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Predicting Genetic Regulatory Response Using Classification

We present a novel classification-based method for learning to predict gene regulatory response. Our approach is motivated by the hypothesis that in simple organisms such as Saccharomyces cerevisiae, we can learn a decision rule for predicting whether a gene is up- or down-regulated in a particular experiment based on (1) the presence of binding site subsequences (``motifs'') in the gene's regulatory region and (2) the expression levels of regulators such as transcription factors in the experiment (``parents''). Thus our learning task integrates two qualitatively different data sources: genome-wide cDNA microarray data across multiple perturbation and mutant experiments along with motif profile data from regulatory sequences. We convert the regression task of predicting real-valued gene expression measurement to a classification task of predicting +1 and -1 labels, corresponding to up- and down-regulation beyond the levels of biological and measurement noise in microarray measurements. The learning algorithm employed is boosting with a margin-based generalization of decision trees, alternating decision trees. This large-margin classifier is sufficiently flexible to allow complex logical functions, yet sufficiently simple to give insight into the combinatorial mechanisms of gene regulation. We observe encouraging prediction accuracy on experiments based on the Gasch S. cerevisiae dataset, and we show that we can accurately predict up- and down-regulation on held-out experiments. Our method thus provides predictive hypotheses, suggests biological experiments, and provides interpretable insight into the structure of genetic regulatory networks.


I. INTRODUCTION
Understanding underlying mechanisms of gene transcriptional regulation through analysis of highthroughput genomic data -for example, gene expression data from microarray experiments and regulatory sequence data -has become one of the central problems in computational biology, particularly for simpler model organisms such as S. cerevisiae. Efforts to identify regulatory elements in non-coding DNA [1,6], models for investigating co-occurrence of regulatory motifs and combinatorial effects of regulatory molecules [11], and attempts to organize genes that appear to be subject to common regulatory control into "regulatory modules" [7,14] all define pieces of this complex problem. Most recent studies of transcriptional regulation can be placed broadly in one of three categories: statistical approaches, which aim to identify statistically significant regulatory patterns in a dataset [1,7,11]; probabilistic approaches, which try to discover structure in the dataset as formalized by probabilistic models (often graphical models or Bayesian networks) [5,9,10,14,15]; and linear network models, which hope to learn explicit parameterized models for pieces of the regulatory network by fitting to data [2,17]. These approaches are all useful exploratory tools in the sense that they allow the user to generate biological hypotheses about transcriptional regulation that can then be tested in the lab. In general, however, these approaches are not yet adequate for making accurate predictions about which genes will be up-or down-regulated in new or held-out experiments. Therefore, it is difficult to compare performance of different approaches or decide, based on cross-validation experiments, which approach is likely to generate plausible hypotheses.
The goal of our method is to learn a prediction function for the regulatory response of genes under different experimental conditions. The inputs to our learning algorithm are the gene-specific regulatory sequences -represented by the set of binding site patterns they contain ("motifs") -and the experiment-specific expression levels of regulators ("parents"). The output is a prediction of the expression state of the regulated gene. Rather than trying to predict a real-valued expression level, we formulate the task as a binary classification problem, that is, we predict only whether the gene is up-or down-regulated. This reduction allows us to exploit modern and effective classification algorithms. The learning algorithm that we use is boosting with a margin-based generalization of decision trees called alternating decision trees (ADTs). Boosting, like support vector machines, is a large-margin classification algorithm that performs well for high-dimensional problems. We evaluate the performance of our method by measuring prediction accuracy on held-out microarray experiments, and we achieve very good classification results in this setting. Moreover, we show that the learned prediction trees contain information that is both statistically significant and biologically meaningful. These significant features, which are associated with accurate generalization rather than simply correlations in the training data, suggest regulators, motifs, and motif-regulator pairs that play an important role in gene transcriptional regulation.
Among recent statistical approaches, the most successful related approach is the REDUCE algorithm of Bussemaker et al. [1] for regulatory element discovery. Given gene expression measurements from a single microarray experiment and the regulatory sequence S g for each gene g represented on the array, REDUCE proposes a linear model for the dependence of log gene expression ratio E g on presence of regulatory subsequences (or "motifs") E g = C + µ∈Sg F µ N µg , where N µg is a count of occurrences of regulatory subsequence µ in sequence S g , and the F µ are experiment-specific fit parameters. We generalize beyond the conditions of a single experiment by considering pairs (motif g ,parent e ), where the parent variable represents over-or under-expression of a regulator (transcription factor, signaling molecule, or protein kinase) in the experiment e, rather than using motif information alone. Note, however, that we use classification rather than regression as in REDUCE.
Similar restriction of potential parents has been used with success in the probabilistic model literature, including in the regression-based work of Segal et al. [14] for partitioning target genes into regulatory modules for S. cerevisiae. Here, each module is a probabilistic regression tree, where internal nodes of the tree correspond to states of regulators and each leaf node prescribes a normal distribution describing the expression of all the module's genes given the regulator conditions. The authors provide some statistical validation on new experiments by establishing that selected module distributions do have non-random correlation with true expression; however, they do not focus on making accurate predictions of differential expression as we do here. In our work, we retain the distinction between regulator ("parent") genes and target ("child") genes, as well as a model that can capture combinatorial relationships among regulators; however, our margin-based trees are very different from probabilistic trees. Unlike in Segal et al. [14], we learn from both expression and sequence data, so that the influence of a regulator is mediated through presence of regulatory element. We note that in separate work, Segal et al. [15] present a probabilistic model for combining promoter sequence data and a large amount of expression data to learn transcriptional modules on a genome-wide level in S. cerevisiae, but they do not demonstrate how to use this learned model for predictions of regulatory response.

A. Adaboost
Adaboost is a general discriminative learning algorithm invented by Freund and Schapire [12]. The basic idea of Adaboost is to repeatedly apply a simple learning algorithm, called the weak or base learner, to different weightings of the same training set. In its simplest form, Adaboost is intended for binary prediction problems where the training set consists of pairs (x 1 , y 1 ), (x 2 , y 2 ), . . . , (x m , y m ), x i corresponds to the features of an example, and y i ∈ {−1, +1} is the binary label to be predicted. A weighting of the training examples is an assignment of a non-negative real value w i to each example (x i , y i ).
On iteration t of the boosting process, the weak learner is applied to the training set with a set of weights w t 1 , . . . , w t m and produces a prediction rule h t that maps x to {0, 1}. The requirement on the weak learner is for h t (x) to have a small but significant correlation with the example labels y when measured using the current weighting of the examples. After the rule h t is generated, the example weights are changed so that the weak predictions h t (x) and the labels y are decorrelated. The weak learner is then called with the new weights over the training examples and the process repeats. Finally, all of the weak prediction rules are combined into a single strong rule using a weighted majority vote. One can prove that if the rules generated in the iterations are all slightly correlated with the label, then the strong rule will have a very high correlation with the label -in other words, it will predict the label very accurately.
The whole process can be seen as a variational method in which an approximation F (x) is repeatedly changed by adding to it small corrections given by the weak prediction functions. In Figure 1, we describe Adaboost in these terms. We shall refer to F (x) as the prediction score in the rest of the paper. The strong prediction rule learned by Adaboost is sign(F (x)).
A surprising phenomenon associated with Adaboost is that the test error of the strong rule (percentage of mistakes made on new examples) often continues to decrease even after the training error (fraction of mistakes made on the training set) reaches zero. This behavior has been related to the concept of a "margin", which is simply the value yF (x) [13]. While yF (x) > 0 corresponds to a correct prediction, yF (x) > a > 0 corresponds to a confident correct prediction, and the confidence increases monotonically with a. Our experiments in this paper demonstrate the correlation between large margins and correct predictions on the test set (see Results section). Adaboost is often used with a decision tree learning algorithms as the base learning algorithm. We use Adaboost both to learn the decision rules constituting the tree and to combine these rules through a weighted majority vote. The form of the generated decision rules is called an alternating decision tree (ADT) [3].

B. Alternating Decision Trees
We explain the structure of ADTs using the example given in Figure 2, reproduced from Freund & Mason [3]. The problem domain is heart disease diagnostics and the goal is to predict whether an individual is healthy or sick based on 13 different indicators. The tree consists of alternating levels of ovals (prediction nodes) and rectangles (splitter nodes). The numbers within the ovals define contributions to the prediction score. In this example, positive contributions are evidence of a healthy heart, negative contributions are evidence of a heart problem. To evaluate the prediction for a particular individual we start at the top oval (0.062) and follow the arrows down.
We follow all of the dotted arrows that emanate from prediction nodes, but we follow only one of the solid-line arrows emanating from a splitter node, corresponding to the answer (yes or no) to the condition stated in rectangle. We sum the values in all the prediction nodes that we reach. This sum represents the prediction score F (x) above, and its sign is the prediction.
For example, suppose we had an individual for which hdl=bad, b.press=0, pain=y, oldpeak=2, weight=300, sex=m. In this case, the prediction nodes that we reach in the tree are 0.062, −0.626, 0.425, −0.444, −0.536, 0.138, and summing gives a score of −0.981, i.e., a very confident diagnosis that the individual has a heart problem.
The ADT in the figure was generated by Adaboost from training data. In terms of Adaboost, each prediction node represents a weak prediction rule, and at every boosting iteration, a new splitter node together with its two prediction nodes is introduced. The splitter node can be attached to any previous prediction node, not only leaf nodes. Each prediction node is associated with a weight α that contributes to the prediction score of every example reaching it. The weak hypothesis h(x) is 1 for every example reaching the prediction node and 0 for all others. The number in front of the conditions in the splitter nodes of Figure 2 indicates the iteration number on which the node was added. In general, lower iteration numbers indicate that the decision rule is more important. We use this heuristic to analyze the ADTs and identify the most important factors in gene regulatory response.

C. ADTs for Predicting Regulatory Response
For the problem of predicting differential gene expression, we start with a candidate set of motifs µ representing known or putative regulatory element sequence patterns and a candidate set of regulators or parents π. For each (gene,experiment) example in our gene expression dataset, we have two sources of feature information relative to the candidate motifs and candidate parent sets: a vector N µg of motif counts of occurrences of patterns µ in the regulatory sequence of gene g, and the vector π e ∈ {−1, 0, 1} of expression states for parent genes π in the experiment e. The data representation is depicted in Figure 3.
Splitter nodes in our ADTs depend on decisions based on (motif,parent) pairs. However, instead of splitting on real-valued thresholds of parent expression and integervalued motif count thresholds, we consider only whether a motif µ is present or not, and only whether a parent π is over-expressed (or under-expressed) in the example. Thus, splitter nodes make boolean decisions based on conditions such as "motif µ is present and regulator π is over-expressed (or under-expressed)". Paths in the learned ADT correspond to conjunctions (AND operations) of these boolean (motif,parent) conditions. Full details on selection of the candidate motifs and regula- tors and discretization into up and down states is given in the Methods section.

Dataset:
We use the Gasch et al. [4] environmental stress response dataset, consisting of cDNA microarray experiments measuring genomic expression in S. cerevisiae in response to diverse environmental transitions. There are a total of 6110 genes and 173 experiments in the dataset, with all measurements given as log 2 expression values (fold-change with respect to unstimulated reference expression). We do not perform a zero mean and unit variance normalization over experiments, since we must retain the meaning of the true zero (no fold change).
Motif set: We obtain the 500 bp 5' promoter sequences of all S. cerevisiae genes from the Saccharomyces Genome Database (SGD). For each of these sequences, we search for transcription factor (TF) binding sites using the PATCH software licensed by TRANSFAC [16]. The PATCH tool uses a library of known and putative TF binding sites, some of which are represented by position specific scoring matrices and some by consensus patterns, from the TRANSFAC Professional database. A total of 354 binding sites are used after pruning to remove redundant and rare sites.
Parent set: We compile different sets of candidate regulators to study the performance and dependence of our method on the set of regulators. We restrict ourselves to a superset of 475 regulators (consisting of transcription factors, signaling molecules and protein kinases), 466 of which are used in Segal et al. [14] and 9 generic (global) regulators obtained from Lee et al. [8].
Due to computational limitations on the number of (motif,parent) features we could use in training, we select smaller subsets of regulators based on the following selection criteria. We use 13 high-variance regulators that had a standard deviation (in expression over all experiments) above a cutoff of 1.2. The second subset consists of the 9 global regulators that are present in the Lee et al. [8] studies but absent in the candidate list of Segal et al. [14]. We also include 50 regulators that are found to be top ranking regulators for the clusters identified in Segal et al. The union of these three lists gives 53 unique regulators.
Target set and label assignment: We discretize expression values of all genes into three levels representing down-regulation (-1), no change (0) and up-regulation (+1) using cutoffs based on the empirical noise distribution around the baseline (0) calculated from the three replicate unstimulated (time=0) heat-shock experiments [4]. We observe that 95% of the samples in this distribution had expression values between +1.3 and -1.3. Thus we use these cutoffs to decide what we define as significantly up-regulated (+1) and down-regulated (-1) beyond the levels of biological and experimental noise in the microarray measurements.
Note that although we train only on those (gene,experiment) pairs which discretize to up-or down-regulated states, we test (make predictions) on every example in a held-out experiment by thresholding on predicted margins. That is, we predict baseline if a prediction has margin below threshold (see Results section).
We reduce our target gene list to a set of 1411 genes which include 469 highly variant genes (standard deviation > 1.2 in expression over all experiments) and 1250 genes that are part of the 17 clusters identified by Gasch et al. [4] using hierarchical clustering (eliminating overlaps).
Software: We use the MLJava software developed by Freund and Schapire, which implements the ADT learning algorithm. We use the text-feature in MLJava to take advantage of the sparse motif matrix and use memory more efficiently.

A. Cross-Validation Experiments
We first perform cross-validation experiments to evaluate classification performance on held-out experiments. We divide the set of 173 microarray experiments into 10 folds, grouping replicate experiments together to avoid bias, and perform 10-fold cross-validation experiments using boosting with ADTs on all 1411 target genes.
We train the ADTs for 400 boosting iterations, during most of which test-loss decreases continuously. We obtain an accuracy of 88.5% on up-and down-regulated examples averaged over 10 folds (test loss of 11.5%), showing that predicting regulatory response is indeed possible in our framework.
To assess the difficulty of the classification task, we also compare to a baseline method, k-nearest neighbor classification (kNN), where each test example is classified by a vote of its k nearest neighbors in the training set. For a distance function, we use a weighted sum of Euclidean distances d((g 1 , e 1 ), (g 2 , e 2 )) 2 = w m ||m g1 − m g2 || 2 + w p ||p e1 − p e2 || 2 , where m g represents the vector of motif counts for gene g and p e represents the parent expression vector in experiment e. We try various weight ratios 10 −3 < (w m /w p ) < 10 3 and values of k < 20, and we use both binary and integer representations of the motif data. We obtain minimum test-loss of 34.4% at k=17 for binary motif counts and 31.3% at k=19 for integer motif counts, both for weight-ratios of 1, giving much poorer performance than boosting with ADTs.
Since ADTs output a real-valued prediction score F (x) = T t=1 α t h t (x), whose absolute value measures the confidence of the classification, we can predict a baseline label by thresholding on this score, that is, we predict examples to be up-or down-regulated if F (x) > a or F (x) < −a respectively, and to be baseline if |F (x)| < a, where a > 0. Figure 4 shows expression values versus  Table I.

B. Extracting features for biological interpretation
We describe below several approaches for extracting important features from the learned ADT models, and we suggest ways to relate these features to the biology of gene regulation.
Extracting significant features: Features at nodes in the ADT consist of motif-parent pairs. We rank motifs, parents and motif-parent pairs by three different methods: by the boosting iteration in which the feature first occurs (iteration score), by the total number of occurrences of the feature in the final tree (abundance score), and by the absolute prediction score associated to the feature (prediction score). Ranking scores are averaged over all ten folds (see supplementary website for detailed results). Note that presence of a strong feature does not necessarily imply a direct binding relationship between parent and motif. Such a pair could represent an indirect regulatory relationship (for example, a kinase and the binding site of the transcription factor that it phosphorylates) or some other kind of predictive correlation, for example, co-occurrence of the true binding site with the motif corresponding to the feature.
The top ranking motif based on iteration score was the STRE element of MSN2/MSN4, which is known to be a regulatory element for a significant number of general stress response target genes [4]. The other high scoring motifs include HSF1 (heat-shock), RAP1 (heatshock and osmolarity), TBP (TATA binding site), ADR1 (glycerol metabolism and osmolarity), MIG1 (glucose metabolism and carbon source based stress), REB1 (Pol-I transcription termination activity), GAL4 (galactose metabolism), YAP1 (peroxide stress) and GCN4 (amino acid biosynthesis and starvation response) binding sites, all of which are known to be active in various kinds of stress responses.
Of the 53 candidate regulators, 37 appear in the ADTs of the ten folds. The top-ranking regulator, based on both iteration score and abundance score, is USV1 (YPL230W); this regulator was found by Segal et al. [14] as the top-ranking regulator in 11 of their 50 regulatory modules. Other top ranking regulators (see Table IV B) include PPT1, TPK1 (SRA3), XBP1 and GCN20. It is interesting to note that while the presence and absence of binding sites of some very important stress factors like MSN2 and HSF1 (heat shock factor) are identified as sig-nificant features (high motif iteration score) in the ADTs, their mRNA expression levels do not seem to be very predictive. HSF1 does not appear as a parent in any of the ADTs, and MSN2 gets low abundance and iteration scores as a parent, despite its importance as a stress response regulator. Similar results are observed in the modules of Segal et al. [14], where HSF1 is not found in any of the regulation programs and MSN2 is found in 3 of the 50 regulation programs but with low significance. If we examine the expression profiles of HSF1, MSN2, USV1 and PPT1, we find that the mRNA levels of MSN2 and HSF1 have quite small fluctuations (rarely greater than 2 fold change) and fall mostly within the baseline state, while the expression levels of USV1 or PPT1 show much larger variation over many experiments (see Figure 5). It is known that MSN2 is regulated posttranslationally by TPK1, which is identified as an important parent in the ADTs and is found associated with the MSN2 binding site as a motif-parent pair. Thus in this case, where the activity of a regulator is itself regulated post-transcriptionally, we see a clear advantage of using motif data along with mRNA expression data. "In silico" knock-outs: By removing a candidate from the regulator list and retraining the ADT, we can evaluate whether test loss significantly decreases with omission of the parent and identify other weaker regulators that are also correlated with the labels. We investigate in silico knock-outs in the biologically-motivated experiments described below.

C. Biological Validation Experiments
We designed 5 different training and test sets of selected microarray experiments based on observations of similarity and differences between stresses by Gasch et al. [4], and we used these experiments to study the response to specific types of stress in our framework. We present results for 3 of these studies below (see supplementary website for the other 2 experiments). By comparative analysis of the trees learned from these sets, we find and validate regulators that are associated to regulation programs activated by different stresses.
Heat-shock and osmolarity stress response: In the first study, we trained on heat-shock, osmolarity, heat-shock knockouts, over-expression, amino-acid starvation experiments, and we tested on stationary phase, simultaneous heat-shock and hypo-osmolarity experiments.
We observe a low test loss of 9.3%, supporting the hypothesis that pathways involved in heat-shock and osmolarity stress appear to be independent and the joint response to both stresses can be predicted easily [4]. We also confirm that the regulatory response for stationary phase (test set) is very similar to that of heat-shock (training set) [4]. The high scoring parents are USV1, XBP1, TPK1, PPT1, GIS1, GAC1 and SLT2. The connection of osmolarity response to the HOG and other MAP kinase pathways is well known, and it is interesting to note that most of these regulators are in fact signaling molecules. Also, the osmolarity response is strongly related to glycerol metabolism and transport and hence closely associated with gluconeogenesis and glucose metabolism pathways. We find the binding sites of CAT8 (gluconeogensis), GAL4 (galactose metabolism), MIG1 (glucose metabolism), GCN4 (regulator of HOG pathway and amino acid metabolism), HSF1 (heat-shock factor), CHA4 (amino acid catabolism), MET31 (methion-ine biosynthesis), RAP1 and MSN2/MSN4 to have high iteration scores; these regulators are all related to the stress conditions in the training set.
USV1 "in silico" knockout: Using the same train and test microarrays as in the heat-shock/osmolarity setup, we perform a second study by removing one of the strong regulators, USV1, from the parent set and retraining the ADT. We get a minor but significant increase in test error from 9.3% to 11%. Regarding structural changes in the ADT, we observe that the overall hierarchy of the features does not change significantly: TPK1, XBP1, PPT1 and GIS1 remain the highest scoring parents. We also find that 305 target genes change prediction labels. GO annotation enrichment analysis of these target genes reveal the terms cell wall organization and biogenesis, heat-shock protein activity, galactose, acetyl-CoA and chitin metabolism and tRNA processing and cell-growth. These match many of the terms enriched by analyzing GO annotations of genes that changed significantly in a microarray experiment by Segal et al. [14] with stationary phase induced in a USV1 knockout.
Pleiotropic response to diamide: For the third study, we trained on heat-shock, heat-shock knockouts, over-expression, H 2 O 2 wild-type and mutant, menadione, DTT experiments, and we tested on diamide experiments.
Gasch et al. [4] consider the diamide response to be a composite of responses to the experiments in the training set. We observe a moderate test loss of 16%, suggesting that this pleiotropic response is more complex than the simpler additive responses to heat-shock and osmolarity. We observe the emergence of an important motif-parent feature: YAP1 is directly associated with its ARE-binding site (Y$TRX2) as a high scoring regulator that is absent in the ADTs of both previous studies. This finding is consistent with known biology, since YAP1 plays a specific role in peroxide and superoxide response (present in the training set) [4]. We also find the PDR3 (menadione-drug response) binding site to be a high scoring motif.

V. DISCUSSION
While encouraged by the performance of our method, we believe further work is likely to yield much more comprehensive and accurate models of the regulatory networks of yeast and other simple organisms.
One main direction for improvement is to increase the computational efficiency of our software so that we can scale up both the size of the training set and the feature space. Since the Gasch dataset that we used here only contains experiments for environmental stress response, many other regulatory pathways are likely not activated and therefore cannot be modeled by analysis of this dataset alone. We plan to pursue more extensive computational experiments on other diverse yeast datasets, such as those available through NCBI's Gene Expression Om-nibus and the Saccharomyces Genome Database (SGD). At the same time, we hope to increase the number of parents to include the complete putative list of about 500 regulators, in order to identify the possible roles of additional regulatory proteins. Since we are using (motif, parent) feature pairs, increasing the number of parents increases the feature space and memory requirements by a multiplicative factor. Two promising directions for improvement are (i) using data structures more appropriate for our pairwise interaction features and (ii) using weighted sampling to reduce the size of the memory required for the training data.
Another potential advance would be a more careful treatment of the raw data. In these preliminary experiments, we used a simple noise model based on wildtype replicates, and we were able to learn to predict large up-or down-regulation response using thresholds based on this model. However, while log expression ratio data (perturbation/wild type) gives a natural input variable for our analysis, better signal to noise is likely to be achieved by taking into account the excitation levels separately. In particular, using an intensity-sensitive noise model could allow us to establish more meaningful thresholds for more of the genes. A more complicated issue is the fact that we do not use baseline expression examples for training, and therefore we restrict to the subset of genes that show variation across stress response experiments for our training and test sets. Ideally, however, we would like to predict regulatory response for all genes (including non-responding genes), which will likely mean changing the formulation of the learning task so that we include baseline examples in training.
A further refinement would be to treat parent and child excitation levels as continuous rather than binary quantities. Similarly, the number of motifs in the regulatory region, rather than merely their presence/absence, and the spatial relationship between them could be taken into account. While these extensions could potentially yield much more realistic models, they require substantial algorithmic changes and should be done carefully so as to avoid overfitting.
While we showed how to extract significant motifs, regulators, and motif-regulator pairs from the ADTs, further work is needed to obtain more detailed information from these predictive models. It is plausible that the trees contain information about combinatorial relationships between regulators or between regulatory elements, but it is not clear how to disambiguate independent effects from combinatorial ones. One possible approach could be to rank collections of two or more features occurring in paths in the ADTs and check whether motifs in over-represented paths tend to co-occur in regulatory regions, giving evidence of combinatorial relationships. Another approach is to examine more carefully the contributions of different features to the prediction score for various target genes. While our learning method does not yield a descriptive network model that can be easily visualized, we believe that the predictive model approach enables new possibilities for analysis and understanding of gene regulation.

VI. ACKNOWLEDGEMENT
AK is supported by NSF EEC-00-88001. CW and MM are partially supported by NSF ECS-0332479 and NIH GM36277. CL and CW are supported by NIH grant LM07276-02, and CL is supported by an Award in Informatics from the PhRMA Foundation.