Transcription factor binding site clusters identify target genes with similar tissue-wide expression and buffer against mutations

Background: The distribution and composition of cis-regulatory modules composed of transcription factor (TF) binding site (TFBS) clusters in promoters substantially determine gene expression patterns and TF targets. TF knockdown experiments have revealed that TF binding profiles and gene expression levels are correlated. We use TFBS features within accessible promoter intervals to predict genes with similar tissue-wide expression patterns and TF targets using Machine Learning (ML). Methods: Bray-Curtis Similarity was used to identify genes with correlated expression patterns across 53 tissues. TF targets from knockdown experiments were also analyzed by this approach to set up the ML framework. TFBSs were selected within DNase I-accessible intervals of corresponding promoter sequences using information theory-based position weight matrices (iPWMs) for each TF. Features from information-dense clusters of TFBSs were input to ML classifiers which predict these gene targets along with their accuracy, specificity and sensitivity. Mutations in TFBSs were analyzed in silico to examine their impact on TFBS clustering and predict changes in gene regulation. Results: The glucocorticoid receptor gene ( NR3C1), whose regulation has been extensively studied, was selected to test this approach. SLC25A32 and TANK exhibited the most similar expression patterns to NR3C1. A Decision Tree classifier exhibited the best performance in detecting such genes, based on Area Under the Receiver Operating Characteristic curve (ROC). TF target gene prediction was confirmed using siRNA knockdown, which was more accurate than CRISPR/CAS9 inactivation. TFBS mutation analyses revealed that accurate target gene prediction required at least 1 information-dense TFBS cluster. Conclusions: ML based on TFBS information density, organization, and chromatin accessibility accurately identifies gene targets with comparable tissue-wide expression patterns. Multiple information-dense TFBS clusters in promoters appear to protect promoters from effects of deleterious binding site mutations in a single TFBS that would otherwise alter regulation of these genes.

site sequences and represents the average binding strength of the TF 3 . Neighboring, likely coregulatory TFBSs were identified by information density-based clustering (IDBC), which takes into account both the spatial organization (i.e. intersite distances) and information density (i.e. R i values) of TFBSs 5 .
TF binding profiles, either derived from in vivo ChIP-seq peaks 6-8 or computationally detected binding sites and CRMs 9 , have been shown to be predictive of absolute gene expression levelsusing a variety of tissue-specific ML classifiers and regression models. Because signal strengths of ChIP-seq peaks are not strictly proportional to strengths of the contained strongest TFBSs and are instead controlled by TFBS counts 3,10 , representing TF binding strengths by ChIP-seq signals may not be appropriate; nevertheless, both achieved similar accuracy 11 . CRMs have been formed by combining two or three adjacent TFBSs 9 , which is inflexible, as it arbitrarily limits the number of binding sites contained in a module, and does not consider differences between information densities of different CRMs. Chromatin structure (e.g. histone modification (HM) and DNase I hypersensitive sites (DHSs)) were also found to be statistically redundant with TF binding in explaining tissue-specific mRNA transcript abundance at a genome-wide level 7,8,12,13 , which was attributed to the heterogeneous distribution of HMs across chromatin domains 8 . Combining these two types of data explained the largest fraction of variance in gene expression levels in multiple cell lines 7,8 , suggesting that either contributes unique information to gene expression that cannot be compensated for by the other.
Previous studies have shown that a small subset of target genes bound by TFs were differentially expressed (DE) in the GM19238 cell line, upon knockdown with small interfering RNAs (siRNAs) 14 . TFBS counts were defined as the number of ChIPseq peaks overlapping the promoter, with the caveat that the number and strengths of the TFBSs in each peak were not known 15 . Correlation between total TFBS counts and gene expression levels across 10 different cell lines was more predictive of which were DE than by setting a minimum threshold count of TFBSs 15 . This has also been addressed by perturbing gene expression with CAS9-directed clustered regularly interspaced short palindromic repeats (CRISPR) of 10 different TF genes in K562 cells 16 . The regulatory effects of each TF were dissected by single cell RNA sequencing with a regularized linear computational model 16 . This revealed DE targets and new functions of individual TFs, some of which were likely regulated through direct interactions at TFBSs in their corresponding promoters. ML classifiers have also been applied to predict targets of a single TF using features extracted from n-grams derived from consensus binding sequences 17 , or from TFBSs and homotypic binding site clusters 5 .
We investigated whether the predicted TFBS strengths, distribution and CRM composition in promoters substantially determines gene expression profiles of direct TF targets. A general ML framework was developed by combining information theory-based TF binding profiles with DHSs. The approach predicts which genes have similar tissue-wide expression profiles, and conversely, DE direct TF targets. Upon selecting DHSs to define accessible

Amendments from Version 1
The manuscript has been extensively edited to improve clarity of the presentation. Sentence lengths were reduced. Duplicate terms and text were eliminated. The titles of the subsections of Results were revised to indicate the primary conclusions. Two paragraphs were moved to the Supplementary Methods. The revised manuscript is shortened by 400 words and approximately 2 pages.
We addressed the impact of covariance between expression levels of developmentally related tissues from the same organ, by sequentially removing 12 of 13 brain tissues from the GTEx dataset prior to recomputing the Bray-Curtis Similarity index. We found multiple covarying brain tissue expression values to not significantly influence the set of most similar genes seen with all 53 tissues in this analysis.
For the Decision Tree classifiers predicting transcription factor target genes, Gini importance values were computed to assess the relative contribution of the six ML features to their predictive power. For the CRISPR-perturbed TFs in the K562 cell line, clustering Features 1-3, particularly the TFBS cluster information densities (Feature 3), were most important. The TFBS-level Feature 5 comprising the distribution of strong binding sites accounts for the largest contribution to classifier performance for the 11 siRNA-perturbed TFs in the GM19238 cell line.
Additional file 1 now contains text from v1 of the manuscript as requested by a reviewer. Additional file 5 now contains the Gini scores for the machine learning features and the accuracy value of each individual round of 10-fold cross validation.
We now cite: • Zabet & Adryan (2015)-indicating properties of TF molecules that contributed to genome-wide binding profiles.
• Ma et al. (2018)-describing spatially colocalized cisclusters of TFs and how these groups of TF constitute tissue specific regulatory subnetworks.

Introduction
The distinctive organization and combination of TFBSs and regulatory modules in promoters dictates specific expression patterns within a set of genes 1 . Clustering of multiple adjacent binding sites for the same TF (homotypic clusters) and for different TFs (heterotypic clusters) defines cis-regulatory modules (CRMs) in human gene promoters. Experimental studies have shown that these clusters can reinforce (and in some instances, amplify) the impact of individual TFBSs on gene expression through increasing binding affinities, facilitated diffusion mechanisms and funnel effects 2 . Because tissue-specific TF-TF interactions in TFBS clusters are prevalent, these features can assist in identifying correct target genes by altering binding specificities of individual TFs 3 . Previously, we derived iPWMs from ChIP-seq data that can accurately detect TFBSs and quantify their strengths by determining the associated R i values (Rate of Shannon information transmission for an individual sequence 4 ). R sequence (the area under the sequence logo) is the average of R i values of all binding promoter intervals, ML features that captured the spatial distribution and information theory-based TFBS compositions of CRMs were extracted from IDBC clusters. The intent of this framework was to provide insight into the transcriptional program of genes with similar profiles by dissecting shared properties of their cis-regulatory element organization, without imposing strict constraints on the strengths and distributions of TFBSs. We first identify genes with comparable tissue-wide expression profiles by application of Bray-Curtis similarity 18 . Using transcriptome data generated by CRISPR-16 and siRNA-based 14 TF knockdowns, we predicted DE target genes with promoters that contain ChIP-seq peaks for these same TFs.

Methods
To identify genes with similar tissue-wide expression patterns, we formally define tissue-wide gene expression profiles and pairwise similarity measures between profiles of different genes. A general ML framework relates features extracted from the organization of TFBSs in these genes to their tissue-wide expression patterns. Since protein-coding (PC) sequences represent the most widely studied and best understood component of the human genome 19 , positives and negatives for deriving ML classifiers of predicted DE direct TF target genes encoding proteins (TF targets, below) were obtained from CRISPR-and siRNAgenerated knockdown data.
Similarity between GTEx tissue-wide expression profiles of genes We used data from the Genotype-Tissue Expression (GTEx, version 6p) project which measured expression levels for each gene in 53 tissues, in different numbers of individuals (5 to 564). For each tissue population, the median expression value is given in RPKM (Reads Per Kilobase of transcript per Million mapped reads) for each gene 20 . Data are available on Zenodo 21 .
To capture the tissue-wide overall expression pattern of a gene instead of within a single tissue, the tissue-wide expression profile of a gene was defined as its median RPKM across GTEx tissues, which is described by a 53-element vector (Equation 1). Note that different isoforms whose expression patterns may significantly differ from each other cannot be distinguished by this approach.
where EP A is the tissue-wide expression profile of Gene A, Prediction of genes with similar tissue-wide expression profiles The framework for predicting whether the tissue-wide expression profile of a gene resembles a particular gene is indicated in Figure 1 (panels A and B The seven information density-related ML features (Additional file 1 22 ) derived from each TFBS cluster included: 1) The distance between this cluster and the transcription start site (TSS), 2) The length of this cluster, 3) The information content of this cluster (i.e. the sum of R i values of all TFBSs in this cluster), 4) The number of binding sites of each TF within this cluster, 5) The number of strong binding sites (R i > R sequence ) of each TF within this cluster, 6) The sum of R i values of binding sites of each TF within this cluster, and 7) The sum of R i values of strong binding sites (R i > R sequence ) of each TF within this cluster.
Each of the Features 1-3 was defined in a gene as a vector, whose size equalled the number of clusters in the gene promoter; each cluster was mapped to a single value in the vector. In Features 4-7, each cluster itself was mapped to a vector corresponding to binding sites for 82 TFs (Additional file 1 22 ). If two genes contained different numbers of clusters, the maximum number of clusters among all instances was determined, and null clusters were added to the 5' end of promoters with the smaller numbers of clusters; this enabled all genes to exhibit the same cluster counts. This allowed all genes to be used as training data for ML classifiers. Default parameter values for these classifiers were used to generate ROC curves with a built-in MATLAB function (Additional file 1 22 ).

Prediction of TF targets
Perturbed target gene expression after CRISPR-based mutation of TF genes. Dixit et al. performed CRISPR-based perturbation experiments using multiple guide RNAs for each of ten TFs in K562 cells, resulting in a matrix of coefficients indicating the effect of each guide RNA on each of 22,046 genes 16 . Data are available on Zenodo 21 . The coefficient of a guide RNA is defined as the log 10 fold change in gene expression level 16 . We previously derived iPWMs for the primary binding motifs of 7 of the ten TFs (EGR1, ELF1, ELK1, ETS1, GABPA, IRF1, YY1) 3 . The framework for predicting TF targets ( Figure 1A and 1C) was applied to these TFs. We defined a positive TF target gene in a cell line as : 1) The fold change in the expression level of this gene for each of the guide RNAs of the TF was consistently greater than (or is less than) 1, which eliminated genes exhibiting both increased and decreased expression levels for different guide RNAs, and increased the possibility that the gene was downregulated (or upregulated) by the TF (Additional file 1 22 ). and 2) The average fold change in the expression level of this gene for all guide RNAs of the TF was greater than the threshold (or is less than 1/ ), and Figure 1. The general framework for predicting genes with similar tissue-wide expression profiles and TF targets. Red and blue contents are respectively specific to prediction of genes with similar tissue-wide expression profiles and prediction of TF targets. (A) An overview of the ML framework. The steps enclosed in the dashed rectangle vary across prediction of genes with similar tissue-wide expression profiles and TF targets. The step with a dash-dotted border that intersects promoters with DHSs is a variant of the primary approach.
In the IDBC algorithm (Additional file 1 22 ), the parameter I is the minimum threshold on the total information contents of TFBS clusters. In prediction of genes with similar tissue-wide expression profiles, the minimum value was 939, which was the sum of mean information contents (R sequence values) of all 94 iPWMs; in prediction of direct targets, this value was the R sequence value of the single iPWM used to detect TFBSs. The parameter d is the radius of initial clusters in base pairs, whose value, 25, was determined empirically. The seven ML features derived from TFBS clusters are described in the Methods section. The performance of seven different classifiers was evaluated with ROC curves and 10-fold cross validation (Additional file 1 22 ). (B) Obtaining the positives and negatives for identifying genes with similar tissue-wide expression profiles to a given gene (Additional file 2 22 ). (C) Obtaining the positives and negatives for predicting target genes of seven TFs using the CRISPR-generated perturbation data in K562 cells (Additional file 3 22 ). (D) Obtaining the positives and negatives for predicting target genes of 11 TFs using the siRNA-generated knockdown data in GM19238 cells (Additional file 4 22 ).
3) The promoter interval (10 kb) upstream of a TSS of this gene overlapped a ChIP-seq peak of the TF in the cell line.
If the coefficients for all guide RNAs of the TF for a gene were zero, the gene was defined as a negative (i.e. a non-target gene).
As the threshold ε increases, the number of positives strictly decreases. As ε decreases, we have lower confidence that the positives were DE as a result of the TF perturbation. We balanced the number of positives obtained against our confidence that they were DE by evaluating different values of ε (i.e. 1.01, 1.05 and 1.1; Additional file 1 22 ). For each TF, all ENCODE ChIP-seq peak datasets from the K562 cell line were merged to determine positives. Data are available on Zenodo 21 . To avoid imbalanced datasets that significantly compromised the classifier performance 27 , the Bray-Curtis function was applied to compute the similarity values in the tissue-wide expression profile between all negatives and the positive gene with the largest average coefficient, and then negatives with the smallest values were selected, resulting in the same number of positive and negative genes ( Figure 1C).
Because TFs may exhibit tissue-specific sequence preferences due to different sets of target genes 3 , the K562 cell line-derived iPWMs of EGR1, ELK1, ELF1, GABPA, IRF1, YY1 were used to detect binding sites in DHS-intersected intervals; for ETS1, we used the only available iPWM from GM12878 3 . Six features (Features 1-5 and 7) were derived from each homotypic cluster (i.e. Feature 6 became identical to Feature 3, because only binding sites from a single TF were used) ( Figure 1A). The results of 10 rounds of 10-fold cross validation were averaged to evaluate the accuracy of the classifier.

Target gene expression changes after siRNA-based knockdown of TFs.
Significant changes in expression of target genes upon knockdown of 59 TFs in the GM19238 line were identified from the probability of differences in expression level (P-value) relative to the null hypothesis of no change 14 . Data are available on Zenodo 21 . DE genes with larger changes exhibited smaller P-values. The distribution of ChIP-seq peaks were considered to be evidence of TF binding to the promoters of these genes 14 . Among these 59 TFs, we have previously derived iPWMs exhibiting primary binding motifs for 11 (BATF, JUND, NFE2L1, PAX5, POU2F2, RELA, RXRA, SP1, TCF12, USF1, YY1) 3 . For this reason, transcription targets of these TFs were predicted in the GM19238 cell line ( Figure 1A, D).
For ML training, we defined a positive (i.e. a target gene) for a TF, if the P-value of this gene was ≤ 0.01, and the promoter interval up to 10 kb upstream of a TSS overlapped one or more ChIP-seq peaks of the TF in GM12878. Other genes with P-values > 0.01 exhibited insufficient support for being TF targets and were labeled as negatives.
The iPWMs from GM19238 were used to detect binding sites for all TFs except for RELA, RXRA and NFE2L1. The iPWM from the GM19099 line was used for RELA, and for RXRA and NFE2L1, the only available iPWMs were derived from HepG2 and K562 cells, respectively. The DHSs in GM19238 were first remapped to the hg38 assembly using liftOver, prior to being intersected with known promoters 28 . Data are available on Zenodo 21 . Although the knockdowns were performed in GM19238, GM12878 and GM19099 are also lymphoblastic cell lines, with GM19099 and GM19238 both being derived from the Yoruban population. For this analysis, the iPWMs derived in GM12878 and GM19099 were more appropriate sources of accessible TFBSs than those from HepG2 and K562, since GM12878 and GM19099 are more likely comparable to GM19238 than HepG2 and K562. ML results were evaluated by averaging cross validation, as described above.

Mutation analyses on promoters of TF targets
To understand the significance of individual binding sites on the regulatory state of TF targets, we evaluated the effects of sequence changes in TFBSs that altered the R i values of these sites, the definition of TF clusters, and whether consequential IDBC-related changes impacted the prediction of TF target genes. For example, mutations were sequentially introduced into the strongest binding sites in TFBS clusters of the EGR1 target gene, MCM7, to determine the threshold for cluster formation and whether disappearing clusters disabled MCM7 expression. For one target gene of each TF from the CRISPR-generated perturbation data, effects of naturally occurring TFBS variants present in dbSNP 29 were also evaluated to explore aspects of TFBS organization that enabled both clusters and promoter activity to be resilient to binding site mutations. This was done by analyzing whether the occurrence of individual or multiple single nucleotide polymorphisms (SNPs) lead to the loss of binding sites and the corresponding clusters, and resulted in changes in the predictions for these targets.

Results
The Bray-Curtis Function can accurately quantify the similarity between tissue-wide gene expression profiles We computed the similarity values (Equation 2) between the tissue-wide expression profiles of the glucocorticoid receptor (GR or NR3C1) gene and all other 18,812 PC genes to find genes with related profiles. NR3C1 is an extensively characterized TF with many known direct target genes 30 . As a constitutively expressed TF activated by glucocorticoid ligands, the protein mediates up-regulation of anti-inflammatory genes by binding as homodimers to glucocorticoid response elements. Transcription of proinflammatory genes is down-regulated by complexing with other activating TFs (e.g. NFKB and AP1), thereby eliminating their ability to bind and activate targets 30 . NR3C1 can bind its own promoter forming an auto-regulatory loop, which also contains functional binding sites of 11 other TFs (e.g. SP1, YY1, IRF1, NFKB) whose iPWMs have been developed and/or mutual interactions have been described previously 3,30 . The tissue-wide expression profile of NR3C1 comprises all different splicing and translational isoforms (GRα-A, GRα-B, GRα-C, GRα-D, GRβ, GRγ, GRδ). However, the profile averages out tissue-specific preferences of some isoforms, for example, GRα-C isoforms are significantly higher in the pancreas and colon, whereas levels of GRα-D are highest in spleen and lungs 30 . We found that SLC25A32 and TANK have the greatest similarity in expression to NR3C1 (0.880 and 0.877 respectively), based on their overall similar expression patterns across the 53 tissues ( Figure 2).
The Decision Tree classifier performed best in prediction of genes with similar tissue-wide expression profiles Several ML classifiers (Naïve Bayes, Decision Tree (DT), Random Forest and Support Vector Machines (SVM) with four different kernels) were evaluated to determine how well TFBS-related features could predict genes with tissue-wide expression profiles similar to NR3C1. Their performance were compared using ROC curves, for complete promoters or for accessible promoter sequences that were first intersected with DHSs ( Figure 3). DT exhibited the largest AUC (area under the curve) under both A comparison of the panels shows that the overall expression patterns of the three genes across the 53 tissues resemble each other (e.g. all three genes exhibit the highest expression levels in lymphocytes and the lowest levels in brain tissues).
scenarios, and was one of two most stable classifiers (i.e. ΔAUC < 0.01), with the other being the SVM with RBF kernel. Consistent with previous findings 10,31,32 , inclusion of DHS information significantly improved AUC values of the other classifiers with the exception of Naïve Bayes. In many instances, all TFBSs in a contiguous DHS interval formed a single binding site cluster.
The Decision Tree classifier was predictive of TF target genes Based on its performance in distinguishing genes with NR3C1like tissue-wide expression profiles, the DT classifier was used to predict TF targets respectively based on the CRISPR-16 and siRNA-generated 14 perturbation data. Performance was assessed with 10 rounds of 10-fold cross validation (Tables 2 & Table 3).
Gini importance values were also used to assess the relative contribution of the six ML features to the predictive power of the classifier (Additional file 5 22 ). For the CRISPR-perturbed TFs in the K562 cell line, clustering Features 1-3, particularly the TFBS cluster information densities (Feature 3), were most important. The TFBS-level Feature 5 comprising the distribution of strong binding sites accounts for the largest contribution to classifier performance for the 11 siRNA-perturbed TFs in the GM19238 cell line. To assess the value of all ML features in capturing the distribution and composition of CRMs in promoters, all but one (TFBS counts) were sequentially removed, and the impact on accuracy of the classifier was determined. In each instance, classifier performance decreased, except for CRISPR-perturbed GABPA, IRF1 and YY1 upon inclusion of DHS information (Additional file 5 22 ).
The DT classifier predicted TF targets with greater sensitivity and specificity, after eliminating TFBSs in inaccessible promoter intervals in the CRISPR-generated knockdown data (Table 2). Specifically, predictions for EGR1, ELK1, ELF1, ETS1, GABPA, and IRF1 were more accurate than for YY1, which itself represses or activates a wide range of promoters by binding to sites overlapping the TSS (Table 2). Accordingly, perturbation results showed that YY1 has ~4-22 fold more PC targets in the K562 cell line than the other TFs (ε = 1.05). Binding of YY1 more significantly impacts the expression levels of target genes. The ratio of the PC targets at ε = 1.1 vs ε = 1.01 was 0.334, which significantly exceeded those of other TFs in this study (0.017-0.082; Additional file 3 22 ). This is consistent with the extensive interactions of this factor with many other TF cofactors in K562 cells, and its central role in specifying erythroid-specific lineage development 3 .
We found that promoters of most TF targets contain accessible, likely functional binding sites that are significantly correlated with changes in gene expression levels. Despite a high accuracy of target recognition, sensitivity did not exceed specificity, except for IRF1 (Table 2), due to a relatively large number of false negative genes. Promoters of non-targets are either devoid of accessible binding sites, or these sites are non-functional. In these instances, the classifier was unable to distinguish between likely functional binding sites in targets and non-functional sites in non-targets. In vivo co-regulation mediated by interacting cofactors, which was excluded by the classifier, assisted in distinguishing these non-functional sites that do not significantly affect gene expression 14 .
As the minimum differential expression threshold ε increased, the accuracy of the classifier for all the TFs monotonically increased, as expected ( Figure 4). In general, more significantly DE genes have been associated with a higher number of TFBSs in their promoters 14 . Thus, at greater ε, there are larger differences in the values of ML features derived from TFBS clusters between direct targets and non-targets.
Some TF target genes also display similar tissue-wide expression profiles to the TFs, themselves To determine how many TF targets have similar tissue-wide expression profiles, we intersected the set of targets with the set of 500 PC genes with the most similar tissue-wide expression profiles for each TF (    subunits of mitochondrial ribosomes), respectively, in the K562 and GM19238 cell lines 33 . YY1 is known to upregulates a large number of mitochondrial genes by complexing with PGC-1α in C2C12 cells 34 , and genes involved in the mitochondrial respiratory chain in K562 cells 16 . Our results are consistent with the idea that YY1 may broadly regulate mitochondrial function within all 53 tissues, in addition to the erythrocyte, lymphocyte and skeletal muscle cell lines.
Between 0.4%-25% of genes with similar tissue-wide expression profiles to the TFs are actually their targets (Table 4). The majority are non-targets whose promoters contain non-functional binding sites that lack co-regulation by corresponding cofactors. For YY1 and EGR1, we contrasted the flanking cofactor binding site distributions and strengths in the promoters of the most similarly expressed target genes (YY1: MRPL9, BAZ1B; EGR1: CANX, NPM1) with non-target genes (YY1: ADNP, RNF25; EGR1: GUCY2F, AWAT1). In these target gene promoters, strong and intermediate TFBSs recognized by SP1, KLF1, CEBPB formed heterotypic clusters with adjacent YY1 sites. Additionally, TFBSs of SP1, KLF1, and NFY tended to be present adjacent to EGR1 binding sites (Additional file 7 22 ). These patterns contrasted with enrichment of CTCF and ETV6 binding sites in gene promoters of YY1 and EGR1 non-targets (Additional file 7 22 ). Previous studies have reported that KLF1 is essential for terminal erythroid differentiation and maturation 35 . Direct physical interactions between YY1 and the constitutive activator SP1 synergistically induce transcription 36 , through activating CEBPB which promotes differentiation and suppresses proliferation of K562 cells by binding the promoter of the G-CSFR gene encoding a hematopoietin receptor 37 . EGR1 and SP1 synergistically cooperate at adjacent non-overlapping sites on EGR1 promoter but compete for binding at overlapping sites 38 , whereas occupied CTCF binding sites often function as an insulator blocking the effects of cis-acting elements and preventing gene activation by mediating long-range DNA loops to alter topological chromatin structure 39,40 . ETV6, a member of the ETS family, is a transcriptional repressor required for bone marrow hematopoiesis and associated with leukemia development 41 .
Transcription factor binding site clusters buffer against expression changes from mutations in single sites These results and previous studies indicate that the promoters of direct target genes contain multiple binding site clusters. We used our ML models of TFBS organization to investigate the effects of mutations in individual binding sites on the predicted expression of TF targets. We hypothesized that alternative TF clusters in the same promoter might stabilize and compensate for the loss of a mutated TF cluster, enabling mutated promoters to retain some capacity to regulate gene transcription upon TF binding. First, we introduced artificial variants into binding sites in silico in the promoter of the target gene MCM7 of EGR1 and examined the effect on the output of the ML classifier ( Figure 5). In the K562 line, MCM7 is upregulated by EGR1. Knockdown of MCM7 has an anti-proliferative and proapoptotic effect on K562 cells 42 and the loss of EGR1 increases leukemia initiating cells 43 , which suggests that EGR1 may act as a tumor suppressor in K562 cells through the MCM7 pathway. chr7:100101977, +, 2.2 bits; chr7:100101984, +, 1.9 bits) were still predicted to compensate for this mutation, so that the promoter maintains the capacity to induce MCM7 expression ( Figure 5). Adjacent sites within the same TFBS cluster, which may individually not have sufficient affinity to strongly bind TFs and activate transcription, are capable of stabilizing binding to adjacent sites 2 . Weaker sites can direct TF molecules to strong sites and extend the duration of physical association, termed the funnel effect 2 . Binding stabilization between adjacent sites and the funnel effect enable CRMs comprised of information-dense clusters to be robust to mutations in individual binding sites 2,44 . In this example, Clusters 2 and 3 were also respectively removed by G->T and C->G mutations abolishing the strongest site in either cluster, altering the prediction of the classifier, that is, EGR1 is expected to fail to induce MCM7 transcription ( Figure 5). The remaining four sparse weak sites do not form a cluster and cannot completely supplant the disrupted strong sites.
We then examined the predicted impacts of natural SNPs on binding site strengths, clusters and predicted the regulatory state of the promoter for a direct target of each of the seven TFs from the CRISPR-generated perturbation data (Table 5). We found that a single SNP (e.g. rs996639427 of EGR1) could affect the strengths of multiple binding sites within a cluster (Table 5). Apart from SNPs that are predicted to abolish binding ( Figure 5), leaky variants that are expected to merely weaken TF binding are also common (Table 5). Neither mutations that abolish TFBSs nor leaky SNPs in flanking weak binding sites would be expected to inactivate TFBS clusters Upon loss of all three clusters, only weak binding sites remained and EGR1 was predicted to no longer be able to effectively regulate MCM7 expression. Multiple clusters in the promoters of TF targets confer robustness against mutations within individual binding sites that define these clusters. (e.g. rs1030185383 and rs5874306 of IRF1), whereas SNPs with large reductions in R i values of strong sites are more likely to abolish clusters (e.g. rs865922947, rs946037930, rs917218063 and rs928017336 of YY1) (Table 5). Multiple TF clusters enable promoters to be resilient to the effects of these mutations; only the complete inactivation of all clusters by concurrent effects of multiple SNPs within TFBSs would be capable of making a promoter to be unresponsive to TF binding (e.g. rs997328042, rs1020720126 and rs185306857 of GABPA) (Table 5). Conversely, a small number of SNPs capable of strengthening TF binding and reinforcing the regulatory effect of the TF were also observed (e.g. rs887888062 of EGR1 and rs751263172 of ELF1) (Table 5).
In addition to deleterious mutations, potentially benign variants may also be found in promoters, consistent with the expectations of neutral theory 45 .

Discussion
In this study, the Bray-Curtis similarity function was initially shown (for the NR3C1 gene) to measure the relatedness of overall expression patterns between genes across a diverse set of tissues (Figure 2). A ML framework distinguished similar from dissimilar genes based on the distribution, strengths and compositions of TFBS clusters in accessible promoters, which can substantially account for the corresponding gene expression patterns (Figure 1 & Figure 3). Using gene expression knockdown data, the combinatorial use of TF binding profiles and chromatin accessibility was also demonstrated to be predictive of TF targets ( Figure 4, Table 2 & Table 3). A binding site comparison confirmed that coregulatory cofactors can be used to distinguish between functional sites in targets and nonfunctional ones in non-targets. Furthermore, in silico mutation analyses on binding sites of targets suggested that the existence of both multiple TFBSs in a cluster and multiple informationdense clusters in the same promoter enables both the cluster and the promoter to be resilient to mutations in individual TFBSs ( Figure 5, Table 5).
The DT classifier improved after intersecting promoters with DHSs in prediction of TF targets with the CRISPR-generated knockdown data (Table 2). This intersection eliminated noisy binding sites that are inaccessible to TF proteins in promoters 10,31,32 ; specifically, it widened discrepancies in feature vectors between positives and negatives. If the 10 kb promoter of a gene instance does not overlap DHSs, its feature vector will only consist of 0; the percentages of negatives whose promoters do not overlap DHSs considerably exceeded those of positives (Additional file 8 22 ), which led to an excess of negatives with feature vectors containing only 0 after intersection. This explains why these negatives are not DE targets of the TFs in the K562 and GM19238 cell lines, because their entire promoters are not open to TF molecules; other regulatory regions besides the proximal promoters (e.g. intronic enhancers 46 ) still enable the TFs to effectively control the expression of the positives with inaccessible promoters. Compared to the other six TFs, the poorer performance of the classifier on YY1 (Table 2) is attributable to its smaller percentage of negatives with inaccessible promoters (Additional file 8 22 ) and the larger number of functional binding sites in the K562 cell line.
Mutation analyses revealed that some deleterious TFBS mutations could be compensated for by other information-dense clusters in the same promoter ( Figure 5, Table 5) 2,47 ; thus, predicting the effects of mutations in individual binding sites might not be sufficient to interpret downstream effects without considering their context. Though other TFBS clusters may compensate and maintain gene expression, the promoter will likely exhibit lower levels of activity than the wild-type promoter, which is a recipe for achieving natural phenotypic diversity 44 . Few published studies in molecular diagnostics have specifically examined the effects of naturally occurring variants within clustered TFBSs. IDBC-based ML provides an alternative approach to predict deleterious mutations that impact (i.e. repress or abolish) transcription of target genes and result in abnormal phenotypes, and to minimize false positive calls of TFBS variants that alone would be expected to have little or no impact.
Apart from these TFs, the Bray-Curtis Similarity metric can be directly applied to identify the ground-truth genes with overall similar tissue-wide expression patterns to any other gene whose expression profile is known. Previous applications of this index include: a) measurement of the ecological transfer of species abundance from dense to sparse plots 48 , b) comparative difference analyses of species quantities between reference and algorithm-derived metagenomic sample mixtures (https:// precision.fda.gov/challenges/3/view/results) and c) improvement of friend recommendations in geosocial networks by using it to compare users' movement history 49,50 .
These results stimulate questions about the biological significance of genes sharing a common expression pattern, including the similarity between other regulatory regions besides proximal promoters in terms of TFBSs and epigenetic markers. This ML framework can also be applied to predict target genes for other TFs and in other cell lines, depending on the availability of corresponding knockdown data.
There are a number of limitations of our approach. The Bray-Curtis function seems unable to accurately measure the similarity between the tissue-wide expression profiles of a gene (e.g. MIR23A) without any detectable mRNA in any tissues and genes that are expressed in at least one tissue (e.g. ubiquitously expressed NR3C1 and stomach-specific PGA3). Intuitively, PGA3 is more similar to MIR23A than NR3C1; however, the Bray-Curtis similarity indicates that both PGA3 and NR3C1 are equally dissimilar to MIR23A. The finite number of TFs analyzed is another possible limitation in the prediction of genes with similar expression profiles. This was due to a lack of iPWMs for other TFs that were knocked down. Given that 2000-3000 sequence-specific DNA-binding TFs are estimated to be encoded in the human genome 51 , the CRMs of many genes under concerted regulation by different TFs will likely reveal complex circuitry that is currently unknown. For example, the iPWMs for several TFs (CREB, MYB, NF1, GRF1) that bind to the NR3C1 gene promoter to activate or repress its expression could not be successfully derived from ChIP-seq data 3,30 . Regarding the CRISPR-generated knockdown data, positives were inferred to be direct targets by intersecting their promoters with corresponding ChIP-seq peaks. This may not be completely accurate, due to the presence of noise peaks that do not contain true TFBSs 3,52,53 . Small fold changes in the expression levels of DE targets could arise from inefficient knockdown due to suboptimal guide RNAs or to limitations of perturbing only a single allele encoding the TF 54 . Finally, the framework presented considers only the 10 kb interval proximal to the TSS. This could not capture long range enhancer effects beyond this point; a potential way of remediating this would be to incorporate correlation-based approaches that have successfully incorporated multiple definitions of promoter length 15 .

Conclusions
We have developed a ML framework with a combination of information theory-based TF binding profiles of the spatial distribution and information contents of TFBS clusters, ChIP-seq and chromatin accessibility data. This framework distinguishes tissue-wide expression profiles of similar vs dissimilar genes (originally defined by the Bray Curtis function) and identified TF targets. Functional binding sites in target genes that significantly alter expression levels upon direct binding are at least partially distinguished by TF-cofactor coregulation from non-functional sites in non-targets. Finally, in-silico mutation analyses suggested that the presence of multiple information-dense clusters in a target gene promoter is capable of mitigating the effects of deleterious mutations that can significantly alter TF-regulated expression levels. Additional file 1. The mathematical definitions of the four other similarity metrics, the workflow of the IDBC algorithm, an example feature vector, the mathematical definitions of five statistical variables to measure classifier performance, the default parameter values of classifiers in MATLAB, and histograms visualizing the first two criteria for selecting positives from the CRISPR-generated knockdown data.
Additional file 2: The lists of positives and negatives in the ML classifiers to predict genes with similar tissue-wide expression profiles to NR3C1.
Additional file 3: The lists of positives and negatives in the DT classifier to predict TF targets based on the CRISPR-generated knockdown data.
Additional file 4: The lists of positives and negatives in the DT classifier to predict DE direct targets based on the siRNA-generated knockdown data.
Additional file 5: The performance of the DT classifier using only TFBS counts, accuracy of each round of 10-fold cross validation, and Gini importance values of the ML features.
Additional file 6: The list of the most similar 500 PC genes to each TF in terms of tissue-wide expression profiles, and the intersection of these 500 genes and target genes of the TF.
Additional file 7: Cofactor binding sites adjacent to YY1 and EGR1 sites in the promoters of their targets and non-targets.
Additional file 8: The percentages of positives and negatives whose promoters do not overlap DHSs for the CRISPR-perturbed TFs.
Data are available under the terms of the Creative Commons Zero "No rights reserved" data waiver (CC0 1.0 Public domain dedication).

Software availability
Source code implementing the ML framework, including generating the figures in this article, is available at: https:// bitbucket.org/cytognomix/information-dense-transcriptionfactor-binding-site-clusters/.
License: GNU General Public License 3.0. In this manuscript, Ru and Rogan use Bray-Curtis Similarity and several machine-learning algorithms to identify genes that have similar expression patterns. They use transcription factor binding sites within promoter regions and DNA accessibility data to train their models. This is a very important question and the authors propose an interesting mechanistic approach to address it. Nevertheless, there are several limitations that need to be addressed.

Specific comments:
While the grammar is at a good level, the way the information is presented makes the text very difficult to read. Some sentences are very long and there are many notations. One suggestion is to move some of the less important parts in the Supplementary Material. On page 3 in the introduction, the authors claim that signal strength of ChIP-seq peaks are not strictly proportional to TF binding strength. This is not always true and we showed in that in fact the number of TF molecules controls the height of the ChIP-seq peak. On page 5, it is not clear why the authors talk of Features 1-3, since it seemed they had 7 features. The way the machine learning information is presented should be improved. The authors test Naïve Bayes, Decision Tree, Random Forest and SVM. I was wondering if they consider also Neural Networks. They don't need to implement that now, but they should at least mention what was behind their selection for the machine-learning algorithms. One of the main findings is that DNA accessibility improves predictions, because it masks potential TF binding sites. This is something that was previously showed in the context of TF binding to the genome by us and other scientists (e.g. References 1,2,3). Figure 4 needs re-plotting (e.g. x axis labels do not fit the figure). In the discussion, none of the statements are referred back to any of the figures in the results section. This makes the reading difficult. The lower performance for YY1 needs to be better explained. The authors claim that this could be explained by lower percentage of negatives in inaccessible promoters. Are there other examples of TFs displaying similar features? What is their performance? One of the main limitations of the manuscript is that the authors use only 82 TFs and claim that there are no iPWM for others. Have they tried to use MotifDB (https://bioconductor.org/packages/release/bioc/html/MotifDb.html), which has approximately 1000 PWMs for human TFs? When talking about the accuracy of the ChIP-seq signal, they could also reference this paper .

If applicable, is the statistical analysis and its interpretation appropriate? Yes
Are all the source data underlying the results available to ensure full reproducibility? Yes

Are the conclusions drawn adequately supported by the results? Partly
No competing interests were disclosed.

I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
Author Response 25 Mar 2019 , University of Western Ontario, Canada Peter Rogan : While the grammar is at a good level, the way the information is presented makes the Comment 1 text very difficult to read. Some sentences are very long and there are many notations. One suggestion is to move some of the less important parts in the Supplementary Material.
: The manuscript has been extensively edited to improve clarity of the presentation. Response Sentence lengths have been reduced. Duplicate terms and text have been eliminated. All abbreviations have been defined. Two paragraphs have been moved to the Supplementary Methods. The revised manuscript has been shortened by 400 words and approximately 2 pages. : On page 3 in the introduction, the authors claim that signal strength of ChIP-seq Comment 2 peaks are not strictly proportional to TF binding strength. This is not always true and we showed in that in fact the number of TF molecules controls the height of the ChIP-seq peak. : In (1), it was discovered that signal strengths of ChIP-seq peaks are not strictly Response proportional to strengths ( values) of the strongest TFBSs contained in the peaks. The finding in R (2) provides a complementary explanation about the determinants of signal strengths of ChIP-seq peaks, which is that 'the number of TF molecules controls the height of the ChIP-seq peak'. Therefore, this sentence is revised to "Because signal strengths of ChIP-seq peaks are not strictly proportional to strengths of the contained strongest TFBSs and are instead controlled by TFBS counts [3, 10], representing…".
: On page 5, it is not clear why the authors talk of Features 1-3, since it seemed they Comment 3 had 7 features. The way the machine learning information is presented should be improved.
: In this sentence, we would like to make it easier for readers to understand the Response generation of classifier predictors, by explaining how the seven high-level features were transformed to low-level predictors that were directly input into the classifiers. Therefore, this sentence was revised to "Each of the Features 1-3 was defined in a gene as a vector, whose size equals the number of clusters in the gene promoter; each cluster was mapped to a single value in the vector. In Features 4-7, each cluster itself was mapped to a vector corresponding to binding sites for 82 TFs (Additional file 1)." Also, Section 5 of Additional file 1 gives a specific example about the predictor vector of a gene instance.
: The authors test Naïve Bayes, Decision Tree, Random Forest and SVM. I was Comment 4 wondering if they consider also Neural Networks. They don't need to implement that now, but they should at least mention what was behind their selection for the machine-learning algorithms.
: We did not select Neural Networks due to two considerations. First, it requires much Response more data to train than traditional machine learning algorithms, as in at least thousands if not millions of labeled samples (3). In this study the numbers of both positives (i.e. protein-coding genes with similar tissue-wide expression profiles to ) and negatives (i.e. dissimilar genes) NR3C1 are 500, which is insufficient to apply Neural Networks. Second, it is more computationally expensive than traditional algorithms (4).
: One of the main findings is that DNA accessibility improves predictions, because it Comment 5 masks potential TF binding sites. This is something that was previously showed in the context of TF binding to the genome by us and other scientists (e.g. References 1,2,3).
: Accordingly, in this revision, the last sentence of the second subsection of the Results Response section was revised to "Consistent with previous findings (2, 5, 6), inclusion of DHS information significantly improved AUC values of the other classifiers with the exception of Naïve Bayes.". And in the second paragraph of the Discussion section, the second sentence was revised to "This intersection eliminated noisy binding sites that are inaccessible to TF proteins in promoters (2, 5, 6),…" : Figure 4 needs re-plotting (e.g. x axis labels do not fit the figure).

Comment 6
: In this revision, Figure 4 was replotted to fix this issue. Response : In the discussion, none of the statements are referred back to any of the figures in the Comment 7 results section. This makes the reading difficult.
: In the first paragraph of the Discussion section of this revision, references to the Response figures in the Results section were added to the following sentences, "In this study, the Bray-Curtis 1 i figures in the Results section were added to the following sentences, "In this study, the Bray-Curtis similarity function was initially shown (for the NR3C1 gene) to measure the relatedness of overall expression patterns between genes across a diverse set of tissues (Figure 2). A ML framework distinguished similar from dissimilar genes based on the distribution, strengths and compositions of TFBS clusters in accessible promoters, which can substantially account for the corresponding gene expression patterns (Figures 1 & 3). Using gene expression knockdown data, the combinatorial use of TF binding profiles and chromatin accessibility was also demonstrated to be predictive of TF targets (Figure 4, Tables 2 & 3). A binding site comparison confirmed that coregulatory cofactors can be used to distinguish between functional sites in targets and non-functional ones in non-targets. Furthermore, in silico mutation analyses on binding sites of targets suggested that the existence of both multiple TFBSs in a cluster and multiple information-dense clusters in the same promoter enables both the cluster and the promoter to be resilient to mutations in individual TFBS ( Figure 5, Table 5)." In the third paragraph, references to the figures in the Results section were added to the following sentence, "Mutation analyses revealed that some deleterious TFBS mutations could be compensated for by other information-dense clusters in the same promoter ( Figure 5, Table 5)" : The lower performance for YY1 needs to be better explained. The authors claim that Comment 8 this could be explained by lower percentage of negatives in inaccessible promoters. Are there other examples of TFs displaying similar features? What is their performance?
: In this sentence, all the seven CRISPR-perturbed TFs were split into two sets; one Response consisting of only YY1, the other consisting of the remaining six TFs. This sentence was comparing the performances of the Decision Tree classifiers on these two TF sets. Seen from Table 3, the classifier's performance on YY1 was markedly lower than that on the other six TFs after intersecting promoters with DHS sites, which is due to the fact that YY1 has a smaller percentage of negatives with inaccessible promoters. To make this clearer, in this revision, this sentence was revised to "Compared to the other six TFs, the poorer performance of the classifier on YY1 (Table 2) is attributable to …" : One of the main limitations of the manuscript is that the authors use only 82 TFs and Comment 9 claim that there are no iPWM for others. Have they tried to use MotifDB (https://bioconductor.org/packages/release/bioc/html/MotifDb.html), which has approximately 1000 PWMs for human TFs?
: We selected to use these 94 iPWMs of 82 TFs that were derived from ENCODE Response ChIP-seq datasets using entropy minimization in (1), since we want to ensure the high quality of the iPWMs used in the analyses.
Compared to the MotifDB PWMs, the reliability and accuracy of these iPWMs were extensively and independently validated using four methods, including detection of experimentally proven binding sites, explanation of effects of characterized SNPs, comparison with previously published motifs and statistical analyses.
These iPWMs were used to scan for 803 experimentally confirmed TFBSs, and there was complete concordance between these true binding sites and those detected with the iPWMs, both in terms of their locations and relative strengths (1). And these iPWMs were further used to explain the experimentally observed effects of 153 SNPs on binding site strengths, based on the changes in the values. For 130 SNPs (∼85.0%), the predictions of the iPWMs and the experimental R observations are completely concordant; for 16 SNPs (∼10.5%), the predicted and observed experimental findings are concordant, but the extents of these changes differ (e.g. TF binding is i experimental findings are concordant, but the extents of these changes differ (e.g. TF binding is predicted to only be weakened, but binding was completely abolished in experiments); for only 7 SNPs (∼4.6%), the predicted and observed experimental changes were discordant.
The PWMs in MotifDB are not information theory-based (i.e. not iPWMs). Instead, they are given in the form of count matrices or frequency matrices. The performance of the iPWMs that used in the present study has been shown to outperform other PWM-based approaches for binding site detection and quantification (7).
: When talking about the accuracy of the ChIP-seq signal, they could also reference Comment 10 this paper .
: In this revision, the reference was added to the following sentence in the last Response paragraph of the Discussion section, "Regarding the CRISPR-generated knockdown data, positives were inferred to be direct targets by intersecting their promoters with corresponding ChIP-seq peaks. This may not be completely accurate, due to the presence of noise peaks that do not contain true TFBSs ."

Daphne Ezer
The Alan Turing Institute for Data Science, London, UK I think that this is an interesting paper that should be published. Often, gene expression patterns are clustered and TF binding sites are used as features to build a classifier for identifying the cluster to which those genes belong or similar schemes such as clustering TFs and gene expression together-see Clements et al and Berman et al . However, a biologist may want to identify what TFs regulate a specific gene of interest. They could then use the 'Bray-Curtis Similarity' index to find a set of genes whose expression pattern is similar to their gene of interest. Then, they can use the pipeline presented here to identify features that are predictive of this kind of gene expression pattern.
They also create a scheme to test how different combinations of features from different experiments influence their predictions.
I think that the text would garner much more interest if it focused more on the research questions that are being addressed. The method details are discussed in depth, but the big picture is hard to find amidst the details.

Main points:
One of the main things that bothers me about the Bray-Curtis Similarity metric is that it seems to assume that tissues are independently sampled. However. we see from Fig.1 that there are many brain samples that seem to (at least in the three genes shown) have similar gene expression values. Is there a lot of covariance between gene expression values in pairs of tissues? If so, is there a way to adjust this metric to acknowledge stratification of the tissues. I don't think that the whole paper needs to be re-written with a new metric, but it would be nice if the authors address this directly. Another issue I have is with this metric is that it uses RPKM gene expression values in the Bray-Curtis Similarity metric. Imagine that two genes have extremely high gene expression values in some tissue (like the brain) and low values in another tissue (like the pancreas). However, one of these genes is always expressed at 10 times the level of the other gene. Lets say that a third gene has almost no change of gene expression value across the tissues but has a mean RPKM that is similar to the first gene's mean RPKM. Would the Bray-Curtis SImilarity metric say that gene 1 and 2 are more similar? Or gene 1 and 3? If gene 1 and 3, then this might be resolved by comparing z-scores or otherwise normalising gene expression values across tissues. Every time a machine learning method is named, it should be clear: (1)  : One of the main things that bothers me about the Bray-Curtis Similarity metric is that Comment 1 it seems to assume that tissues are independently sampled. However. we see from Fig.1 that there are many brain samples that seem to (at least in the three genes shown) have similar gene expression values. Is there a lot of covariance between gene expression values in pairs of tissues? If so, is there a way to adjust this metric to acknowledge stratification of the tissues. I don't think that the whole paper needs to be re-written with a new metric, but it would be nice if the authors address this directly.
: There are 13 brain tissues among all the 53 tissues investigated by GTEx. Admittedly, Response genes tend to exhibit closer expression values between some of these brain tissues; for example, seen from Figure 2, the gene has close, low expression values in multiple brain tissues NR3C1 (Amygdala, Anterior cingulate cortex (BA24), Caudate (basal ganglia), etc).
To investigate how much this covariance can influence similarity values between tissue-wide expression profiles of genes computed by the Bray-Curtis function, using the brain tissues as an example, we retained only one brain tissue and removed all other brain tissues at one time, and recomputed the Bray-Curtis similarity values between and all other protein-coding genes. NR3C1 Thus, there are 13 variant cases due to the presence of 13 brain tissues. Then we compared the resultant set of 500 most similar genes in each variant case to that when all 53 tissues were used (given in Additional file 2).
All of the top 100 most similar genes when using all 53 tissues were among the top 500 genes in every variant case. The top 200 genes when using all 53 tissues differed by 0-3 genes from the top 500 genes in variant cases. The top 500 genes when using all 53 tissues differed by approximately 22% (112-117) from top 500 genes in variant cases. This suggests that the increased number of brain tissues does not significantly influence the results of the Bray-Curtis metric for the most similar genes but does affect results at lower similarity threshold.
Especially, in all 14 cases (i.e. the 13 variant cases and using all 53 tissues), the three most similar genes to are the same ( , , ). Therefore, this covariance between NR3C1 SLC25A32 TANK CDC27 these brain tissues is not a dominant factor in identifying genes with similar tissue-wide expression profiles to a particular gene using the Bray-Curtis Function.
On the other hand, the situation is also present that a gene has closer expression values between two tissues from two different organs, than between two more similar tissues from the same organ. For example, both the Cerebellar Hemisphere (CH) tissue and the Amygdala tissue are from the brain; the Visceral Adipose (VA) tissue and the Adrenal Gland (AG) tissue are not. Seen from Figure 2, for the gene's expression, there is a larger difference between CH and NR3C1 Amygdala. Instead, CH is closer to VA, whereas Amygdala is closer to AG.
Despite well established developmental lineages for these tissues, we prefer not to make assumptions regarding the covariance in expression values between similar tissues from the same organ. The null hypothesis should not discriminate between tissues or weight them differently, without explicit prior information about tissue-specific expression, which is what we are trying to organ. The null hypothesis should not discriminate between tissues or weight them differently, without explicit prior information about tissue-specific expression, which is what we are trying to measure. For this reason, when computing similarity values between tissue-wide expression profiles of genes using the Bray-Curtis Function or other metrics, it may be more appropriate to assign the same weight to every tissue and treat every tissue equally.
: Another issue I have is with this metric is that it uses RPKM gene expression values Comment 2 in the Bray-Curtis Similarity metric. Imagine that two genes have extremely high gene expression values in some tissue (like the brain) and low values in another tissue (like the pancreas). However, one of these genes is always expressed at 10 times the level of the other gene. Lets say that a third gene has almost no change of gene expression value across the tissues but has a mean RPKM that is similar to the first gene's mean RPKM. Would the Bray-Curtis SImilarity metric say that gene 1 and 2 are more similar? Or gene 1 and 3? If gene 1 and 3, then this might be resolved by comparing z-scores or otherwise normalising gene expression values across tissues. Then the Bray-Curtis similarity value between Gene 1 and Gene 2 is: 2/11. sim (G1,G2) = The Bray-Curtis similarity value between Gene 1 and Gene 3 is: However, this is not unreasonable. In other words, this is not a problem, thus it does not need to be resolved. There is no ground-truth relationship between and . The sim (G1, G2) sim (G1,G3) reason is described below.
When measuring the similarity between two vectors, there are two factors to be considered: 1. the sizes of the vectors (i.e. the distance between the two vectors), 2. the directions of the vectors (i.e. the angle between the two vectors). In this context of measuring similarity between tissue-wide expression values of genes (each gene is mapped to a vector), both factors matter.
It is stated in the Methods section that Bray-Curtis Similarity satisfies three desirable properties. In fact, Property 2 (achieving the maximal similarity value 1 if and only if two vectors are identical) ensures Factor 1 to be considered, and Property 3 (larger values having a larger impact on the resultant similarity value) ensures Factor 2 to be considered.
Thus, Table 1 shows that Bray-Curtis Similarity is more appropriate than the other five metrics, which is exactly due to the fact it takes both factors into account. In contrast, Euclidean Similarity does not take vectors' directions into account; Cosine Similarity, Pearson Correlation and Spearman Correlation do not take the sizes of the vectors into account.
Thus, to be able to infer a ground-truth similarity relationship, on both Factor 1 and Factor 2 the intuitive comparison results must be concordant. In Example 1 (see Additional File 1), the angle between Gene and Gene is identical to that between Gene and Gene , and the distance A C B C between and is larger than that between and ; thus, . Similarly, the A C B C sim (A,C) < sim (B,C) distance between and is identical to that between and , and the angle between and is distance between and is identical to that between and , and the angle between and is A D E F A D larger than that between and ; thus, .

E F sim(A,D) < sim(E,F)
But in this case, the distance between Gene 1 and Gene 2, i.e. 9*sqrt( ), is larger than that a + b between Gene 1 and Gene 3, i.e. ( )/sqrt(2), but the angle between Gene 1 and Gene 2 (i.e. 0) is b-a smaller than that between Gene 1 and Gene 3 (>0). Thus, a ground-truth similarity relationship is unable to be inferred. Thus, the result given by Bray-Curtis Similarity, i.e.
: Every time a machine learning method is named, it should be clear: (1) what are the Comment 3 input features (ii) what are the labels --i.e. what is being classified (iii) what is the cross-validation or training-testing-validation scheme. Since there are so many machine learning things being done, it is hard sometimes to make sense of what is being done in each specific case.
: In the module to predict genes with similar tissue-wide expression profiles to a Response particular gene, to make these points clearer, the following changes were made: (i) Using the red color Figure 1A shows that seven features were derived from TFBS clusters. In addition, in the legend of Figure 1A, the following sentence was added "The seven ML features derived from TFBS clusters were described in the Methods section." The second paragraph of the second subsection of the Methods section details the seven features; its first sentence was revised to "The seven information density-related ML features derived from each TFBS cluster included …" (ii) The first sentence of the 'Prediction of genes with similar tissue-wide expression profiles" subsection of the Methods section was revised' to 'The framework for predicting whether the tissue-wide expression profile of a gene resembles a particular gene is indicated in Figure 1A, B.", so that it is clear that the two labels are 'similar to the particular gene' and 'dissimilar to the particular gene'. In addition, Figure 1B also indicates that 500 most similar genes and 500 most dissimilar genes were selected as positives and negatives.
(iii) The last step ('Performance evaluation') of Figure 1A was revised to 'Performance evaluation (ROC curve/10-fold cross validation)'; the red color indicates that ROC curves were used to validate the classifiers in this module. In addition, the last sentence of the legend of Figure 1A was revised to "The performance of ML classifiers was evaluated with ROC curves and 10-fold cross validation".
The last sentence of the second subsection of the Methods section was revised to "This allowed all genes to be used as training data for ML classifiers. Default parameter values for these classifiers were used to generate ROC curves in MATLAB", and also the first sentence of the corresponding second subsection of the Results section was revised to "Several ML classifiers (Naïve Bayes, Decision Tree (DT), Random Forest and Support Vector Machines (SVM) with four different kernels) were evaluated to determine how well TFBS-related features could predict genes with tissue-wide expression profiles similar to NR3C1. Their performance were compared using ROC curves…". Thus, it is now clear that ROC curves were used to validate the classifiers and all instances were used as training data (i.e. there were no test sets).
In the module to predict TF target genes, to make these points clearer, the following changes were made: (i) Using the blue color Figure 1A shows that six features were derived from TFBS clusters. Also, 2 2 BC BC (i) Using the blue color Figure 1A shows that six features were derived from TFBS clusters. Also, the penultimate sentence of the last paragraph of the "Using gene expression in the CRISPR-based perturbations" subsection of the Methods section states "Six features (Features 1-5 and 7) were derived from each homotypic cluster (i.e. Feature 6 became identical to Feature 3, because only binding sites from a single TF were used) ( Figure 1A).". Combining with the detailed descriptions about what the features are in the second paragraph of the previous subsection, it is clear that these six features (Features 1-5 and 7) were used.
(ii) The last sentence of the first paragraph of the 'Using gene expression in the CRISPR-based perturbations" subsection of the Methods section was revised to "We defined a positive TF target gene in a cell line as:…" And the sentence in the fifth paragraph was revised to "If the coefficients of all guide RNAs of the TF for a gene are zero, the gene was defined as a negative (i.e. a non-target gene)." Thus it is clear that the two labels are "TF target genes" and "non-target genes". Combining with the last sentence of the first paragraph of the Methods section, 'Since protein-coding (PC) sequences represent the most widely studied and best understood component of the human genome [19], positives and negatives for deriving machine learning classifiers for predicting DE direct TF target genes that encode proteins (TF targets, below) were obtained from CRISPR-and siRNA-generated knockdown data', it is clear that the 'target genes' here stands for 'PC, direct, DE target genes'.
(iii) As stated above, the last step ('Performance evaluation') of Figure 1A was revised to 'Performance evaluation (ROC curve/10-fold cross validation)'; the blue color indicates that 10-fold cross validations were used to validate the classifiers in this module. In addition, the last sentence of the legend of Figure 1A was revised to "The performance of ML classifiers was evaluated with ROC curves and 10-fold cross validation". The last sentence of the last paragraph of the "Using gene expression in the CRISPR-based perturbations" subsection of the Methods section was revised to "The results of 10 rounds of 10-fold cross validation were averaged to evaluate the accuracy of the classifier." Thus it is clear that the validation scheme is 10-fold cross validation.
: For the method described in (B) in Fig 1: Does it necessarily make sense to compare Comment 4 the 'most similar' to the 'least similar'? Genes that have exactly the opposite gene expression pattern to the one you are interested might be tightly regulated by a different set of TFs. You might be picking up this signal instead of the one you care about! This might be an even bigger issue since you are using raw gene expression values--genes that are very highly or very lowly expressed in all tissues might always come up in your negative set.: : Yes, it makes sense. As stated in the above response to Comment 3, in this module to Response predict genes with similar tissue-wide expression profiles to a particular gene, the two labels are 'similar to the given gene' and 'dissimilar to the given gene'. Therefore, it makes the most sense that the most similar genes were selected as positives and the most dissimilar genes were selected as negatives.
The first sentence of the last paragraph of the Background section, "…the distribution and composition of -regulatory modules in promoters substantially determines gene expression cis profiles…, is exactly the underlying rationale why this machine learning framework is able to distinguish between "similar genes" and "dissimilar genes". In other words, "similar genes" and "dissimilar genes" have different expression patterns, presumably because they have different organizations and compositions (i.e. different TF sets) of TFBSs in their promoters. Therefore, the potential fact that "similar genes" and "dissimilar genes" are regulated by different TF sets was exactly what we expected to see and validate. exactly what we expected to see and validate.
: Biologists don't just want good classifiers, they want feature selection! Can you show Comment 5 the Gini scores of the features in a supplemental table?: : In the module to predict TF target genes based on CRISPR-and siRNA-generated Response knockdown data, to assess the relative importance of the six features to the Decision Tree classifiers, we computed their Gini importance values, which are added to Additional file 5.
For the seven CRISPR-perturbed TFs in the K562 cell line, the cluster-level Features 1-3, especially Feature 3 capturing the information density of TFBS clusters, have the largest contribution to the classifiers' predictive power. By contrast, for the 11 siRNA-perturbed TFs in the GM19238 cell line, the binding site-level Feature 5 capturing the spatial distribution of strong TFBSs has the largest contribution.
Accordingly, in this revision, this observation is described in the second and third sentences of the first paragraph of the third subsection of the Results section.
: Is all the code for generating every figure available online? Let's help make research Comment 6 reproducible.
: As stated in the Software availability section, the code that implemented this machine Response learning framework and produced all the results has been deposited at https://bitbucket.org/cytognomix/information-dense-transcription-factor-binding-site-clusters/src and . The input of the code to derive the figures is directly https://doi.org/10.5281/zenodo.1892051 taken from the output of the ML framework code. There are no intermediate steps or variable required to generate the figures in MATLAB.
The code for generating the figures is used to visualize the results. in this revision, we also deposited the MATLAB code for generating all the figures at https://bitbucket.org/cytognomix/information-dense-transcription-factor-binding-site-clusters/src : If you have 10 values (from cross validation), why don't you show them all in Figure 4 Comment 7 so we can evaluate the spread.
: To avoid making Figure 4 too complicated, in this revision, the accuracy values of all Response individual rounds of 10-fold cross validations in prediction of TF target genes were added to Additional file 5. Accordingly, the legends of Table 2, Figure 4 and Table 3 were revised to indicate this.
: "Our in-silico mutation analyses revealed that some deleterious TFBS mutations Comment 8 could be compensated for by other information-dense clusters in the same promoter(2); thus, predicting the effects of mutations in individual binding sites might not be sufficient to interpret downstream effects without considering their context." This is something that me and my collaborators have recently studied3. Don't feel pressure to add this citation--I just thought it would be interesting for you to read! (Also, thanks for discussing IDBC in this paper--I hadn't heard of it before but it would be relevant to my research.) : In this revision, this publication has now been referenced (number 47) in the Response manuscript. manuscript.
: It would be great if you discussed how Bray-Curtis is used in other fields in the Comment 9 Discussion.
:The following sentences were added to the penultimate paragraph, "Previous Response applications of this index include: a) measurement of the ecological transfer of species abundance from dense to sparse plots and comparative difference analyses of species quantities between reference and algorithm-derived metagenomic sample mixtures ( ). b) improvement of friend recommendation in https://precision.fda.gov/challenges/3/view/results geosocial networks by using it to compare users' movement history .." : Better subsection names in the results section -emphasizing the biological Comment 10 conclusions rather than what was done.
: In the Results section of this revision, the title of each subsection was revised as Response follows, now summarizing the primary conclusion from this subsection.
The title of the first subsection was revised from 'Similarity between GTEx tissue-wide expression profiles of genes' to 'The Bray-Curtis Function can accurately quantify the similarity between tissue-wide gene expression profiles'.
The title of the second subsection was revised from 'Prediction of genes with similar GTEx tissue-wide expression profiles' to 'The Decision Tree classifier performed best in prediction of genes with similar tissue-wide expression profiles'.
The title of the third subsection was revised from 'Prediction of TF targets" to 'The Decision Tree classifier was predictive of TF target genes'.
The title of the fourth subsection was revised from 'Intersection of genes with similar tissue-wide expression profiles and TF targets' to 'Some TF target genes also display similar tissue-wide expression profiles to the TFs, themselves.
The title of the fourth subsection was revised from 'Mutation analyses on promoters of direct targets' to 'Transcription factor binding site clusters buffer against expression changes from mutations in single sites'. none

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