A set of methods is presented for normalization, quantification of noise and co-expression analysis for gene expression studies using deep sequencing. With the advent of ultra high-throughput sequencing technologies, increasingly researchers are turning to deep sequencing for gene expression studies. Here we present a set of rigorous methods for normalization, quantification of noise, and co-expression analysis of deep sequencing data. Using these methods on 122 cap analysis of gene expression (CAGE) samples of transcription start sites, we construct genome-wide 'promoteromes' in human and mouse consisting of a three-tiered hierarchy of transcription start sites, transcription start clusters, and transcription start regions. In recent years several technologies have become available that allow DNA sequencing at very high throughput - for example, 454 and Solexa. Although these technologies have originally been used for genomic sequencing, more recently researchers have turned to using these 'deep sequencing' or '(ultra-)high throughput' technologies for a number of other applications. For example, several researchers have used deep sequencing to map histone modifications genome-wide, or to map the locations at which transcription factors bind DNA (chromatin immunoprecipitation-sequencing (ChIP-seq)). Another application that is rapidly gaining attention is the use of deep sequencing for transcriptome analysis through the mapping of RNA fragments -4.MmeI. Recent development of the deepCAGE protocol employs the EcoP15 enzyme, resulting in approximately 27-nucleotide-long sequences. The 'CAGE tags' thus obtained can then be sequenced and mapped to the genome. In this way a genome-wide picture of transcription start sites (TSSs) at single base-pair resolution can be obtained. In the FANTOM3 project [An alternative new high-throughput approach to gene expression analysis is cap analysis of gene expression (CAGE) sequencing . CAGE is project  this appThere are several advantages that deep-sequencing approaches to gene expression analysis offer over standard micro-array approaches. First, large-scale full-length cDNA sequencing efforts have made it clear that most if not all genes are transcribed in different isoforms owing both to splice variation, alternative termination, and alternative TSSs . One of However, whereas for micro-arrays there has been a large amount of work devoted to the analysis of the data, including issues of normalization, noise analysis, sequence-composition biases, background corrections, and so on, deep sequencing based expression analysis is still in its infancy and no standardized analysis protocols have been developed so far. Here we present new mathematical and computational procedures for the analysis of deep sequencing expression data. In particular, we have developed rigorous procedures for normalizing the data, a quantitative noise model, and a Bayesian procedure that uses this noise model to join sequence reads into clusters that follow a common expression profile across samples. The main application that we focus on in this paper is deepCAGE data. We apply our methodology to data from 66 mouse and 56 human CAGE-tag libraries. In particular, we identify TSSs genome-wide in mouse and human across a variety of tissues and conditions. In the first part of the results we present the new methods for analysis of deep sequencing expression data, and in the second part we present a statistical analysis of the human and mouse 'promoteromes' that we constructed.et al. [The first step in the analysis of deep-sequencing expression data is the mapping of the (short) reads to the genome from which they derive. This particular step of the analysis is not the topic of this paper and we only briefly discuss the mapping method that was used for the application to deepCAGE data. CAGE tags were mapped to the human (hg18 assembly) and mouse (mm8 assembly) genomes using a novel alignment algorithm called Kalign2  that mapet al.  was emplet al. , this maOnce the RNA sequence reads or CAGE tags have been mapped to the genome we will have a  collection of positions for which at least one read/tag was observed. When we have multiple samples we will have, for each position, a read-count or tag-count profile that counts the number of reads/tags from each sample, mapping to that position. These tag-count profiles quantify the 'expression' of each position across samples and the simplest assumption would be that the true expression in each sample is simply proportional to the corresponding tag-count. Indeed, recent papers dealing with RNA-seq data simply count the number of reads/tags per kilobase per million mapped reads/tags . That ist and on the vertical axis the number of TSS positions to which at least t tags map. As the figure shows, the distributions of tags per TSS are power-laws to a very good approximation, spanning four orders of magnitude, and the slopes of the power-laws are a very similar across samples. These samples are all from THP-1 cells both untreated and after 24 hours of phorbol myristate acetate (PMA) treatment. Very similar distributions are observed for essentially all CAGE samples currently available (data not shown).For our CAGE data the mapped tags correspond to TSS positions. Figure 4 tags, that is, close to 1% of all tags in the sample. Manual inspection confirms that these correspond to TSSs of genes that are likely to be highly expressed, for example, cytoskeletal or ribosomal proteins. It is quite remarkable in the opinion of these authors that both low expression background transcription, whose occurrence is presumably mostly stochastic, and the expression of the highest expressed TSSs, which is presumably highly regulated, occur at the extremes of a common underlying distribution. That this power-law expression distribution is not an artifact of the measurement technology is suggested by the fact that previous data from high-throughput serial analysis of gene expression (SAGE) studies have also found power-law distributions [Drosophila shows that the number of reads per position follows an approximate power-law distribution as well . These observations strongly suggest that RNA expression data generally obey power-law distributions. The normalization procedure that we present here should thus generally apply to deep sequencing expression data.The large majority of observed TSSs have only a very small number of tags. These TSSs are often observed in only a single sample, and seem to correspond to very low expression 'background transcription'. On the other end of the scale there are TSSs that have as many as 10ibutions . For ChIibutions . In addiFor each sample, we fitted  the reverse-cumulative distribution of tags per TSS to a power-law of the form:n0 the inferred number of positions with at least t = 1 tag and α the slope of the power-law. Figure n0 and α for all 56 human CAGE samples.with n0 varies significantly with the depth of sequencing; that is, the dots on the right are from the more recent samples that were sequenced in greater depth. In contrast, the fitted exponents vary relatively little around an average of approximately -1.25, especially for the samples with large numbers of tags.We see that, as expected, the inferred number of positions α = -1.25 and, for convenience, we chose the offset n0 such that the total number of tags is precisely 1 million. We then used the fits for all samples to transform the tag-counts into normalized 'tags per million' (TPM) counts . Figure In the analysis of micro-array data it has become accepted that it is beneficial to use so-called quantile normalization, in which the expression values from different samples are transformed to match a common reference distribution . We follAlthough the changes that this normalization introduces are generally modest, the collapse of the distributions shown in Figure In the remainder we will use the normalized tag counts to compare the expression at individual positions in the genome across samples. We also retain the raw tag-counts because, as we will see below, the noise on the observed tag count depends on these raw counts.In order to analyze expression profiles, it is necessary to analyze the distribution of the noise on deepCAGE and other deep-sequencing expression measurements. To our knowledge, such an analysis has not yet been performed. Instead of determining noise on expression measurements, existing work has focused on defining models of the background distribution of tags/reads, which can be used to identify regions that have significantly more mapped tags/reads than expected from the background model. These background models assume that the number of tags in a given region follows either a simple Poisson distribution, or a Poisson distribution with gamma-distributed rate .To quantitatively investigate the noise in the expression measurements, we compared tag-counts across replicate data-sets. Among the currently available CAGE data-sets there is one pair in which two libraries were prepared from a common mRNA sample and Figure e4 ≈ 55), the scatter has an approximately constant width whereas at low TPM the width of the scatter increases dramatically. This kind of funnel shape is familiar from micro-array expression data where the increase in noise at low expression is caused by the contribution of non-specific background hybridization. However, for the deepCAGE data this noise is of an entirely different origin.The figure shows that, at high TPM  is given by:where the variance σ2) plus one over the raw number of measured tags. The approximation (Equation 3) breaks down for n = 0. The probability to obtain n = 0 tags is approximately given by :That is, the measured log-TPM is a Gaussian whose mean matches the log-TPM in the input sample, with a variance equal to the variance of the multiplicative noise  and find σ2 = 0.085. To illustrate the impact of the normalization, determining σ2 on the same unnormalized data-set, we obtained σ2 = 0.11, that is, a 29% increase in the apparent noise between the replicates. In addition to this replicate, among the human CAGE data-sets there is a time course of THP-1 cells after PMA treatment, measured in triplicate, which includes samples before PMA treatment and after only 1 hour of PMA treatment. Manual inspection shows that the correlation of tags per TSS for these two samples is as large as for the technical replicate. This makes sense because, on the time scale of 1 hour, the expression of most transcripts can probably not change appreciably [σ2 as well for the three 0/1 hour sample pairs. The values we estimate are, respectively, σ2 = 0.048, σ2 = 0.116, and σ2 = 0.058.We used the CAGE technical replicate  to estimate the variance reciably . Using aσ2 ranging from 0.048 to 0.116. Although this analysis provides some evidence that the size of the multiplicative noise varies between samples, the range of inferred values is small and we will make the assumption that σ2 is the same for all samples. As an estimate of σ2 we took an intermediate value of σ2 = 0.06 for the rest of our CAGE analysis.In summary, using four pairs of samples that are  replicates, we find estimates of We next validated this noise model as follows. According to our noise model, for TSSs that have non-zero expression in both samples, the z-statistic:m' the normalized expression at 1 hour and n' at zero hours, should be Gaussian distributed with standard deviation 1 . We tested this for the three biological replicates at 0/1 hour and for the technical replicate. Figure z-values for the four replicates.with z, that is, z < -4, which appears only for the 0/1 hour comparisons. These correspond to the small fraction of positions that are significantly up-regulated at 1 hour. In summary, Figure Although the data are noisy, it is clear that all three curves obey a roughly Gaussian distribution. Note the deviation from the theoretical curve at very low Drosophila mRNA samples that were sequenced using Solexa sequencing and estimated a value of σ2 = 0.073 for these replicate samples . This fitted value of σ2 is similar to those obtained for the CAGE samples.To verify the applicability of our noise model to RNA-seq data, we used two replicate data sets of σ2 values that we infer for the deep sequencing data are somewhat larger than what one typically finds for replicate expression profiles as measured by micro-arrays. However, it is important to stress that CAGE measures expression of individual TSSs, that is, single positions on the genome, whereas micro-arrays measure the expression of an entire gene, typically by combining measurements from multiple probes along the gene. Therefore, the size of the 'noise' in CAGE and micro-array expression measurements cannot be directly compared. For example, when CAGE measurements from multiple TSSs associated with the same gene are combined, expression profiles become significantly less noisy between replicates . This applies also to RNA-seq data .Finally, the Using the methods outlined above on CAGE data, we can comprehensively identify TSSs genome-wide, normalize their expression, and quantitatively characterize the noise distribution in their expression measurements. This provides the most detailed information on transcription starts and, from the point of view of characterizing the transcriptome, there is, in principle, no reason to introduce additional analysis.However, depending on the problem of interest, it may be useful to introduce additional filtering and/or clustering of the TSSs. For example, whereas traditionally it has been assumed that each 'gene' has a unique promoter and TSS, large-scale sequence analyses, such as performed in the FANTOM3 project , have maad hoc clustering method employed in the FANTOM3 analysis.These observations raise the question as to what an appropriate definition of a 'basal promoter' is. Should we think of each individual TSS as being driven by an individual 'promoter', even for TSSs only a few base-pairs apart on the genome? The answer to this question is a matter of definition and the appropriate choice depends on the application in question. For example, for the FANTOM3 study the main focus was to characterize all distinct regions containing a significant amount of transcription initiation. To this end the authors simply clustered CAGE tags whose genomic mappings overlapped by at least 1 bp . Since CBoth clustering methods just mentioned cluster CAGE tags based only on the overall density of mapped tags along the genome - that is, they ignore the expression profiles of the TSSs across the different samples. However, a key question that one often aims to address with transcriptome data is how gene expression is regulated. That is, whereas these methods can successfully identify the distinct regions from which transcription initiation is observed, they cannot detect whether the TSSs within a local cluster are similarly expressed across samples or that different TSSs in the cluster have different expression profiles. Manual inspection shows that, whereas there are often several nearby TSSs with essentially identical expression profiles across samples/tissues, one also finds cases in which TSSs that are only a few base-pairs apart show clearly distinct expression profiles. We hypothesize that, in the case of nearby co-expressed TSSs, the regulatory mechanisms recruit the RNA polymerase to the particular area on the DNA but that the final TSS that is used is determined by an essentially stochastic (thermodynamic) process. One could, for example, imagine that the polymerase locally slides back and forth on the DNA and chooses a TSS based on the affinity of the polymerase for the local sequence, such that different TSSs in the area are used in fixed relative proportions. In contrast, when nearby TSSs show different expression profiles one could imagine that there are particular regulatory sites that control initiation at individual TSSs.Whatever the detailed regulatory mechanisms are, it is clear that, for the study of transcription regulation, it is important to properly separate local clusters of TSSs that are co-regulated from those that show distinct expression profiles. Below we present a Bayesian methodology that clusters nearby TSSs into 'transcription start clusters' (TSCs) that are co-expressed in the sense that their expression profiles are statistically indistinguishable.A second issue is that, as shown by the power-law distribution of tags per TSS Figure , we findFinally, for each significantly expressed TSC there will be a 'proximal promoter region' that contains regulatory sites that control the rate of transcription initiation from the TSSs within the TSC. Since TSCs can occur close to each other on the genome, individual regulatory sites may sometimes be controlling multiple nearby TSCs. Therefore, in addition to clustering nearby TSSs that are co-expressed, we introduce an additional clustering layer, in which TSCs with overlapping proximal promoters are clustered into 'transcription start regions' (TSRs). Thus, whereas different TSSs may share regulatory sites, the regulatory sites around a TSR only control the TSSs within the TSR.Using the normalization method and noise model described above, we have constructed comprehensive 'promoteromes' of the human and mouse genomes from 122 CAGE samples across different human and mouse tissues and conditions  by first clustering nearby co-regulated TSSs; second, filtering out background transcription; third, extracting proximal promoter regions around each TSS cluster; and fourth merging TSS clusters with overlapping proximal promoters into TSRs. We now describe each of these steps in the promoterome construction.π (d) that these TSCs should be fused, which depends on the distance d along the genome between the two TSCs. For each pair of TSCs we calculate the likelihoods of two models for the expression profiles of the two TSCs. The first model assumes that the two TSCs have a constant relative expression in all samples (up to noise). The second model assumes that the two expression profiles are independent. Combining the prior π (d) and likelihoods of the two models, we calculate, for each contiguous pair of TSCs, a posterior probability that the two TSCs should be fused. We identify the pair with highest posterior probability and if this posterior probability is at least 1/2, we fuse this pair and continue clustering the remaining TSCs. Otherwise the clustering stops.We define TSCs as sets of contiguous TSSs on the genome, such that each TSS is relatively close to the next TSS in the cluster, and the expression profiles of all TSSs in the cluster are indistinguishable up to measurement noise. To construct TSCs fitting this definition, we will use a Bayesian hierarchical clustering procedure that has the following ingredients. We start by letting each TSS form a separate, 1-bp wide TSC. For each pair of neighboring TSCs there is prior probability xs the logarithm of the TPM in sample s of one TSC, and by ys the log-TPM in sample s of a neighboring TSC, then we want to calculate the probability P of the two expression profiles assuming the two TSCs are expressed in the same way, and the probability P({xs}), P({ys}) of the two expression profiles assuming they are independent.The details of the clustering procedure are described in Materials and methods. Here we will briefly outline the key ingredients. The key quantity for the clustering is the likelihood ratio of the expression profiles of two neighboring TSCs under the assumptions that their expression profiles are the same and independent, respectively. That is, if we denote by xs as the sum of a mean expression μ, the sample-dependent deviation δs from this mean, and a noise term:For a single TSS we write P(xs|μ + δs) is given by the noise-distribution (Equation 3). To calculate the probability P({xs}) of the expression profile, we assume that the prior probability P(μ) of μ is uniformly distributed and that the prior probabilities of the δs are drawn from a Gaussian with variance α, that is:The probability δs} and μ:The probability of the expression profile of a single TSC is then given by integrating out the unknown 'nuisance' variables {α, which quantifies the a priori expected amount of expression variance across samples, is determined by maximizing the joint likelihood of all TSS expression profiles .The parameter P, we assume that even though the two TSCs may have different mean expressions, their deviations δs are the same across all samples. That is, we write:To calculate the probability andP is then given by integrating out the nuisance parameters:The probability As shown in the Materials and methods section, the integrals in Equations 9 and 12 can be done analytically. For each neighboring pair of TSCs we can thus analytically determine the log-ratio:a priori more likely that they are driven by a common promoter than for distant pairs of TSCs. To test this, we calculated the log-ratio L of Equation 13 for each consecutive pair of TSSs in the human CAGE data. Figure L as a function of the distance of the neighboring TSSs.To perform the clustering, we also need a prior probability that two neighboring TSCs should be fused and we will assume that this prior probability depends only on the distance between the two TSCs along the genome. That is, for closely spaced TSC pairs we assume it is π (d) that two neighboring TSCs are co-expressed falls exponentially with their distance d, that is:Figure l is a length-scale that we set to l = 10.where L and we calculate a prior log-ratio:For each consecutive pair of TSCs we calculate d between two TSCs is defined as the distance between the most highly expressed TSSs in the two TSCs. We iteratively fuse the pair of TSCs for which L + R is largest. After each fusion we of course need to update R and L for the neighbors of the fused pair. We keep fusing pairs until there is no longer any pair for which L + R > 0 (corresponding to a posterior probability of 0.5 for the fusion).where the distance If one were principally interested in identifying all transcription initiation sites in the genome, one would of course not filter the set of TSCs obtained using the clustering procedure just described. However, when one is interested in studying regulation of expression then one would want to consider only those TSCs that show a substantial amount of expression in at least one sample and remove 'background transcription'. To this end we have to determine a cut-off on expression level to separate background from significantly expressed TSCs. As the distribution of expression per TSS does not naturally separate into a high expressed and low expressed part - that is, it is power-law distributed - this filtering is, to some extent, arbitrary.According to current estimates, there are a few hundred thousand mRNAs per cell in mammals. In our analysis we have made the choice to retain all TSCs such that, in at least one sample, at least ten TPM derive from this TSC, that is, at least 1 in 100,000 transcripts. With this conservative cut-off we ensure that there is at least one mRNA per cell in at least one sample. Since for some samples the total number of tags is close to 100,000, a TSC may spuriously pass this threshold by having only 2 tags in a sample with low total tag count. To avoid these, we also demand that the TSC has one tag in at least two different samples.Finally, for each of the TSCs we want to extract a proximal promoter region that contains regulatory sites that control the expression of the TSC, and, in addition, we want to cluster TSCs with overlapping proximal promoter regions. To estimate the typical size of the proximal promoters, we investigated conservation statistics in the immediate neighborhood of TSCs. For each human TSC we extracted PhastCons  scores 2We observe a sharp peak in conservation around the TSS, suggesting that the functional regulatory sites are highly concentrated immediately around it. Upstream of the TSS the conservation signal decays within a few hundred base-pairs, whereas downstream of the TSS the conservation first drops sharply and then more slowly. The longer tail of conservation downstream of the TSS is most likely due to selection on the transcript rather than on transcription regulatory sites.Based on these conservation statistics, we conservatively chose the region from -300 to +100 with respect to the TSS as the proximal promoter region. Although the precise boundaries are, to some extent, arbitrary, it is clear that the conserved region peaks in a narrow region of only a few hundred base-pairs wide around the TSS. As a final step in the construction of the promoteromes, we clustered together all TSCs whose proximal promoter regions  overlap into TSRs.To characterize the promoteromes that we obtained, we compared them with known annotations and we determined a number of key statistics.Using the collection of all human mRNAs from the UCSC database , we compBy far the most common situation is that there is a known mRNA start within a few base-pairs of the TSC. We also observe a reasonable fraction of cases where a known mRNA start is somewhere between 10 and 100 bp either upstream or downstream of the TSC. Known TSSs more than 100 bp from a TSC are relatively rare and the frequency drops further with distance, with only a few cases of known mRNA starts 1,000 bp away from a TSC. For 37.7% of all TSCs there is no known mRNA start within 1,000 bp of the TSC, and for 27% there is no known mRNA start within 5 kb. We consider these latter 27% of TSCs novel TSCs. To verify that the observed conservation around TSSs shown in Figure We observe a similar peak to that for all TSCs, although its height is a bit lower and the peak appears a bit more symmetrical, showing only marginally more conservation downstream than upstream of TSSs. Although we can only speculate, one possible explanation for the more symmetrical conservation profile of novel TSCs is that this class of TSCs might contain transcriptional enhancers that show some transcription activity themselves. In Additional data file 1 we present analogous figures for the mouse promoterome.Table The 56 human CAGE samples identify about 74,000 TSCs and the 66 mouse samples identify about 77,000 TSCs. Within these TSCs there are about 861,000 and 608,000 individual TSSs, respectively, corresponding to about 12 TSSs per TSC in human and about 8 TSSs per TSC in mouse. Note that, while large, this number of TSSs is still much lower than the total numbers of unique TSSs that were observed. This again underscores the fact that the large majority of TSSs are expressed at very low levels.Next we investigated the hierarchical structure of the human promoterome . Figure Figure This observation is further supported by the distribution of the lengths of TSCs and TSRs Figure . In partIn Additional data file 1 we compare the promoteromes obtained with our clustering procedure with those that were obtained with the simple single-linkage clustering procedures used in FANTOM3. The key difference between our clustering and the single-linkage clustering employed in FANTOM3 is that, in our procedure, neighboring TSSs with significantly different expression profiles are not clustered. Although TSSs within a few base-pairs of each other on the genome often show correlated expression profiles, it is also quite common to find nearby TSSs with significantly differing expression profiles. Figure Within a region less than 90 bp wide our clustering identifies 5 different TSCs that each (except for the furthest downstream TSC) contain multiple TSSs with similar expression profiles. Any clustering algorithm that ignores expression profiles across samples would likely cluster all these TSSs into one large TSC. However, as shown in Figure Since clustering procedures that ignore expression profiles, such as the single-linkage clustering employed in FANTOM3, cluster nearby TSSs with quite dissimilar expression profiles, one would expect that this clustering would tend to 'average out' expression differences across samples. To test this, we calculated for each TSC the standard deviation in expression (log-TPM) for both our TSCs and those obtained with the FANTOM3 clustering. Figure Our promoterome statistics above suggest that there are two classes of promoters. That there are two types of promoters in mammals was already suggested in previous CAGE analyses , where tFigure To study the association between promoter class and its length distribution, we selected all TSRs that with posterior probability 0.95 or higher belong to the high-CpG class, and all TSRs that with probability 0.95 or higher belong to the low CpG class, and separately calculated the length distributions of the two classes of TSRs.Figure Finally, we compared the promoter classification of known and novel TSRs. Of the 43,164 TSRs, 37.7% are novel - that is, there is no known transcript whose start is within 5 kb of the TSR. For both known and novel TSRs the classification into high-CpG and low-CpG is ambiguous for about 8% of the TSRs. However, whereas for known TSRs 56% are associated with the high-CpG class, for novel TSRs 76% are associated with the low-CpG class. This is not surprising given that high-CpG promoters tend to be higher and more widely expressed than low-CpG promoters - that is, they are much less likely to not have been observed previously.It is widely accepted that gene expression is regulated to a large extent by the rate of transcription initiation. Currently, regulation of gene expression is studied mostly with oligonucleotide micro-array chips. However, most genes initiate transcription from multiple promoters, and while different promoters may be regulated differently, the micro-array will typically only measure the sum of the isoforms transcribed from the different promoters. In order to study gene regulation, it is, therefore, highly beneficial to monitor the expression from individual TSSs genome-wide and deepCAGE technology now allows us to do precisely that. The related RNA-seq technology similarly provides significant benefits over micro-arrays. We therefore expect that, as the cost of deep sequencing continues to come down, deep sequencing technologies will gradually replace micro-arrays for gene expression studies.Application of deep sequencing technologies for quantifying gene expression is still in its infancy and, not surprisingly, there are a number of technical issues that complicate interpretation of the data. For example, different platforms exhibit different sequencing errors at different rates and, currently, these inherent biases are only partially understood. Similarly, it is also clear that the processing of the input samples to prepare the final libraries that are sequenced introduces biases that are currently poorly understood and it is likely that many technical improvements will be made over the coming years to reduce these biases.Apart from the measurement technology as such, an important factor in the quality of the final results is the way in which the raw data are analyzed. The development of analysis methods for micro-array data is very illustrative in this respect. Several years of in-depth study passed before a consensus started to form in the community regarding the appropriate normalization, background subtraction, correction for sequence biases, and noise model. We expect that gene expression analysis using deep sequencing data will undergo similar development in the coming years. Here we have presented an initial set of procedures for analyzing deep sequencing expression data, with specific application to deepCAGE data.a priori reason that mammalian cells should have a common power-law expression distribution across all tissues and conditions. It is conceivable that, as more extensive data become available in the future, we may find significant differences between the expression distributions in different tissues.Our available data suggest that, across all tissues and conditions, the expression distribution of individual TSSs is a universal power-law. Interestingly, this implies that there is no natural expression scale that distinguishes the large number of TSSs that are expressed at very low rates - so-called background transcription - from the highly regulated expression of the TSSs of highly expressed genes. That is, background transcription and the TSSs of the most highly expressed genes are just the extrema of a scale-free distribution. As we have shown, by assuming that a common universal power-law applies to all samples, we can normalize the expression data from different deep sequencing data-sets. The fact that expression profiles from SAGE and from RNA-seq using the Solexa platform also show power-law distributions strongly suggests that this normalization scheme is applicable to deep sequencing expression data in general. It should be noted that although all observed distributions are power-laws, there is no Drosophila showed multiplicative noise of similar size. However, we expect that it is a simplification to assume that the size of the multiplicative noise is identical in all experiments, and in the future we will want to apply a more refined analysis that takes into account the differences in the size of the multiplicative noise for different samples. To this end it will be important to design experiments such that at least one replicate is available to estimate the size of the multiplicative noise associated with a given experimental procedure.The noise in the expression measured across different deepCAGE samples can be accurately modeled by a convolution of multiplicative noise and Poisson sampling and we derived a practical analytical approximation to the resulting noise distribution. Using replicate data-sets, we inferred the size of the multiplicative noise for different samples and found it to vary in a small range. In addition, analysis of Solexa RNA-seq data from The noise model allows us to rigorously assess the statistical significance of measured expression differences across different samples. In particular, we developed a Bayesian procedure that calculates the probability that two TSSs have identical expression profiles. Interestingly, we found that TSSs that are less than 10 bp apart on the genome are much more likely to be co-expressed than more distal neighboring TSSs. Using these results, we clustered sets of nearby co-expressed TSSs into TSCs that we propose are each regulated by a common 'promoter'. Of course, our ability to detect significant expression differences is limited by the number of available samples and we expect that, as the number of available deepCAGE samples increases, the number of TSCs will increase as well.Comparative genomic analysis shows a strong peak in sequence conservation restricted to a few hundred base-pairs around TSSs. This suggests that the proximal promoter associated with each TSC extends a few hundred base-pairs around the TSSs in the TSC. Besides clustering nearby co-expressed TSSs into TSCs, we also clustered TSCs whose proximal promoters overlap into TSRs. Comparing the sequence composition and widths of TSRs, we find that there are two classes of promoters in the human and mouse genomes. The first class corresponds to TSRs that are narrow, almost always less than 10 bp wide, and that have low CG content as well as low CpG content. The second class corresponds to TSRs that are wide, that is, anywhere from 25 to 250 bp wide, and that are associated with CpG islands, that is, having both a high CG content as well as a high CpG content. It seems plausible that different mechanisms may be involved in the regulation of these two classes of promoters.All the samples used in this study were provided by the RIKEN Genomic Sciences Center as well as its successor, the Omics Science Center, and come from the FANTOM3, the FANTOM4, and several smaller projects. Each human sample has at least 100,000 mapped tags, and each mouse sample at least 50,000. The lists of all 56 human and 66 mouse samples, with tissue/cell line name, treatment and accession numbers are included in Additional data files 2 and 3. Whenever assigned, accession numbers of the DNA Data Bank of Japan are listed. Raw CAGE data of the FANTOM4 project are available at .The CAGE protocol that was used has been described in . The 143Drosophila Kc cells using Trizol reagent. Purification of mRNA and the generation of the cDNA library were performed following the Illumina protocol for mRNA sequencing. Primary sequencing data analysis was done following the Illumina Genome Analyzer software pipeline. ELAND (part of the Illumina suite) was used for the alignment of short reads to the Drosophila genome (release 5).For the RNA-seq data total RNA was isolated from n(t) of the number of TSSs with at least t tags to a power-law. To robustly fit these power-laws across different samples with different total numbers of tags, we remove the data from the first and last order of magnitude along the vertical axis and apply simple linear regression to the remaining data. As a result, for each sample s there will be a fitted exponent α (s) and a fitted offset n0 (s).For each CAGE sample we fit the reverse-cumulative distribution nr (r0 tα-) the total number of tags is given by:For a reference distribution of the form ζ (x) is the Riemann-zeta function. That is, the total number of tags is determined by both r0 and α . For the reference distribution we chose α = 1.25 and 6. Setting α = 1.25 in Equation 16 and solving for r0 we find:where t in each sample into a tag-count t' according to:To map tag-counts from different samples to this common reference, we transform the tag-count n(t') for this sample will match the reference distribution, that is, n(t') = nr (t'). If the observed distribution has tag-count distribution:such that the distribution t' this becomes:then in terms of n(t') = nr (t') gives:Demanding that α/β = 1.25, that is:This equation is satisfied when λ we find:Using this and solving for f of the tags in the input pool. Let x = log(f) and let y be the log-frequency of the tag in the final prepared sample that will be sequenced, that is, for CAGE after cap-trapping, linking, PCR-amplification, and concatenation. We assume that all these steps introduce a Gaussian noise with variance σ2 so that the probability P is given by:We model the noise as a convolution of multiplicative Gaussian noise and Poisson sampling noise. Assume that tags from a given TSS position correspond to a fraction n tags for this position, given y and given that we sequence N tags in total is given by:We assume that the only additional noise introduced by the sequencing is simply Poisson sampling noise. That is, the probability to obtain n tags given that the log-frequency in the input pool was x is given by:Combining these two distributions, we find that the probability to obtain x is high enough such that the expected number of tags ⟨n⟩ = Nex is substantially bigger than 1, then the Poisson distribution over y takes on a roughly Gaussian form over the area where (y - x)2 is small enough to contribute substantially to the integral. We thus decided to approximate the Poisson by a Gaussian, that is, we use:This integral can unfortunately not be solved analytically. However, if the log-frequency y can be performed analytically. Since the integrand is already close to zero at y = 0 , we can extend the region of integration to y = ∞ without loss of accuracy. We then obtain:Then the integral over where the variance is given by:n/N) matches the input log-frequency x, and has a noise variation of the size σ2 plus one over the tag-count n.In summary, the expected tag-count is such that the expected log-frequency log is given by the integral:Although this approximation is strictly only good for large y = ∞ without appreciable error. In addition, we introduce a change of variables to:We can again extend the integration range to m, which represents the expected number of tags, that is:and we introduce the variable With these definitions the integral becomes:z = 0. We therefore expand eσz to second order, that is:The Gaussian second term in the exponent ensures that the main contribution to the integral comes from the region around The integral then becomes a Gaussian integral and we obtain the result:σ this is in fact very close to:For small x.Both Equations 35 and 36 are reasonable approximations to the probability of obtaining zero tags given an original log-frequency n times in the first replicate sample and m times in the second replicate sample. Assume also that both n and m are larger than zero. A little calculation shows that the probability P is given by:Assume a particular TSS position was sequenced n and m we mean the raw tag-counts or the normalized version. For the comparison of expression levels - that is, the difference log(n/N) - log(m/M) - it is clear we want to use the normalized values n' and m' . However, since the normalized values assume a total of 1 million tags, the normalized values cannot be used in the expression for the variance. Therefore, we use the raw tag-counts n and m in the expression for the variance. That is, the probability takes the form:Note that we have not yet specified if by σ2 by maximizing the probability of the data over all positions for which both n and m are larger than zero. Writing:We estimate the variance L of the data can be written as:the log-probability i. We can now find the maximum of L with respect to σ2. Doing this on the replicate CAGE data set we find:where the sum is over all TSS positions σ2 by comparing expression across TSSs in the CAGE samples of THP-1 cells before and after 1 hour of PMA treatment. We assume that a large fraction of the TSS positions should be expressed equally in the two experiments but allow for a small fraction of TSS positions to be expressed differently across the two time points.Using the assumption that few TSSs change their expression within 1 hour of treatment with PMA, we can also estimate P(x) = 1/Δ over log-frequency x. Assume a TSS position has expression m at zero hours and n at 1 hour. The probability of this expression given that both are expressed the same is P that we calculated above (Equation 13). In contrast, if the expression is different between the two time points, then the probability is just the prior 1/Δ. Let π denote the (unknown) fraction of all positions that is expressed differently between the two time points. Under these assumptions the likelihood of the data is:Let Δ denote the size of the range in log-expression - that is, the difference between highest and lowest log tag-count - which is about 20,000 in our experiments. We assume a uniform prior distribution π and σ2. Doing this on zero and one time points of the three replicates gives us estimated σ2 values of 0.048, 0.116, and 0.058. Note that two of these are less than the σ2 values inferred from the replicate.We now maximize this likelihood with respect to both n is, to a good approximation, Gaussian in the log-expression log(n) with a variance (σ2 + 1/n), where σ2 is the variance due to the replicate noise and 1/n is the variance due to the Poisson sampling. However, this Gaussian form breaks down when n = 0 and this makes analytic derivations impossible when data-points with zero counts are included. To circumvent this, we make two approximations when considering the expression profiles of neighboring TSCs. First, we discard all samples s in which both TSSs have zero tag-count ns = 0, that is, we assume, in effect, that samples for which both TSCs have count zero are equally likely under both models. In addition, for samples s where one of the two TSCs has a zero count we replace the count zero with a pseudo-count of one-half of a tag .We want to calculate the likelihoods of two neighboring TSCs under the assumption that they have fixed relative expression, and assuming the two profiles are independent. As discussed above, the probability of the observed tag-count s denote a sample, ts the normalized TPM of the TSC in the sample, and ns the un-normalized CAGE tag count in the sample. The log-expression values are given by:We focus first on the probability of the expression profile of a single TSC (considering only the samples in which at least one of the TSCs has non-zero tag count). Let ns is zero and Ns is the total number of tags in sample s . We now assume a model of the following form:where the Kronecker delta function is 1 if and only if the tag-count μ is the true average log-expression of this TSC and δs is the true deviation from this mean in sample s. Given our noise model we have:where where:σ2 is the variance of the multiplicative noise, and we set ns = 1/2 whenever ns = 0. We need a prior probability distribution for the true expression variation δs and we will assume this prior to be Gaussian with mean zero, that is, we assume:α sets the scale of the variation that TSCs show. As discussed below, we choose α so as to maximize the likelihood of all the expression profiles from all TSSs (assuming each TSS is independent).where xs given μ and α, we perform the integral:To obtain the marginal probability of This is a Gaussian integral that can be easily performed and we obtain:where:xs given only α, we integrate over the mean log-expression μ and to do this we need a prior P(μ). For simplicity we use a uniform prior probability over some fixed range, that is:Next, to obtain the marginal probability of μ/2 ≤ μ ≤ Δμ/2, and zero outside of this range. We then obtain:when -Δμ is large compared to the region over which the probability takes on its maximum so that we can let the integral run from minus infinity to infinity without affecting the result. The precise value of Δμ is not important since it will eventually cancel out of the calculation. The result of the integral over μ is:We will assume that ΔS is the number of samples (for which at least one of the two neighboring TSCs has non-zero tag-count) and the averages are defined as follows:where andα we extract, for each TSS p, all samples s for which the TSS has non-zero tag-count ns and we calculate P(x|α) for each of the expression profiles of these TSSs. The total likelihood of α is then simply the product of P(x|α) over all TSSs:To estimate α .and we maximize this expression with respect to δs are the same. That is, we assume:The key quantity that we want to calculate is the probability that the expression profiles of two neighboring TSCs are proportional. That is, that the 'true' expression of the one TSC is a constant times the expression of the other TSC. Mathematically, we assume that the means of the log-expressions may be different for the two TSCs, but the deviations andxs and ys are the log-expression values of the neighboring pair of TSCs. Again, as described above, we restrict ourselves to those samples for which at least one of the neighbors has non-zero expression, and add a pseudo-count of half a tag whenever ns = 0.where For a single sample we have:where:ms is the raw tag-count of the TSC with log-expression ys. The integral over δs is still a Gaussian integral but the algebra is quite a bit more tedious in this case. To simplify the expressions we write:and andThen we can write:μ and Next we want to integrate over where we again use uniform priors:μ and r =  the joint distribution of log-CG and log-CpG contents of all TSRs to a mixture of two two-dimensional Gaussians of the form:where the components of The center of the low-CpG Gaussian is given by:and the center of the high-CpG Gaussian by:The fitted variance of the low-CpG Gaussian is given by:and the fitted variance of the high-CpG Gaussian is given by:Using the fitted mixture of Gaussians we can calculate, for each TSR at position GAT  tags per million; TSC: transcription start cluster; TSR: transcription start region; TSS: transcription start site.Drosophila Kc cell RNA-seq experiments and WVB provided the genome mappings. All authors read and approved the final manuscript.PB and EvN developed the data normalization procedure, the noise model, and the hierarchical clustering procedure, and applied these to the human and mouse CAGE data. PC and JK produced the CAGE data, CD was responsible for the initial CAGE data processing, and YH coordinated the production and initial processing of the CAGE data. CB performed the Drosophila RNA-seq data, CAGE replicate data, comparison with FANTOM3 clustering, and statistics on the mouse promoterome (Additional data file The following additional data are available with the online version of this paper: a collection of supplementary materials containing 13 supplementary figures and one supplementary table with additional results on the Drosophila RNA-seq data, CAGE replicate data, comparison with FANTOM3 clustering, and statistics on the mouse promoterome.Additional results include the Click here for fileData for the 56 human CAGE samples, with tissue/cell line name, treatment and accession numbers.Click here for fileData for the 66 mouse CAGE samples, with tissue/cell line name, treatment and accession numbers.Click here for file


Gene expression patterns in the brain are strongly influenced by the severity and duration of physiological stress at the time of death. This agonal effect, if not well controlled, can lead to spurious findings and diminished statistical power in case-control comparisons. While some recent studies match samples by tissue pH and clinically recorded agonal conditions, we found that these indicators were sometimes at odds with observed stress-related gene expression patterns, and that matching by these criteria still sometimes results in identifying case-control differences that are primarily driven by residual agonal effects. This problem is analogous to the one encountered in genetic association studies, where self-reported race and ethnicity are often imprecise proxies for an individual's actual genetic ancestry.post hoc sample matching or covariate analysis. While gene expression patterns are generally correlated across different brain regions, we found strong region-region differences in empirical ASRs in many subjects that likely reflect inter-individual variabilities in local structure or function, resulting in region-specific vulnerability to agonal stress.We developed an Agonal Stress Rating (ASR) system that evaluates each sample's degree of stress based on gene expression data, and used ASRs in Variation of agonal stress across different brain regions differs between individuals, revealing a new level of complexity for gene expression studies of brain tissues. The Agonal Stress Ratings quantitatively assess each sample's extent of regulatory response to agonal stress, and allow a strong control of this important confounder. Occasionally, the major factors affecting the phenotypic outcome may be truly strong and well known, such as cigarette smoking as a risk factor for lung cancer, or older age for Alzheimer's disease. In most other situations, however, particularly those concerning multifactorial diseases such as cancer and psychiatric disorders, there are usually numerous contributing factors for the observed phenotype, but their relative importance is not always known beforehand. While many case-control studies automatically include age and gender in sample matching, additional variables that are important for the phenotype need to be chosen on a case-by-case basis, and sometimes only after the data have been collected and analyzed. In genetic association studies, for example, the ancestral background of human subjects can have a strong confounding effect . A paexample, ,7. The ipost hoc sample matching [per se, and are less susceptible to survey errors or recall bias.Despite the widespread use and general success of these sample matching strategies, the risk of residual confounding remains. The key pH-sensitive genes or pathways, such as components of mitochondrial electron transport chain and proteasome genes, are highly variable between samples , and oftmatching ,18. In ematching , in whicmatching -22. The a priori reason to assume that altered pH and agonal factors would impact all these brain regions in a uniform manner. Consequently, sample matching based on a parameter derived from a single brain area or the entire brain may not be reliable for all regions examined, whereas gene expression data for individual regions can be used to assess specific regional patterns of agonal stress.In this study, we applied a similar strategy to an ongoing gene expression study in which we compare postmortem brain tissues between normal controls and subjects who suffered from major depression, bipolar disorder, or schizophrenia. In a previous report , we descpre hoc indicators such as pH and clinically derived Agonal Factor Scores (AFS), compared the stress ratings across six brain regions, and assessed the performance of different sample matching strategies. We also developed rigorous data pre-processing methods, compared different options of defining the ASRs, evaluated the robustness of ASRs in terms of the between-lab and between-platform reproducibility, and explored several related analysis algorithms.To this end, we developed Agonal Stress Rating (ASR), a quantitative system that measures the degree of stress of each RNA sample on a continuous scale based on gene expression data. We examined the relationship between ASRs and conventional Before we begin to characterize biological confounding factors, non-biological sources of variation must be identified. The microarray data used in this study were collected in multiple experimental batches, representing the mixed use of two types of Affymetrix Genechips (U133A/B and U133Plus_2), experiments run at three laboratories , RNA samples from six brain regions , and six cohorts of approximately 20 subjects each (four Mood Disorder Cohorts and two Schizophrenia Cohorts), for up to 126 subjects, about half of which were normal controls, the other half were cases of major depression, bipolar disorder, or schizophrenia. Cohort assembly, tissue dissection and RNA extraction took place in multiple stages, typically several months apart. The RNA samples were labeled and hybridized one cohort at a time, one region at a time, in two or three laboratories  separately. As a result of these technical variabilities, the entire dataset contained systematic differences between sites, chip types, and sometimes, cohorts, although the cohort-cohort technical differences are blended with genuine sample-sample differences across cohorts. This type of technical variation warrants careful scrutiny, and must be adequately controlled to ensure the accuracy of analyzing biological differences.After array scanning and Affymetrix Genechip data summary , we examined chip-to-chip similarity in each region by plotting the pairwise correlation matrices as color-coded heatmaps, where red indicates high similarities between pairs of chips, blue indicates low similarity, and the samples are ordered by site and by cohort. Figure E. coli transcripts, the data still exhibit the same block structure as seen with the use of all genes [see Additional File At least two other lines of evidence suggest that the "blocks" are derived from technical variation between experimental batches rather than due to genuine biological differences between samples in different cohorts. First, when we set aside data for all human transcripts, and plot chip-chip correlations by using only the 68 Affymetrix control probe sets, which target spiked-in The correlation matrices not only provide a means to visualize sample heterogeneity, but also allowed us to define a most parsimonious set of blocks for each region for the purpose of data normalization. To adjust for the block effect, we subtracted from each sample's logged expression value the median value of the block, and did so for each block and for every transcript. For example, for each gene, expression values for all Block 1 samples would subtract the median value of Block 1, and likewise for all other blocks, such that after the centering, the median of each block is at zero, effectively transforming the original data into the deviations from the block medians, in a procedure that is similar to adding a Block factor as a categorical variable in robust linear modeling (particularly the median polish method). The goal of this procedure is to remove a block-wide fixed factor, most of which, as we argued above, came from technical sources. The benefit of this adjustment, particularly the assumption of a fixed block-specific effect, can be evaluated by an objective criterion: how well the adjusted data increase the technical reproducibility of the same samples that were run at two or more sites. We found that after removing the block effect by median centering, we improved the between-site similarity for replicate chips run at multiple sites Figure . For samAlthough the systematic differences between blocks can be adjusted in this way, the assumption of a fixed effect is not expected to hold for all genes in all samples equally well. Other types of variation, including within-block heterogeneity, however, are not readily discernible in the data, and are probably impossible to control. Our analysis showed that a major portion of the between-block differences have been accounted for by a fixed technical effect affecting all samples within the block, for most of the genes studied. In the example of 201 AnCg chips, the median proportion of variance explained by the "block" factor, across all 12,734 genes, is 2.5% of the total variance. Because the 2.5% between-block variance has one degree of freedom, while the 97.5% within-block variance has 199 degrees of freedom, the F test showed that more than half of the genes had significant between-block differences. In this case, 56% of the genes satisfy P < 0.05 (one-way ANOVA) for the Block factor.Previously we showed that most of the brain samples in our study can be classified into two main types of expression patterns : those f-13), the clinical agonal factors, as well as with the previously determined Type 1-Type 2 designations; whereas PC2 and PC3 scores have almost no correlation. For example, in AnCg, r is 0.04 (P > 0.35) and 0.07 (P > 0.25) for pH-PC2 and pH-PC3, respectively. Note that with n = 126, r needs only to be approximately 0.18 to be significantly non-zero at p = 0.05). This result not only confers a biological meaning to PC1, but also suggests that a single continuous variable is likely to be sufficient to capture most of the gradual progression of expression patterns from the low-pH prototype to the normal-pH prototype.Because pH/agonal stress acts as an exceedingly strong confounder in gene expression studies, a dichotomous classification may not be sufficient to ensure that cases and controls are well-stratified, or balanced within each stratus. In addition, different brain regions may carry different stress outcomes; whereas this aspect of data heterogeneity is not well informed by pH values measured in one brain region, nor by the clinical indicators. One possible approach for dealing with residual heterogeneity is to subdivide the main classes further, such as into Types 1A, 1B, 2A, 2B, etc, effectively classifying samples in multiple tiers to establish nested subsets, within each of which the cases and controls are more homogeneous and better balanced. Figure Not all genes contributed equally to the placement of individual samples along the gradient of membership. We selected the 20% strongest Type 1-like samples  with tissue pH Figure  reveals After calculating ASR for all six regions and for two sites in each region, we obtained twelve series of ASR values. As AMY and CB had larger numbers of missing chips , we plotted the eight ASR series for the four remaining brain regions in color codes along with pH values and AFS (in two levels)  in AnCg, and normal to high ASRs in the other regions. The third and sixth subjects, indicated by the next two arrows, have unusually low ASRs in DLPFC and HC, respectively. These strong region-region differences in ASRs are robustly observed (see the next section) and suggest genuine differences in stress outcome across different parts of the brain. Such differences may arise due to inter-individual variabilities in local structure or function, resulting in region-specific vulnerability to agonal stress. An additional possibility is that the nature of the illness that caused the death, such as hepatic, renal, or cardiac failures, may have triggered a region-specific brain response. These results underscore the value of using ASRs to carry out per-region sample matching, as pH and clinical indicators are measures for the entire brain.It is difficult to know how much between-region differences arise from variabilities in tissue dissection, but this factor is unlikely to explain most of the differences we observed here, as the effect is seen even for relatively large, easy-to-dissect regions such as DLPFC and CB. Although the nature of the observed regional differences is still not clear, most of such differences are likely due to actual biological differences rather than to technical variability in performing RNA labeling and hybridization or to data analysis methods. There are several reasons for making this conclusion. First, while regional differences of ASRs are often large (+/- 0.5), ASRs varied to a much lesser degree (1) between sites, (2) between different numbers of informative genes used, (3) between different distance measures , (4) with another round of normalization after median centering, (5) following the selection of only the high ASR samples as the basis for re-calculating block medians, or (6) importantly, following the use of only normal controls rather than both cases and controls for ranking genes by t scores. Secondly, we examined the possibility that some regions may actually have a greater Type 1-Type 2 difference than the other regions, and different samples may have different regional differences. To this end, we calculated additional versions of ASR by using (1) the same ten Type 1 samples and the same 14 Type 2 samples to determine the informativeness of genes in all six regions; (2) combined all six regions (more than 1200 chips) in designating the canonical samples on the two extremes, defining most informative genes, and calculating ASR across all 1200 samples . These alternative versions did not significantly alter the ASR patterns across samples and regions, and did not explain most of the observed regional differences. Thirdly, with our 700-gene Illumina data, we were able to compare the ASRs based on data from two different platforms. For each sample, we averaged the Affymetrix ASR values from two sites to obtain the six values for six regions, and calculated their correlation to the corresponding six ASR values from the Illumina data. We obtained 67 such correlations in 67 samples for which we had both the Affymetrix and Illumina data. Of these 67, 58 correlations were above 0.33, 43 were above 0.67, and 28 were above 0.8, with most of the smaller correlations explained by very low between-region variations, that is, when the six scores are similar to begin with for a given sample, it is more difficult to observe a highly correlated pattern for this sample in a different platform.Many gene expression analyses have shown that agonal stress at the time of death can significantly alter expression patterns in postmortem tissues -33. BecaOur results revealed striking between-region differences in stress outcome. This complexity presents additional challenges to gene expression analyses of the brain, especially if the goal is to not only study each region separately, but also to study biological regulation across brain regions, as well as their disruption in the diseased state. During our initial analysis, we had hoped that all regions of the same brain would have a similar stress profile, making it possible to use one or more regions as the same-subject control for the other regions. In this scheme, between-region differences in gene expression, instead of gene expression levels in each region separately, are compared between cases and controls, under the assumption that agonal stress is acting more extensively across the entire brain, whereas expression signatures of psychiatric disorders are restricted in some regions. This approach is reminiscent of the genetic method of using family controls to remove the impact of population structure. Our analysis, however, revealed considerable heterogeneity between brain regions in stress-related expression patterns, suggesting that this between-region analysis method is still problematic and requires further investigation.independent of the genetic basis of the other risk factors, even though in the long run it is ideal to be able to study all the contributing factors in conjunction with each other. By the same token, the near-term goal of our study is to discover gene expression signatures of psychiatric disorders independent of gene expression changes due to confounding factors, especially when these factors (stress at death) are not likely to be closely related to the biology of mental illness.One of the concerns in adopting this approach is that gene expression changes in response to near-death conditions may overlap with those affected by chronic psychiatric states. If the Agonal Stress Ratings reflect the blending of both effects, how do we know whether we have under- or over-corrected the main effect of interest? Unfortunately, at the present time we do not know many genes or pathways that are clearly and reproducibly altered by major depression and bipolar disorder; as a result we currently do not have a definitive set of "true positives" to fine-tune the stringency of the sample matching strategy. To address this type of question would require a sufficiently large collection of samples to directly investigate whether patients of mental disorders are more likely than the healthy controls to have more severe terminal stress, lower tissue pH values, and more pronounced changes in gene expression patterns. When the sample size is below or near 100, as is currently the norm in expression profiling of human brains, a study is not properly powered to formally answer this question, and the gene expression signature due to mental disorders, if it overlaps with that due to agonal stress, will be easily obscured. However, despite this uncertainty, it is widely recognized that the effects due to agonal stress usually have a much more potent influence on gene expression patterns than do mental disorders. In such a situation, the chance of finding false positives due to residual imbalance is quite high. A continuous, quantitative rating system, like the ASR that we developed here, can greatly reduce the number of false positives in such studies by allowing a quantitative assessment of the broadly recognizable outcome of the most prominent confounder. By applying the ASR, it remains possible to detect a true signal for psychiatric disorders as long as it is strong enough or sufficiently independent of the confounding effect, particularly if the disease related changes involve a small number of transcripts whereas the agonal conditions usually affect a large number of genes . In esseIn this study, we found that the Agonal Stress Ratings are sometimes at odds with tissue pH values or clinically-recorded medical factors. These indices, though useful in most situations, have several shortcomings when serving as surrogates for the underlying biological heterogeneity. First, different brain regions may carry different stress outcomes, while pH values were usually measured in one region. Likewise, the clinical indicators do not inform regional heterogeneity. Secondly, these conventional variables inevitably contain measurement errors or incomplete information. Thirdly, brain pH is both the outcome of prior episodes of stress and the trigger for subsequent physiological responses. As a result, even if pH is measured in all regions, and even if pH is similar across regions , the samIt is also important to point out that the tissue pH measurements and clinical records are still of immense value in sample matching. They provide biological meaning to the ASR values, and allow an integrated strategy that combines these different indicators in sample selection . We beliper se to detect sample heterogeneity is a practically useful yet ultimately exploratory method, especially when true positives are not known beforehand.An implicit assumption of using inferred ancestry to control population stratification in genetic studies is that most of the genetic markers tested are phenotypically neutral; that is, not associated with the disease under study. Under this assumption, when data have been collected for a large number of loci , the majority of these loci can be used to infer population structure ,16,36,37post hoc strategies, such as stratified analysis, or incorporating covariates in regression analysis. We have found that the main differences due to agonal stress can be robustly observed, i.e., are highly similar between study sites and across two microarray platforms. This means that the canonical patterns that we describe here, featuring prominently energy metabolism genes and stress response pathways, can be transferred to other studies of postmortem tissues even if these studies characterized a narrower range of the confounding effect. In Additional files In inferring individual ancestry from genetic data, it is helpful to know the genetic profile of the putative ancestral populations, for example, the allele frequencies determined from samples that represent the progenitors of the admixed individuals. Without these "pure" canonical profiles, while it is still theoretically possible to simultaneously determine both the canonical ancestral patterns and the mixing ratios of each sampled individual, the results are less reliable and often improperly scaled . Similara priori the fractional composition of different cell types in each sample. Conversely, Lu et al. [The situation would be much simpler if the mixing ratios are known by other, independent methods, or if the canonical patterns were profiled in independent studies. Such an "expression signature bank" can be established by studying the response to controlled stress treatment in animal models, or by analyzing "pure" classes of brain cells, such as laser-captured defined cell populations. Stuart et al.  gave an u et al.  used expu et al. -46 have u et al. ,16,47. Ipost hoc sample matching. We found that ASR-based matching provides tighter control of the agonal effect than by using pH. We also found that different brain regions exhibited different stress outcomes and that such regional patterns also varied between individuals. Our results once again highlight one of the main challenges in gene expression studies of psychiatric disorders: transcript levels are under the influence of a large number of confounding factors. Agonal stress undoubtedly plays a major role; as a result the stress-related, pH-sensitive genes or pathways are prone to appear as the top findings in case-control comparisons. We propose to adopt a conservative approach for the genes and pathways that are clearly altered by the confounding factors, even if it is possible that they are also influenced by the disease of interest. Deriving an ASR from gene expression data and using it for sample matching is one example of such an approach. This approach involves using continuous ratings as opposed to categorical assignments, thus represents an early attempt to apply graded classification methods to a sample heterogeneity problem for brain tissues, similar to the application of dimensional models in psychiatric diagnosis. In practice, we believe that this method can and should be expanded to the characterization of other sources of biological variation, such as medication, age, and cell-type composition of the dissected brain tissues. Drug use by psychiatric patients is likely to affect gene expression, regardless whether the medication was effective in treating the disease or not. But medication history is one of the most elusive aspects of clinical information to accurately record and quantify. Likewise, an individual's chronological age may vary greatly from the actual physiological age of the tissue under study, while the neuronal-glial ratios of the dissected tissues may also vary from brain region to brain region, from subject to subject. Proper monitoring of these additional sources of phenotypic variation is an important prerequisite for the eventual identification of the true gene expression signature of mental disorders, and in this regard, animal models of either drug treatment or stress, independently applied, in the absence of psychiatric history and genetic heterogeneity, represents a powerful alternative strategy for defining canonical expression patterns and assessing their relative contributions.In this study we developed an Agonal Stress Rating (ASR) system that evaluates each sample's degree of stress based on gene expression data, and used ASRs in Sample acquisition, RNA labeling, and microarray hybridization were carried out as described previously ,48. We uSince the original Affymetrix probe definitions require frequent updates, and are known to contain errors and redundancies, we developed a custom probe definition method that involves re-annotating all Affymetrix probes by sequence alignment to the most recent build of genomic DNA sequences and a variety of transcribed sequence collections, including Unigene, Refseq, ENSEMBL Genes/Transcripts/Exons, and Entrez, etc . For eacWe calculated chip-chip correlation in each region by using RMA summaries values and defined blocks by visual inspection of the correlation heatmaps. Logged expression values for each gene were centered within each block. Median centered values were used for the Principal Component Analysis, whereby the PC1 scores were used to rank samples so that a proportion of samples at one extreme were designated canonical Type 1 samples, while a proportion of samples at the other extreme were designated canonical Type 2 samples. These two groups of samples were compared by the Student's t test, so that all genes can be ranked by the t scores. The ASR of each sample is then calculated as the "distance" to canonical Type 1 pattern minus its distance to the canonical Type 2 pattern by using a proportion of the genes with the largest absolute t scores. A range of parameter values were tested, including different proportion of samples used to define canonical patterns, different number of genes used for calculating ASRs, and different measured of chip-chip distance. For example, most results in this report were based on using approximately 20% of samples at each extreme of PC1 scores, 25% of the genes of largest t scores, and Pearson's correlation as distance measures. The nearest Shrunken Centroid Classification was carried out by using the Predictive Analysis of Microarrays (PAM) package in R. All R scripts used in the analysis are available from the authors.The Illumina custom Beadchips were designed to cover ~700 transcripts that represent both biologically candidate genes and preliminary Affymetrix results to be validated. Sample labeling and hybridization were performed according to manufacturer's specifications. In all, about 67 samples were analyzed in each brain region, except for AMY, which we analyzed only 54 samples. All of the nearly 400 RNA samples were randomized with regard to cohort and region. The calculation of ASRs was carried out in a similar fashion as with the Affymetrix data except that there were only 700 genes used in the analysis.AnCg, anterior cingulate cortex; DLPFC, dorsal lateral prefrontal cortex; AMY, amygdala; HC, hippocampus; CB, cerebellum; NACC, nucleus accumbenThe authors are members of the Pritzker Neuropsychiatric Disorders Research Consortium, supported by the Pritzker Neuropsychiatric Disorders Research Fund L.L.C. There exists a shared intellectual property agreement between the academic and philanthropic entities of the consortium for potential findings.SJE, PVC, MPV supervised the collection of gene expression data by using the Affymetrix Genechips. LT, VS, TC collected gene expression data by using the Illumina custom Beadchips. FM and SJW developed data management and analysis infrastructure and the Affymetrix custom CDF files. DW and WEB collected and compiled sample information that includes diagnosis, agonal stress and other clinical/demographic variables. MPV and WEB collected brain pH data. JL developed the analysis method in this work and performed the statistical analyses. JL and RMM wrote the manuscript. SJE, PVC, HT, MPV, WEB, EGJ, HA, SJW participated in data analysis and drafting of the manuscript. WEB, EGJ, HA, SJW, RMM conceived, coordinated, and supervised the overall study. All authors read and approved the final manuscript.E. coli transcripts. Sample order was the same as in Figure Technical batch effects. a. The color-coded correlation matrix among the same 201 AnCg samples as in Figure Click here for fileHeatmap of normalized expression levels for "top 25%" genes in 201 AnCg samples. Shown are log-transformed, normalized expression levels of 3184 transcripts across 201 AnCg samples. These genes have the highest 25% of Type 1- Type 2 absolute t scores, and have been used to calculate the sample-sample correlations shown in Figure Click here for fileExpression levels of 3841 most changed genes. Normalized expression levels for 3841 genes in 201 samples as shown in Additional File Click here for fileCross-validation errors in classifying samples. Number of cross-validation errors as a function of number of genes used in the nearest Shrunken Centroid classification  where thClick here for fileComparison of Type 1-Type 2 differences across brain regions. Scatter plots of t scores for 12,734 transcripts on the U133A chips across six regions, showing that the Type-1 versus Type-2 comparisons in these brain regions are highly correlated. The t scores are calculated by comparing about 20% strongest Type 1 samples against about 20% strongest Type 2 samples in each region. The samples are ranked by a Principal Component Analysis by using all transcripts.Click here for fileMost strongly changed genes upon agonal stress. The spreadsheet "1000Up_LowpH" listed 1000 most strongly up-regulated genes among the Type-2, low-pH samples and their t scores in five regions. The second spreadsheet "1000Down_LowpH" listed the corresponding 1000 most strongly down-regulated transcripts. The Unigene ID's are from Unigene Build 176.Click here for file