Bioinformatics Advance Access originally published online on July 5, 2005
Bioinformatics 2005 21(17):3490-3500; doi:10.1093/bioinformatics/bti558
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Discrimination of yeast genes involved in methionine and phosphate metabolism on the basis of upstream motifs
1Service de Conformation des Macromolécules Biologiques et de Bioinformatique, Université Libre de Bruxelles CP 263, Campus Plaine, Blvd du Triomphe, B-1050 Bruxelles, Belgium
2Unité de Chronobiologie Théorique CP 231, Campus Plaine, Blvd du Triomphe, B-1050 Bruxelles, Belgium
3Projet Méthodes et Algorithmes pour la Bioinformatique, LIRMM-CNRS 161 rue Ada, 34392, Montpellier, France
*To whom correspondence should be addressed.
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Abstract |
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 TOP Abstract INTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Motivation: In yeast, methionine and phosphate metabolism are regulated by the complexes Met4p/Met28p/Cbf1p and Pho4p, respectively. The binding sites for these factors share a common core CACGTG. We evaluate our capability to discriminate phosphate- and methionine-responding genes on the basis of putative regulatory elements, despite the similarity between Met4p/Met28p/Cbf1p and Pho4p consensus.
Results: We scanned upstream regions of methionine, phosphate and control genes with position-specific weight matrices for Pho4p, Met4p/Met28p/Cbf1p and Met31p/Met32p, and applied discriminant analysis to classify genes according to matrix matching scores. This analysis showed that matrix scores provided a good discrimination between phosphate, methionine and control genes. The optimal parameters have then been used to predict phosphate and methionine regulation at a genome scale. The genome-scale analysis predicts 37 genes as methionine-regulated and 40 as phosphate-regulated. We compare the predictive results with high throughput data and discuss the difference.
Availability: The programs for sequence retrieval and analysis, as well as the complete data and results, are available on the website on regulatory sequence analysis tools (http://rsat.scmbb.ulb.ac.be/rsat/).
Contact: jvanheld{at}scmbb.ulb.ac.be
Supplementary information: The complete datasets and results are available at http://rsat.scmbb.ulb.ac.be/rsat/data/published_data/Gonze_MET_PHO/
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INTRODUCTION |
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TOPAbstractINTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Living cells respond to changes in their environment by activating or repressing the expression of selected genes. For example, when the intracellular concentration of a given metabolite is too low, a specific transcription factor starts activating the expression of enzymes and transporters involved in the biosynthesis and uptake of this metabolite. Each factor binds to specific sites on the chromosomes and interacts with RNA polymerase to modify the level of expression of the neighbour gene. The specificity of protein–DNA binding is thus the key for restricting the transcriptional response to the appropriate target genes.
The binding specificity of a transcription factor can be described by a pattern, which can be used to detect putative binding sites in new sequences. On the basis of a set of known binding sites, a position-specific scoring matrix (PSSM) can be built to represent the binding specificity of a given transcription factor, and this matrix can be used to scan new sequences to predict putative binding sites (Hertz et al., 1990; Hertz and Stormo, 1999; Wasserman and Sandelin, 2004). However, not all matches correspond to effective regulatory elements. Indeed, binding motifs are generally short (typically 5–10 conserved positions) so that, when scanning large sequences, many spurious matches are expected by chance. In addition, the highest specificity does not always correspond to the highest regulatory activity.
A particularly challenging case is the recognition of phosphate- and methionine-responding genes in the yeast Saccharomyces cerevisiae. Methionine metabolism is regulated by several transcription factors, with distinct binding sites. The main regulator is the Met4p/Met28p/Cbf1p complex, whose binding consensus is TCACGTGA. Two additional transcription factors have been isolated, Met31p and Met32p, on the basis of their binding to the motif AAACTGTGG (Thomas and Surdin-Kerjan, 1997; Blaiseau et al., 1997). Phosphate metabolism is regulated by the transcription factor Pho4p, whose binding sites show two variants : high affinity binding sites are centred on the core CACGTG followed by a short GC-rich region (2–3 nt), whereas medium affinity binding sites have a CACGTT motif followed by a T-rich region (Oshima et al., 1996). These two variants of Pho4p binding sites can be summarized with the consensus CACGTKkk, where K means ‘G or T’, and the two last letters are in lowercase to highlight the fact that they are less conserved.
Thus, Pho4p and Met4p share a common core, CACGTG, and their mutual specificity relies on the flanking bases of this core. Due to this similarity of their consensi, one could expect cross-predictions between Met4p and Pho4p targets. However, we can take benefit from our additional knowledge of phosphate and methionine regulation to establish multi-variate criteria, taking into account the following aspects of the regulation: (1) binding diversity (specificity of the core-flanking bases, two variants of Pho4p binding sites); (2) self-synergy (many genes contain multiple binding sites for either Pho4p or Met4p); (3) heterologous synergy (cooperative regulation by Met4p and Met31p).
In this paper, we apply a discriminant analysis to test whether phosphate- and methionine-responding genes can be discriminated on the basis of putative Met4p, Met31p and Pho4p binding sites. We optimize the parameters on the basis of a set of genes known to be submitted to phosphate and methionine regulation, as well as a control group. Optimal parameters are then used for predicting phosphate and methionine regulation for each gene of the genome. The results of this genome-scale prediction are compared with high-throughput data from ChIP–chip and microarray experiments.
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SYSTEMS AND METHODS |
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TOPAbstractINTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Position-specific scoring matrices
Binding sites were collected from TRANSFAC, SCPD and the literature. Altogether, we obtained 21 binding sites for Pho4p, 16 for Met4p and 18 for Met31p. The sizes of the binding sites varied between 16 and 22 bp. The complete data and the sources are provided in the Supplementary material.
PSSMs were constructed by aligning the binding site sequences with the program consensus (matrix width w = 15, include both strands as a single sequence) (Hertz et al., 1990; Hertz and Stormo, 1999). The resulting matrix M indicates the counts nr,j of each residue r at each position j of the aligned binding sites. This count matrix is automatically converted into weights Wr,j by patser:
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High-scoring segments (large Xi) correspond to putative binding sites for the transcription factor. Matrix-based pattern matching was performed with patser (Hertz and Stormo, 1999). This program takes as input a sequence S and a PSSM M of width w, and assigns a score to each position of the sequence as described in Hertz and Stormo (1999). The search was performed on both strands, and the program returned the three top scores per sequence.
DNA–chip data and ChIP–chip data
The phosphate microarray data published by Ogawa et al. (2000) was downloaded from http://cmgm.stanford.edu/pbrown/phosphate/ (October 2000). A list of target genes for 106 transcription factors found by a ChIP–chip experiment (Lee et al., 2002) were downloaded from http://web.wi.mit.edu/young/regulator_network/ (October 2002). The dataset from Harbison et al. (2004) were downloaded from http://web.wi.mit.edu/young/regulatory_code/ (September 2004).
Composition of the training sets
For training and evaluation, we selected 16 genes known to respond to a stress in methionine (MET family), 8 genes submitted to phosphate regulation (PHO family) and a control family (CTL family) containing 80 genes, which are supposed to respond neither to methionine nor to phosphate (Table 1). Note that there are less training genes than binding sites for each transcription factor. This is due to the fact that a promoter generally contains multiple binding sites for the same factor (for example, the 21 sites used for building the Pho4p matrix belong to not more than 8 genes).
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Discriminant analysis
Leave-one-out evaluation
Before using the discriminant function for predicting phosphate and methionine regulation for all the genes of a genome it is essential to evaluate its accuracy. Classically, the evaluation relies on a testing set, which must be independent from the training set. Given the restricted number of genes with known class membership (8 PHO and 16 MET genes) splitting them into even smaller subsets would strongly bias the training. To circumvent this, we applied the leave-one-out (LOO) procedure (Huberty, 1994): one element is discarded from the training set, a discriminant function is built on the basis of the remainders and this function is used to predict the class of the discarded element. The predicted class is compared with the training class, and the procedure is iterated over all the elements of the training set.
Variable selection
Another classical problem, when working with a very small training set, is the risk of over-fitting: the accuracy of prediction decreases when the number of variables increases [see Huberty (1994) for a detailed discussion]. With our datasets, there is a risk of over-fitting since the number of variables (15 matrix scores, see Results) is higher than the number of elements in some training classes (8 genes in the PHO group). To circumvent this problem, we implemented a forward stepwise procedure, which selects a subset of variables by optimizing the hit rate (Huberty, 1994): the program first compares the rate of error obtained by using each variable alone and selects the most discriminating one. Additional variables are then successively incorporated by selecting, at each step, the variable that returns the smallest rate of error when combined to the variables retained in the preceding steps. For the evaluation of error rates, the forward stepwise variable selection was performed inside the LOO loop in order to prevent a possible bias on the selected variables. For genome-scale prediction, variable selection was performed with all the training objects.
Linear versus quadratic discriminant analyses
We systematically compared the results obtained with the linear discriminant analysis (LDA) and the quadratic discriminant analysis (QDA). Both methods rely on an hypothesis of multinormality, and LDA (but not QDA) assumes that the training classes have the same covariance matrix. Although these hypotheses are rarely satisfied with real data (and certainly not in the case of pattern counts), discriminant analysis generally gives good results, especially LDA, which requires very few parameter estimates.
Principal component analysis
Since we suspected a problem of over-dimensionality, we compared the results of variable selection in the original data space (matrix scores) and in the principal component analysis (PCA)-transformed data. PCA includes the transformation of a p-dimensional space of variables into a p-dimensional space of components, where each component is a linear combination of the original variables. The contribution (weight) of each variable to each component is calculated in order to maximize the variance associated with the first component. PCA is often used as a method to reduce the dimensionality of a variable space.
Permutation test
The error rate by itself is not sufficient to evaluate the benefit of the discriminant analysis. Indeed, even a random assignation of class membership would still lead to a certain percentage of correct classification by chance. The random expectation depends on the dataset (relative size of the training groups) and on the parameters of the analysis (linear versus quadratic, selected variables). We performed a permutation test to evaluate the random expectation for the error rate. For this test, we randomly permuted the group labels and applied the same discriminant procedure as with the real labels. For each condition, 100 independent permutation tests were performed and the average error rates were calculated.
Availability and supplementary material
Multivariate analysis and figure drawings were performed with the freeware statistical package R (http://cran.r-project.org/). The programs for sequence retrieval and analysis are available on the web site on regulatory sequence analysis tools (http://rsat.scmbb.ulb.ac.be/rsat/) (van Helden et al., 2000; van Helden, 2003). The complete datasets and results are available on the same site (http://rsat.scmbb.ulb.ac.be/rsat/data/published_data/Gonze_MET_PHO/).
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RESULTS |
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TOPAbstractINTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Position-specific scoring matrices
A position-based matrix was built for each transcription factor: Met4p [Table 2(A)], Met31p [Table 2(B)] and Pho4p [Table 2(C)]. In addition, we made a specific treatment for the Pho4p factor, which shows two variants of binding sites: high affinity sites, containing a CACGTG core, and medium-affinity sites, centred around a CACGTT core (Oshima et al., 1996).
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Generally, CACGTG-based sites are followed by a short GC-rich region (2–3 bp), whereas CACGTT-based sites are followed by several other Ts (see Supplementary material). Such dependencies between neighbouring positions are not taken into account by PSSM. As a consequence, a matrix built with all the CACGTG- and CACGTT-based sites [Table 2(x)] would assign a very high score to a sequence like CACGTGTTT, despite the fact that this sequence contains a CACGTG core followed by a T-rich region, a situation which has not yet been observed in any experimentally-proven sites.
In order to better reflect the dependency between the core and the flanking region, we built two separate matrices, regrouping the CACGTG-based [Table 2(D)] and CACGTT-based [Table 2(E)] sites, respectively. The drawback is that each of these matrices is based on a very small number of observations, which might reduce its capability to recognize new sites. We thus combined information obtained with the generic (Pho4p, combining all sites) and the two specific (Pho4p.g and Pho4p.t) matrices. This induces some redundancy, and correlations are to be expected between the matching scores obtained with the generic and each specific matrix. Fortunately, inter-column correlations are taken into account by the discriminant analysis, and should thus not provoke any bias. The utilization of three matrices for Pho4p also increases the number of variables, which increases the risk of over-fitting, but this is not problematic since we apply a forward stepwise variable selection.
Each alignment matrix was converted by patser to a weight matrix and used to scan the whole set of yeast upstream sequences for putative matches. Upstream sequences of all yeast genes were retrieved over 800 bp from the start codon. For each PSSM, the three top scores were collected in order to detect multiple binding sites for the same transcription factor. Each upstream sequence is thus characterized by a 15-dimensional (3 scores x 5 matrices) vector of scores.
Comparison of matrix scores on upstreamsequences of the training set
Figure 1 plots the scores assigned to the training genes with the different matrices. A simple visual inspection already reveals interesting properties of the PSSM.
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Most PHO genes have a high score (
10) with the Pho4p matrix (Fig. 1A), whereas such a score is observed only once for a MET gene. Reciprocally, most MET genes have a high Met31p score, which is rarely observed in PHO genes. The Pho4p and Met31p matrix thus provide a reasonably good, but not perfect, separation between PHO and MET genes. A few MET genes are mixed with the CTL genes. Figure 1B shows that there is no apparent correlation between Pho4p and Met4p scores, despite the fact that they share the same binding core CACGTG. The difference between flanking residues (compare Table 2A and C) are thus informative. Figure 1C shows that most MET genes have a high scoring match for both Met31p and Met4p, highlighting the cooperative effect of the two factors. However, some MET genes seem to have binding sites for Met4p alone, or Met31p alone. As expected, PHO genes are mixed with CTL as shown in Figure 1C. The combination of Met4p and Met31p matrices separates thus reasonably well MET from non-MET genes.
Figure 1D–F show the two top scoring matches obtained with the Pho4p, Met4p and Met31p matrices, respectively, on each sequence of the training set. It is striking that seven of the eight PHO genes have two very high-scoring matches (Fig. 1D), suggesting the presence of multiple Pho4p binding sites in their upstream sequences. Similarly, most MET genes have at least two very good matches for the Met4p matrix (Fig. 1E). The effect is less pronounced for the Met31p matrix (Fig. 1F): the majority of the MET genes have a very high (>10) first score, but a low (<7) second score.
In summary, PSSMs seem reasonably specific for their expected gene families (Met31p and Met4p matrices are specific for MET genes, and the Pho4p matrices for PHO genes), but each matrix only provides a partial information on the way a gene is regulated. Thus, for classifying genes on the basis of their upstream sequence motifs, one would like to combine information provided by all the matrices. The problem is obviously to find an optimal criterion for weighting the different matrix scores. This can be done with the discriminant analysis, as shown in the next section.
Discriminant analysis with matrix scores
In order to evaluate whether PHO, MET and CTL genes can be discriminated on the basis of upstream motifs, we applied LDA and QDA. We performed two separate analyses for predicting phosphate (PHO against MET + CTL), and methionine (MET against PHO + CTL) regulation, respectively. The evaluation was performed with a LOO test. To prevent the risk of over-fitting, we applied a forward stepwise variable selection.
Error rates were calculated as a function of the number of variables, with different discriminant methods (linear or quadratic). We also tested the effect of data transformation by PCA.
Figure 2 summarizes the results of this evaluation. Each curve represents the rate of error for one discriminant method as a function of the number of selected variables.
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For both PHO and MET predictions, better results are obtained with LDA than with QDA. Let us consider the PHO against CTL + MET classification (Fig. 2A): with LDA, the error rate decreases when the 5 first variables are incorporated, after which it remains constant until the 10th variable is incorporated. Optimal discrimination (1% errors) is obtained with 5–9 variables. Under the same condition, a random classification would return 7.7% of errors (LDA permutation curve). The increases of the error rate with the last variables suggests an effect of over-fitting. This is not surprising since the training uses more variables (15) than objects in the PHO training group (eight genes). A similar behaviour is observed for the error curves of the MET against PHO + CTL discrimination (Fig. 2B). It is interesting to note that the error rate increases with the number of variables even with the permuted dataset, which is typical of a situation of over-fitting: when the training is done with more variables than objects, the discriminant function is over-fitted to the training set, even if there is nothing to be learned from it (permuted dataset), and tends to misclassify new objects.
The order of incorporation of the variables is indicative of the information contained in the matrix scores. Not suprisingly, for the PHO against MET + CTL discrimination, the seven first variables correspond to the different scores of Pho4 matrices [Table 3(A)]. The eighth and ninth variables (which neither decrease nor increase the error rate) are the second and third top scores of the Met31 matrix. Consistently, a different subset of variables is used for the MET against PHO + CTL discrimination [Table 3(B)]: the first three selected variables are the top scores for the Met4 matrix and the first and third scores of Met31. The next variables are mostly Pho4 scores.
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In general, QDA is more powerful than LDA, but in our case the results are opposite. This probably results from the over-fitting problem: the dimensionality of the discrimination criterion increases quadratically with the number of selected variables. QDA could not incorporate more than five variables due to the restricted size of the smallest training class (eight genes for the PHO group). With QDA, over-fitting is already perceptible in the permutation test when the second (Fig. 2A) or third (Fig. 2B) variable is incorporated.
Beyond the raw error rate, it is important to evaluate the types of prediction errors. Table 4 summarizes the number of correct and wrong assignations obtained by LDA for each class of the training set. For the two-group classifications (PHO against MET + CTL and MET against PHO + CTL), all errors consist of ‘false negatives’, i.e. one PHO and three MET genes are assigned to the CTL group, giving error rates of 1.0 and 2.9%, respectively.
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We also tested the direct three-group classification (PHO against MET against CTL), but this raised an error rate of 5.8% [Table 4(E)]. In addition, from the biological point of view, the regulation of a given gene might be achieved by multiple transcription factors. There is thus no reason to impose a priori that a gene belongs to only one class. Indeed, from their experimental observations, O'Connell and Baker (1992) have postulated a possible cross-regulation between phosphate and sulfate metabolism in yeast.
The permutation test shows that the random expectation for the error rate is markedly higher for the three-group classification (23.1%) than for the two-group classifications (15.4% for MET and 7.6% for PHO). The confusion tables [Table 4(B, D and F)] show that when the program is trained with randomly permuted labels the classifier tends to assign all objects to the most frequentclass (CTL).
The types of errors returned by QDA (Table 5) show similar trends as with LDA (Table 4), but the results are slightly poorer.
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Data transformation by PCA did not improve the performances of the classification (Fig. 2).
In summary, two-group classifications with LDA provides a quite stringent discrimination criterion (few false positives), which is essential for the genome-scale prediction.
Genome-scale prediction of methionine andphosphate responding genes
We used the optimal method (LDA) and the variables selected by the stepwise procedure for predicting methionine and phosphate regulation in all yeast genes. This resulted in the prediction of 40 phosphate- and 37 methionine-regulated genes.
Among the PHO-predicted genes (Table 6), all training genes but PHO8 are recovered. The non-training gene predicted with the highest probability is STB3. Almost nothing is known about this gene except that its product binds to Sin3p, a global transcription factor affecting expression of many genes including INO1, which itself is involved in phospholipid biosynthesis (Slekar and Henry, 1995). Also predicted with a high probability are VTC4, which was recently proposed as a target for PHO4 (Huang et al., 2002), PHO87, coding for a phosphate permease, PHM6, which might have a role in phosphate metabolism and is regulated by phosphate (Standford Genome Database) and PMP2, coding for an H+-ATPase subunit. These genes are interesting candidates for the experimental analysis.
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Among the MET-predicted genes (Table 7), 11 of the 16 training genes are recovered. There are thus five false negatives in the genome-scale prediction, i.e. two more than in the LOO evaluation. This is due to a change in prior probabilities: for the evaluation, the frequencies of training classes were used as priors, whereas during genome-scale predictions we intentionally reduced MET prior probability to 1% in order to minimize false positives.
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Some of the predicted genes are interesting targets to look for in effective binding to MET4 and/or MET31/MET32. In particular, genes predicted with a high probability include CYS3 and CYS4, both involved in cystathionine metabolism, MUP1, coding for a methionine permease and MET32. This latter gene is particularly interesting since it codes for a transcription factor involved in methionine regulation. Its classification among MET genes suggests that it is itself regulated at the transcriptional level, and this might be mediated by Met4p, Met31p or by auto-activation. We did not find any evidence for such a regulation in the literature, but the MET32 upstream sequence contains a high scoring site for Met31p/Met32p. In constrast, the gene MET31 is not classified in the MET group by the discriminant procedure and its upstream region does not seem to contain any match for Met31p/Met32p or Met4p. This raises the intriguing hypothesis that the two homologous genes MET31 and MET32 could be regulated differently, and this might enable the cell to activate methionine biosynthesis in response to different conditions.
Comparison with experimental genome-scaledetection of transcription factor target genes
In order to assess the reliability of our predictions, we compared the results of the discriminant procedures with high-throughput experiments reporting the binding of transcription factors to DNA (Lee et al., 2002) and the transcriptional response to phosphate stress (Ogawa et al., 2000).
Lee et al. (2002) applied a ChIP–chip approach to detect binding between 106 yeast transcription factors and all the yeast intergenic regions, and characterized the reliability of each measurement by a P-value. From this dataset, we selected the ChIP–chip experiment P-values for Pho4p, Met4p and Met31p.
Ogawa et al. (2000) performed eight DNA chip experiments to test the transcriptional response of yeast to various phosphate stress conditions (low concentrations or PHO mutants) and selected 21 genes showing a consistent transcriptional response (at least 2-fold regulation in at least five of the eight experiments).
We first compared microarray data from Ogawa et al. (2000) with ChIP–chip provided by Lee et al. (2002). Suprisingly, the comparison reveals a striking discrepancy between these two datasets (Fig. 3A): genes showing transcriptional response are not detected by the ChIP–chip experiment, and reciprocally. Some PHO training genes appear among the regulated genes, but none of them is detected in the ChIP–chip experiment.
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A closer analysis of the ChIP–chip experiment reveals that 62 genes have a P-value < 10–3, but that none of these genes corresponds to known Pho4p target genes (Zhu and Zhang, 1999), and, in addition, the upstream sequences of the genes detected by ChIP–chip do not contain the Pho4p binding motif (Simonis et al., 2004). The most likely reason for the absence of PHO genes is that Lee and co-workers used the same rich medium for all their experiments. Since it is well known that, in presence of phosphate, Pho4p is inactivated by sequestration in the cytoplasm (Oshima et al., 1996) there was not much chance to detect real Pho4p targets in the experimental conditions used, and the 62 reported genes are thus likely to be experimental artefacts. For a similar reason, the Met4p ChIP–chip experiment should also be considered with caution since Met4p is inactivated by methionine (Kuras and Thomas, 1995; Thomas and Surdin-Kerjan, 1997). These ChIP–chip data also show a large inconsistency between target genes detected for Met4p and Met31p (Supplementary material).
In a more recent study, Harbison et al. (2004) detected the binding regions of yeast transcription factors in different culture media. This study includes detection of PHO4 targets in phosphate-poor medium (Pi–) and of MET4 targets in methionine-poor medium (SM). Figure 3B shows a better consistency between ChIP–chip detection (Pho4p targets in Pi- medium) and expression data, although many genes are detected with ChIP–chip but not by microarray experiments.
Not suprizingly, we found not a single common gene between our PHO predicted genes and the Pho4p targets detected by Lee et al. (2002) in the rich medium (Fig. 3C). The comparison with Harbison et al. (2004) results is more informative: several genes are detected by both our motif-based PHO predictions and the ChIP–chip detection (Fig. 3D), among which a good fraction is of the annotated Pho4p targets.
The comparison between our PHO predictions and the gene expression data (Fig. 3E) shows that almost all the genes showing a high transcriptional response are detected by the discriminant analysis (top-right corner). These genes include most of the training genes (PHO12, PHO84, PHO86, SPL2, PHO89, PHO5 and PHO11) as well as some of our de novo predictions (VTC2, VTC4 and PHM6). However, many other predicted genes do not show any response to phosphate in Ogawa's experiments. These genes include one of the training genes, PHO81, suggesting that some real phosphate genes can escape detection in Ogawa's experiment. However, motif-based predictions also contain a certain rate of false positive (see Discussion).
Genes classified as MET by the discriminant procedure poorly correspond to those detected by the ChIP–chip data in methionine-poor medium (Fig. 3F). Only five genes are detected by both our predictions and the ChIP–chip experiment, including two of the MET training genes. Nine other training genes are detected by our predictions but not in the ChIP–chip experiment, whereas one is detected by the ChIP–chip and not predicted by our method.
Discriminant analysis with an expanded training set
It is somewhat surprising to notice that the simplest method (LDA) gives better performances than more elaborate treatments (QDA, PCA-transformation before LDA or QDA) (Fig. 2). This effect might result from the small number of training objects, in particular for the PHO group (eight genes). In order to test this possibility, we performed the same analysis with a larger training set, regrouping the original training set (proven PHO and MET genes) with those predicted by our LDA procedure.
On the error curves obtained with the expanded training set (Fig. 4), QDA indeed gives better results than with the small training sets, and its performances are similar to LDA. The differences between PCA-transformed and non-transformed data are also less sensitive with the expanded dataset, and, for PHO against CTL + MET classification, the best results are obtained with LDA on the PCA-transformed data.
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DISCUSSION |
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TOPAbstractINTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The first question addressed in this paper was whether PSSMs would allow us to distinguish PHO and MET genes, despite the high similarity between the consensus of their main regulator (TCACGTGA for Met4p and CACGTKkk for Pho4p). Discriminant analysis using the LOO evaluation shows that there is no confusion between the training PHO and MET genes. The PSSMs are thus sufficiently informative, despite the small number of sites used for building them (no more than seven sites for Pho4p.t). An essential reason for the absence of cross-predictions is the integration of multiple criteria. For the MET family, two distinct PSSMs were used to reflect the synergic regulation by multiple transcription factors (Met4p and Met31p, respectively). The comparison of scores obtained with Met31 and Met4 matrices shows that some genes are essentially regulated by Met4p, some by Met31p and some by both factors. The combination of matrices thus provides better information to distinguish MET sequences from the PHO and CTL groups. We also used multiple scores to reflect the binding diversity due to the specificity of the core-flanking bases (e.g. Pho4p.t and Pho4p.g matrices) and self-synergy assured by multiple binding sites (selection of the three top scores for each sequence). This multi-variate representation gives better classification than any matrix taken alone. However, it is essential to restrict the number of predictive variables in order to avoid the trap of over-fitting (Fig. 2).
The second question was whether the classification based on putative binding motifs would allow to predict phosphate or methionine response at a genome-scale. These genome-scale predictions should be taken with caution, for various reasons. (1) The number of genes is so large (6345) that even a small risk of error would result in many misclassifications. To avoid this, we deliberately chose low prior probabilities (1%) for PHO and MET classes, and this has a cost in terms of sensitivity (we miss 5 out of the 16 MET genes). The predictions can thus certainly not be considered as exhaustive. (2) When two neighbour genes are transcribed in divergent directions they share the same intergenic region. In such cases, we cannot predict whether the binding sites are involved in the regulation of the gene at their left, at their right, or both. (3) The binding of a transcription factor is not always sufficient to confer a transcriptional regulation. Note that the restrictions (2) and (3) also apply for the interpretation of ChIP–chip data, since this method detects the binding of a transcription factor to an intergenic region.
Having in mind all the restrictions above, genome-scale predictions can nevertheless give some useful information. It is interesting to note that among the 6345 yeast genes not a single one is predicted as both phosphate and methionine regulated. Another observation is that, despite the simplicity of its underlying model, LDA gives better results than QDA. Paradoxically, our attempts to use more sophisticated methods (SVM) resulted in a lower hit rate (not shown). It is well known that each classifier has its own range of applications, and apparently with the type of data treated here good results can be obtained with one of the simplest classifiers. It is likely that the accuracy of LDA observed in this case comes from the very small size of the training set. In cases where larger training sets are available, other methods that rely on the estimation of more parameters (SVM, QDA) might become more efficient. This hypothesis seems to be supported by our observation that the differences between LDA and QDA are reduced when the classification is performed with the expanded training set combining annotated and predicted genes.
The comparison between our predictions and the gene expression and ChIP–chip data suggests that pattern-based prediction of gene regulation can be very helpful as a complement to high-throughput data. The high rate of false-positives returned by some methods can be reduced by selecting the most consistent results (intersection between sets of genes detected by the different methods). Alternatively, sequence-based predictions could be used to detect potential targets, which for some biological (culture conditions) or technical (noise) reason escaped the detection by high-throughput methods. These predicted targets could then be submitted to a more precise experimental characterization.
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Acknowledgments |
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The authors are grateful to Jerry Hertz, who kindly adapted his patser program in order to report multiple top matches per sequence. D.G. is Chargé de Recherches du Fonds National Belge de la Recherche Scientifique. This research was partly funded by the Actions de Recherche Concertée de la Communauté Française de Belgique (contracts ARC-02/07–291 and ARC-04/09–307). S.P. and O.G. were supported by the Fench Réseau National des Génopoles (RNG).
Conflict of Interest: none declared.
Received on January 16, 2005; revised on June 15, 2005; accepted on June 27, 2005
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REFERENCES |
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TOPAbstractINTRODUCTIONSYSTEMS AND METHODSRESULTSDISCUSSIONREFERENCES |
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