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Condition-Specific Modeling of Biophysical Parameters Advances Inference of Regulatory Networks Graphical Abstract

Authors Konstantine Tchourine, Christine Vogel, Richard Bonneau

Correspondence [email protected] (K.T.), [email protected] (C.V.), [email protected] (R.B.)

In Brief This work demonstrates that extending the biophysical accuracy of the assumed model of transcriptional regulation improves large-scale regulatory network inference. As a proof of concept, Tchourine et al. show that incorporating RNA degradation into the model results in better network recovery while simultaneously predicting accurate RNA degradation rates.

Highlights d

Explicitly accounting for RNA degradation improves regulatory network inference

d

Network-based optimization of RNA half-lives predicts correct RNA stability values

d

Resulting networks are specific to groups of similar genes and conditions

d

Importance of accounting for RNA half-lives is shown for yeast and B. subtilis

Tchourine et al., 2018, Cell Reports 23, 376–388 April 10, 2018 ª 2018 The Authors. https://doi.org/10.1016/j.celrep.2018.03.048

Cell Reports

Article Condition-Specific Modeling of Biophysical Parameters Advances Inference of Regulatory Networks Konstantine Tchourine,1,2,* Christine Vogel,1,2,6,* and Richard Bonneau1,2,3,4,5,6,7,* 1Center

for Genomics and Systems Biology, New York University, New York, NY 10003, USA Department, New York University, New York, NY 10003, USA 3Courant Institute of Mathematical Sciences, Computer Science Department, New York University, New York, NY 10003, USA 4Center for Data Science, New York University, New York, NY 10003, USA 5Flatiron Institute, Center for Computational Biology, Simons Foundation, New York, NY 10010, USA 6Senior author 7Lead Contact *Correspondence: [email protected] (K.T.), [email protected] (C.V.), [email protected] (R.B.) https://doi.org/10.1016/j.celrep.2018.03.048 2Biology

SUMMARY

Large-scale inference of eukaryotic transcriptionregulatory networks remains challenging. One underlying reason is that existing algorithms typically ignore crucial regulatory mechanisms, such as RNA degradation and post-transcriptional processing. Here, we describe InfereCLaDR, which incorporates such elements and advances prediction in Saccharomyces cerevisiae. First, InfereCLaDR employs a high-quality Gold Standard dataset that we use separately as prior information and for model validation. Second, InfereCLaDR explicitly models transcription factor activity and RNA half-lives. Third, it introduces expression subspaces to derive condition-responsive regulatory networks for every gene. InfereCLaDR’s final network is validated by known data and trends and results in multiple insights. For example, it predicts long half-lives for transcripts of the nucleic acid metabolism genes and members of the cytosolic chaperonin complex as targets of the proteasome regulator Rpn4p. InfereCLaDR demonstrates that more biophysically realistic modeling of regulatory networks advances prediction accuracy both in eukaryotes and prokaryotes. INTRODUCTION Inference of large-scale transcription regulatory networks is an active research area with many broad applications. Network inference typically assumes that changes in RNA expression levels inform of regulatory relationships between transcription factors (TFs) and their target genes. Ideally, orthogonal data on protein-protein and protein-DNA interactions, such as protein binding assays (Valouev et al., 2008; Mundade et al., 2014), DNA accessibility assays (Davie et al., 2015), and motif enrichment analysis (Setty and Leslie, 2015; Guo et al., 2012), com-

plement these expression data. Various machine learning approaches are then used to infer the network. The approaches have multiple levels of complexity, ranging from Boolean networks and network module approaches (Shmulevich et al., 2002; La¨hdesma¨ki et al., 2003; Segal et al., 2003; Pe’er et al., 2001) to approaches that explicitly or implicitly model dynamics, TF interactions, and activity (Honkela et al., 2010; Aïjo¨ et al., 2013; Intosalmi et al., 2016; Studham et al., 2014). Recent comprehensive, blind assessments of various network inference approaches concluded that inference in eukaryotes is systematically more challenging than in prokaryotes, with nearly random performance in yeast (Marbach et al., 2012). Other recent studies showed that results from incorporating prior interaction data also dramatically differ between prokaryotes and eukaryotes, and performance in yeast remained poor (Greenfield et al., 2013; Wilkins et al., 2016; Siahpirani and Roy, 2016; Aïjo¨ and Bonneau, 2016). This discrepancy is likely due to increased complexity of eukaryotic transcriptional regulation, but most existing inference methods, such as those based on random forest (Huynh-Thu et al., 2010; Petralia et al., 2015), cannot directly incorporate new parameters. The Inferelator is a method based on constrained regression (Bonneau et al., 2006; Greenfield et al., 2013; Arrieta-Ortiz et al., 2015). In contrast to other large-scale inference methods, it allows explicit modeling of biophysical processes via differential equations (see Inferelator Implementation in the Experimental Procedures). We and others have shown that inference of transcription- and translation-related parameters via ordinary differential equations produces robust genome-wide models in various organisms (Tchourine et al., 2014; Schwanhaüsser et al., 2013; Peshkin et al., 2015). Importantly, the differential equations also allow for incorporation of additional regulatory parameters. One such crucial regulatory component is RNA degradation. For yeast, experimental data highlight the large range in RNA half-lives and their extensive changes across different conditions and genetic backgrounds (Miller et al., 2011; Schwalb et al., 2012; Sun et al., 2012; Neymotin et al., 2014; Munchel et al., 2011). In addition, high correlation between degradation and

376 Cell Reports 23, 376–388, April 10, 2018 ª 2018 The Authors. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Figure 1. Network Inference Is Sensitive to RNA Half-Lives in Both Eukaryotes and Prokaryotes in a Condition- and Gene-Specific Manner (A and B) AUPR is shown as a function of preset RNA half-life (A) in Saccharomyces cerevisiae and (B) in Bacillus subtilis. Each line denotes one of the 20 independent gold standard re-samples, and colored dots represent the maximum AUPR for a given re-sample. (C) Over two thousand expression datasets group into 20 bi-clusters (unrelated to 20 Gold Standard re-samples) with gene- and condition-specific properties. Red and blue denote high and low expression levels, respectively. Gene cluster names correspond to the most highly enriched function category. Condition cluster names represent the most highly enriched terms in the meta-data. The heatmap shows the 997 genes from the Gold Standard. Note that the final network was derived from expression data of 5,716 genes mapped onto these clusters. (D) Shades of red denote the optimal half-life, in minutes, for each of the 20 bi-clusters. The color scale is devised to discriminate half-lives < 50 min, which contain 16/20 of the predictions. For the full plot of AUPR and AUROC trajectories for every bi-cluster, see Figures S4 and S5, respectively. See also Figures S1 and S6A–S6H.

transcription rates across mutant strains suggests extensive feedback between the two processes, controlled by factors such as XRN1 (Sun et al., 2013). Because expression regulation also depends on external conditions, networks are remodeled in a condition-specific manner (Lehtinen et al., 2013; Shivaswamy and Iyer, 2008) and can be captured in a low-dimensional space of expression clusters that correspond to different biological function that are highly utilized under those conditions (Hart et al., 2015). These findings render the inclusion of RNA half-lives into condition-specific modeling of transcription regulation critical. Here we developed InfereCLaDR, an inference framework derived from the Inferelator, with the addition of expression sub-space clustering and explicit modeling of RNA degradation rates. InfereCLaDR infers the RNA degradation rate for every gene and condition cluster in the expression data by optimizing the cluster’s network inference accuracy and then combines the networks derived using optimized RNA half-lives. InfereCLaDR also uses a high-quality Gold Standard (GS) dataset we created. We showed that InfereCLaDR not only improved inference but also resulted in accurate conditionand gene-specific RNA half-life predictions. The final, combined network produced by InfereCLaDR has an area under the precision-recall curve (AUPR) of 0.33, which is far larger than other existing approaches in yeast, providing insights into various regulatory mechanisms. InferCLaDR is generalizable, as demonstrated by estimation of global RNA half-lives

in other systems, such as Bacillus subtilis, and provides the first proof of concept that explicitly accounting for RNA degradation is necessary for accurate regulatory network inference from large and heterogeneous datasets. RESULTS Curation and Assembly of Comprehensive Datasets for High-Quality Network Inference To develop InfereCLaDR, we leveraged the information available for baker’s yeast across a broad range of experimental conditions. We first assembled a list of 563 potential TFs from various sources, a Gold Standard of interactions, and an RNA expression dataset (see Data Acquisition and Normalization and Curation of the Gold Standard of Regulatory Interactions in the Experimental Procedures). The expression data originated from 119 labs and diverse experimental conditions but used the same transcriptomics platform throughout. With 5,716 genes and 2,577 samples (Figure 1C), it is one of the largest expression datasets used for network inference in yeast (Marbach et al., 2012; Danziger et al., 2014; Petralia et al., 2015; Siahpirani and Roy, 2016). We developed a new Gold Standard of regulatory interactions that combines multiple types of regulatory evidence from several databases (Table S1). It includes 1,403 signed interactions that distinguish between activation and repression, which is important for accurate calculation of TF activities (TFAs) (Arrieta-Ortiz et al., 2015). Although the Gold Standard represents only a fraction of all potential regulatory interactions in yeast, it is highly

Cell Reports 23, 376–388, April 10, 2018 377

Figure 2. InfereCLaDR Recapitulates Known Differences between RNA Half-Lives of Different Genes and Conditions and Identifies New Relationships (A–H) The boxes show median RNA half-lives with the first and third quartiles. (A)–(D) show the distribution of predicted values across 20 Gold Standard re-samples, and (E)–(H) show values measured experimentally across genes. Predicted values are produced by InfereCLaDR; observed values are from experimental datasets. Magenta color denotes minimally perturbed conditions (i.e., chemostat and log phase growth) (predicted) and Neymotin et al. (2014) experimental data for subsets of genes; i.e., nucleobase-containing small-molecule metabolism (NCSM) and translation. We highlight the NCSM category because its high half-lives was the most prominent predicted pattern under minimally perturbed conditions. Light blue denotes all genes predicted or observed under unperturbed conditions. Green denotes half-lives of all genes predicted or observed under conditions of transcription inhibition (Shalem et al., 2008). See also Figure S4.

enriched in true positives: each interaction is confirmed by at least three orthogonal sources, one of which is direct (e.g., chromatin immunoprecipitation with DNA microarray [ChIP-chip]) and two are indirect (e.g., based on TF knockout expression changes). Further, Figures 3A and S3 show that a small, highquality gold standard provides more self-consistent regulatory networks than larger and lower-quality reference sets, such as those commonly used (MacIsaac et al., 2006; Marbach et al., 2012; Ma et al., 2014; Petralia et al., 2015; Siahpirani and Roy, 2016). InfereCLaDR Accurately Estimates RNA Degradation Rates for Condition and Gene Clusters To assess whether network prediction is, in general, sensitive to RNA degradation rates, we first tested the original Inferelator on the entire dataset for a range of preset half-lives. Indeed, prediction was sensitive to RNA half-lives and affected the AUPR. The AUPR was maximized for an RNA half-life of 20 to 50 min (Figure 1A; Figures S1A–S1D). Intriguingly, this range is highly consistent with experimental measurements (Miller et al., 2011; Neymotin et al., 2014; Munchel et al., 2011). To demonstrate that network inference is sensitive to transcript stability across organisms, we also estimated the optimal half-life for B. subtilis (Figures 1B and S1B), predicting 6–13 min as the optimal half-life. Again, this range is similar to experimentally measured RNA half-lives of < 7 min for about 80% of the transcripts (Hambraeus et al., 2003). These results, derived entirely from changes in RNA expression, encouraged the inclusion of RNA half-life in network prediction. Because the data used in our work span a variety of conditions, we extended RNA half-life optimization and network inference to 20 bi-clusters consisting of four condition and five gene clusters (Figures S1E and S1G; Expression Data Clustering in

378 Cell Reports 23, 376–388, April 10, 2018

the Experimental Procedures). This simultaneous clustering of genes and conditions with the subsequent optimization of RNA half-lives comprises the core of the InfereCLaDR. To maximize the accuracy of RNA half-life predictions, we used the Split A approach (Figure S2), which makes use of connectivity information from the entire gold standard. In the Split A approach, we use the entire gold standard for training TFAs and half-life fitting but exclude the validation step. For most bi-clusters, the AUPR trajectory peaked inside a narrow range of half-lives (Figure S4), and the median half-lives for each bi-cluster are summarized in Figure 1D. For some bi-clusters, especially in the ‘‘fermentation’’ cluster, the AUPR trajectory did not peak at a specific half-life, indicating that accurate regulatory network modeling is not contingent on RNA degradation in these regimes. We excluded the RNA half-life predictions made in the fermentation cluster from the following analyses. To validate the newly predicted RNA degradation rates, we compared them with measured RNA half-lives. Note that our approach predicted bi-cluster and not gene-specific RNA half-lives, therefore preventing direct gene-wise comparison with experimental measurements (see RNA Half-Life Estimation in the Experimental Procedures; Figure S1I). Therefore, we tested whether predicted RNA degradation rates for condition and gene clusters that are significantly different from the norm are similarly different for distributions of experimentally measured RNA half-lives across the genes in the corresponding clusters. Figure 2 shows that this is indeed the case; e.g., when comparing all genes under minimally perturbed conditions (Figures 2A and 2E) with all genes under ‘‘transcription inhibition’’ conditions (Figures 2D and 2H). The predicted increase in RNA stability under transcriptional inhibition conditions (Wilcoxon p < 13 1010) is corroborated by the fact that experimental designs that used transcription inhibition to

measure RNA decay rates vastly overestimated true RNA halflives (Neymotin et al., 2014). In another example, ribosomal mRNAs are known to be more stable than other transcripts under normal conditions (Neymotin et al., 2014; Munchel et al., 2011). Indeed, the predicted half-life for the 115 ribosomal genes in the ‘‘translation’’ gene cluster was signifycantly higher than that of other genes (Figure 2C; Wilcoxon p < 4 3 103; see RNA Half-Life Estimation in the Experimental Procedures), confirming our approach. InfereCLaDR’s half-life optimization also revealed new trends across bi-clusters. Most prominently, ‘‘nucleic acid metabolism’’ genes under the ‘‘chemostat’’ and ‘‘log phase’’ conditions showed very high RNA half-lives (Figures 1D and 2B; Wilcoxon p < 0.02). Genes in this cluster function in nucleobase-containing small-molecule metabolism (NCSM), a category of genes that has not been noted for increased RNA half-lives in existing literature. We extracted the 207 NCSM genes from experimental RNA half-life measurements (Neymotin et al., 2014) and confirmed that, in line with the InferCLaDR predictions, the NCSM mRNAs were significantly more stable than all transcripts (Figure 2F; Wilcoxon p % 5 3 1010). The increase in RNA halflives for both the translation and nucleic acid metabolism gene categories under normal conditions, as well as the global increase in RNA half-lives under the transcription inhibition conditions, was also confirmed when area under the receiver operating characteristic curve (AUROC) was used as an alternative measure for half-life fitting (Figure S1H), as well as by correlation analysis (Figure S1I; rs = 0.7). These examples support our confidence in accurate predictions of RNA half-lives within the InfereCLaDR framework. InfereCLaDR Improves Network Inference by Recovering Condition-Specific Interactions Next we tested whether rank-combining the bi-cluster-specific networks improves prediction accuracy. To avoid circularity, we used non-overlapping, randomly chosen subsets of the gold standard to train the model, fit RNA half-lives for individual bi-clusters, and validate the predictions (Figure S2, Split B). We repeated the procedure for each of the 20 re-samples (the choice of 20 is unrelated to the number of bi-clusters, which is also 20), and compared InfereCLaDR with other methods (Figure 3A; Table 1). We calculated the AUPR on the respective validation subset of the gold standard, using the single value of half-life optimized on the corresponding fitting subset of the gold standard. RNA Half-Life Estimation in the Experimental Procedures details this method. The two algorithmic modifications of the InfereCLaDR (bi-cluster-specific network inference and RNA half-life optimization) improve accuracy significantly over inference without these advances (p < 0.05; Figures 3A and S1F; Tables 1 and S2). In total, 115 of 120 pairwise comparisons resulted in larger AUPRs when these modifications were used together and separately (Table 1), showing that half-life estimation and bi-clustering result in significantly improved network inference and that combining the two significantly improves inference further. The final AUPR value of 0.33 represents an almost 8-fold increase compared with Genie3 (Table 1), the best-performing method in a recent competition (Marbach et al., 2012). Using AUROC yielded a

similar outcome (Figure S1; Table S2). Sub-Sampling the Gold Standard for RNA Half-Life Fitting and Error Estimation in the Experimental Procedures and the Supplemental Experimental Procedures provide further details. To maximize the size and accuracy of the final integrated network, we repeated the whole procedure with the Split A approach (Figure S2). At 50% precision, this final network contained a total of 2,924 interactions (Figure 4; Data S1), 1,462 of which were ‘‘new’’; i.e., absent from the Gold Standard. Of these 1,462 interactions, 631 (43%) were validated by independent data that had been excluded from the modeling (Figure 3B). The high fraction of independently confirmed interactions suggests that the remaining 831 new interactions are also strongly enriched in true positives. Next we compared InfereCLaDR with original Inferelator predictions. We focused on three categories of interactions: those that were predicted by InfereCLaDR but not the Inferelator (‘‘gained’’), those that were predicted by both InfereCLaDR and the Inferelator (‘‘conserved’’), and those that were not predicted by InfereCLaDR but were by the Inferelator (‘‘removed’’) (Figure 3C). Conserved interactions correlated in rank; i.e., both approaches had similar confidence in accuracy of these predictions. InfereCLaDR predicted more interactions than Inferelator, both outside of the Gold Standard (Figures 3B and S6I– S6K) and in total; the number of gained interactions was much larger than that of removed ones (Figure 3C). Notably, this increase was not due to overfitting or error because orthogonal support for the gained interactions also increased in InfereCLaDR compared with the original approach (Figure 3D). These lines of evidence suggest that bi-clustering and RNA half-life fitting implemented in InfereCLaDR resulted in hundreds of new high-quality interactions and also removed many false positives. One of InfereCLaDR’s major strengths lies in recovering condition-specific regulatory interactions. For example, most of the gained interactions passed the precision = 0.5 cutoff (Supplemental Experimental Procedures) in only one or two condition clusters; i.e., they were highly condition-specific. In contrast, most conserved interactions were above threshold in 3 or 4 condition clusters; i.e., they were more general (Figure 3E). We examined these gained interactions more closely to determine which bi-clusters accounted for new predictions (Figure 3F). Consistent with our expectations, gained interactions occurred frequently among NCSM metabolism genes in the chemostat cluster, which uses one of the longest RNA half-lives (Figures 1D, 2F, and S4). Similarly, gained interactions involved target genes from protein catabolism and cell wall biogenesis when predicted under perturbed conditions but not under normal conditions; e.g., during log phase growth (Figure 3F), confirming predicted transcript stabilization for these genes under perturbed conditions (Figures 1D and S4). In comparison, other gained interactions occurred in bi-clusters with short RNA half-lives; i.e., for protein catabolism genes and cell wall biogenesis genes in the chemostat cluster, confirming that InfereCLaDR also captured condition-specific network rewiring events that were independent of RNA half-life changes. In sum, InfereCLaDR not only outperformed Inferelator and other methods in terms of accuracy of newly gained interactions but


Figure 3. InfereCLaDR Outperforms Previous Network Inference Approaches by Predicting New High-Confidence Condition-Specific Interactions (A) The improvement in the precision-recall curve is a result of the use of a high-quality Gold Standard, bi-cluster specific network inference, and optimization of bi-cluster specific RNA half-lives. We compare InfereCLaDR (red line) with Inferelator without bi-clustering or half-life optimization (black dotted line), with the Inferelator using the MacIsaac gold standard of interactions (orange dashed line), and with context likelihood of relatedness (CLR), Genie3, and iRafNet (purple dash-dotted line, blue dashed line, and green dash-dotted line, respectively). Each curve is constructed using median precision and recall values across 20 resamples. For improvement based on AUROC, see Figure S1F. (B) The number of new predicted interactions (i.e., interactions not in the Gold Standard), obtained using the optimized bi-cluster-specific half-lives and the full Gold Standard for training, compares favorably with new predictions from the original Inferelator and from Genie3. The height of a section within each bar corresponds to the number of new interactions that were confirmed by the corresponding type of evidence in orthogonal data. Direct evidence refers to physical protein-DNA interactions, and indirect evidence refers to knockout and overexpression assays (Table S1). The number above each bar denotes the fraction of new interactions supported by at least one orthogonal source. Prec, precision. (C) High-scoring regulatory interactions correlate between InfereCLaDR and Inferelator, but InfereCLaDR predicts many new interactions. The vertical and horizontal blue lines show the precision = 0.5 rank cutoff for InfereCLaDR and Inferelator, respectively (Supplemental Experimental Procedures). The lower the rank, the higher the confidence in the prediction. The red line maps the InfereCLaDR rank to the same rank in Inferelator. See also Figures S6I–S6K. (D) Most (56%) regulatory interactions that were newly predicted by InfereCLaDR have orthogonal support to validate them. In comparison, Inferelator’s predictions that were removed in InfereCLaDR have little support, suggesting that they had been false positives. Black bars denote the bottom right quadrant in (C) (gained), gray bars denote the top left quadrant in (C) (lost), and white bars denote the interactions in the bottom left quadrant of (C) (conserved). (E) InfereCLaDR’s gained interactions are often specific to experimental conditions. Each bar displays how many regulatory interactions were above the rankbased cutoff (Supplemental Experimental Procedures) for the given number of clusters. Interactions that only appear in one cluster are very condition-specific, whereas interactions that appear in all four clusters are more general and independent of experimental conditions. The graph shows only the high-confidence predictions that were above the cutoff for at least one cluster prior to rank-combining. (F) InfereCLaDR’s gained predictions are often specific to non-standard conditions. Each interaction was assigned a bi-cluster based on the gene cluster of the target gene and a condition cluster in which this interaction had the best rank. Red cells represent bi-clusters with significantly more gained interactions, blue cells represent bi-clusters with significantly fewer gained interactions, and white cells represent no enrichment (Supplemental Experimental Procedures).

did so by recovering interactions that only appear under specific conditions, under which RNA half-lives typically deviated from the norm. New Predictions Are Corroborated by Literature To illustrate the value of new interactions, we list the top new targets of highly and medium-connected TFs (Tables 2 and S3). Importantly, many of the predictions are validated by indepen-


dent datasets (Tables 2 and S3) and function annotation. For example, Sfp1p is a known regulator of ribosomal protein genes (Marion et al., 2004; Cipollina et al., 2008; Reja et al., 2015), and all of its top predicted targets are ribosomal subunits and are supported independently (Table S3). Rpn4p is known to activate proteasome expression (Karpov et al., 2008a, 2008b), and, indeed, most of its predicted targets of activation are proteasomal genes, consistent with known biology.

Table 1. Expression Data Bi-clustering, RNA Half-Life Fitting, and a High-Quality Gold Standard Underlie InfereCLaDR’s Superior Performance Re-samples Outperforming Inferelator + GS

Re-samples Outperformed by InfereCLaDR

Median AUPR

InfereCLaDR (GS + clustering + RNA half-life)

19/20

–

0.328

Inferelator + GS + clustering

20/20

17/20

0.319

Inferelator + GS + RNA half-life

19/20

19/20

0.305

Method

Inferelator + GS

–

19/20

0.290

Inferelator + MacIsaac

0/20

20/20

0.146

Genie3 + GS

0/20

20/20

0.042

iRafNet + GS

0/20

20/20

0.031

Each modification independently outperforms the original Inferelator using the Gold Standard (second column). ‘‘Inferelator + MacIsaac’’ shows the results of the Inferelator when the MacIsaac standard of interactions was used for training and Gold Standard for evaluation. Combining all modifications optimizes performance compared with using them separately (third column). Columns two and three show the number of times one method outperformed the other in a re-sample, as specified by the corresponding row and column, in terms of AUPR. The fourth column shows the median AUPR. See Sub-sampling the Gold Standard for RNA Half-Life Fitting and Error Estimation, RNA Half-Life Estimation, and Supplemental Experimental Procedures for further details. See also Table S2.

In contrast, InfereCLaDR also predicted that Rpn4p activates the expression of four previously unknown targets, CCT2, CCT3, CCT4, and CCT8, which are not part of the proteasome but subunits of the cytosolic chaperonin Cct ring complex and are required for actin and tubulin function (Chen et al., 1994; Vinh and Drubin, 1994). These four interactions were largely absent from the existing databases listed in Table S1, and InfereCLaDR detected them in a subset of regulatory regimes (Data S1). We found additional evidence that supports the validity of the prediction. Rpn4p is known to bind the proteasome-associated control element (PACE; 50 -GGTGGCAAA-30 ; Mannhaupt et al., 1999) and also regulates proteasome assembly chaperones through binding to a smaller region, 50 -(A/G)GTGGC-30 , known as the PACE core region (Shirozu et al., 2015). Examining the promoter region of the CCT genes, all four contained the PACE core element (Supplemental Experimental Procedures). These interactions were specific to the transcription inhibition and fermentation clusters (Figure 4; Supplemental Notes), explaining why they were undetected in previous studies, which typically excluded the condition-specific regulatory regimes tested here. Of the 100 new interactions in Table S3, 13 were absent from the orthogonal validation datasets discussed above. We examined some of these interactions further and found evidence supporting their validity. For example, Hsf1p is a key regulator of diverse stresses and monitors the cell’s translation status by interacting with the ribosome quality control (RQC) complex (Brandman et al., 2012). InfereCLaDR predicts that Hsf1p acti-

vates LSB1 and SAF1 in a condition-specific manner (Figure 4, transcription inhibition cluster). SAF1 has four other transcription regulators (Bur6p, Med6p, Spt10p, and Sua7p), which are all, similarly to Hsf1p, detected under various stresses, especially heat shock (Mendiratta et al., 2006; Venters et al., 2011), suggesting that Hsf1p could also be a member of the heat shock regulators of SAF1. In comparison, Lsb1p controls actin assembly and prion modulation in yeast (Ali et al., 2014) and has not been reported as a target of Hsf1p. Several recent studies have linked Hsf1p to actin assembly. Yeast deficient in the RQC-Hsf1 regulatory system has altered actin cytoskeletal structures (Yang et al., 2016), overexpressing HSF1 in worms increases actin cytoskeleton integrity and lifespan (Baird et al., 2014), and active Hsf1p affects the actin cytoskeleton in mammalian cells (Toma-Jonik et al., 2015). Therefore, it is tempting to hypothesize that LSB1 is the missing link by which Hsf1p affects actin skeleton assembly. The Supplemental Notes outline additional examples that validate InfereCLaDR’s new predictions, including condition-specific interactions and combinatorial regulation of gene categories, which we summarize in Figure 4. In sum, InfereCLaDR predicted hundreds of novel high-confidence interactions in yeast that are consistent with previously known roles of the regulators and suggest new regulatory relationships. DISCUSSION We present InfereCLaDR, a network inference framework with several conceptual advances over existing methods (Greenfield et al., 2013; Arrieta-Ortiz et al., 2015; Ciofani et al., 2012), demonstrating, for the first time, that biophysically relevant models that incorporate RNA degradation improve large-scale network prediction. InfereCLaDR includes a new, high-quality Gold Standard of regulatory interactions and infers separate networks across subsets of genes and conditions. We built the Gold Standard that accompanies this work from several benchmark datasets (Teixeira et al., 2006, 2014; Monteiro et al., 2008; Abdulrehman et al., 2011; Cherry et al., 2012; Costanzo et al., 2014; Kemmeren et al., 2014), and, importantly, accounted for the direction of the interaction (i.e., activation versus repression) and our confidence in the data source. We show that this approach, which improved the quality of a gold standard but not necessarily its size, vastly outperformed alternative approaches (Figure S3). In addition, InfereCLaDR showed that bi-clustering expression data, cluster-specific network inference, and optimization and use of cluster-specific RNA half-lives improved prediction accuracy and sensitivity even further (Figures 3 and S1). Using these advances, InfereCLaDR resulted in a genomewide regulatory network that is more accurate and comprehensive than previous approaches. At 50% precision, InfereCLaDR predicts >1400 new interactions in yeast (Figure 4), 43% of which are validated by independent datasets, and 57% are entirely new (Figure 3B). Approximately 80% of these interactions were activating and 20% were repressive. Compared with other approaches (e.g., Genie3), this was an 8-fold improvement. We validated new interactions using existing direct (i.e., TF-DNA contact) and indirect (i.e., knockout/overexpression) evidence. The success of rank-combining cluster-specific networks


Figure 4. Condition-Specific Networks Reveal New Predictions and Regulatory Relationships beyond What a Global Network Can Show The figure displays the final high-confidence regulatory network split into four parts, based on the four experimental condition clusters, where each interaction was detected with the strongest confidence. Transcription factors are shown in black (center), and target genes are colored (periphery). Different colors indicate different gene clusters, as shown in the legend. The colors of the edges correspond to predicted transcriptionally activating (red) and repressive (blue) regulation, respectively. A stronger color denotes high confidence. A large font size denotes the five transcription factors that are most specific to each condition cluster. TFs that were not among the top 5 in terms of cluster specificity in any of the clusters are not shown.

suggested that previous approaches often missed conditionspecific regulatory interactions (Figures 3 and S2; Tables 1), especially for conditions with altered RNA half-lives (Figures 2D and 2H and 3F). The result was consistent with the findings that both RNA degradation and transcription regulation are specific to different gene sets and adjust to changing environmental conditions (Munchel et al., 2011; Miller et al., 2011; Lehtinen et al., 2013; Hart et al., 2015; Yang and Leskovec, 2014). Most importantly, we showed that including RNA degradation in network prediction boosts inference of transcriptional regulatory networks. To the best of our knowledge, InfereCLaDR is the only approach capable of doing so on a genome-wide scale. InfereCLaDR does not make prior assumptions on RNA stability but learns optimal degradation rates directly from expression data. The resulting rates were similar to experimentally measured rates, validating our approach. In addition, optimized (predicted) half-lives accurately reflected expected trends across conditions and across organisms; e.g., for ribosomal genes


(Figure 2). InfereCLaDR is also generalizable to other organisms. In B. subtilis, it accurately predicted that bacterial RNA transcripts are less stable than yeast transcripts (Figure 1), as confirmed by experiments (Neymotin et al., 2014; Sun et al., 2012; Pelechano and Pe´rez-Ortıń, 2008; Hambraeus et al., 2003). InfereCLaDR has several applications. First, it can predict RNA degradation rates for different gene clusters or conditions from expression data alone. Such predictions are valuable because it is still challenging to measure RNA degradation, and only a few datasets exist (Miller et al., 2011; Schwalb et al., 2012; Sun et al., 2012; Neymotin et al., 2014; Munchel et al., 2011). Second, InfereCLaDR can reveal new trends, such as the long half-lives of genes in nucleic acid metabolism (Figure 2). Third, InfereCLaDR can predict new regulatory interactions missed before. We showed that even the predicted interactions not seen in other studies are likely valid. To the best of our knowledge, our approach is the first attempt at incorporating RNA degradation into large-scale automated

Table 2. InfereCLaDR Top-Ranking Predictions and Their Precision Values

(A) New targets (i.e., interactions not in the Gold Standard) of the ten transcription factors (top row) that are most connected in the Gold Standard. The table also lists the precision values of these interactions, with darker green denoting higher precision. (B) New targets of ten TFs of medium connectivity. Precision values are calculated using the entire matrix of prediction confidence scores, containing 5,716 genes and 557 TFs. The list of true positives was defined by the Gold Standard. Bold targets correspond to interactions that were not found in any of the four orthogonal datasets listed in Table S1; i.e., these regulatory interactions are entirely new. See Table S3 and Data S1 for more details.

network learning. Our work should therefore be viewed primarily as a proof of concept, demonstrating that expanding the biophysical complexity of the underlying model of regulation improves network prediction accuracy while also accurately estimating the dynamic parameters of transcriptional regulation. This step brings the field of machine learning-based network inference closer to the field of detailed mathematical modeling of biophysical processes. However, InfereCLaDR also has limitations that need to be addressed in future versions. One such limitation is the requirement of a large enough RNA expression dataset to distinguish between different modes of regulation under different conditions or cell types. A substantial portion of the data needs to stem from time series experiments, and the condition cluster label assignments require semi-manual inspection of the meta-data for heterogeneous expression datasets for better interpretability. Another limitation is the availability of a reliable gold standard of interactions. Both of these requirements are already met in wellstudied model organisms, such as E. coli (Fang et al., 2017), C. elegans (Cheng et al., 2011), and some human cell lines (ENCODE Project Consortium, 2012). As more experimental data become available through technological advances such as assay for transposase-accessible sequencing (ATAC)-seq, InfereCLaDR in its current form will be applicable to other systems. In addition, future research will determine the sensitivity of InfereCLaDR to the quality of the collection of prior known interactions and to the technique employed for bi-clustering the data, which are beyond the scope of the present study. Other extensions could expend the Inferelator framework to infer RNA degradation rates from a continuous distribution and using the same prior known interactions for both RNA degradation rate fitting and TFA estimation, which would address limitations

regarding the size of the Gold Standard and the requirement to select a discrete set of potential RNA half-lives. Finally, future extensions could eliminate the need for gene-wise clustering by estimating the optimal RNA half-life separately for every gene through application of the same Bayesian model selection the Inferelator uses to select the best regulatory model for every gene. In a broader context, InfereCLaDR advances inference methods through improved biophysical modeling of biological processes by approximating the rates of synthesis and degradation using mass action laws and experimental designs that include time series. This approach outperforms other methods that are agnostic of underlying mechanisms (and unaware of underlying temporal designs), such as Random Forest (Huynh-Thu et al., 2010; Petralia et al., 2015), conditional entropy (Karlebach and Shamir, 2012), partial correlation (Yuan et al., 2011), or probabilistic graphical models (Siahpirani and Roy, 2016). The results of this study encourage further incorporation and recovery of biophysical parameters, such as interaction terms between co-regulating TFs, separation of transcriptional activators and repressors, which has only been done on a small scale (Noman and Iba, 2005; Liu and Wang, 2008; Aïjo¨ and Bonneau, 2016; Intosalmi et al., 2016), and modeling protein modifications that affect TF activity. Given the growing body of literature on RNAbinding proteins (Hogan et al., 2008; Mittal et al., 2009; Janga and Mittal, 2011), our results also inspire potential approaches to model the RNA decay term explicitly as a sum of contributions from RNA degradation factors. Therefore, we argue that it is time to move inference of transcription regulatory networks toward more biophysically relevant models, and the work presented here provides an important step toward this goal.


EXPERIMENTAL PROCEDURES Data Acquisition and Normalization We acquired four regulatory interaction datasets (known priors) from the sources listed in Table S1, originating predominantly from ChIP-chip, chromatin immunoprecipitation sequencing (ChIP-seq), knockout, and overexpression assays (Teixeira et al., 2006, 2014; Monteiro et al., 2008; Abdulrehman et al., 2011; Cherry et al., 2012; Costanzo et al., 2014; Kemmeren et al., 2014). The list of 563 TFs includes all genes annotated as either ‘‘DNA-binding’’ or ‘‘Regulation of transcription, DNA-templated’’ in the Saccharomyces Genomes Database (SGD) (Cherry et al., 2012; Costanzo et al., 2014) and all regulators in the YEASTRACT database of regulatory interactions (Teixeira et al., 2006, 2014; Monteiro et al., 2008; Abdulrehman et al., 2011). We downloaded 179 RNA expression datasets from 119 different labs from the GEO (Edgar et al., 2002; Barrett et al., 2013) using the R Bioconductor package GEOquery (Huber et al., 2015; Davis and Meltzer, 2007). To obtain a high-quality, consistent dataset and to avoid platform-specific batch effects, we exclusively used the Yeast Affymetrix 2.0 platform (GPL2529) because it contained the largest number of unique samples in the GEO database. Raw CEL files for every GEO sample (GSM) measured on this platform were downloaded on March 23, 2015, along with their meta-data. We processed and normalized the raw CEL files using the R packages affy (Gautier et al., 2004) and gcrma (Wu et al., 2004), adjusting for background intensities, optical noise, and non-specific binding in a probe sequence-specific fashion. Methods correcting for batch/lab effect did not improve inference performance (data not shown). The meta-data were processed manually to identify time series experiments. The full meta-data, as downloaded from the GEO, are included in the Data S1. The final yeast RNA expression dataset used for the work described here included 2,577 samples, each containing the expression data for 5,716 genes. For B. subtilis, all relevant data, including the gold standard of interactions, the list of TFs, expression data, and the meta-data, were taken from ArrietaOrtiz et al. (2015). We used the BSB1 expression dataset employed in Arrieta-Ortiz et al. (2015), which was measured on the B. subtilis strain BSB1, a derivative of strain 168. This dataset can be found under GEO: GSE27219 (Nicolas et al., 2012). Expression Data Clustering We scaled the expression data so that every row (gene) had mean 0 and variance 1. The 2,577 expression samples were then clustered using the Euclidean distance metric. We then performed principal-component analysis on the entire RNA expression matrix and excluded all but the first 16 dimensions to remove the cumulative effect of noisy low-variance components and facilitate condition-wise clustering. We then performed k-means clustering with k = 4. This number was optimized as described in the Supplemental Experimental Procedures (Figure S1E). We performed all downstream analyses on the resulting clusters using the original (normalized but unscaled) expression data. To annotate the four condition clusters, we parsed the meta-data from the GEO, employing the R packages tm (Feinerer and Hornik, 2015; Feinerer et al., 2008) and SnowballC (Bouchet-Valat, 2014). First, we used the binomial test to determine which words are enriched in a given condition cluster compared with the remaining clusters. To avoid words with a p value of 0 and to minimize lab-specific effects, we then excluded words that had zero counts in all but one cluster. This resulted in a list of words sorted by p value enrichment in each cluster. The p values were then corrected for multiple hypotheses testing using the Bonferroni correction. Word clouds were created from terms with p values smaller than 1020 using the wordcloud package in R (Fellows, 2012). The final label assignments were determined via a detailed, manual inspection of enriched terms in the word clouds (Supplemental Notes). See the Supplemental Experimental Procedures for more details and Data S2 for the complete lists of terms. In addition to condition-wise clustering, we also performed row (gene-wise) clustering. To do so, we first hierarchically clustered the 997 genes in the Gold Standard and then generalized these clusters to the 5,716 genes present in the entire expression dataset. This procedure resulted in five clusters, for which we performed gene ontology enrichment analysis as described in the Supplemental Experimental Procedures. See the Supplemental Experimental Procedures for more details.


The bi-clustering of genes and conditions was used to separate genes with heterogeneous functions and samples coming from heterogeneous conditions into several broad classes based on gene function and type of condition. The goal of this bi-clustering was to capture the known condition and gene specificity of RNA half-lives (Neymotin et al., 2014; Munchel et al., 2011) and condition-specific network remodeling (Lehtinen et al., 2013; Hart et al., 2015). Note that this is unrelated to the bi-clustering used in Bonneau et al. (2006) to identify co-regulated genes and conditions. Curation of the Gold Standard of Regulatory Interactions A key aspect of the work was the construction of a high-quality Gold Standard of regulatory interactions, which we used as prior interactions data for transcription regulatory network (TRN) training, for fitting RNA half-lives, and for validating the predicted interactions (GS-train, GS-fit, and GS-fit/GS-validate in Figure S2, respectively). The Gold Standard was derived by combining binding and expression information from three major sources (Table S1). We obtained the core data from the YEASTRACT repository (Teixeira et al., 2006, 2014; Monteiro et al., 2008; Abdulrehman et al., 2011), which is a curated repository of > 200,000 regulatory interactions in yeast with >1,300 bibliographic references. The repository contains two types of evidence for each potential regulatory interaction: direct and indirect. Direct evidence denotes an interaction coming from an assay that directly established a physical binding event, such as ChIP-seq or one-hybrid assay. Indirect evidence comes from differential expression analysis of a TF knockout or overexpression experiment. We first filtered these data to obtain a conservative list of 2,577 regulatory interactions that have at least one source of direct evidence and two sources of indirect evidence. At this stage, these interactions were unsigned; i.e., they did not include information about whether the regulatory interaction is positive or negative. Because TFA estimation performs best when all prior known interactions are signed (Supplemental Experimental Procedures), we processed the list further to maximize the number of signed interactions. YEASTRACT provides information on the signs for some interactions; e.g., those derived from expression analysis of knockout mutants. To add signs from the YEASTRACT database, we used the following rule: a regulatory interaction was deemed ‘‘positive’’ when the target gene was downregulated upon TF knockout, and ‘‘negative’’ for the opposite case. Because some interactions were detected in multiple experiments with opposite sign annotations, we only considered the signs that were measured in assays conducted under normal conditions, labeled as ‘‘YPD medium; mid-log phase’’ in the YEASTRACT database. In case there was still a conflict, we employed the majority rule, and in the case of a tie, the interaction was discarded (set to 0). This procedure resulted in 1,155 signed interactions in total. To expand this dataset, we obtained additional, curated regulatory interactions from the SGD (Cherry et al., 2012; Costanzo et al., 2014) and from a published dataset of 1,484 knockout experiments (Kemmeren et al., 2014). We used these interactions only to assign signs to interactions that were still unsigned in the list of 2,577 interactions with one direct and two indirect evidence types in YEASTRACT (see above). These additions expanded our list of signed interactions to 1,403. These 1,403 interactions constitute the set of signed prior known interactions used throughout this paper, which we denote as the ‘‘Gold Standard.’’ The Supplemental Experimental Procedures, Figure S3, and Data S1 describe more details about the creation of Gold Standard and its performance compared with other collections of interactions. Inferelator Implementation We used and modified code for the Inferelator version 2015.03.03 (Bonneau et al., 2006; Greenfield et al., 2013; Arrieta-Ortiz et al., 2015). We describe the original Inferelator core model in this section, and more details can be found in the Supplemental Experimental Procedures. The Inferelator algorithm calculates the optimal model of regulation for each target gene independently of other genes. The model for each gene i is based on the assumption that the dynamics of transcription regulation are governed by the following relation: X dXi ~i;j Aj ; b = ai Xi + dt j˛P i

(Equation 1)

where Xi is the RNA expression level of gene i, Pi is the set of potential regu~i;j is the coefficient of regulatory interlators of gene i, Aj is the activity of TF j, b action between TF j and gene i, and ai is the RNA degradation rate of gene i. ~i;j , we can approximate Equation 1 using finite To estimate the parameters b differences and divide both sides by ai : ti

X Xi ðtk + 1 Þ Xi ðtk Þ + Xi = bi;j Aj ðtk Þ; tk + 1 tk j˛P

(Equation 2)

i

where the time axis t has been broken up into discrete time points at which the data was collected, indexed by k. The left side of Equation 2 is the response and variable, whereas the right side is the design variable. Note that t i = a1 i ~i;j . is related to the RNA transcript half-life HLi via HLi = ti logð2Þ and bi;j = t i b Also note that, throughout our analysis, no corrections for cell division times were made because it was impossible to determine them for each of the 2,577 experiments coming from 119 labs. Given that median RNA half-lives are much shorter than cell doubling times, we consider the omission tolerable. In the original Inferelator framework, the RNA half-life had been set to 14 min for all yeast genes and conditions (i.e., t = 20). Furthermore, note that Equation 1 holds true for both steady-state data and time series data, which can be used to perform regression simultaneously. For steady-state conditions, the first term on the left side of the equation is 0, and Aj ðtk Þ becomes Aj;k , where k denotes the steady-state condition. In the datasets employed in this paper, 963 of the 2,577 (37%) yeast data points and 160 of the 266 (60%) B. subtilis data points were derived from time series experiments; the remainder were derived from steady-state conditions. The response variable is first used together with prior known interactions to calculate TFAs for every TF (Supplemental Experimental Procedures). TFA is derived from expression changes of the prior known targets of a TF and has been shown to improve TRN inference dramatically in prokaryotes (ArrietaOrtiz et al., 2015). The same prior known interactions are then used in a constrained regression step that selects the most likely model of regulation for every gene using a data-driven approach called Bayesian best subset regression (BBSR). To calculate TFA and BBSR, we used the entire gold standard or a subset of it as prior known interactions. Figure S2 and Sub-Sampling the Gold Standard for RNA Half-Life Fitting and Error Estimation in the Experimental Procedures outline the workflows employed in this paper, specifying how the gold standard was split, sub-sampled, and used for inference. The procedure does not use any training data for testing. The new framework, InfereCLaDR, is defined by bi-cluster-specific network inference using the Inferelator and explicit modeling and optimization of the RNA half-life descriptor t for each gene and condition cluster. The final output of the Inferelator and InfereCLaDR is a list of confidence scores for all possible regulatory interactions, determined by a ‘‘computational knockout assay.’’ Each Inferelator run was performed on 50 bootstraps of the RNA expression data, and the final confidence scores for all interactions were computed by rank-combining the confidence scores across bootstraps. For more detail, see the Supplemental Experimental Procedures.

Sub-sampling the Gold Standard for RNA Half-Life Fitting and Error Estimation To use our gold standard for both parameter fitting and method evaluation without overfitting, we used two strategies for re-sampling the gold standard (Figure S2). For assessing the overall dependency of inference accuracy on RNA half-life (Figures 1A and 1B) and obtaining optimal gene- and condition-specific RNA half-lives (Figures 1D, 2, and S4), we used Split A. This method involved randomly selecting a pre-specified fraction of gold standard interactions to be in the training set (GS-train), with the rest of the interactions to be used for fitting half-lives (GS-fit). We set the fraction of data used in the ‘‘training’’ set to 0.5, although all results also hold for other values (Figures S6A–S6H). The procedure was repeated 20 times, and for each re-sample, RNA half-lives were fit as described in RNA Half-Life Estimation in the Experimental Procedures. Note that the choice of 20 re-samples is unrelated to the number of bi-clusters in the yeast expression dataset used here, which is also 20.

To assess whether fitting condition- and gene-specific RNA half-lives in this manner improves performance (Figures 3A; Table 1), we used Split B, where a third set of Gold Standard interactions (GS-valid) was held out and used only for estimating the accuracy of our algorithm’s predictions. We created GS-valid to avoid over-fitting, and this set was exclusively used to estimate the accuracy of the network computed using prior known interactions in GS-train and half-lives obtained using GS-fit. In other words, the evaluation set GS-valid was completely separate from the training sets. Each interaction was assigned one of the three categories randomly (GS-train, GS-fit, or GS-validate), with probabilities of 0.34, 0.33, and 0.33, respectively. This way of splitting the gold standard was also applied to the other methods (Genie3 and iRafNet), keeping the random assignments of interactions into GS-train, GS-fit, and GS-valid identical across the methods for each Gold Standard re-sample. In both splitting approaches, the random separation of interactions into two or three categories was performed on the basis of regulatory interactions between TFs and target genes. It is also possible to perform the separation on the basis of target genes. However, in the yeast dataset, 695/993 (70%) of all genes in the yeast Gold Standard have only one interaction in the Gold Standard (i.e., they are only known to be regulated by one TF). This number also comprises 50% of all interactions in the Gold Standard. Hence, splitting the training, fitting, and validation networks based on target genes is essentially equivalent to splitting them based on interactions, and so the two approaches are basically equivalent. We used two measures of network prediction accuracy to assess the quality of our predictions: AUPR and AUROC. The two measures were calculated in the standard way, as described in the Supplemental Experimental Procedures. All results are similar for both measures (Figures S1C–S1D, S1F, S5, and S6; Table S2). We focus here on AUPR because it is more sensitive for highscoring interactions compared with AUROC, which distributes the weights more equally across the entire list of predictions. A model with maximal AUPR is desirable for small-scale, targeted validation experiments. Further, AUPR is superior to AUROC in a class-imbalanced (skewed) regime, in which the sizes of true positives and false positives differ substantially (Davis and Goadrich, 2006), which is the case for our data. RNA Half-Life Estimation The primary advance described here is the explicit modeling and incorporation of RNA degradation rates into large-scale network inference. To do so, we first developed a procedure to compare different models across parameter settings. As shown in Figure S2, Split A involves sub-sampling two equal sets of interactions from the gold standard: one for training TFA and BBSR (GS-train) and one for calculating AUPR (GS-fit). We pre-specified values of the RNA half-life parameter t at 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 140, 160, 200, and 250 min, designed to span the range of expected half-lives in yeast (Neymotin et al., 2014; Munchel et al., 2011; Sun et al., 2013; Schwalb et al., 2012; Miller et al., 2011). Splitting the Gold Standard into a training and a fitting set is required because our RNA half-life estimations rely on optimization of network inference. Because our algorithm already uses some interactions for TFA and BBSR estimation (GS-train), a second leave-out set of interactions is necessary for unbiased evaluation of network inference accuracy (GS-fit) and, subsequently, for RNA half-life optimization. InfereCLaDR uses the Inferelator while setting t to a given value (as specified above) for every gene under every condition either in the given bi-cluster (Figures 1D and S4, S1H, and S5) or for the entire dataset (Figures 1A and 1B and S1C and S1D), using GS-train as the prior known interactions. Precision and recall curves were computed for each run corresponding to a re-sample and a value of t, using GS-fit as the set of true interactions. We compared precision-recall curves across RNA half-lives by taking the element-wise median of the precision and recall vectors across Gold Standard re-samples for a given value of RNA half-life (Figures S1A and S1B). Conversely, to create a half-life-versus-AUPR curve for each re-sample, we compared AUPRs measured for different t’s, without changing GS-train and GS-fit between t values or bi-clusters. These comparisons are represented by isochromatic curves in Figures 1A and 1B and S4. We chose an optimal t for each re-sample by maximizing AUPR along the corresponding curve. We also compared performances between models with different RNA half-lives using AUROC instead of AUPR, yielding similar optimal half-lives (Figures S1C, S1D, and S5). For


best RNA half-life inference results, we recommend that at least 30% of samples belong to time series of reasonable spacing (i.e., measured in minutes or hours but not days or weeks). Finally, we considered the distribution of optimal RNA half-lives across the 20 re-samples for each condition and gene bi-cluster using the Split A procedure in Figure S2. These distributions are shown in Figure 2, and their medians are shown in Figure 1D (and in Figure S1F for AUROCs). The median values of AUPR constitute the RNA half-life predictions for each gene and condition bi-cluster. Comparisons of predicted and observed RNA half-lives in the minimally perturbed condition clusters were performed by comparing median predicted RNA half-lives across re-samples with the median experimentally measured RNA half-lives across genes. Predicted and observed median values for each gene cluster were averaged across the chemostat and log phase growth condition clusters (Figure S1I). To predict RNA half-lives for translation genes only (Figures 2C and S4), we applied the same AUPR maximization procedure to each condition cluster, using only known cytoplasmic translation genes and their known regulators for AUPR calculations. To predict RNA half-lives for nucleotide metabolism genes, we used the entire gene cluster because it was strongly enriched in the respective genes. Data S3 contains the final RNA half-life predictions for each gene and condition cluster. For more detail, see the Supplemental Experimental Procedures. To demonstrate the improvement in TRN inference gained in InfereCLaDR compared with the original framework, we first split the gold standard according to Split B into GS-fit, GS-train, and GS-validate. For a given re-sample, we predicted RNA half-lives by maximizing AUPR (as measured on GS-fit) on each bi-cluster, using GS-train for training TFA and BBSR. Using those half-life values and the same re-sample of the gold standard, the model was trained again, but now using a union of GS-train and GS-fit (GS-train+fit) for TFA and BBSR computation. We calculated the final precision-recall curve by adding confidence scores across condition clusters for each re-sample, estimating precision and recall only on the GS-valid set corresponding to that re-sample (because GS-valid was not used to produce the predicted network) and then taking the element-wise median of the precision and the recall vectors across the 20 re-samples (Figure 3A). Figure S1F was calculated the same way but with number of true positives and number of false positives instead of precision and recall in the last (validation) step. Note that the Split B approach (Table 1) underestimates the magnitude of the increase in inference accuracy because of half-life fitting compared with the actual increase in accuracy of our final predicted network, which is produced using the Split A approach (Supplemental Experimental Procedures).

DATA AND SOFTWARE AVAILABILITY The InfereCLaDR InfereCLaDR.

code

is

available

at

https://github.com/kostyat/

SUPPLEMENTAL INFORMATION Supplemental Information includes Supplemental Notes, Supplemental Experimental Procedures, six figures, and three tables and can be found with this article online at https://doi.org/10.1016/j.celrep.2018.03.048. ACKNOWLEDGMENTS C.V. acknowledges funding by NIH/NIGMS Grant 1R01GM113237-01 and the NYU Women Faculty Science Research Challenge Grant. R.B. acknowledges funding from the Simons Foundation. AUTHOR CONTRIBUTIONS K.T. assembled and processed the data, conducted the computational experiments, prepared the figures, and wrote the paper. C.V. and R.B. equally contributed to supervising the entire process, guiding the project, and writing and editing the paper.


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Cell Reports, Volume 23

Supplemental Information

Condition-Specific Modeling of Biophysical Parameters Advances Inference of Regulatory Networks Konstantine Tchourine, Christine Vogel, and Richard Bonneau

S1

Supplemental Tables

Table S1: A survey of the databases of regulatory interactions used in this study. Related to Experimental Procedures Section. The first column denotes the name of the interactions database. The second column lists the number of interactions in each database. An interaction may be duplicated within a database if the database contains multiple entries for the same interaction (e.g. coming from different labs or different conditions), so in the parentheses we specify the number of unique interactions for each database. The third column lists the most common types of regulatory evidence in each database, including the number of interactions for each type of evidence. These top types of evidence account for over 98% of interactions in each database. Database

Total number of interactions (unique)

YeastractDirect

55,653 (41,654)

YeastractIndirect

194,083 (172,929)

SGD

33,838 (32,338)

Kemmeren

193,253 (193,253)

Top types of evidence for interactions ChIP (Chip: 47,535, Seq: 2,302, unspecified: 5382), EMSA: 267, DNA footprinting: 61 Microarray expression level (WT vs. TF mutant: 167,288, WT vs. TF overexpression: 15,916, WT vs. TF loss of function mutant: 3,711, WT vs. TF chimera: 1,511), Northern Blot – WT vs. TF mutant: 1,406, Proteomics – WT vs. TF mutant: 993, lacZ – WT vs. TF mutant: 875 ChIP (Chip: 16,638, Seq: 154, unspecified: 11), Microarray expression level: 13,165, computational combinatorial: 3,782 Microarray expression level – WT vs. TF mutant: 193,253

Table S2: Expression data bi-clustering, RNA half-life fitting, and a high-quality gold standard underlie InfereCLaDR’s superior performance. Related to Table 1. Each modification independently outperforms the original Inferelator using the GS (second column). ”Inferelator + MacIsaac” shows the results of the Inferelator when the MacIsaac standard of interactions was used for training and GS for evaluation. Combining all modifications improves performance as compared to using either one of them separately (third column). Columns two and three show the number of times the AUROC measured on GS-fit from the same re-sample was higher for one method than the other, given a pair of Experimental Procedures specified by the row and the column. The fourth column shows the median area under the receiver operating characteristic curve (AUROC). See Experimental Procedures 4.5, 4.6, and Suppl. Experimental Procedures S3.10 for further details. Method InfereCLaDR (GS + Clustering + RNA half-life) Inferelator + GS + Clustering Inferelator + GS + RNA half-life Inferelator + GS Inferelator + MacIsaac Genie3 + GS iRafNet + GS

Re-samples outperforming Inferelator + GS

Re-samples outperformed by InfereCLaDR

Median AUROC

20/20

-

0.775

20/20

20/20

0.745

19/20

19/20

0.746

0/20 0/20 0/20

20/20 20/20 20/20 20/20

0.718 0.615 0.573 0.555

27

Table S3: Top 10 new predicted targets for various TFs. Related to Table 2. The top half of the table lists the 10 TFs that have the highest number of targets (outdegree) in the Gold Standard. For each TF, the number of known targets in the GS is shown in the parentheses. The table then lists for each TF the top 10 predicted interactions that are not in the GS and therefore most likely new. The bottom half displays the median 10 TFs in terms of the number of known targets, out of the 97 TFs with at least one target in the GS. For each TF, targets are listed in the order of decreasing prediction confidence. Superscripts denote whether a given interaction was also present in any of the four large-scale collections of interactions: Yeastract-Direct (1), Yeastract-Indirect (2), SGD (3), and Kemmeren et al. 2014 (4). Bold targets correspond to interactions that are seen in at most one of these four data bases, highlighting completely new interactions. Table 2 displays the precision-based confidence ranks of these interactions, and SuppNetwork3.tsv in Supplemental File SuppData1.zip lists precision and orthogonal validation scores for all 97 TFs in the GS. TF Name

Targets

Rap1p (192)

SEC142 , YEL11 , PMT42,3 , FEN12,3 , ALG72,3 , RBD2, RPL18B1,2,3 , RPL16B1,2,3 , YLR412CA1 , HXK22,3 LYS11,2,3 , HOM22 , BAT12 , HIS22 , STR22 , SDT12 , RIB32 , PSF21,2,3 , POS52 , SRY12 RPS24A1,2,3 , RPL18B1,2,3,4 , RPS16A1,2,3 , RPL8A2,3 , RPS18B1,2,3 , RPS18A2,3 , RPL40B2,3 , RPL42B2,3 , RPS22A2,3,4 , RPL9A2,3 YDR391C2,3,4 , CMK22,3 , YLR257W2 , STF22,4 , RCN22 , HAL51,2 , OXR12 , PNC12,4 , DOA11 , MRP82 YRO22 , UIP2 , YNL194C1,2,4 , GAD12 , JIP42,4 , MSC12,4 , TFS12 , YNL195C2,4 , YJR096W2 , OM452 GAC1, TAH181,2 ISF12 , YNR034W-A1,2 , MBR12 , MRK1, TCB21,3 , GAT22 , YLR460C1,2,3 , ATR11,2 OPI102,3 , GGA12 , RTC32,3 , YRO22,3 , APJ11 , LSB1, YGR127W, YGR250C1,2,3 , CUR11 , SAF1 RPN122,4 , RPT21,4 , PRE102,4 , RPT51,2,4 , RPN71,2,3,4 , RPN12,4 , RPN102,4 , PRE72,4 , YBR062C2,4 , PUP11,2,3,4 YER010C, COA33 , GET22 , BSD21,2 , YAH1, TDA5, MIM12 , YDR541C1 , MGR2, SLC12 TRX2, CRH11,2 , YOL019W1 , RAX21,3 , YOL014W2 , TGL22 , YPS32 , PHM82 , YBL111C, RIB4

Gcn4p (143) Sfp1p (128) Msn2p (61) Sok2p (60) Yap1p (51) Hsf1p (48) Rpn4p (44) Abf1p (33) Tec1p (31) Mga2p (6) Mot3p (6) Ino2p (5) Msn4p (5) Fkh2p (5) Flo8p (5) Rtg3p (4) Stp1p (4) Leu3p (4) Nrg1p (3)

PLB22,4 , TDA42,4 , YLR413W2,4 , ALE1, FAS11,2 , HEM13, SUR22,4 , NEM1, PEX31, FHN1 FIG24 , PRM12 , SAG14 , TIR12 , PAU242,4 , AAC32,3,4 , TIR42,4 , EUG14 , TIR22,3 , FIG12,4 HNM11,4 , SAH11,2,4 , FAS11,2,3,4 , SAM24 , CHO12,4 , EPT12,4 , ADO11,3,4 , OPI32,4 , EHT12,4 , YIP34 YHR022C1,2 , CRS52 , JLP1, SNO42 , FRE72 , PUG12 , YEL073C1,2 , PDC62,3 , GCY12 , FMP482,3 AIM201,2 , HOF11,2 , ALK11,2,3 , CLB11,2 , YMR030W-A, BUD41,2,3 , CDC52 ,YMR001C-A, KIN31 , HST31 FLO91 , TIR4, DED81, PAU7, MSC7, PAU5, ERG24, PAU24, NCP1, YGL108C IDH21,2,3,4 , PDH12,4 , AAT22 , CPR4, ARP3, WTM12 , IDP11,3,4 , URA8, ADE3, SLP1 VHR22,3,4 , MET17, MET32 , SUL1, MET102,3 , MET52,3 , MEP24 , PET8, GNP11,2,3,4 , DAL802,4 OAC12,3,4 , BAT12,3,4 , FRS22 , ILV52,3 , LEU12,3,4 , SSB1, MAE12,3 , PAB13 , YPL260W, ILV1 PDE2, PRM7, VTS1, YLR407W2 , GFD2, YGR079W, YNL095C, TRM5, PHO90, MCH51

28

S2

Supplemental Figures

29

Figure S1: Network inference is sensitive to RNA half-life and the number of condition clusters, and is improved when both are combined in the InfereCLaDR, in terms of both AUPR and AUROC. Related to Figures 1 and 3. 30

Figure S1: Network inference is sensitive to RNA half-life and the number of condition clusters, and is improved when both are combined in the InfereCLaDR, in terms of both AUPR and AUROC. Related to Figures 1 and 3. Precision-recall curves for A) S. cerevisiae, and B) B. subtilis. Each line corresponds to a different pre-set value of RNA half-life, and displays the median precision and recall across 20 Gold Standard (GS) re-samples. C) True positives vs. false positives curves, with each line corresponding to a different pre-set value of RNA half-life. Each line displays the median number of true positives and true negatives across 20 GS resamples. D) AUROC as a function of pre-set RNA half-life. Different lines denote 20 independent GS re-samplings, and colored dots represent the maximum AUROC for a given GS re-sample. E) Network inference performance (measured in AUPR) depends on the number of condition clusters the expression data is split into. The red line shows the AUPR of the confidence scores combined across the clusters, the black dash-dotted line shows the highest AUPR across the clusters, and the dotted blue line shows the lowest AUPR across the clusters. F) The improvement in the ROC curve is a result of the use of a high-quality gold standard (GS), bi-cluster specific network inference, and optimization of bi-cluster specific RNA half-lives. We compare InfereCLaDR (red line) to Inferelator without bi-clustering or half-life optimization (black dotted line), to the Inferelator using the MacIsaac gold standard of interactions (orange dashed line), and to CLR, Genie3 and iRafNet (purple dash-dotted line, blue dashed line and green dash-dotted line, respectively). Each curve is constructed using median precision and recall values across 20 re-samples. G) Terms enriched in the annotation data for each condition cluster (see Experimental Procedures). Larger font corresponds to higher enrichment. Terms with a p-value over 10−20 (after the Bonferroni correction) are excluded. H) A heatmap of median RNA half-lives that maximized network inference performance with respect to Area Under the Receiver Operating Characteristic curive (AUROC), for every bi-cluster (i.e. peaks of every curve in Figure S5). I) Correspondence between the predicted and measured RNA half-lives. Spearman correlation coefficient is shown in the top right corner. ”Translation” refers to the entire gene cluster enriched in translation, whereas ”translation genes” refers only to the genes in that cluster that are involved in protein translation (see Suppl. Experimental Procedures S3.7). A, C-I show analyses performed on yeast data.

31

Figure S2: Outline of the InfereCLaDR workflows used for testing and for creating the final network. Related to Experimental Procedures Section. We used two strategies for splitting the Gold Standard (GS) of interactions. Split A was used to optimize predictions of condition- and gene-specific RNA half-lives, which were then used to predict the final network. Split B was used during method development to evaluate the improvement in network inference accuracy conferred by bi-clustering and estimating RNA half-lives. In both cases, GS was randomly re-sampled into two or three equal sets of interactions. GS-train was used to estimate Transcription Factor Activity (TFA) and to run Bayesian Best Subset Regression (BBSR). GS-fit was used to find the optimal conditionand gene- specific prediction of RNA half-lives, based on maximum area under precision-recall curve (AUPR).

32

Figure S3: Combining multiple sources of evidence creates a consistent and high-quality collection of prior known regulatory interactions. Related to Experimental Procedures Section.

33

Figure S3: Combining multiple sources of evidence creates a consistent and high-quality collection of prior known regulatory interactions. Related to Experimental Procedures Section. Each of the collections of interactions listed in the legend was split into two equal parts, one for training the Inferelator (A-E) or CLR (F) and one for validation. Each line or bar represents statistics calculated on the 50% leave-out set of the corresponding collection of interactions. A-D: Black, gray, purple, and green lines correspond to the collections of interactions described in Table S1. The green line includes only the signed portion of the SGD collection (where positive and negative regulation is pre-specified). Blue line corresponds to the interactions that appear at least once in the Yeastract-Direct collection and at least twice in the Yeastract-Indirect collection, without positive and negative regulation specified. The red line shows the final signed Gold Standard we use throughout this study. A) Precision vs. recall for the six collections of interactions. B) Precision as a function of number of predictions. C) Receiver Operating Characteristic curve for each collection of interactions. D) Number of true positives as a function of the number of predictions. Note that in B and D, performance on the Gold Standard decreases more quickly after several hundred interactions because the positives exhaust all true interactions more quickly due to the smaller size of the Gold Standard as compared to other collections shown. E) The number above each bar indicates the number of interactions in the collection, after removing genes and TFs that do not appear in our RNA expression dataset. The color of each bar represents whether it is an existing dataset or a combination of these datasets, either based solely on knock-out evidence (orange), or on an intersection of knock-out and a ChIP binding evidence (red). The shaded pattern represents whether none, some, or all interactions are signed. Except for (the final) GS, signed interactions came from the signed database in the intersection (Kemmeren or SGD). For the partially signed collection (the rightmost bar), which is a superset of the GS, the same signs as in GS were used when available, and all other interactions were set to 1 (1GS the indicator function of GS, i.e. the GS with all of its interactions set to 1). Standard notation for set theory was used, with ∪ denoting union, ∩ denoting intersection, and \ denoting set difference. F) Precision vs. recall for the six collections of interactions, as generated from predictions made using CLR instead of Inferelator.

34

Figure S4: Network inference accuracy is sensitive to RNA half-lives in a condition-specific manner. Related to Figures 1D and 2. Each panel shows 20 AUPR plots as as a function of pre-set RNA half-life, when the InfereCLaDR is trained on the the genes specific to the gene cluster (shown on the right) and on conditions specific to the condition cluster (shown on top). Each of the 20 lines corresponds to the 20 Gold Standard re-samples, where 50% of the GS was used for training, and the remaining 50% for calculating AUPR. ”translation clust.” refers to the whole cluster enriched in translation genes, and ”translation” refers only to known translation genes, shown in Figures 1D and 2.

35

Figure S5: Network inference accuracy is sensitive to RNA half-lives in a condition-specific manner, in terms of area under the ROC curve (AUROC). Related to Figure 1D. Each panel shows 20 AUROC plots as as a function of pre-set RNA half-life, when the InfereCLaDR is trained on the the genes specific to the gene cluster (shown on the right) and on conditions specific to the condition cluster (shown on top). Each of the 20 lines corresponds to the 20 Gold Standard re-samples, where 50% of the GS was used for training, and the remaining 50% for calculating AUROC.

36

Figure S6: Improvements due to RNA half-live variation and incorporation are independent of the choice of various parameters and evaluation metric. Related to Figures 1 and 3.

37

Figure S6: Improvements due to RNA half-live variation and incorporation are independent of the choice of various parameters and evaluation metric. Related to Figures 1 and 3. A) and B) The precisionrecall curves and the AUPRs as a function of RNA half-life, respectively, for the regime in which 34% of the GS was used for training the Inferelator, and the rest as a leave-out for validation. C) and D) The same metrics but for a regime in which 67% of the GS was used for training, and the rest for validation. E) and F) The true positives vs. false positives curves and the AUROCs as a function of RNA half-life, respectively, for the regime in which 34% of the GS was used for training, and the rest for validation. G) and H) The same metrics as E and F, but with 67% of GS as the training set. I-K: Interactions predicted by the InfereCLaDR vs the Inferelator, in terms of rank (lower rank is higher confidence). The horizontal and vertical blue lines show the precision=0.5 cutoff for Inferelator and InfereCLaDR, respectively. The red line maps the InfereCLaDR rank to the same rank in Inferelator. Hexagonal bins correspond to the number of counts of I) Gold Standard interactions, J) interactions not in the Gold Standard, but present in an orthogonal interactions database, and K) interactions in neither the Gold Standard nor any of the orthogonal interactions databases.

38

S3

Supplemental Experimental Procedures

Abbreviations: AUROC: Area Under the Receiver Operator Characteristic curve AUPR: Area Under the Precision and Recall curve FP: False Positives GO: Gene Ontology GS: Gold Standard of interactions NCSM: Nucleotide-Containing Small Molecule (metabolism genes) PR: Precision-Recall SGD: Saccharomyces Genomes Database TF: Transcription Factor TFA: Transcription Factor Activity TP: True Positives TRN: Transcription Regulatory Network

S3.1

Inferelator Worfklow

The Inferelator is a multi-step framework that aims to predict a TRN from expression data (Bonneau et al., 2006; Greenfield et al., 2013; Arrieta-Ortiz et al., 2015). As inputs, it takes RNA expression data as well as orthogonal sources of data. This orthogonal data can originate from Pol II binding, DNA accessibility, knock-out, overexpression assays, or motif data, and is normally compiled into a matrix of prior known interactions to be used for training and validation of the resulting network. The main idea behind the Inferelator is that the rate of change of RNA levels of a gene i can be expressed as a difference between its transcription and degradation of its transcript, where the transcription term is approximated as a linear combination of the activities of the gene’s potential TFs. This section describes additional details of how we implemented the original Inferelator and modified its workflow to develop InfereCLaDR. The general approach is described in Experimental Procedures 4.4. This document expands on this description. S3.1.1

Estimation of Transcription Factor Activities

We calculate TF activities (TFA) of a given TF from the expression levels of its prior known targets in the respective conditions, as described in (Liao et al., 2003; Arrieta-Ortiz et al., 2015). The primary motivation for calculating TFA, rather than using a TF’s RNA expression levels, is that the expression level of a TF is a poor proxy for its activity, and the activity is much better estimated by examining the expression level changes of a TF’s known targets, as demonstrated in Arrieta-Ortiz et al. (2015). As described in reference Arrieta-Ortiz et al. (2015), we calculate TFA by expressing the response variable, as defined in Equation 2 (Experimental Procedures 4.4), as a linear combination of TFA levels of each of its known regulators. Mathematically, this relation is expressed as such: Resp = P A,

(3)

where P is the connectivity matrix, A is the full, desired TFA matrix (with rows corresponding to TFs and columns to samples), and Resp is the response matrix with each row corresponding to the response variable as defined in Equation 2. The elements of the connectivity matrix P come from the GS or its subset, such that a value of 0 corresponds to no known interaction, 1 to a known positive interaction (activation), and -1 to a known negative interaction (repression). We calculate the activity matrix A by multiplying both sides by the pseudoinverse of P (i.e. the Moore–Penrose inverse, using the R function pseudoinverse from the corpcor package).

39

S3.1.2

Model Selection and Prediction Confidence Score

Selecting the set of TFs that regulate a specific gene involves several steps and is the essence of TRN inference, because this is the process in which we select the most likely regulatory network for every gene in the genome. The first step involves narrowing down the list of all genes known to be acting as TFs in the organism to a small set of p TFs that are specific to a given gene. This step is completed using timelagged Context Likelihood of Relatedness (tlCLR), a method for calculating context-dependent mutual information between gene i and its potential TF (Greenfield et al., 2010; Madar et al., 2010). Typically when using the Inferelator, this value is set to p = 10, which is what we also use here. In addition to these p regulators, TFs known to regulate gene i from prior known interactions are appended to its set of potential regulators. Denote this set as Pi . Selecting the most accurate model of regulation for a gene i is thereby equivalent to selecting the set of regulators Pi ⊂ Pi that optimizes an objective function. The choice of the objective function is a version of the Bayesian Information Criterion (BIC), modified with a Zellner’s g-prior, which incorporates prior known interactions into the model by reducing the sparsity penalty for prior known regulatory interactions. This approach, known as Bayesian Best Subset Regression (BBSR), is described in more detail in Greenfield et al. (2013). Note that for this step, we linearly scaled and shifted every gene in the response matrix and every TF in the design (TFA) matrix such that every row has mean 0 and variance 1 across samples, which was necessary to avoid having to estimate an extra y-intercept parameter corresponding to basal transcription rate. Once the model Pi that minimizes the BIC is selected, we employ a computational knock-out approach to calculate the confidence we have in each predicted regulatory interaction. The confidence score of the predicted interaction between gene i and TF j ∈ Pi is determined in the following manner. We first determine the parameters βi,k for all k ∈ Pi by performing linear regression on Equation 2, and use them to calculate the right-hand side of Equation 2. We denote this entity as the predicted profile. Accordingly, 2 be the variance of residuals the left-hand side of Equation 2 is denoted as the observed profile. Let σi,j between the predicted profile and the observed profile. Let Pi¬j be the same model of regulation of gene 2 be the variance of residuals between the observed profile and the i, but without TF j. Then let σi,¬j predicted profile as calculated using Pi¬j . Then the confidence score of the interaction between TF j and gene i is defined as confi,j = 1 −

2 σi,j 2 σi,¬j

(4)

To avoid overfitting and derive empirical confidence intervals for model parameters, tlCLR and BBSR are repeated on different but possibly overlapping subsets of the response matrix, denoted as bootstraps of the expression data. Every such bootstrap is a column-wise (i.e. sample-wise) subset of the response matrix. The columns are selected randomly using the R function sample with default settings. Using this command, we sample n columns with replacement, where n is the total number of columns in the full response matrix. For each bootstrap of the response matrix, the confidence score of every possible interaction is determined using Equation 4. The final combined confidence score for every interaction is determined by adding the ranks of the confidence scores of that interaction across bootstraps. Note that a high score corresponds to a low rank, i.e. a high-confidence prediction. We use 50 bootstraps for all analyses in this paper, except when specified otherwise. S3.1.3

Estimating Network Prediction Accuracy

We define validation set as the set of known true interactions that we validate our prediction against. Because the output of the Inferelator (and consequently, the InfereCLaDR) is a list of predicted interactions, ranked by their combined confidence scores from highest to lowest, we may define precision and recall as functions of i in the following way: precision is the fraction of the interactions in the top i lowest-ranked

40

(highest-scoring, best) predicted interactions that are also in the validation set, whereas recall is the number of interactions in the top i lowest-ranked predicted interactions divided by the total number of interactions in the validation set. We calculate precision and recall for every value of i in the full list of predicted interactions. Every PR curve is plotted by connecting the precision and recall values for consecutive values of i with straight lines, and the reported Area Under Precision-Recall curve (AUPR) is the area under this curve. True Positives (TPs) is a function of i that maps i to the number of interactions among the top i highest-ranked predicted interactions that are also in the validation set, whereas False Positives (FPs) is the number of interactions among the top i highest-ranked predicted interactions that are not in the validation set. We plot all TP-FP curves by connecting the TP and FP values for consecutive values of i with straight lines. We report Area Under the ROC curve (AUROC) by dividing the area under the TP-FP curve by the product of the total number of TPs and the total number of FPs. For calculating precision and recall, as well as TPs and FPs, on a leave-out set (i.e. when a certain leave-in set of interactions was used for training the network prediction algorithm, i.e. the TFA step and the BBSR step), we use the leave-out set as the validation set for calculations described above. The confidence scores of predicted interactions that appear in the leave-in set are set to 0, effectively moving them to the end of the ranked list of predicted interactions. This removes the effect of penalizing the leavein interactions that are correctly predicted by the algorithm when only using the leave-out for evaluation. The sign of the interactions is not taken into account in any of the AUPR and AUROC calculations. Predictions involving TFs and genes with no prior known interactions in the leave-out set are excluded from AUPR and AUROC calculations.

S3.2

Primary Data Processing

The meta data for every whole-genome expression sample (GSM) was downloaded using the R function getGEO from the GEOquery package (Edgar et al., 2002; Barrett et al., 2013). These GSMs were filtered such that the final list only contained samples measured in Saccharomyces cerevisiae using the Yeast Affymetrix 2.0 platform (GPL2529). For each expression series (GSE) that contained at least one of those GSMs, a TAR file was downloaded from the GEO website on March 23, 2015, using the R function download.file. The raw CEL files for every sample in that GSE (filtering for S. cerevisiae and GPL2529) were furthermore extracted from the associated TAR file. For processing and normalizing the raw CEL files, we used the R packages affy (Gautier et al., 2004) and gcrma (Wu et al., 2004), using the functions ReadAffy and gcrma. All samples were processed simultaneously as one batch. For time series meta data, all time differences were converted into minutes. To test for batch effects, we used ComBat (Johnson et al., 2007; Leek et al., 2012), treating either laboratory of origin or experiment series as batches, but did not observe an improvement in network prediction (data not shown). All computations were made in R programming language, version 3.1.2 (R Core Team, 2014).

S3.3

Condition Clustering

Principal Component Analysis (PCA) of the entire expression matrix was performed using the R command prcomp, treating each expression sample as a 5, 716-dimensional vector. K-means clustering of the dimensionally reduced (post-PCA) expression samples was performed using the R function kmeans, using the default parameters with nstart=25, and iter.max=1000, corresponding to 25 initial random configurations (among which the best one is automatically picked by the built-in algorithm in R) and a maximum of 1,000 iterations. PCA and k-means clustering was performed on scaled expression data (mean shifted to 0 and variance scaled to 1), and all subsequent analysis was done on the resulting clusters using the original (processed and normalized, but not scaled) expression data. We also performed some of the downstream analyses using clusters that were obtained the same way but without scaling, which did not lead to any significant differences in terms of inference performance (not shown).

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The number of condition clusters was determined by rank-combining the confidence score outputs of InfereCLaDR (pre-half-life-fitting) across a pre-specified number of clusters, and maximizing the prediction accuracy of this procedure as a function of the number of condition clusters. Rank-combining across the predictions obtained from a set of disjoint expression clusters was done by taking the sum of the confidence score matrices (combinedconf*.RData files). We used the AUPR of the rank-combined prediction as a proxy for prediction accuracy. The pre-specified numbers of clusters that we tested were n = 2-10, 12, 14, 16, 18, 22, 26, 30, 40, 50, 60, 70, and 80. For a given n, the entire expression data set was first clustered into n clusters (as described in the paragraph above). For each n, we ran the InfereCLaDR separately for each of n expression clusters, using 50% of the GS as the leave-in set for TFA and model selection steps, and the rest as the leave-out set for calculating AUPR. We did not resample the GS for this analysis, we used 10 response matrix bootstraps, and set τ = 60 for this analysis. The same randomly sampled leave-in set was used across the InfereCLaDR runs for all clusters. Figure S1E shows AUPR as a function of the number of clusters n. Furthermore, it shows the AUPR of the worst-performing and the best-performing cluster among the n clusters. We notice that the AUPR is maximized around n = 4 and n = 7, where it is approximately equal to 0.35. We selected n = 4 as our optimal number of clusters because after n = 4, there is a sharp drop in the AUPR of the worst-performing cluster, rendering it uninformative. In addition, 4 clusters is optimal as it also minimizes overfitting in our modeling, leaving each cluster with a large number of diverse data points. Given that for every gene, we test approximately 500 potential TFs (jointly during the tlCLR step and the Bayesian regression step), we aim for at least 500 conditions in each cluster. However, clustering with n > 4 resulted in some clusters with much fewer than 500 conditions. This reasoning further solidifies our choice of the number of clusters. All downstream analyses were performed on these four clusters. To annotate the condition clusters, all text that was provided in every available sample of the meta data table was sorted into four bins according to the sample’s assigned cluster. We processed the list of words in every cluster as follows using the R package tm (Feinerer and Hornik, 2015; Feinerer et al., 2008). First, common English words, commas, and numbers were removed. All text was converted to lower case. Unnecessary white spaces were removed, and term frequency statistics were calculated using the R package SnowballC (Bouchet-Valat, 2014). Multiple hypothesis testing for enriched terms in each cluster was performed using the Bonferroni correction. To foster visualization and interpretability, we removed spurious terms, which we did not consider biologically relevant, from these lists. The final word clouds were made using the R function wordcloud from the package wordcloud (Fellows, 2012). To assign each cluster with a final label and to ensure that each topic is not enriched in its cluster as a result of lab bias in term usage, we compared the occurrence of enriched terms in each cluster and assessed whether they come only from one lab or from multiple labs (Supplemental File SuppData2.zip). See Supplemental Notes Section SN1 for a detailed discussion of primary and secondary enrichments in each condition cluster, and the justification for the final condition cluster naming scheme. Our condition cluster label assignments were also supported by GO enrichments in genes that had the highest relative variance compared to other genes in their cluster (not shown).

S3.4

Gene Clustering

Gene clustering was performed as described in Experimental Procedures 4.2. The reason for scaling expression data before clustering is that this approach results in more evenly-sized gene clusters. Since our method for determining gene- and condition-cluster specific RNA half-lives relies on the availability of prior known interactions with the target genes, we first performed gene clustering for the 997 genes that were present in our Gold Standard of interactions. We performed hierarchical clustering using the R function hclust with default arguments (e.g. euclidean distance metric). We determined the number of clusters by comparing several qualities of the resulting gene clusters as a function of the number of clusters. Given a pre-specified number of clusters k, we used the R function cutree to cut the similarity tree into k clusters. For each of the k resulting gene clusters, we performed Gene Ontology (GO) enrichment analysis (see Suppl. Experimental Procedures S3.5). After performing this analysis for k ranging from 2 to 8, we 42

determined that setting k > 5 does not result in any new clusters with meaningful new GO enrichments as compared to the enrichments obtained with k = 5 clusters. Additionally, having more than 5 clusters and small cluster sizes was unfavorable because the RNA half-life inference for a given gene cluster relies on AUPR maximization calculated on a leave-out list of prior known interactions involving the genes in that cluster. AUPR calculation gets increasingly noisy when the number of known true positives is small. For k = 5, the smallest number of prior known interactions with the genes in one of the five clusters was 101, and the largest was 592. This range was sufficient for producing relatively smooth half-life vs. AUPR curves (Figure S4). Picking a larger k resulted in the breaking down of the smallest cluster into smaller clusters. Therefore, we used 5 gene clusters for the analysis. Importantly, for the final yeast network, we included regulatory network predictions for all 5,716 genes in our expression data set. To this end, we assigned each gene with one of the clusters that was determined using the 997 genes from the GS (as described above). We denote the set of those 997 genes as gGS. For a given gene g, its cluster membership was assigned by finding the gene gprior ∈ gGS that minimizes the Euclidean distance between g and gprior , and assigning the cluster membership of gene gprior to gene g. This approach was superior to clustering all 5,716 genes, because the latter approach resulted in highly unevenly distributed cluster sizes within the 997 genes in gGS, and therefore very noisy AUPR calculations.

S3.5

Function Enrichment Analysis

For determining Gene Ontology (GO) enrichments, we employed the hypergeometric test using the hyperGTest function from the R Bioconductor package ‘GOstats’ and the R Bioconductor package ‘org.Sc.sgd.db’ (Carlson et al., 2014). We used the 997 genes that have at least one interaction in the GS as the background set. We corrected p-values for multiple hypothesis testing using the Bonferroni correction. For each gene cluster, we reported the top GO terms, all of which were statistically significant (p < 0.05). For the full list of gene ontology terms enriched in each cluster, see Supplemental File SuppData1.zip.

S3.6

Gold Standard Curation

The new, high-quality Gold Standard was created as described in Experimental Procedures 4.3 in the main text. Here we specify some further details. For example, in the YEASTRACT dataset, in case the sign of an interaction was specified, it appeared in the ”Association Type” column. When ”Association Type” had a label ”Negative”, it denoted a decrease in abundance after a TF knock-out (and a positive sign according to our convention), and ”Positive” denoted an increase (resulting in a negative sign according to our convention). To obtain interactions from Saccharomyces Genome Database, we downloaded 32,338 unique regulatory interactions using Yeastmine (Balakrishnan et al., 2012; Costanzo et al., 2014). We refer to these 32,338 interactions as the SGD standard (such as in Table S3). The SGD website provided signs for 10,022 of those interactions. We observed 363 agreements and 12 disagreements in signs of the overlapping signed interactions between the list of 1,155 high-confidence signed interactions obtained from YEASTRACT (as described in Experimental Procedures 4.3) and the 10,022 interactions from SGD. We used the signed portion of the SGD standard to expand our list of signed GS interactions in the following way. If the signed interaction from SGD was already in the list of 1,155 from YEASTRACT, we kept the sign that we obtained from YEASTRACT regardless of its sign in the SGD standard. If it was among the 2,577 high-confidence interactions obtained from YEASTRACT, but without a sign from YEASTRACT, we assigned it with the sign from SGD. This procedure provided an additional 117 signed interactions towards the final Gold Standard of interactions. Furthermore, we used the data from Kemmeren et al. (2014), which contained the results of a study that measured genome-wide expression level changes for 1,484 knock-outs, including most TFs in yeast. First, we created a collection of interactions by considering all knock-out-induced expression changes that were reported in the original publication with a p-value of p < 0.01 after the Bonferroni correction, yielding 43

> 193, 000 interactions (which we furthermore denote as the Kemmeren standard). Of these, 131 were present amongst the 2,577 high-confidence interactions described above. Adding these 131 interactions expanded our high-confidence set of interactions to 1,403. To identify the best set of possible prior known interactions in a consistent manner, we used a procedure estimating how effectively the Inferelator trained on one half of a collection of interactions can recover the other half of the same collection of interactions. Figure S3 compares the performance of the Inferelator on the 50% leave-out set of seven different collections of prior known interactions, when trained on the 50% leave-in set of the same seven collections (respectively). According to both the precision-recall curve and the Receiver Operating Characteristic curve, the final Gold Standard of 1,403 signed interactions is by far the most consistent, i.e. it has the highest area under the curve as compared to any of the sources of interactions shown in Table S1. The biggest improvement in AUPR is achieved by restricting the collection of interactions from YEASTRACT to the 2,577 unsigned interactions that have 1 piece of evidence in Yeastract-Direct and 2 pieces of evidence in Yeastract-Indirect (blue line, AUPR=0.20, AUROC=0.70). Reducing those interactions to only those for which we have evidence of the direction of the regulation in either of the three sources of interactions (YEASTRACT, SGD, and Kemmeren) further improves performance (Gold Standard, red line, AUPR=0.30, AUROC=0.73). Our Gold Standard also outperformed the MacIsaac regulatory interactions database (MacIsaac et al., 2006), which is commonly employed for evaluating network inference algorithms in yeast (Marbach et al., 2012; Siahpirani and Roy, 2016). We extended this comparison to other possible combinations of these collections of interactions (Figure S3E). We confirmed our observations using CLR (Context Likelihood of Relatedness, see below) instead of the Inferelator, confirming that combining one direct and two indirect sources of evidence results in the most self-consistent collection of interactions (Figure S3F). Our results led us to conclude that the 1,403 interactions of our Gold Standard constitute the most consistent and reliable collection of interactions in yeast known to date.

S3.7

Gene Cluster Half-Life Prediction and Validation

The gene cluster that was most prominently enriched in cytoplasmic translation was also the largest cluster (409 genes), and also contained many genes unrelated to translation. Therefore, for predicting RNA half-lives for cytoplasmic translation genes, we used only the genes that were annotated as ”cytoplasmic translation” genes in the Saccharomyces Genome Database (GO:0002181). This consisted of 171 unique gene names, 127 of which were ribosomal protein coding genes (either RPLs or RPSs). These genes were used to calculate the predicted translation gene RNA half-lives in Figure 2 (see Experimental Procedures 4.6). The predicted RNA half-life values for nucleobase containing small molecule (NCSM) metabolism genes were obtained using the genes in the ”nucleic acid metabolism” gene cluster in ”log-phase growth” and ”chemostat” condition clusters. We used the AmiGO 2 website (Carbon et al., 2009) to obtain 207 genes contained as members of the nucleobase containing small molecule metabolic process category (GO:0055086). These genes have experimentally measured RNA half-lives reported in Figure 2 (Neymotin et al., 2014). The list of ”cytoplasmic translation” and ”NCSM metabolism” genes here can be found in Supplemental File SuppData1.zip.

S3.8

Combining Condition-Specific Networks to Create the Final Yeast Network

The final network of regulatory interactions predicted by InfereCLaDR was created in several steps (Figure S2). First, bi-cluster specific RNA half-lives were determined by re-sampling the Gold standard into GStrain and GS-fit 20 times (i.e. employing the Split A approach). The predicted half-life for each bi-cluster was determined by taking the median across the half-lives that optimized AUPR in each of the 20 GS re-samples. Then the TFA and BBSR were trained on each bi-cluster using the full Gold Standard and the corresponding, predicted RNA half-life. The final combined confidence scores were obtained by adding the confidence scores across the condition clusters for every gene. To convert the final (combined) ranked 44

list of interactions into a set of predicted interactions, we set a rank cutoff based on the rank at which precision=0.5 for TFs and their targets in the GS. We applied this rank cutoff of 2,359 to all predictions (regardless of whether the TF or target gene had data in the GS), to obtain the final InfereCLaDR network (Figure 4). The procedure resulted in 1,462 new interactions that were not in the GS. These new interactions are listed in SuppNetwork1.tsv in Supplemental File SuppData1.zip. SuppNetwork2.tsv in Supplemental File SuppData1.zip contains all predictions and their precision values. We determined the rank cutoff for Genie3 network in the same way but using precision=0.15, as Genie3 predictions did not reach a precision over 0.20. We used same procedure to determine rank-based cutoffs for each condition cluster as we did for the full InfereCLaDR network, as well as for the final network predicted by the original Inferelator (yielding 1,922 interactions). To assign each interaction to a condition-cluster in the final InfereCLaDR network (Figure 4), we used the cluster with the lowest predicted rank determined. For each TF, we estimated the skewness of the distribution of the TF’s targets across the four condition clusters using the binomial test. Specifically, we compared the number of targets of each TF in a given cluster with the total number of its targets across all clusters, assuming using the ratio of all interactions in that cluster to all interactions across clusters as the null hypothesis. For each cluster, the five TFs with the highest skewness towards that cluster are shown in Figure 4 in large font. We also used the binomial test to calculate the enrichment of ”gained” interactions in each bi-cluster, treating the distribution of the sum of ”conserved” and ”removed” interactions as the null hypothesis (Figure 3F). The gene cluster of each interaction was assigned from the cluster of the target gene. The networks were visualized using the R packages igraph (Csardi and Nepusz, 2006) and network (Butts, 2008, 2015).

S3.9

Motif Enrichment Analysis

To validate the presence of the PACE-core motif 5’-(A/G)GTGGC-3’ (Shirozu et al., 2015) in CCT2, CCT3, CCT4, and CCT8 promoter regions, we used the online tool on the Yeastract website (http: //www.yeastract.com/searchbydnamotif.php) (Teixeira et al., 2006; Abdulrehman et al., 2011; Monteiro et al., 2008; Teixeira et al., 2014). We found that CCT2 and CCT4 each contain two exact matches for 5’-GGTGGC-3’ in the main and the complementary strand of their promoter regions, respectively. Furthermore, CCT8 and CCT3 each contained an exact match for 5’-AGTGGC-3’ in the main and the complementary strand of their promoter regions, respectively. Neither gene contained an exact match with the longer PACE sequence (Mannhaupt et al., 1999).

S3.10

Methods Comparisons

For implementing Genie3 (Huynh-Thu et al., 2010), we used the R code downloaded from the Genie3 website (http://www.montefiore.ulg.ac.be/∼huynh-thu/software.html) on September 22, 2016. We modified the original R code to allow for parallel processing, such that calculations on different genes could be performed on separate processors simultaneously. The implementation of the code was conducted as instructed in the README file downloaded from the same website. The R code for iRafNet (Petralia et al., 2015) was downloaded from the iRafNet website (http: //research.mssm.edu/tulab/software/irafnet.html) on January 27, 2016. We implemented it using the parameter specifications recommended in the original iRafNet paper (Petralia et al., 2015). In particular, we built the iRafNet weight matrix W using the leave-in portion of the Gold Standard by setting all values of 0 in our leave-in to 0.1 in the weight matrix, and all values of -1 and 1 to 1.1. We set the number of trees � ntree to 1,000, and number of potential regulators to be sampled from every node to mtry=round( ng − 1), where ng is the number of genes, and round is the rounding function. We implemented the Context Likelihood of Relatedness (CLR) method (Faith et al., 2007) by incorporating it into an Inferelator-like procedure analogous to Greenfield et al. (2010) and Madar et al. (2010). CLR scores for every potential interaction were calculated between the response of the target (left hand side of Equation 2 in Experimental Procedures 4.4) and the activity of the potential regulator (calculated as in Suppl. Experimental Procedures S3.1.1), using τi = 20. The BBSR and confidence score calculation steps 45

were entirely bypassed, and so the CLR score was used as the final confidence score for every interaction. Bootstrapping was performed as described in Suppl. Experimental Procedures S3.1.2. InfereCLaDR uses the original Inferelator framework, a new, high-quality GS, expression bi-clustering, and RNA half-life fitting (main text, Figure S2). Figure 3 (main text), Tables 1 (main text) and S2 show increases in performance based use of individual advances. For the ”Inferelator + GS” and ”Inferelator +MacIsaac” in Figure 3 (main text), Table 1 (main text) and Table S2, we set τi = 20 for all genes i and all conditions (see Equation 2 for a definition of τi ), which roughly corresponds to an assumed half-life of 14 minutes. This number was based on the median experimentally measured RNA half-life from various recent studies (Neymotin et al., 2014; Munchel et al., 2011; Miller et al., 2011). For the ”Inferelator + Clustering” (no half-life fitting) approach, we also used τi = 20 for all genes i and all four condition clusters. For the ”Inferelator + RNA half-life” (but no clustering) approach, we used the optimal value of RNA half-life as determined by maximizing the AUPR on the GS-fit collection of leave-out interactions from Split B approach (Figure S2), using the entire RNA expression data set as the input, rather than doing this analysis separately for each condition cluster. For each of these methods, training was done on the same set of 20 re-samples of the Gold Standard, as described in Experimental Procedures 4.5 and 4.6, using the Split B approach, and the AUPRs and AUROCs were calculated using the GS-validate set using the same 20 re-sampes (Figure S2). For each re-sample, individual comparisons in terms of AUPRs and AUROCs between different methods were made, and the number of times, out of 20, that the AUPR (or AUROC) of one method was higher than the other is shown in Table 1 (in terms of AUPR) and Table S2 (in terms of AUROC). Note that the calculation of RNA half-lives differs between the Split A and Split B approaches. The Split A approach reports a single value for each bi-cluster, which is obtained by taking the median of optimal half-lives across the 20 re-samples, where the optimal half-life is the one that maximizes the AUPR calculated on the GS-fit that corresponds to the given re-sample. Taking the median predicted half-life reduces half-life prediction error due to noise and re-sample specific effects, i.e. biases that arise from the particular interactions included in a given re-sampling of the Gold Standard. In the Split B approach, each RNA half-life prediction is derived from only one GS re-sample, because we prioritized guaranteeing the statistical significance of comparisons between methods in terms of network inference accuracy over RNA half-life prediction accuracy. That is, comparisons between methods were made for each GS re-sample separately, which resulted in 20 points of comparison for each pair of methods. Thus, Split B approach simultaneously inferred RNA half-life for each bi-cluster by maximizing AUPR over GS-fit produced from only one re-sample of the Gold Standard. Therefore, the magnitude of the increase in inference accuracy due to half-life fitting that we calculate using the Split B approach (Table 1) is an underestimate of the actual increase in accuracy of our final predicted network, which is produced using the Split A approach. We calculated the p-values in Figure 3F using the binomial test. The number of interactions predicted by the InfereCLaDR but not Inferelator (”gained”, top left quadrant in Figure 3C) in each bi-cluster (representing k, the ”number of successes”) was compared to the number of interactions falling into all three quadrants (”gained”, ”conserved”, and ”removed”) in the same bi-cluster (representing n, the ”number 1,076 of trials”). We assumed a null probability of 1,076+1,283+639 , or the total number of interactions in the ”gained” quadrant divided by the total number of interactions in all quadrants, independent of the bicluster. The sign by which the p-value was multiplied denoted whether the enrichment was on the upper tail (positive sign, i.e. higher than expected) or the lower tail (negative sign, lower than expected). All of the InfereCLaDR, Inferelator, iRafNet, Genie3, and CLR runs that involved the 20x re-sampling of the Gold Standard were performed on the NYU High Performance Cluster (https://wikis.nyu.edu/ display/NYUHPC), using the PBS job scheduling system (Henderson, 1995).

46

SN1

Supplemental Notes: Cluster Interpretation

This section discusses the clusters shown in Figure S1G which lists the most enriched terms of each of the condition clusters using the associated meta-data. Briefly, condition cluster 1 is from cells grown in chemostats, with experiments on nutrient limitation and long time series. Condition cluster 2 comprises experiments that examine oxidative stress or inhibit transcription, which usually relate to early measurements of RNA degradation rates (Shalem et al., 2008, 2011), with treatments such as methyl methane sulfonate (MMS) and phenanthroline. Cluster 3 is enriched in comparisons of mutant strains to wildtype, with cells grown in rich medium. Finally, condition cluster 4 includes fermentation involving industrial strains. The time series experiments in this cluster often last several days. The analysis of the enrichments shown in word clouds was only the first step in determining the most aptly fitting, biology-motivated name for each cluster. After the enrichment analysis, we examined each enriched term individually and counted its appearance in the cluster in which it was enriched compared to other clusters. We also counted from how many separate data series and laboratories the experiments whose meta data contained the term originated. The results of this analysis are summarized in the table in top-words_by-clust.pdf in Supplemental File SuppData2.zip. Specifically, while cluster 1 was more enriched in the terms “oscillation” and “cenpkd” (as shown in Figure S1G), the 195 samples that contained each of these terms came from only 6 and 11 series (from 3 and 6 labs), respectively. The next three most significant terms (aside from “period”, which is arguably redundant with “oscillation”) - “fermentor”, “continuous” and “chemostat” - were all related to cells growing in continuous culture, i.e. a chemostat or biofermentor. “Chemostat” is in the meta data of 187 samples coming from 14 series and 11 different labs. These numbers suggests that the enrichment in chemostat-grown cultures might be more biologically meaningful than the enrichment in the “oscillation” conditions, because it is supported by 3-4 times as many independent laboratories, and twice as many as for “cen.pk”. Given these considerations, the cluster was named “chemostat”. In cluster 2, “decay” was by far more enriched than any other term. The experiments that contained this term came from studies in which decay rates were measured by suppressing and inhibiting transcription, e.g. Shalem et al. (2008) (GSE12221) and Shalem et al. (2011) (GSE26829). Inhibiting transcription to measure RNA degradation is now recognized as a highly invasive method, delivering results very different from non-invasive, labeling-based methods that measure RNA degradation (Neymotin et al., 2014). To mark the fact that the cluster contained invasive methods for RNA degradation measurements, we name it the “transcription inhibition” cluster. The term “oxidative” was also enriched in this cluster, but to a much lower degree, and the cluster contained other smaller studies with unrelated stresses that nevertheless induced similar RNA expression levels. The most enriched terms in cluster 3 were “wild type” and “midlog”, referring to the growth of wild type yeast cells in mid-log phase growth conditions. Upon further inspection, we determined that around half of the experiments in this condition cluster involved cells grown in mid-log phase or in rich medium, YPD, or YEPD. Furthermore, approximately half of these cells were wild type, and subsequent inspection revealed that a lot of the studies compared mutants with wild-type cells in rich conditions. Because our naming convention is condition-focused rather than genotype-focused, we chose “log-phase growth” as the name of this cluster. Finally, for cluster 4, the top two enriched terms, “wort” and “fermentation”, are related to use of yeast for industrial-scale, fermentation-based brewing. “Day” was enriched only because a lot of these studies comprised of time-series with time differences between consecutive time points measured in days, as is typical for brewing. Fermentation/brewing related terms such as “lager”, “riesling”, “wine”, “malt”, and others, were also enriched, coming in total from 7 series and 5 different labs. Given the dominance of this theme in cluster 4, it was named the ”fermentation” cluster. Next, we clustered the data by gene expression patterns and tested for enriched gene functions (Experimental Procedures 4.2). The most significant enrichments in the five gene clusters included cytoplasmic translation, cell wall biogenesis, nucleic acid metabolism, and protein catabolism, respectively (p-value

47

< 0.05, Figure 1C). We used these categories to name the clusters. Large clusters contained additional enrichments. For example, in the ”translation” cluster, translation genes only occupy a fraction of the cluster, and the rest of the cluster is enriched in protein and ncRNA biosynthesis (p-value < 10−22 and p-value < 10−12 , respectively). See Supplemental File SuppData1.zip for the full list of tested GO terms and their corresponding enrichments for every gene cluster.

SN2

Supplemental Notes: Condition Cluster Half-Lives

Figures 2A and E shows that the optimal RNA half-life, as estimated by maximal AUPR, differed between condition clusters. Further, the shape of the distribution varies across condition clusters (Figure S4), suggesting different degrees of half-life dependence under different conditions. The unperturbed condition clusters have comparatively low RNA-half-lives of approximately 10 to 25 minutes. This prediction is consistent with experimental half-life estimates of 10 to 15 minutes for unperturbed conditions (Miller et al., 2011; Neymotin et al., 2014; Munchel et al., 2011), which we expect to be similar to ”chemostat” and ”log-phase growth” conditions. In comparison, the half-lives in the “transcription inhibition” cluster in Figure 2D cluster are longer than those under unperturbed conditions (Wilcoxon p < 10−10 ). The “transcription inhibition” cluster contains many studies that measured RNA decay rates by inhibiting transcription, e.g. Shalem et al. (2008). Indeed, it has recently been shown that these studies identify significantly longer RNA half-lives than those using less invasive metabolic labeling methods (Neymotin et al., 2014; Pelechano and Pérez-Ort´ın, 2008) (Wilcoxon p < 2 × 10−16 ).

SN3

Supplemental Notes: New Predictions

SN3.1

CCT Targets of Rpn4p

The four interactions (i.e. Rpn4p regulating CCT2, CCT3, CCT4, and CCT8 ) were absent from the Kemmeren database; only CCT4 was present in Yeastract-Direct database as directly bound by Rpn4p; only CCT3 and CCT8 were in the Yeastract-Indirect database; and only CCT4 was in the SGD database with computational support (see SuppNetwork2.tsv in Supplemental File SuppData1.zip). Several reasons explain why these interactions have so far gone undetected, but are strongly predicted by the InfereCLaDR. For example, the four mRNAs have optimal half-lives between 42 and 83 min, far longer than the median half-life of 10-20 minutes used in the original Inferelator. Further, these interactions are very condition-specific, that is, they are restricted to only one cluster, explaining why they are missed in global inference.

SN3.2

New Predictions With Indirect Validation

Another form of validation arises from gene knockout phenotypes. For example, the Tec1p transcription factor regulates filamentation genes, but also positively affects lifespan (Mösch and Fink, 1997; Garay et al., 2014). Its predicted target TRX2 (predicted to be repressed) is a thioredoxin isoenzyme involved in the oxidative stress response (Garrido and Grant, 2002; Greetham et al., 2010). A screen by Postma et al. (2009) demonstrated increased lifespan in a TRX2 null mutant strain Postma et al. (2009), supporting indirectly our predicted repression of TRX2 by Tec1p. A second example relates to MRK1, which InfereCLaDR predicts as a new repression target of Yap1p, which is required for tolerance to oxidative stress and cadmium exposure (Kuge and Jones, 1994; Wemmie et al., 1994; Lee et al., 1999). Mrk1p itself activates stress response genes (Hardy et al., 1995; Hirata et al., 2003). Further, cellular cadmium levels increase in the MRK1 knockout (Yu et al., 2012), again supporting a repression link between MRK1 and Yap1p and response to cadmium.

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SN3.3

Condition-Specific Predictions

Next, we explored interactions that were predicted due to InfereCLaDR’s condition specificity. Figure 4 shows the list of top five most condition-responsive TFs in each cluster. For many of these TFs, condition specificity is in line with their cellular function. For example, the ”chemostat” cluster is enriched in experiments related to glucose limitation (Figure S1G, Supplemental Data SupData2.zip). Both Cat8p and Adr1p are InfereCLaDR predicted regulators for which literature already describes a link to glucoselimiting conditions (Turcotte et al., 2010), but screens have missed them so far. The Cat8p TF is known to bind carbon source responsive elements in absence of glucose, and Adr1p is related to glucose-limiting conditions. Sok2p regulates growth under nitrogen limitation (Ward et al., 1995) and is a new, InfereCLaDR predicted regulator specific to the chemostat cluster (Figure 4). Indeed, the chemostat cluster contains all nitrogen-limitation experiments we used (Figure S1G, Supplemental Data SupData2.zip). Finally, Spt10p is an S-phase specific transcription factor (Xu et al., 2005), and we predict most of its targets within the chemostat cluster. Consistent with this prediction, the cluster contains 195 out of 210 samples related to cell cycle (Supplemental Data SupData2.zip). In sum, InfereCLaDR recognized the condition-specific activities of Cat8p, Adr1p, Sok2p, and Spt10p that previous approaches failed to predict. Another example arises from Mtf1p and Mhr1p, which were predicted as highly specific to the ”logphase growth” condition cluster. Mitochondrial Transcription Factor 1 (Mtf1p) facilitates high levels of transcription by bending and unbending their promoter and non-promoter regions, respectively (Lisowsky and Michaelis, 1989; Tang et al., 2011; Velazquez et al., 2012). While the mechanism of Mtf1p activity as a polymerase specificity factor is well-understood, its pattern of activity and targets are not. We predict that Mtf1p transcriptionally activates 24 mitochondrial genes (20 of which are ”gained” by InfereCLaDR). Of these interactions, 19 are among the most significant predictions in the ”log-phase growth” cluster, i.e. its interactions are highly condition-specific (Figure 4). The example of Mhr1p illustrates the opposite case, a regulator with many ”conserved” interactions for which InfereCLaDR predicts targets across diverse conditions. Note that similarly to Mtf1p, Mhr1p is predicted to regulate a large proportion of mitochondrial genes. Mhr1p is known for its role in different contexts, ranging from mitochondrial DNA replication and homologous recombination (Ling and Shibata, 2002; Hori et al., 2009) to nuclear transcriptional repression (Emili et al., 1998; Traven et al., 2002). Our results show that Mhr1p targets are distributed across different condition clusters (Figure 4), and that about half of them are also predicted by the original Inferelator, whereas almost none of Mtf1p’s targets were also predicted by the Inferelator. Taken together, InfereCLaDR predicts Mtf1p and Mhr1p to regulate mitochondrial genes in a dynamic, combinatorial way, with Mtf1p acting under few, specific and Mhr1p under multiple conditions.

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