinformatics 17:S243–S252

  36. 36.

    Segal E, Raveh-Sadka T et al (2008) Predicting expression patterns from regulatory sequence in Drosophila segmentation. Nature 451:535–540

  37. 37.

    Spellman PT, Sherlock G, Zhang MQ et al (1998) Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol Cell Biol 9:3273–3297

  38. 38.

    Wang Y et al (2002) Precision and functional specificity in mRNA decay. Proc Natl Acad Sci USA 99:5860–5865

  39. 39.

    Werhli AV, Grzegorczyk M, Husmeier D (2006) Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models and Bayesian networks. Bioinformatics 22:2523–2531

  40. 40.

    Yu T, Li KC (2005) Inference of transcriptional regulatory network by two-stage constrained space factor analysis. Bioinformatics 21:4033–4038

  41. 41.

    Zou M, Conzen SD (2004) A new dynamic Bayesian network (DBN) approach for identifying gene regulatory networks from time course microarray data. Bioinformatics 21:71–79

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Correspondence to Hui Liu.

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Liu, H. Quantifying transcriptional regulatory networks by integrating sequence features and microarray data. Bioprocess Biosyst Eng 33, 495–505 (2010).

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  • Transcription regulation
  • Quantitative model
  • Transcription rate