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Introduction Top

Importance of cis-Regulatory Elements

The rapidly emerging field of systems biology is helping us to understand the molecular determinants of phenotype on a genomic scale [1]. Cis-regulatory elements are major sequence-based determinants of biological processes in cells and tissues [2]. For instance, during transcriptional regulation, transcription factors (TFs) bind to very specific regions on the promoter DNA [2],[3] and recruit the basal transcriptional machinery, which ultimately initiates mRNA transcription (Figure 1A).

Figure 1. Basic Tenets of Modeling cis-Regulation Using a Regression Approach.

(A) A schematic of transcriptional regulation is shown. Motifs 1, 2, and 3 are bound by their respective TFs and thus are active, while motif 4 is not. Furthermore, TFs 1 and 2 are shown to be interacting. (B) Box plots of the logarithm of expression ratio (E_g/E_gC) of genes containing the MCB element ACGCGT (marked as >0, group 1) and genes that do not contain the element (marked as 0, group 2) are shown for the alpha arrest experiment [8] of yeast cell-cycle. The ratio E_g/E_gC is the expression of the gene relative to its average across all time points. During 21 min (G1/S phase), there is a statistically significant difference (p<1.0e-16, t-test) in expression level between the genes in groups 1 and 2. Average log₂(E_g/E_gC) of these two groups is 0.27 and −0.02, respectively. During the 35 min (G2/M phase), there is no such association (p = 0.02, average log₂(E_g/E_gC) = 0.04 vs 0.01). This type of approach is elucidated in detail in [57]. (C) The same data as in (B) is shown, except that the motif counts are no longer binary. There is a statistically significant association between the motif count and expression during the 21 min (p = 3.3e-12 (F-test), y = −0.02+0.28x), but not during the 35 min (p = 0.006, y = 0.01+0.04x) time point. Each point in the figure represents a gene, characterized by a count of ACGCGT in its promoter (x-axis) and log₂(expression ratio) (y-axis).

doi:10.1371/journal.pcbi.1000269.g001

Learning cis-Regulatory Elements from Omics Data

A vast amount of work over the past decade has shown that omics data can be used to learn cis-regulatory logic on a genome-wide scale [4]–[6]—in particular, by integrating sequence data with mRNA expression profiles. The most popular approach has been to identify over-represented motifs in promoters of genes that are coexpressed [4],[7],[8]. Though widely used, such an approach can be limiting for a variety of reasons. First, the combinatorial nature of gene regulation is difficult to explicitly model in this framework. Moreover, in many applications of this approach, expression data from multiple conditions are necessary to obtain reliable predictions. This can potentially limit the use of this method to only large data sets [9]. Although these methods can be adapted to analyze mRNA expression data from a pair of biological conditions, such comparisons are often confounded by the fact that primary and secondary response genes are clustered together—whereas only the primary response genes are expected to contain the functional motifs [10].

A set of approaches based on regression has been developed to overcome the above limitations [11]–[32]. These approaches have their foundations in certain biophysical aspects of gene regulation [26], [33]–[35]. That is, the models are motivated by the expected transcriptional response of genes due to the binding of TFs to their promoters. While such methods have gathered popularity in the computational domain, they remain largely obscure to the broader biology community. The purpose of this tutorial is to bridge this gap. We will focus on transcriptional regulation to introduce the concepts. However, these techniques may be applied to other regulatory processes. We will consider only eukaryotes in this tutorial.

Regression Methods for Learning the Active cis-Regulatory Elements Top

What is a Regression Method?

A regression method is essentially a curve-fitting approach. When there is one observed variable (y-axis) and one predictor variable (x-axis), regression consists of drawing a line or a curve that best fits the data. The challenge arises when there are multiple candidate predictors, among which only a selected few are relevant. This is the case for cis-regulation, where relatively few cis-elements are differentially activated between two conditions while the number of candidate elements is large [2],[5]. Regression methods provide efficient ways to select this set of active elements via a curve-fitting exercise.

How To Learn Which cis-Regulatory Elements Are Active

Let us consider the case of a single cis-element, a DNA word. Before we introduce the regression method, let us first proceed by dividing the genes into two groups, according to whether a gene has the word in its promoter or not. If under a biological condition the expression levels of genes in these two groups are significantly different from each other, it implies that the cis-element is most likely bound by its cognate TF, which is regulating its target genes. In other words, the cis-element is active. However, if there is no significant difference in expression between these two groups, then, analogously, the cis-element is likely inactive. Furthermore, if the genes with the cis-motif have higher expression levels on average than those without the motif, then the TF is an activator, and in the reverse situation an inhibitor. The case of the MCB element, a G1/S regulator of the yeast cell-cycle [8], is illustrated in Figure 1B. We observe that there is indeed a statistically significant association between the presence of the MCB element and mRNA expression in the G1/S phase of the cell-cycle (p<1.0e-16), but not in the G2/M phase (p = 0.02). Furthermore, this analysis indicates that the MCB element has an activating role in the G1/S phase, as expected [8].

A regression approach is a generalized version of the method described above. Here, the data is not binary any more. Instead, we plot the actual motif counts against the mRNA levels for all genes genome-wide (Figure 1C). To examine if there is any association between the occurrence of the MCB element and mRNA expression, we fit a straight line through these data points. Next, we check if the observed linear fit to the data could be obtained by random chance. If the fit is statistically significant, then the motif is considered active, just as in the binary data above, and inactive otherwise. Furthermore, if the slope of the fitted line is positive, then the element is an activator—a high number of elements are indicative of high expression on average, while fewer or no copies imply low expression. For the MCB element (Figure 1C), we notice that the fit is significant in the G1/S phase, but not in the G2/M phase, as expected of a G1/S-specific element. The positive slope of the line indicates that the MCB element is an activator.

The best fit shown in Figure 1C leads to a direct quantitative relation between the logarithm of observed expression E_g and motif count n_g of any gene g [11]:
(1)
where C indicates a reference condition. The parameters a and b, the intercept and slope of the line, respectively, are estimated from the input data via a least squares fit. a and b are constant across all genes. We can use Equation 1 to estimate how much of the mRNA expression levels are explained by this motif. We note that expression data from one experimental condition and one control condition are used in this analysis.

How To Learn Multiple cis-Regulatory Elements

Under any specific condition, multiple cis-elements are usually active [2],[36],[37]. Moreover, cis-regulation has been shown to be inherently combinatorial. Thus, often distinct combinations of such elements regulate the genes. To learn which specific combinations are active out of the many possible candidate elements, the simplest strategy is to repeat the above curve-fitting procedure for each such element. The elements that meet a significance threshold are considered to be active. However, this simple approach does not account for combinatorial regulation. Namely, it does not specify which particular elements act collectively to regulate gene expression. To overcome this limitation, we build a multivariate model (Equation 2 below with d₁₂ = 0). This involves two steps: (a) feature selection, i.e., identifying which specific elements are active, and (b) model building, i.e., specifying the regression model involving these elements. These two steps may be executed simultaneously [11]. Alternatively, one can first select the cis-element features, and then build a regression model using these features [13]. A representative flowchart for multivariate modeling is shown in Figure 2. The elements that appear in a multivariate model are, then, hypothesized to be functional [11],[13].

Figure 2. A Flow Chart for Modeling Combinatorial cis-Regulation Using Regression Methods.

The steps are shown for constructing a model with linear functions; however, with some small modifications, they are applicable to nonlinear functions as well. P_motif indicates the p-value of the association of the best motif with mRNA expression. P_motif>p₀ is one possible termination condition. Other alternative strategies can also be used instead. In this example, feature selection and model building are done simultaneously.

doi:10.1371/journal.pcbi.1000269.g002

An additional complexity is that functional interactions among TFs are often essential to transcriptional control [2]. This is especially true in higher organisms. In regression models, we introduce the interactions via a product of word counts. This reflects the fact that a pair of elements has a stronger effect than the sum of the elements in the pair. The strategy for including these terms is similar to the methodology described above [12]. For example, to describe the three motifs and interactions between motifs 1 and 2 in Figure 1A, the equation would be [12]:
(2)
n_ig is the count of motif i for gene g. The parameters a, b₁, b₂, b₃, and d₁₂ are learnt from the data, again using a least squares fit. d₁₂>0 implies a synergistic interaction, while d₁₂<0, a competitive interaction.

How To Model Regulation by Degenerate Motifs

cis-Regulatory elements are often not simple words, especially in higher eukaryotes. Instead, the cis-elements bound by a specific TF may have small differences in their sequences in different promoters [4]–[6]. This variability, referred to as degeneracy of the motifs, is often represented by a position weight matrix (PWM) [3],[5]. PWMs are probabilistic representations of cis-motifs (Figure 3).

Figure 3. Position Weight Matrix (PWM) Logo for E2F-1.

The sequence logo for the PWM of E2F-1, a key transcription factor for regulating the mammalian cell-cycle, is shown (http://jaspar.genereg.net/). The figure shows the bases that may occur at each position of this 8-nucleotide long motif. The height of each base quantifies the bits of information content, which is related to the probability of its occurrence at that position [3]. For example, there is a 100% chance of observing a T at position 1, while at position 8, a 90% chance of observing a C, and a 10% of G.

doi:10.1371/journal.pcbi.1000269.g003

To use PWMs in regression methods, we would first score each promoter sequence against each PWM. The probabilities of each base at each position are used to compute the scores. These scores are related to the binding affinity of a TF for the DNA sequence [3],[35],[38]. There are multiple scoring schemes available 13,18,22,33 (see also [3],[35],[39]), but often the maximum score of a PWM for each promoter is used. We then use the same regression methods described above to construct a model, but with PWM scores instead of word counts. JASPAR [40] and TRANSFAC [41],[42] are among the most popular databases of PWMs. However, PWMs may also be generated using de novo motif discovery tools [4],[13],[43].

Nonlinear models.

Although one can use linear methods with PWM scores [13], such methods are not ideal since the relation between motif scores and gene expression is not always linear. Furthermore, previous studies indicate that linear methods may not be optimal for modeling degenerate motifs when interactions are included [11]. This is a significant limitation since interactions among degenerate motifs are pervasive in mammalian transcriptional regulation [2],[5]. Instead, based on biophysical models, we expect the transcriptional response to be sigmoidal [44],[45] (Figure 4A). To account for such complexities, nonlinear methods have been developed. We model the expression ratios in terms of sums of sigmoidal functions of PWM scores [28],[31], or, alternatively, their variants, linear splines [15],[22]. Linear splines are related to sigmoidal functions by a logarithmic transformation (Figure 4B). They allow more efficient modeling when data is sparse since they require fewer parameters, while sigmoidal functions yield a more accurate model when sufficient data is available. The modeling procedure is similar to multivariate linear regression (see above). For the example shown in Figure 4C, we obtain an equation of the form:
(3)
Here, s denotes the PWM score. is a linear spline function or a sigmoidal function in s. Because of the increased number of fitting parameters, these more complex models require that we control for overfitting of the data. Although the implementation details are beyond the scope of this tutorial, they involve various forms of cross-validation (see the references in Table 1). These overfitting effects can also be significant in multivariate linear models with interactions. Because PWM scores are related to binding affinities, and sigmoidal functions model the essential biophysics of transcriptional regulation, these nonlinear approaches have strong biophysical underpinnings [26],[33],[34],[46].

Figure 4. Nonlinear Regression Models of cis-Regulation.

(A) mRNA expression (E_g) as a function of TF binding free energy often has a sigmoidal pattern. There is an activation threshold, below which the transcriptional response is flat. Above the threshold, it grows exponentially, and finally saturates. For an inhibitory pattern, the curve is inverted along the y-axis. PWM scores are proportional to the binding free energies. (B) A logarithmic transformation of the sigmoidal function leads to a sum of linear splines. Each linear spline function has the shape of a hockey stick: It is zero below (or above) a threshold, called knot, and rises linearly above (or below) it. The smoothness of the transition from the flat part to the exponential part of the curve is not modeled in linear splines. A linear model is realized if the activation threshold is ignored, i.e., the sigmoidal function is replaced by an exponential function in (A). In a linear spline approach, the target determination threshold is set to the knot [22] or the gene activation threshold. While for the sigmoidal function, the threshold is typically set by the point at which the curve reaches half its maximal value [28]. (C) A model comprising linear splines for three functional motifs and one interacting motif pair is shown.

doi:10.1371/journal.pcbi.1000269.g004

Table 1. Regression Tools for cis-Regulatory Element Identification Currently Reported in the Literature.

doi:10.1371/journal.pcbi.1000269.t001

How To Identify Target Genes

In a regression method, the input is a candidate motif. Thus, once we have identified the active motif, we have an additional task of determining which genes are targets of the cognate TF. Thus, in contrast to coexpression-based approaches where we assume that groups of co-expressed genes are co-regulated, co-regulation of genes is inferred in this approach a posteriori in regression methods. In the case of DNA words, it may seem that all promoters containing an instance of the word will always be bound by its partner TF. However, such a word may represent only the core of the motif. Thus, to discriminate the true targets, additional sequence information flanking the core motif may be essential [17],[32].

The challenge with the PWM scores is that they are generally continuous and nonzero (on a scale from zero to one, zero indicating that the motif is absent). Thus, most promoters often contain a low-scoring instance of each PWM. This is especially true for motifs of high degeneracy, as in humans [5]. Nonlinear regression methods provide a straightforward solution to select which instances of the motifs are active, since they allow one to define a cutoff threshold [22],[28] for each motif—promoters scoring above the threshold are then the targets, while those below are not (Figure 4B). There are alternative strategies to target determination, which are either more complex [23],[24],[31] or require information from ChIP-chip data [16],[25].

How To Assess the Statistical Significance of the Fit

A popular metric to assess the quality of a regression model is how much of the variation in the expression data it can explain. This is parameterized as R², sometimes referred to as the percent reduction in variance [11]:
(4)
where V_original is the variance in the input expression data, and V_residual is the variance of the differences between the input expression data and the fitted model. V_residual represents the unexplained part of the variation in expression data. R² is directly related to the F-statistic [47], which is often used to evaluate the significance of the fit.

Validity of the Premises

A large number of studies have shown that the motifs identified by regression methods are indeed functional motifs. The organisms where these methods have been applied include yeast [11]–[13], [15]–[18], [20], [21], [23], [25], [28]–[30],[32],[48], C. Elegans [32], Drosophila [14],[31], and human [22],[30]. Some of this work has been previously reviewed [26],[34],[49], and we refer to these publications for details.

Which Kinds of Problems Can These Methods Be Applied to?

In this tutorial, we have focused on transcriptional regulation. However, regression methods may also be applied to other stages of gene regulation that are mediated by cis-elements. Regression approaches have been used to model chromatin remodeling [28], 3′ UTR mediated mRNA stability [50], and the regulation of alternative splicing of pre-mRNAs[27]. These methods can also be applied to DNA binding data, such as those generated by ChIP-chip [16],[51], DamID [14], or PBM [21],[52] experiments. In these cases, the binding ratios from TF binding profiles may be used in place of either expression ratios or motif scores, depending on the application.

Available Software Based on Regression Methods

We have summarized the currently available software based on regression along with their key features in Table 1. The basic aspects of a regression method can be easily implemented in R or MATLAB.

Conclusion Top

In this tutorial, we have described the basic aspects of regression methods. These are complementary to alternative approaches for motif discovery, such as comparative genomics [53]–[55] or motif over-representation methods [4],[56]. In particular, regression methods are optimal for evaluating the activity of cis-elements among a set of candidate elements. They are better suited for modeling combinatorial regulation and nonlinear responses and are more closely tied to the biophysical models of transcriptional regulation. With some modifications, regression methods can also be adapted for de novo motif discovery [21],[25],[50]. Finally, although most regression methods are used to model the observed changes in gene expression between a pair of conditions, recently this methodology has been extended to include information from multiple conditions as well [29].

Acknowledgments Top

We thank Sam Ng for a careful reading of the manuscript.

Note Added in Proof

During the preparation of this manuscript, a new regression approach based on the Fast Orthogonal Search (FOS) method [58] was published to identify active cis-regulatory elements. As new algorithms get published, we will continue to maintain an updated version of Table 1 on our Web site http://vision.lbl.gov/People/ddas/Regres​sionPrimer/ .

References Top

1. Wolf DM, Arkin AP (2003) Motifs, modules and games in bacteria. Curr Opin Microbiol 6: 125–134. Find this article online
2. Levine M, Tjian R (2003) Transcription regulation and animal diversity. Nature 424: 147–151. Find this article online
3. Stormo GD (2000) DNA binding sites: representation and discovery. Bioinformatics 16: 16–23. Find this article online
4. Tompa M, Li N, Bailey TL, Church GM, De Moor B, et al. (2005) Assessing computational tools for the discovery of transcription factor binding sites. Nat Biotechnol 23: 137–144. Find this article online
5. Wasserman WW, Sandelin A (2004) Applied bioinformatics for the identification of regulatory elements. Nat Rev Genet 5: 276–287. Find this article online
6. Pennacchio LA, Rubin EM (2001) Genomic strategies to identify mammalian regulatory sequences. Nat Rev Genet 2: 100–109. Find this article online
7. Eisen MB, Spellman PT, Brown PO, Botstein D (1998) Cluster analysis and display of genome-wide expression patterns. Proc Natl Acad Sci U S A 95: 14863–14868. Find this article online
8. Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, et al. (1998) Comprehensive identification of cell cycle regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol Biol Cell 9: 3273–3297. Find this article online
9. Niehrs C, Pollet N (1999) Synexpression groups in eukaryotes. Nature 402: 483–487. Find this article online
10. Kirmizis A, Farnham PJ (2004) Genomic approaches that aid in the identification of transcription factor target genes. Exp Biol Med (Maywood) 229: 705–721. Find this article online
11. Bussemaker HJ, Li H, Siggia ED (2001) Regulatory element detection using correlation with expression. Nat Genet 27: 167–171. Find this article online
12. Keles S, van der Laan M, Eisen MB (2002) Identification of regulatory elements using a feature selection method. Bioinformatics 18: 1167–1175. Find this article online
13. Conlon EM, Liu XS, Lieb JD, Liu JS (2003) Integrating regulatory motif discovery and genome-wide expression analysis. Proc Natl Acad Sci U S A 100: 3339–3344. Find this article online
14. Orian A, van Steensel B, Delrow J, Bussemaker HJ, Li L, et al. (2003) Genomic binding by the Drosophila Myc, Max, Mad/Mnt transcription factor network. Genes Dev 17: 1101–1114. Find this article online
15. Das D, Banerjee N, Zhang MQ (2004) Interacting models of cooperative gene regulation. Proc Natl Acad Sci U S A 101: 16234–16239. Find this article online
16. Gao F, Foat BC, Bussemaker HJ (2004) Defining transcriptional networks through integrative modeling of mRNA expression and transcription factor binding data. BMC Bioinformatics 5: 31. Find this article online
17. Wang W, Cherry JM, Nochomovitz Y, Jolly E, Botstein D, et al. (2005) Inference of combinatorial regulation in yeast transcriptional networks: a case study of sporulation. Proc Natl Acad Sci U S A 102: 1998–2003. Find this article online
18. Zhong W, Zeng P, Ma P, Liu JS, Zhu Y (2005) RSIR: regularized sliced inverse regression for motif discovery. Bioinformatics 21: 4169–4175. Find this article online
19. Smith AD, Sumazin P, Das D, Zhang MQ (2005) Mining ChIP-chip data for transcription factor and cofactor binding sites. Bioinformatics 21: (Suppl 1)i403–i412. Find this article online
20. Cokus S, Rose S, Haynor D, Gronbech-Jensen N, Pellegrini M (2006) Modelling the network of cell cycle transcription factors in the yeast Saccharomyces cerevisiae. BMC Bioinformatics 7: 381. Find this article online
21. Foat BC, Morozov AV, Bussemaker HJ (2006) Statistical mechanical modeling of genome-wide transcription factor occupancy data by MatrixREDUCE. Bioinformatics 22: e141–e149. Find this article online
22. Das D, Nahle Z, Zhang MQ (2006) Adaptively inferring human transcriptional subnetworks. Mol Syst Biol 2: 2006 0029. Find this article online
23. Nguyen DH, D'Haeseleer P (2006) Deciphering principles of transcription regulation in eukaryotic genomes. Mol Syst Biol 2: 2006 0012. Find this article online
24. Bonneau R, Reiss DJ, Shannon P, Facciotti M, Hood L, et al. (2006) The Inferelator: an algorithm for learning parsimonious regulatory networks from systems-biology data sets de novo. Genome Biol 7: R36. Find this article online
25. Tanay A (2006) Extensive low-affinity transcriptional interactions in the yeast genome. Genome Res 16: 962–972. Find this article online
26. Bussemaker HJ, Foat BC, Ward LD (2007) Predictive modeling of genome-wide mRNA expression: from modules to molecules. Annu Rev Biophys Biomol Struct 36: 329–347. Find this article online
27. Das D, Clark TA, Schweitzer A, Yamamoto M, Marr H, et al. (2007) A correlation with exon expression approach to identify cis-regulatory elements for tissue-specific alternative splicing. Nucleic Acids Res 35: 4845–4857. Find this article online
28. Pham H, Ferrari R, Cokus SJ, Kurdistani SK, Pellegrini M (2007) Modeling the regulatory network of histone acetylation in Saccharomyces cerevisiae. Mol Syst Biol 3: 153. Find this article online
29. Wang L, Chen G, Li H (2007) Group SCAD regression analysis for microarray time course gene expression data. Bioinformatics 23: 1486–1494. Find this article online
30. Wu RZ, Chaivorapol C, Zheng J, Li H, Liang S (2007) fREDUCE: detection of degenerate regulatory elements using correlation with expression. BMC Bioinformatics 8: 399. Find this article online
31. Segal E, Raveh-Sadka T, Schroeder M, Unnerstall U, Gaul U (2008) Predicting expression patterns from regulatory sequence in Drosophila segmentation. Nature 451: 535–540. Find this article online
32. Yu RX, Liu J, True N, Wang W (2008) Identification of direct target genes using joint sequence and expression likelihood with application to DAF-16. PLoS ONE 3: e1821. doi:10.1371/journal.pone.0001821. Find this article online
33. Djordjevic M, Sengupta AM, Shraiman BI (2003) A biophysical approach to transcription factor binding site discovery. Genome Res 13: 2381–2390. Find this article online
34. Das D, Zhang MQ (2007) Predictive models of gene regulation: application of regression methods to microarray data. Methods Mol Biol 377: 95–110. Find this article online
35. Stormo GD, Fields DS (1998) Specificity, free energy and information content in protein-DNA interactions. Trends Biochem Sci 23: 109–113. Find this article online
36. Pilpel Y, Sudarsanam P, Church GM (2001) Identifying regulatory networks by combinatorial analysis of promoter elements. Nat Genet 29: 153–159. Find this article online
37. Elemento O, Slonim N, Tavazoie S (2007) A universal framework for regulatory element discovery across all genomes and data types. Mol Cell 28: 337–350. Find this article online
38. Berg OG, von Hippel PH (1987) Selection of DNA binding sites by regulatory proteins. Statistical-mechanical theory and application to operators and promoters. J Mol Biol 193: 723–750. Find this article online
39. O'Flanagan RA, Paillard G, Lavery R, Sengupta AM (2005) Non-additivity in protein-DNA binding. Bioinformatics 21: 2254–2263. Find this article online
40. Sandelin A, Alkema W, Engstrom P, Wasserman WW, Lenhard B (2004) JASPAR: an open-access database for eukaryotic transcription factor binding profiles. Nucleic Acids Res 32: D91–D94. Find this article online
41. Matys V, Fricke E, Geffers R, Gossling E, Haubrock M, et al. (2003) TRANSFAC: transcriptional regulation, from patterns to profiles. Nucleic Acids Res 31: 374–378. Find this article online
42. Fu Y, Weng Z (2004) Improvement of TRANSFAC matrices using multiple local alignment of transcription factor binding site sequences. Conf Proc IEEE Eng Med Biol Soc 4: 2856–2859. Find this article online
43. Zhang MQ (2007) Computational analyses of eukaryotic promoters. BMC Bioinformatics 8: (Suppl 6)S3. Find this article online
44. Carey M (1998) The enhanceosome and transcriptional synergy. Cell 92: 5–8. Find this article online
45. Veitia RA (2003) A sigmoidal transcriptional response: cooperativity, synergy and dosage effects. Biol Rev Camb Philos Soc 78: 149–170. Find this article online
46. Chin CS, Chubukov V, Jolly ER, DeRisi J, Li H (2008) Dynamics and design principles of a basic regulatory architecture controlling metabolic pathways. PLoS Biol 6: e146. doi:10.1371/journal.pbio.0060146. Find this article online
47. Hastie T, Tibshirani R, Friedman JH (2001) The Elements of Statistical Learning. New York: Springer.
48. Wang W, Cherry JM, Botstein D, Li H (2002) A systematic approach to reconstructing transcription networks in Saccharomyces cerevisiae. Proc Natl Acad Sci U S A 99: 16893–16898. Find this article online
49. Hannenhalli S (2008) Eukaryotic transcription factor binding sites—modeling and integrative search methods. Bioinformatics 24: 1325–1331. Find this article online
50. Foat BC, Houshmandi SS, Olivas WM, Bussemaker HJ (2005) Profiling condition-specific, genome-wide regulation of mRNA stability in yeast. Proc Natl Acad Sci U S A 102: 17675–17680. Find this article online
51. Kim TH, Ren B (2006) Genome-wide analysis of protein-DNA interactions. Annu Rev Genomics Hum Genet 7: 81–102. Find this article online
52. Mukherjee S, Berger MF, Jona G, Wang XS, Muzzey D, et al. (2004) Rapid analysis of the DNA-binding specificities of transcription factors with DNA microarrays. Nat Genet 36: 1331–1339. Find this article online
53. Nardone J, Lee DU, Ansel KM, Rao A (2004) Bioinformatics for the ‘bench biologist’: how to find regulatory regions in genomic DNA. Nat Immunol 5: 768–774. Find this article online
54. Dubchak I (2007) Comparative analysis and visualization of genomic sequences using VISTA browser and associated computational tools. Methods Mol Biol 395: 3–16. Find this article online
55. Blanchette M, Tompa M (2002) Discovery of regulatory elements by a computational method for phylogenetic footprinting. Genome Res 12: 739–748. Find this article online
56. Bulyk ML (2003) Computational prediction of transcription-factor binding site locations. Genome Biol 5: 201. Find this article online
57. Boorsma A, Foat BC, Vis D, Klis F, Bussemaker HJ (2005) T-profiler: scoring the activity of predefined groups of genes using gene expression data. Nucleic Acids Res 33: W592–W595. Find this article online
58. Minz I, Korenberg MJ (2008) Modeling Cooperative Gene Regulation Using Fast Orthogonal Search. The Open Bioinformatics Journal 2: 80–89. Find this article online