In this study, we present a robust and reliable computational method for tag-to-gene assignment in serial analysis of gene expression (SAGE). The method relies on current genome information and annotation, incorporation of several new features, and key improvements over alternative methods, all of which are important to determine gene expression levels more accurately. The method provides a complete annotation of potential virtual SAGE tags within a genome, along with an estimation of their confidence for experimental observation that ranks tags that present multiple matches in the genome.Saccharomyces cerevisiae genome, producing the most thorough and accurate annotation of potential virtual SAGE tags that is available today for this organism. The usefulness of this method is exemplified by the significant reduction of ambiguous cases in existing experimental SAGE data. In addition, we report new insights from the analysis of existing SAGE data. First, we found that experimental SAGE tags mapping onto introns, intron-exon boundaries, and non-coding RNA elements are observed in all available SAGE data. Second, a significant fraction of experimental SAGE tags was found to map onto genomic regions currently annotated as intergenic. Third, a significant number of existing experimental SAGE tags for yeast has been derived from truncated cDNAs, which are synthesized through oligo-d(T) priming to internal poly-(A) regions during reverse transcription.We applied this method to the We conclude that an accurate and unambiguous tag mapping process is essential to increase the quality and the amount of information that can be extracted from SAGE experiments. This is supported by the results obtained here and also by the large impact that the erroneous interpretation of these data could have on downstream applications. Serial Analysis of Gene Expression (SAGE) technology  has beeni.e. determining the UniGene cluster that most likely represents the gene from which the experimental SAGE tag was derived. Each UniGene cluster contains a collection of expressed sequences, which consists of well-characterized mRNA/cDNA sequences and expressed sequence tags (ESTs) that might represent a unique transcript. Unfortunately, this strategy allows only for the partial assignment of tags to transcripts, because the current resources for transcriptome data are incomplete for most species and organisms. Therefore, a significant fraction of the experimentally measured tags remains unidentified. In addition, there are several drawbacks of using this strategy for the mapping of SAGE tags to transcripts. First, a single gene may be represented in several clusters, resulting in ambiguous assignments. Second, EST sequences, which are the major components of the UniGene clusters, have an approximated error rate estimated at 1% (1 in 100 nts), resulting in a tag error assignment rate close to 10% [i.e. hypothetical and unknown genes). For example, SAGE studies in human have shown that 60% of the 14 bp tags do not have any match to sequences in the UniGene clusters [A critical step in the SAGE methodology is the tag mapping process, which refers to the unambiguous assignment of an experimentally measured tag to a given transcript. Currently, the tag mapping process frequently involves the search of the observed tag sequences within the known transcriptome. Commonly employed databases available for tag mapping -10 use Ue to 10% . Third, clusters . The corclusters . Fourth,SAGE can be very efficient for gene discovery and annotation -5. For tIn this work, we designed a bioinformatic method that gives different confidence values to each of the multiple hits in the genome for a tag sequence. Our method allows to fully exploit the abovementioned benefits while using genomic sequences for the tag mapping process in SAGE. The confidence values were assigned according to several parameters that were obtained by the analysis of experimental SAGE tags from previous studies in yeast -17. We dIn this work, we describe a new method, HGA, for tag mapping in SAGE. The method combines existing knowledge of a genome sequence and its current annotation, along with known data from previous SAGE experiments, to increase the accuracy and reduce the ambiguity of the tag mapping process.Saccharomyces cerevisiae. Some of these parameters are highly specific to yeast and may not be as crucial for other organisms, and viceversa.Though this methodology can be applied to any organism, we describe it here with some parameter values that have been specifically tuned for HGA consists of four main steps, which are described below. A detailed flowchart of the HGA method is illustrated in Figure Saccharomyces cerevisiae, its protein tables only specify the coding regions of each gene  and do not contain the assignment of the untranslated regions (UTRs) at the 5' and 3' ends. Therefore it was necessary to assign them. The precise assignment of these regions is particularly relevant in the case of the 3'-UTRs, because it is expected that a significant fraction of experimental SAGE-tags will be obtained from these regions. With better knowledge of the transcriptome, a larger fraction of the UTRs can be accurately assigned. For most model organisms, a large number of expressed sequence tags (ESTs) are available even though only a small fraction of full length cDNAs is known. Therefore, the precise assignment of UTRs for most of the coding genes is not possible. For yeast, about half of the known genes have a predicted 3'-UTR with high confidence. These are mainly due to the identification of downstream polyadenylation signals [The complete genomic sequence of an organism is first searched for occurrences of the recognition site of the anchoring enzyme used in SAGE. The virtual potential SAGE-tags are then extracted by combination with a given tagging enzyme. These potential tags are then compared all-against-all in a pairwise fashion and the frequency of occurrence of each of the potential tags in the genome is determined  of less than 100 nts . At thisAfter the assignment of complete coding transcripts to the genome, the RNA tables are used to map and assign the non-mRNA transcripts (see methods). This feature of the HGA method is new, because previous works in SAGE have not explicitly used the non-coding transcripts to map experimental tags. Though most non-coding transcripts do not contain poly(A) tails, and thus should not be observed in SAGE experiments, a recent study has shown that some ribosomal RNAs are polyadenylated in yeast, even in the absence of a canonical polyadenylation signal . FurtherOnce all transcripts have been assigned, the remaining intergenic regions of the genome are categorized into two types, depending on whether an annotated transcript is present in the complementary strand or not .The structured genome information generated above is crossed against all the potential tags, generating a genome based annotation of virtual SAGE-tags. The resulting virtual tags are categorized into one of seven classes, depending on the genomic position, annotation and frequency of occurrence of each virtual SAGE-tag in the genome Figure , center.de novo. The remaining tags are labelled as 'non-spliced-tags'.As an important complement for this new tag classification scheme, the HGA method also incorporates two additional tag features, which are intended to reduce some potential distortions that can affect the interpretation of SAGE results. First, all continuous stretches of eight or more adenines within each annotated transcript are recorded to account for oligo-dT priming to internal poly(A) regions of RNA molecules during reverse transcription. It has been demonstrated that this process occurs at a high frequency, causing that about 12% of ESTs are truncated due to internal poly(A) priming . TherefoThe resulting tag classification, along with the abovementioned additional tag features, are used to select particular tags from the genome, the occurrences of which are searched for among known experimental SAGE-tags obtained previously and described in the literature for the studied organism. Table To summarize, all the potential tags are assigned with a value according to the genomic regions they map and to their specific features. For example, the tags mapping into a certain transcript will have different values according to the transcript position and the proximity of internal poly(A) sequences, whereas the tags mapping to intergenic regions have a single value.ie. among all occurrences of a tag sequence that is observed multiple times in the genome, there is not a case where a particular virtual tag always has an odds ratio equal or higher than five when compared against all other instances). In these cases, the tags could still be ranked based on the odds ratios that they exhibit, which is provided by the annotation generated by the HGA method. Some examples illustrating how the tag confidence assignment process is carried out by the HGA method are shown in Figure The estimated probability functions described above are then crossed against all virtual genomic tags, to obtain a tag confidence assignment for each potential virtual SAGE-tag in the genome Figure . The oddSaccharomyces cerevisiae , or on the 3'-UTRs (15%) and a small fraction of the tags were found at the 5'-UTRs (5%). As should be expected, these figures correlate with the observed lengths of these elements.The total number of virtual tags shows an inverse linear relationship to its position within the transcript, as expected, based on the fact that position number correlates with distance from the 3'-UTR end, which is directly related to the probability of finding a downstream recognition site for the anchoring enzyme used in SAGE.Only a small fraction of the virtual tags map onto annotated introns (1%) and non-coding RNAs (1%). Very few tags map onto exon-intron boundaries (0.02%), accounting for a total of 13 new tag sequences generated by splicing.When we considered potential unique virtual tag sequences within the genome, most of the results described above remain unchanged  region within a transcript are observed in all SAGE experiments reported. Third, in all experiments, SAGE-tags mapping onto non-coding RNAs are observed. Almost all these cases consist of tags belonging to the class 'non-poly(A)-next' and mapping to the first position within the transcripts, suggesting that typical polyadenylation occurs at the 3' end of these transcripts . Fourth, analogous to what was observed for introns, spliced-tags are observed in all SAGE experiments. This is the first time that experimental SAGE-tags are mapped onto virtual and potential spliced-tags from a genome. Fifth, a significant fraction of experimental SAGE-tags map onto regions in the genome that currently are annotated as intergenic. Though this has already been observed, it must be mentioned that it is for the first time that this analysis is carried out by considering the confidence of the assigned tags, and thus the figures obtained here should be more accurate. These intergenic tags could represent new genes not yet described in yeast. Using the HGA-based annotation they can now be easily ranked according to their estimated confidence, which will facilitate and optimize the experimental planning of the gene discovery process. Finally, a large fraction of the experimental tags that map onto an intergenic region has an annotated transcript on the opposite strand. These tags could correspond either to new genes or to new regulatory elements such as antisense RNA ,23. The i.e. those with several assignments by other authors), independently for each tag class, the obtained figures are highly significant  aSeveral new features that improve the accuracy and completeness of the tag mapping process in SAGE have been incorporated by the HGA method, and are detailed below.First, instead of using only the coding regions of known and hypothetical genes, we assigned, as precisely as possible, the 3' and 5' UTRs, thus generating more accurate putative transcripts. Mature and immature transcripts were generated, by considering exon-intron boundaries, thus keeping and using all the relevant available genomic information and annotation. When no information about UTRs was available for a given gene, we used a fixed maximal length estimated from experimental data. It is noteworthy that most conflicting assignments of unique tags observed between HGA and other authors' assignments resulted from the large length of 3'-UTRs previously used by these authors -17 Tabl. The preSecond, non coding RNAs, in addition to known and hypothetical genes, were also included in the genomic annotation. Though the amount of tags mapping to these transcripts is low Table  and mostS. cerevisiae constitutes one of the best annotated genomes available today. If EST data were used to map experimental SAGE-tags, this information would not be obtained. Hence, a method that considers these elements explicitly in the annotation process would accelerate the discovery of new regulatory elements. The identification of regulatory elements of this kind is important for a complete and accurate interpretation of the gene expression patterns.Third, tags mapping to intergenic regions in the genome, where an annotated transcript is found in the opposite strand, were also considered in the HGA method. These supposedly intergenic tags, if experimentally observed, could account for unknown elements, such as antisense RNA. We showed that a significant fraction of these tags were observed in SAGE experiments with yeast Table , even thFourth, by using genomic information in the tag mapping process, the HGA method identifies tags mapping onto regions where no gene annotations exist in either of the DNA strands. In this work, we demonstrated that a significant fraction of these tags were observed in SAGE experiments with yeasts Table . It is aFifth, the combined use of genomic information along with the generation of new putative splicing tags not explicitly available in the genome sequence, allows a more accurate estimation of tag uniqueness and, therefore, of potentially ambiguous mappings.Sixth, the inclusion of internal poly(A) regions within annotated transcripts as possible reverse transcription initiation sources is another important feature of the HGA method. This was included because recent EST data analyses have shown that a significant fraction of the reverse transcription processes are initiated at internal poly(A) regions of more than 8 consecutive adenines . The resSeventh, the new definition of tag classes considered by the HGA method Table  facilitaFinally, the calculation of tag probabilities from experimental data based on the new tag classification, along with other tag features, allows the HGA method to get the odds or confidence that a tag would be experimentally observed when several instances of a tag sequence are present in the genome. This constitutes the core of the HGA method and one of the most important contributions of this work to reduce the number of unambiguous tag assignments in SAGE. In addition, we also demonstrated that about 20% of the experimental tags mapping onto a transcript are located from the second tag position and above. If this information is not considered in the tag-to-gene mapping process, a substantial fraction of the experimental tags will be missed. Finally, it is important to note that even in those cases where the ambiguity could not be completely removed, the HGA method could reduce the number of possible assignments, thus reducing the overall ambiguity for a particular tag with multiple occurrences in the genome.The score of intergenic tags is strongly dependent on the quality of the genome annotation. In poorly annotated genomes, intergenic tags will have a higher probability of being observed by the HGA methodology. This is a desirable feature for tag probability estimation in the discovery of new genes. In yeast, 11.3% of all experimental SAGE-tags obtained to date and searched against the current annotation of the yeast genome map into an intergenic region, suggesting that new coding or non-coding transcripts are still to be discovered. This figure will be even larger for poorly annotated genomes.Xenopus genome). Therefore, the main problem of using genome sequences for tag-to-gene assignment in long genomes is that with their increased size and complexity tag uniqueness and unambiguous tag-mapping becomes increasingly difficult. It is in these cases that HGA would be most useful, because it will significantly reduce unambiguous tag mappings.In this work, we achieved an 8–10% increase in unambiguous tag assignments when considering all experimental yeast SAGE-tags Table . This imLong-SAGE has been proposed to reduce the ambiguity of tag mapping for large genomes ,25. HoweXenopus tropicalis genome . This genome has 1.5 billion base pairs, half the size of the human genome and 125 times larger than the yeast genome. Our preliminary analysis of all potential tags for X. tropicalis genome showed that tag uniqueness for short (14 nts) virtual tags is around 9.1%, small compared to the 80.6 % of uniqueness for the long (21 nts) virtual tags. When a histogram of occurrence for each tag sequence was constructed, we found that 60% of the virtual short tags have less than 7 matches to the genome and 90% of the tags have less than 20 matches. This low number of genome hits per tag for a significant amount of the potential short tags suggests that the use of HGA tag-mapping should allow proper tag-to-gene assignment when typical SAGE technology with tags of 14 nts is used. More importantly, when we built a virtual reference database for SAGE-tags from X. tropicalis genome using only some of the parameters involved in the HGA method described here, we have found that 40% of the short virtual tags are included in the high confidence class. This indicates that after using the HGA method, a significant fraction of the short tags will be unambiguously mapped with a high confidence to the genome and represents a total potential gain of unambiguous assignments of about 31%. This figure is significantly higher than the 8–10% obtained for yeast, though its estimation for X. tropicalis was based on the virtual genomic tags instead of the experimental SAGE-tags, where this figure will increase, as it was shown for yeast  A significant increase of unambiguous assignments for experimental SAGE-tags in yeast is achieved when using this method Figure .2) Using a genome-based annotation of virtual SAGE-tags like the one described here shows that a significant fraction of experimental SAGE-tags comes from intergenic regions, from partially digested cDNA, from the opposite strand of annotated transcripts, and from truncated cDNAs Figure .3) In all SAGE experiments reported for yeast, tags map onto introns, exon-intron boundaries and onto non-coding RNAs Table .4) In all SAGE experiments reported for yeast, it was observed that the largest fraction of tags map to the coding regions of transcripts and not to the 3' UTR elements Table .Saccharomyces cerevisiae organism was obtained from the July 2005 release available at the Saccharomyces genome database (SGD) web site [The full genome sequence of the web site . The fulweb site .th 2005 release of the genomic annotation available at the SGD web site was used [The July 26was used . This orwas used .subsequence. This process was carried out for the forward and reverse DNA strands, and the results concatenated into a single file. Second, the 14 bp sequences were filtered, selecting only those that matched the pattern CATG at their 5' end. This procedure resulted in a total of 76,516 tags that represent the theoretical product of a complete genome digestion by using a combination of the NlaIII and BsmFI restriction enzymes . In this process, the position and strand where each tag was found in the genome were stored. For this purpose, we set up a new computer program called pattern. Finally, an all-against-all pairwise tag comparison without mismatches was performed and the frequency of occurrence for each tag sequence at the different genomic positions on both strands stored with another computer software: freqtag. All these computer programs for the LINUX operating system are freely available as supplemental material at our web site [Several computer programs in C++ and ANSI C languages were written to perform specific tasks. First, the full DNA sequence of each chromosome in the genome was fragmented in a computer into all possible overlapping oligonucleotide sequences of a length of 14 base pairs (bp) using the computer program web site .ie. the 3'-UTR was defined with a length of zero nts; its end position was therefore assigned to the same position of the end of the annotated ORF). A total of 78 3'-UTRs with a length of zero nts were assigned.Only the records containing the 'ORF' word in the feature type field identifier from the filtered genome annotation table were considered for the annotation and prediction of 5' and 3' UTRs. This restriction yielded a total of 6,591 ORF candidates for the 3' and 5' UTR assignments. The 3'-UTR ends were first assigned to all those cases that cross-matched the previously described annotation . The latie. the 5'-UTR was defined with a length of zero nts and therefore its initial position was assigned to the first nucleotide corresponding to the first codon of the annotated ORF). 265 5'-UTRs with a length of zero nts were assigned.After all 3'-UTR assignments were completed, the 5'-UTRs were assigned as follows: as 5' UTRs of most of yeast ORFs are unknown, a fixed 5'-UTR length of 100 nts was assigned for all those ORFs where the previous annotated transcript was located at a larger distance than 100 nts. In those cases where an ORF was located upstream, then the previously assigned 3'-UTR end position was considered as the end position of the upstream ORF. 100 nts was chosen because more than 95% of the experimental tags that map into the 5'-UTR are observed at an upstream distance from the initial codon of the ORF of less than 100 nts . A totalIn addition to the putative coding transcripts, all non-coding RNAs available in the genomic annotation table were selected. Then, all the virtual genomic SAGE tags were mapped against these annotated elements, based on their genomic positions. Both complete and partial tag matches to a transcript were recorded. A complete match was defined when the virtual tag was totally contained within the transcript. A partial tag match was defined only if the previous condition was not fulfilled and if the most 5' nucleotide was contained within the transcript; otherwise the virtual tag was defined as intergenic. The same criterion described above was used to define those tags mapping to introns. A total of 775 introns are currently annotated within known transcripts in the yeast genome. The virtual tags partially mapping an exon-intron boundary were annotated as such, but in these cases the potential new tags not present in the genomic sequence that could be obtained by the splicing process were also generated and stored into the database. Only 13 potential new tags fulfilling these conditions were generated.All virtual tags defined as intergenic in the previous step were assessed for their occurrence in the opposite strand of an annotated transcript. All virtual tags located within an intergenic region but fully contained in the opposite strand of an annotated transcript were also annotated as such. These tags could be important for the discovery of new interference RNA elements .Virtual tags located within a transcript, but not at the most 3' end position, were observed with a high frequency experimentally due to internal poly(A) priming of oligo-d(T) primer during reverse transcription . TherefoThe class of virtual tags was defined based on three characteristics: 1) the frequency of occurrence of the tag sequence in the genome (whether it is unique or not), 2) the number of annotations for the tag, and 3) the type of annotations of the tag. Using these three distinct features we have defined seven different quality classes for any virtual tag occurring in the genome. The naming and definition of tag classes are described in Table The confidence of virtual tags was defined based on a combination of the tag class, the frequency of occurrence in the genome and the position of mapping within the transcript. All potential tags in the genome were classified as high, low, or undefined confidence. High confidence tags correspond to those that can be unambiguously assigned to a single known gene or to a single intergenic position in the genome. Low confidence tags correspond to those that should not be visible by experiment, because another tag of identical sequence but mapping at a different location in the genome should be. Undefined confidence tags correspond to those that are fuzzy and cannot be assigned clearly to a single gene or intergenic region in the genome. The procedure that we used to define tag confidence is as follows:First, the probability of observation by experiment was calculated for those tags belonging to the class platinum, copper and iron. In the case of the class platinum, the tags were subdivided into two groups depending if the tag was or was not located upstream from an internal poly(A) region. In the case of those tags that were not defined as next to an internal poly(A) site we calculated their frequency of occurrence at different positions in the transcript from the 3'-UTR end, using the currently known experimental SAGE data Figure . To miniie. tags belonging to the silver class), an assessment of the confidence was carried out based on some tag features and on the previously obtained probabilities. The probability of occurrence is obtained from the previous data for all the instances of a particular tag sequence. If an instance of a tag maps to an intergenic region in the genome, then the probability of observing copper and iron tag sequences is used. If an instance of a tag maps into a transcript, then it is first evaluated if it is located upstream from an internal poly(A) region or not. In the case of the former, the probability of a tag mapping upstream from an internal poly(A) region is used; otherwise, the probability is obtained based on the position within the transcript that the tag is found. Once the individual probabilities are obtained for all the instances of the tag sequence, a pairwise comparison table is built, which contains all-against-all odds ratios among the instances. Then, if a single instance of a tag has odd ratios higher than 5.0 against all other instances, this tag is defined as a high confidence tag, and all other instances as low confidence. Otherwise, all tag instances are assigned an undefined confidence.Second, all tags belonging to the classes platinum and copper were defined as high confidence. In the case of non-unique tags in the genome, or in the case of unique tags with multiple annotations (We compiled all experimental information available from SAGE experiments in yeast. These include three independent works -17, accoThe mapping process of experimental SAGE-tags against the virtual library was performed by assigning to the experimental tag the annotation of the high confidence virtual tag, when possible; otherwise, the experimental tag was assigned to multiple transcripts and/or intergenic regions with an undefined confidence.A web server that uses the HGA-based annotation described in this manuscript for the genomic mapping of experimental SAGE tags from yeast or for the exploration of the virtual SAGE-tags on this organism has been implemented and it is freely accessible.Project home page: Operating systems: MacOSX, Linux, WindowsProgramming language: C++, ANSI C, PERL, PHP, MySQLOther requirements: noneLicense: noneAny restrictions to use by non-academics: none


During gene expression analysis by Serial Analysis of Gene Expression (SAGE), duplicate ditags are routinely removed from the data analysis, because they are suspected to stem from artifacts during SAGE library construction. As a consequence, naturally occurring duplicate ditags are also removed from the analysis leading to an error of measurement.An algorithm was developed to analyze the differential occurrence of SAGE tags in different ditag combinations. Analysis of a pancreatic acinar cell LongSAGE library showed no sign of a general amplification bias that justified the removal of all duplicate ditags. Extending the analysis to 10 additional LongSAGE libraries showed no justification for removal of all duplicate ditags either. On the contrary, while the error introduced in original SAGE by removal of naturally occurring duplicate ditags is insignificant, it leads to an error of up to 3 fold in LongSAGE. However, the algorithm developed for the analysis of duplicate ditags was able to identify individual artifact ditags that originated from rare nucleotide variations of tags and vector contamination.The removal of all duplicate ditags was unfounded for the datasets analyzed and led to large errors. This may also be the case for other LongSAGE datasets already present in databases. Analysis of the ditag population, however, can identify artifact tags that should be removed from analysis or have their tag count adjusted. Serial Analysis of Gene expression (SAGE) is a global and digital gene expression profiling method ,2. It reHowever, duplicate ditags will be encountered naturally with a certain frequency, depending on abundance of the two transcripts from which the ditag is derived ,9. For eHowever, recent developments in SAGE technology have accentuated the problem of discarding duplicate ditags. First, there has been a drive towards using smaller samples for construction of SAGE libraries, facilitating the analysis of cells with specialized functions such as pancreatic cells obtained from biopsies . Such saA prediction of the number of duplicate ditags as a function of the abundance of the two monotags in SAGE and LongSAGE is shown in figure As can be seen in figure However, the assumption of equal proportions of compatible overhangs in LongSAGE is unrealistic. The genome sequence is not a random distribution of nucleotides  and furtet al. have argued that up to 5% false ditags, so-called quasi-ditags should be removed from SAGE analyses [et al. is exclusively affecting rare tags, whereas we are concerning with an error increasingly affecting tags the more abundant they get.The experimental dataset derived from RNA isolated from pancreatic acinar cells by the aRNA-LongSAGE procedure was therefore analyzed in greater detail . It contanalyses . In our The corrective measures suggested by Welle and SnydeIn this study, an algorithm implemented in Perl was developed  which extracts both monotags and ditags from phred or fasta formatted sequence files, defines the two nt overhang of tag pairs in the ditags, and counts and sorts these ditags into compatible overlapping classes. Of the 44,276 tags in total, 34,464 were seen twice or more. Considering these tags only (thus excluding most tags originating from sequencing error) 12,408 (36%) were present in duplicate ditags. A major complication of the analysis is the presence of most abundant tags in several forms differing in length by one or rarely by two nucleotides. Thus a single tag may be split into two or more compatible overlapping classes. For this analysis, only tags between 40 and 42 nt were considered . These accounted for 98.6% of all ditags  using equation 3  for each ditag. Assuming normal distribution of the standardized residuals, the standard deviation is calculated for all ditags observed more than once. An observation is classified as an outlier if the standardized residual is larger than three standard deviations (99% confidence). The standardized residuals are plotted in figure found in the TIGR Human Gene Index  and five other libraries derived from pancreatic tissue . The anaAlso, it is important to consider how the removal of duplicate ditags influences the initial identification of a gene as regulated in a comparison of two transcript profiles. To assess whether this changes by exclusion of duplicate ditags, we compared the pancreatic acinar library with one derived from pancreatic ductal cells with and without the inclusion of duplicate ditags. Excluding duplicate ditags, 122 tags was identified as statistically significantly regulated (P < 0.05 with Bonferroni correction). Including duplicates yielded 56 new tags, while three fell below the statistical cut-off   are representative of the actual distribution of tag molecules, the expected occurrence of a duplicate ditag AB in SAGE can be approximated bywhere D is the number of ditags, P the probability, and T the number of monotags observed.The expected occurrence of a duplicate ditag AB in LongSAGE, assuming even distribution of compatible overlapping classes is then (including duplicate ditags).The expected occurrence of a duplicate ditag AB in LongSAGE, using dataset specific distributions of compatible overlapping classes can be approximated byPPT is the sum of all possible partner tags.where TStandardized residuals was calculated as follows A SAGE experiment is performed by digesting cDNA with the frequent cutting restriction enzyme NlaIII, isolating the most 3' fragment and ligating a linker containing the sequence TCCGAC, which is recognized the restriction enzyme MmeI. Tags are generated by MmeI which cleaves the DNA strand 20/18 nt or 21/19 nt downstream of this sequence. Ligated ditags have the general structure CATGXXXXXXXXXXXXXXXX(X)(Y)YYYYYYYYYYYYYYYYCATG, where X denotes tag A and Y denote the reverse complement of tag B. The parentheses indicate that most tags exist in both a short and a long form. Hence, the ditag AB can have the length 40, 41 or 42 nucleotides. Two central base pairs are common to both tag A and tag B and originate from the overlap used during ligation. The Perl script, LongSAGEbias.pl [additional file In the case of 41 nucleotide ditags, the ditag AB is first analyzed. Since A can exist in a 41 nt ditag both in the long and a short form, two predictions are made and the one closest to the observed is chosen. Then, the ditag BA is considered in an identical manner. The standardized residuals are calculated and the results are written to tabulator separated files easily imported into any spreadsheet for further analysis. Assuming the ditag counts are Poisson distributed, the mean can be estimated as the observed count and the standard deviation as the square root of the observed. The confidence interval of ditag counts can thus be estimated as mean ± 2*standard deviation. For small ditag counts this confidence interval extends below zero. Consequently, the standard deviation of the standardized residuals is calculated from ditags observed four or more times only (4-2*√4 = 0).The algorithm can be set to include all duplicate ditags, remove all duplicate ditags and adjust the observed ditag counts that fall outside the confidence interval to the prediction value.In sum, libraries derived from pancreatic acinar cells, ductal cells, and four libraries from different grades of pancreatic intraepithelial neoplasia were analyzed from pancreas. In addition, 5 potato tuber libraries derived from 6 week old minitubers, at harvest, two libraries from 60 days post harvest dormant tubers, and from tuber tissue excised from under an emerging sprout.LongSAGE tags of 17 nt + CATG were extracted from the human RefSeq v. 16 fasta file and the dinucleotide overlap distributions determined using the PERL script dinuccount.pl .LongSAGE tags from libraries generated from all potato and pancreatic tissue were extracted using the Perl script sage-phred.pl. For pancreatic acinar and ductal cells the tags were mapped to the Human Gene Index  using saJE, AMH and KLN have designed the analysis of duplicate ditags. JE have produced scripts and performed the analysis. SAH and AMH have performed the LongSAGE studies on pancreatic tissue. ALH carried out the LongSAGE analyses on the potato. KLN drafted the manuscript, which was extensively discussed and modified by KLN, AMH, JE and KGW. Finally, all authors read and approved the final manuscript.Pancreatic acinar LongSAGE. Additional file Click here for fileObserved and predicted LongSAGE ditags of pancreatic acinar cells. Additional file Click here for fileMost abundant transcripts with and without the removal of duplicate ditags. Additional file Click here for filelongsagebias.pl. This file contains the PERL script that performs the ditag analysis described.Click here for file


The growth of sequencing-based Chromatin Immuno-Precipitation studies call for a more in-depth understanding of the nature of the technology and of the resultant data to reduce false positives and false negatives. Control libraries are typically constructed to complement such studies in order to mitigate the effect of systematic biases that might be present in the data. In this study, we explored multiple control libraries to obtain better understanding of what they truly represent.First, we analyzed the genome-wide profiles of various sequencing-based libraries at a low resolution of 1 Mbp, and compared them with each other as well as against aCGH data. We found that copy number plays a major influence in both ChIP-enriched as well as control libraries. Following that, we inspected the repeat regions to assess the extent of mapping bias. Next, significantly tag-rich 5 kbp regions were identified and they were associated with various genomic landmarks. For instance, we discovered that gene boundaries were surprisingly enriched with sequenced tags. Further, profiles between different cell types were noticeably distinct although the cell types were somewhat related and similar.We found that control libraries bear traces of systematic biases. The biases can be attributed to genomic copy number, inherent sequencing bias, plausible mapping ambiguity, and cell-type specific chromatin structure. Our results suggest careful analysis of control libraries can reveal promising biological insights. Sequencing-based Chromatin-Immunoprecipitation (ChIP) study has been rapidly gaining traction. Introduced around late 2004 with ChIP-SACO Many interesting techniques proposed thus far have been successfully applied to a host of high-throughput sequencing ChIP (htsChIP) data. We can loosely classify these techniques into (i) those that uses single htsChIP library solely  genomic copy number variations, (b) mapping bias, (c) sequencing bias, and (d) chromatin and/or experimental bias. This study intends to explore the extent of these systematic biases.To investigate how much genomic copy number influence the control library, an in-house array CGH data (unpublished data – N.P.) of the MCF-7 cells was used as the benchmark for copy number variations in MCF-7. A whole cell extract library was also generated from MCF-7 and followed by direct ultra high-throughput sequencing using Solexa Genome Analyzer platform. Using Equation (1) and 1 Mbp sliding window see , we estiet al.Similar analyses were also performed using three mouse WCEseq libraries published by Mikkelsen Another likely source for systematic bias lies in the mapping procedures. For the purpose of assessing this bias, we used the repeat regions as a surrogate for heavily biased regions. We found that a number of repeat classes were significantly enriched (p<1e-3) for WCEseq tags, while some were unexpectedly depleted of tags . The depNext, we examined the tag density distribution across the genome. From this analysis, we noticed that some of the spikes did not fall into any repeat regions. This led us to ask the following questions: How many significantly deviating spikes are there in a typical WCEseq library? Could they be all explained by Satellite or other repeat? Or are they coming from other genomic features? To answer this, we took the mouse WCEseq libraries and analyzed them at 5 kbp resolution. For each 5 kbp non-overlapping window, a p-value was computed for tag enrichment within the 5 kbp window assuming random uniform distribution of tags found in the overarching 1.5 Mbp region. Even after FDR-adjustment of multiple hypotheses In all the mouse WCEseq libraries used in this study, the TSS was correlated with a sharp spike of tag population , howeverThe dense 5 kbp regions were also pervasive among intragenic regions. Around 88.26% of the significantly dense 5 kbp regions of the NP WCEseq library were found to be associated with intragenic regions . This obUsing the accompanying expression data in It has been reported that the sequencing efficiency of next generation sequencers is influenced by the nucleic acid composition of the DNA fragment being sequenced We started our analyses by comparing genome-wide profiles of various libraries at low 1 Mbp resolution. The fact that we could reasonably estimate the copy number using fragment density at low 1 Mbp resolution supports the assumption that a significant proportion of the fragments are random noise from the genome and that these random noise are predominantly influenced by the underlying genomic copy number. Consequently, this also supports the notion that WCEseq library should be able to negate bias from underlying chromosomal abundance (copy number). Having said that, though, copy number did not appear to be the sole component in influencing genome-wide profiles of WCEseq. When comparing three WCEseq libraries, which are from very similar and relatively normal genomes, we saw that they were not extraordinarily correlated even at low resolution. The observation suggested the presence of other biases. This was further confirmed by analyses at higher resolution, in which we found that tag-rich 5 kbp regions were non-randomly associated with repeats and gene boundaries (TSS and TES).From our analyses of localized spikes and dips around the TSS and TES, one might suspect that these features are primarily due to mapping bias. If this is the case, the three mouse WCEseq libraries should have roughly the same profile. However, we instead observed clearly distinct shapes of tag density at the TSS. Furthermore, the consistent phased profiles of sense and antisense tags  suggesteAll the evidence gathered thus far strongly suggests that WCEseq profile is cell-type specific. Since sequencing and mapping biases are expected to be similar among libraries of the same species, the cell-type specific signals should be coming from the other two sources of bias (i.e. copy number or chromatin/experiment bias); although it has to be noted that the degree of tag enrichment or scarcity in repeat regions (which are the archetypic regions with mapping bias) were not completely uniform among the mouse WCEseq libraries. Obviously, WCEseq profiles will be different if the different cell types have distinct copy number profiles. However, chromatin bias was apparent in WCEseq from ES, NP, and MEF cells, which are expected to be normal and non-amplified. Tag densities near gene boundaries were distinct in the three libraries and were correlated to the genes' expression levels. For example, only 8.63% of the significantly dense 5 kbp regions found in NP WCEseq library was also found to be significantly dense in MEF WCEseq library  were obtained from a published work An array comparative genomic hybridization readout  was also obtained to measure the genomic copy number of MCF-7.c is the estimated copy number, d is the number of tag counts within the region, w is the length of the region, and λ is the expected number of tags per base pair computed as the total number of tags in the library divided by the total gap-less genome length.The following method was used to generate genomic copy number estimation using WCEseq library. With the assumption that other biases are minimal and should not greatly affect the distribution of the tags, the genomic copy number of a given region can be estimated as:d and copy number c can be described using Equation 2 below:Genomic copy number estimation from ChIP-PET data requires two fundamental steps. First, as the library contains both signal and noise fragments, we need to first be able to extract the noise part. For this we consider only singleton PETs λ is the expected number of tags per base pair computed locally for each region being considered. The second term denotes the fraction of random PETs expected not to overlap with other fragments The first term of equation 2 denotes the amount of singletons expected had there be no overlapping of random PETs in a region, where In our analysis, we used sliding windows  to compute the average copy number from MCF-7 ER ChIP-PET, MCF-7 WCEseq, as well as from the three mouse WCEseq libraries. The same sliding windows were used in averaging the copy number readouts from the MCF-7 aCGH data, which was used as the benchmark in the MCF-7 study. Pearson's correlation was employed to assess the signal concordance within these windows among every pair of libraries. Comparison of MCF-7 aCGH and MCF-7 ER ChIP-PET was done based on hg17. To compare the aCGH data to WCEseq estimate, we first converted the aCGH data into hg18 assembly using the liftOver tool of UCSC Genome Browser.Tag densities computed in our study were based on 50 bp averaging and normalized against the total number of regions inspected. Tags mapped to sense strand and tags mapped to antisense strand were considered separately in As a proxy for mapping bias, we looked for irregularities in the number of tags mapped to different repeat classes. Repeat annotations were taken from UCSC Genome Browser database Having observed that copy number variation explains the coarse-scale profile of WCEseq libraries, we asked whether there exist finer-scale irregularities beyond what can be explained by copy number. To do this, we divided the genome into 5 kbp non-overlapping windows and assessed overabundance of tags while taking into account the local tag density within 1.5 Mbp window. For each window, we compute a p-value of tag overabundance using Poisson distribution as a null hypothesis, with the expected rate of tags based on the 1.5 Mbp window. After calculating the p-values for all 5 kbp windows, the p-values were corrected for multiple hypotheses using the FDR method The identified tag-rich 5 kbp regions were then associated with gene regions and boundaries , x could be uniquely mapped, and x.Let x in a given library. Clearly, x, or x could be mapped back with confidence to x, denoted as Following the above definitions, let We sought to roughly measure the bias that is correlated with the CG content. As a null hypothesis, libraries of simulated tags were constructed for tags of length 26 bp, 27 bp, and 29 bp, through random sampling of the genome sequences. Tags from H3K4me3 ChIPseq libraries were used as positive control. Comparing the resultant cumulative distributions, the WCEseq libraries were found to be relatively closer to the random tags compared to that of the H3K4me3 libraries  experiment is to infer the first factor, i.e. the underlying fragment distribution Given a hts library, we can measure the distribution of CG-content distribution of the DNA fragments associated with the observed tags, i.e. Table S1Testing a model of gene profile bas on WCEseq tag density. A proxy test for tag density model around genes (Supplementary (0.01 MB PDF)Click here for additional data file.Table S2Sequencing depth of the libraries analyzed in this study(0.01 MB PDF)Click here for additional data file.Figure S1Comparative density profiles of tags mapped to forward strand (black lines) and reverse strand (blue lines) in a 5 kbp window centered around middle of Satellite repeats. As the enrichment of tags in Satellite repeats were likely to be resulted from mapping issues and other random noise, no well-positioned fragment was expected, resulted in closely correlating density profile of forward tags and reverse tags.(0.09 MB PDF)Click here for additional data file.Figure S2Comparison of 5 kbp tag-rich regions across WCEseq libraries. (a) A Venn diagram showing the tag-rich regions from the three Wcseq libraries. Regions from ES WCEseq library is negligible due to its shallow sequencing depth. Only 374 dense regions were found to be common in NP and MEF sets. It represented only 8.63% and 26.7% of tag-rich regions from NP and MEF libraries respectively. (b) Comparison of tag-rich regions that are associated with TSS. 296 TSS-associated tag rich regions were common, representing 20.6% and 28.6% of the total TSS-associated tag-rich regions found in the NP and MEF libraries. Common tag-rich regions of NP and MEF were mostly  TSS-associated.(0.02 MB PDF)Click here for additional data file.Figure S3A schematic model of WCEseq fragments distribution across a typical gene, based on observations in (0.01 MB PDF)Click here for additional data file.Figure S4Cumulative distributions of tags based on their C+G content. Distributions of WCEseq tags (red curves) were relatively close to simulated tags , indicating that sequence composition bias is relatively mild. As a comparison, similar curves generated from H3K4me3 ChIPseq tags were also drawn (green curves).(0.06 MB PDF)Click here for additional data file.Figure S5Tag density (50 bp average) profiles after CG-content normalization. The normalization assumed that each tag represents a 150 bp fragment, taking into account the tag direction. Each tag was reweighted such that the CG-content distribution of the fragments matched that of randomly sampled uniquely-mapped simulated tags. Shown above are profiles around transcription start sites (TSS) and transcription end sites (TES) across three mouse WCEseq libraries. The black and blue curves denote density of tags mapped on the sense and antisense strands respectively.(0.12 MB PDF)Click here for additional data file.Figure S6Expression levels of genes were correlated with CG-content normalized tag density in WCEseq libraries. Density profiles (50 bp average) of tags around TSS and TES of highly expressed (red) and lowly expressed (green) genes. The curves show combined density of sense- and antisense-mapped tags. Tags were reweighted based on the CG-content of the corresponding 150 bp fragments.(0.13 MB PDF)Click here for additional data file.


Tag-based techniques, such as SAGE, are commonly used to sample the mRNA pool of an organism's transcriptome. Incomplete digestion during the tag formation process may allow for multiple tags to be generated from a given mRNA transcript. The probability of forming a tag varies with its relative location. As a result, the observed tag counts represent a biased sample of the actual transcript pool. In SAGE this bias can be avoided by ignoring all but the 3' most tag but will discard a large fraction of the observed data. Taking this bias into account should allow more of the available data to be used leading to increased statistical power.Three new hierarchical models, which directly embed a model for the variation in tag formation probability, are proposed and their associated Bayesian inference algorithms are developed. These models may be applied to libraries at both the tag and aggregate level. Simulation experiments and analysis of real data are used to contrast the accuracy of the various methods. The consequences of tag formation bias are discussed in the context of testing differential expression. A description is given as to how these algorithms can be applied in that context.Several Bayesian inference algorithms that account for tag formation effects are compared with the DPB algorithm providing clear evidence of superior performance. The accuracy of inferences when using a particular non-informative prior is found to depend on the expression level of a given gene. The multivariate nature of the approach easily allows both univariate and joint tests of differential expression. Calculations demonstrate the potential for false positive and negative findings due to variation in tag formation probabilities across samples when testing for differential expression. Tag-based transcriptome sequencing libraries consist of a collection of short sequences of DNA called tags along with tabulated counts of the number of times each tag is observed in a sample. These observed tag counts represent a sample from a much larger pool of mRNA tags in a tissue or organism. In the past, Serial Analysis of Gene Expression (SAGE) was the most commonly used technology for generating libraries of tag counts. SAGE libraries have been used to address a number of biological questions including: estimating transcriptome size, and estimating the density of relative expression levels. Most frequently, SAGE was used to assess differential expression across cells from different tissues or strains, or cells grown under different experimental conditions. Next generation methods such as Digital Gene Expression (DGE) tag profiling  now provAs has been repeatedly noted in both SAGE and DGE studies e.g. -4, the mWhile it is intuitively sensible to analyze the prevalence of an mRNA by aggregating multiple tags derived from it, such tags are often analyzed separately . At bestSaccharomyces cerevisiae  o o9] offeThe goal of a SAGE experiment  is to saIn both technologies the restriction enzymes used to create the tags cut at very specific sites within the cDNA. For example, the restriction enzyme used by  cleaves While some genes will have no AE sites, many genes have multiple sites at which the AE could cleave the cDNA. Given that the AE is expected to act in a site-independent manner, a single cDNA molecule can be cut by the AE in multiple places. However, because only the fragment of cDNA that is attached to a streptavidin bead is retained during the experimental process, the site closest to the bead (i.e. the 3' most site) that is actually cleaved is the only site that can lead to an observable tag j-1p. This corresponds to the probability of no cleaving in sites 1 to j - 1, and a cleaving at site j. Note that this probability is independent of what happens at the AE sites 5' from the jth site. The fact that the expected distribution of tags varies with AE cleavage probability p can be used to estimate p from the library of tag counts; see [Because only cDNA that is attached to a streptavidin bead is retained during the experimental process, tags are created from the 3' most AE site that is actually cleaved Figure . Let ki nts; see .ith category of mRNA follows a geometric distributionIt follows that the probability of generating any of the possible tags from the tag formation probability.where the sum is over all non-ambiguous tagging sites. We refer to this quantity as the p is known to a very high precision. The variation in the tag formation probability between genes stems from variation in the number of AE sites as well as the number of ambiguous tagging sites. Given p, the only uncertainty in the estimate of ϕi results from ambiguous tags; this problem may be partially eliminated through techniques that generate longer tags; see [ϕi to be known constants  allows us to accurately estimate this sampling bias and correct the inferences made from tag libraries.t =  represent the aggregated observed tag counts for individual genes. Here l is the number of genes that contain at least one unambiguous AE site and ti is the total number of observed tags that can uniquely be attributed to an AE site in gene i. .) It is natural to view this vector as a sample from a multinomial distribution with l categories, t ~Multi  where θ = , θi represents the frequency of tags from gene i in the tag pool, and ϕi distorts the abundances of observed tags, it is clear that θi represents a biased estimate of the true proportion of mRNA from gene i in the overall pool. Unfortunately, this true proportion of mRNA, denoted mi, is clearly the quantity of interest. [θi to mi with the following simple expression:Before the tag counts are considered, we assume that the data is processed to retain only informative tags, i.e. all ambiguous or orphan tags are removed, as is standard practice. Let the vector nterest.  relates ϕi is the known tag formation probability based on Eq. (1) and the proportions mi are positive and sum to one. The bias corrected likelihood model is then,where mi is straightforward due to the fact that the likelihood function is maximized at the same location irrespective of the way the model is parameterized. Consider the observed sample proportion ti/ttot. The fact that the mi are positive and must sum to one along with Eq. (2) force the maximum likelihood estimates of Direct maximization of the likelihood with respect to the parameters m is difficult. The existence of the normalization term ∑jmjϕj in the denominator of the left hand side of Eq. (4) makes computation of Fisher's information matrix taxing, particularly for the large dimensional vectors encountered when working with SAGE data (i.e. l is of the order 103 to 104). In addition, because the number of categories is generally within an order of magnitude of, or possibly even greater than, the number of tags sampled, most categories have either zero or only a few observations. These relatively small counts call into question inferences such as chi-squared tests which are based on asymptotic approximations.While computation of the maximum likelihood estimates (MLE's) is relatively straightforward, constructing confidence intervals for m,As an alternative, we consider a Bayesian approach to the problem. The constraints lead naturally to the assumption of a Dirichlet prior on αi is the parameter describing any prior information we have on the value of mi. Combining this prior distribution with the likelihood function given in Eq. (3) leads to a posterior distribution proportional to the productwhere mi. However, a number of difficulties severely limit the range of prior parameters that can be used; i.e. those priors with appreciable weight relative to the observed sample sizes. Given the bias in the observed data, the Gibbs sampling based approaches for inference based on the posterior of the mRNA proportions introduced here are more flexible, and require fewer assumptions than analytic techniques. The methods are also highly computationally efficient. While the assumption of independent cleaving resulted in a geometric model, it is important to note that alternative models of tag formation can be substituted into the Bayesian algorithms without making any further adjustments to the model. introducflat priors , they note that while the posterior mean provide improved average accuracy with respect to sums of squared errors across all categories, estimates of categories where large counts are observed were shrunk excessively in order to boost the estimated probabilities of cells with few or no counts. Due to the massive number of categories and the extreme imbalance in observed frequencies , the estimates for frequently observed genes tend to consistently underestimate the true proportions while the reverse is true of genes with very low expression proportions. This observation highlights the main weakness of shrinkage estimators such as the posterior mean. While they perform better on average across categories, they may perform poorly on particular categories that may be of primary interest. [Joint estimators of the relative proportions of individual tags in SAGE experiments based on posterior means from a conjugate Dirichlet-Multinomial model were explored by  and haventerest.  addresser, were known then the data could be modeled as a standard Dirichlet-Multinomial model. By proposing a Poisson distribution for r, posterior inferences can be made. Detailed descriptions for these algorithms are given in the Methods section. Gibbs samplers based on these algorithms all produce posterior samples of m, the vector of relative proportions of each gene in the mRNA population. In addition, DPB produces samples representing N, the hypothetical total number of mRNA transcripts in the population while MD produces posterior samples of r, the number of unconverted transcripts. These quantities may be relevant in studies of the number of unique transcripts.Three hierarchical approaches are proposed to model aggregate tag counts while taking into account the tag formation probability. The Dirichlet-Poisson-Binomial model (DPB) extends the method of , who modm in all three algorithms. Two parameter vectors α1, ..., αl) were tested. The flat prior sets αi = 1 for all i while the tub prior sets αi = 1/l. The flat prior effectively assumes that a hypothetical previous experiment produced 1 tag for each category. As the name suggests, the flat prior represents a uniform density over the parameter space. The tub prior assumes that the prior information is equivalent to that of a single tag. The density of this prior takes a bowl or tub shape. The preponderance of mass along the edges forces the estimates of mi to be small unless significant counts are observed for that gene.A Dirchlet prior distribution was assumed for the proportion vector S. cerevisiae and analyzed by [l = 6, 178 is the number of genes in the sample. For each of the three methods, we compared posterior means from the Gibbs sampler to unadjusted multinomial MLE's, corrected MLE's based on Eq. (4), and the analytically derived joint posterior mode given in [flat prior are plotted versus rank for the 20 genes with largest tag counts. Equations (3) and (5) dictate that the corrected MLE and the posterior mode coincide perfectly in this case. Both posterior means and posterior modes based on the DPB bias correction deviate as much as 40% from the unadjusted MLE for many of the most frequently tagged genes indicating the importance of the correction. Posterior modes and means follow nearly identical trends but with the modal estimates being uniformly larger. Figure tub prior in the DPB case. Here one can see the ithcorrected MLE and posterior mean now coincide up to simulation precision (≈ 1%). As with the flat prior, all estimators generated using the tub prior deviate significantly from the unadjusted MLE's.To analyze performance, we applied each algorithm to data collected from the log-phase growth of lyzed by . Here, lquations  and (5) Both Figures Graphical displays based on the results of the DMB and MD algorithms had very similar appearances and so are not shown. However, meaningful differences in posterior means generated by the methods and across the two priors do exist and are discussed in the following section.m3, which corresponds to the open reading frame YAL003W, were investigated for all approaches. This gene was observed in 32 of the 14,285 tags and was selected randomly among the set of genes with medium to large tag counts. Autocorrelations of both sequences were tested at various lags. Results given in Table flat prior may generate slightly larger correlations than the tub but in both cases autocorrelations are very low between samples with lags as small as 10.In order to ensure that autocorrelation did not adversely effect parameter estimates, convergence analysis was performed. Posterior samples for the proportion N in the DPB algorithm and the number of unconverted transcripts r from the MD method. When using the flat prior, high correlation among posterior simulations of N exist at all tested lags leading to unreliable inferences. Interestingly, the tub prior leads to negligible correlations among samples at all measured lags. Using the MD method, the autocorrelation in samples of r decreases to 0 after 50 simulations when using the flat prior. Samples are uncorrelated at lags as small as 10 when using the tub prior.Table l = 6, 178, 5 million samples from the DPB algorithm required 21.7 and 19.3 minutes with the flat and tub priors respectively. The DMB was slightly slower taking 30.7 and 25.2 minutes to run. Finally, the MD method completed 5 million samples in 20.2 and 19.3 minutes, respectively.In terms of computational efficiency, with m is usually the quantity of interest, far fewer samples would be needed in practice. This would significantly reduce the computation times for the algorithm.In order to avoid any effects due to autocorrelation our real data experiments stored only the last of every hundred samples for analysis. Inference for means was based upon the final 1000 of these stored samples drawn after an extensive burn-in period of 400,000 simulations. Because the vector mi from simulated libraries. The proportion of times the computed interval covers the true known simulation proportion mi is then recorded. Accuracy is assessed by how close the observed coverage percentage is to the desired level of 95%. The average interval length of the 95% posterior intervals was considered as a second criteria of inferential accuracy but no meaningful differences in average interval length were observed among the three methods.Although all methods produce similar trends in their estimates, quantitative differences do exist. It is also important to quantify the effects of the prior distributions on the analysis. Because the inferential quality is often more relevant in scientific investigations of relative and differential expression than point estimates, we attempt to contrast inferential quality of the three methods by examining marginal 95% posterior intervals constructed for mi values for library sizes l = 6, 178 and l = 1, 000. One clear conclusion is that under the simulation protocol and the priors considered, the DPB method has the best general performance across the range of mi values for both priors. In contrast, the DMB and MD methods, which have very similar performance with almost identical coverage values across all categories and priors, offer poor coverage for medium and large categories under the flat prior. All methods provide accurate coverage under the flat prior for the intermediate values of mi (i.e. .0000167 - 0.000912) which represent the bulk of the genes used in our simulations. Below this range, all three methods have a tendency to overestimate the true mi. This is due to the fact that the magnitude of αi for the flat prior is on the same order of magnitude as the observed tag counts and leads to poor coverage performance. In contrast, all three methods tend to underestimate the true mi value in the abundant categories. This shrinkage effect was discussed earlier; see [Table shrinkage effects become more pronounced as the number of genes l increases further degrading the quality of the estimates. This shrinkage is most acute for DMB and MD methods applied to larger library sizes, which perform poorly for the segments with the. As noted above, the flat prior works well across a wide range of values but performs poorly in the extremes. Figure tub prior works well for the majority of genes where the flat prior fails. For example, the tub works well in large mi categories because it shrinks the estimates very little. Its weakness; it adds almost no mass to categories with small positive values of mi and, if no counts are observed, intervals are produced with both endpoints near 0. Figures mi gene. Focusing on the left panel of Figure mi systematically underestimate its true value. This leads to upper interval endpoints being systematically too small. The tub prior on the right corrects this phenomenon well. On the left of Figure mi being drawn well above their actual values by the reversing of the shrinkage for small mi categories. This leads to reasonably accurate coverage. In the right panel we see that tub prior fails miserably in this case. Intervals for genes with 0 counts collapse close to zero systematically underestimating the true mi values.Not surprisingly, tub prior being relied upon for larger count categories while the flat prior is used for the remaining categories.Because these methods are very efficient to compute, both methods can be applied to analyze a single library with the Tag based transcriptome sequencing such as SAGE is most commonly used to identify differential expression of genes across groups of libraries. It is important to point out the consequences of differences in tag formation probabilities in such studies along with the advantages of the proposed methods in this context.p is experiment dependent [A and B. Letting pa and mia represent the cutting probability and relative proportion of mRNA for the ith tag in experiment A and similarly for B, the theoretical odds ratio for the tag proportions across libraries A and B isBecause the anchoring enzyme AE cutting probability ependent , it is sj in experiment A, Ω is the true odds ratio, and kj is the number of AE positions upstream from which the tag was derived. The approximation holds when both pa and pb are large (i.e. > 0.5) and the ith expression level mi is small in an absolute sense for both experiments, conditions that are almost universally met in SAGE studies.where k = 0, and ϕja = pa then the odds simply reduces to (mia(1 - mib))/(mib(1 - mia)), the exact odds ratio desired. However, suppose all tags are allowed and the experimenter tests differential expression for the ith tag, which derives from an AE site 1 position upstream from the 3' end. The tag formation probability now takes the form p(1 - p). Assuming cutting probabilities pa = .92 and pb = .96 we see that our estimate of the odds ratio is overestimated by a factor of ~1.9 potentially leading to a false positive diagnosis. In fact, this phenomenon could result in a sizeable proportion of both false positive and false negative conclusions. If SAGE analysis were restricted to 3' most AE sites and all data from upstream tags were eliminated from the library, ϕi would be constant and sampling bias would be eliminated by analysis using odds ratios (logistic regression coefficients are estimated log-odds ratios). Once again, the caveat to this approach is that a significant proportion of the observed tags may be discarded. The need for the adjustments we propose stems from an effort to accurately combine multiple tags arising from the same mRNA and offers the ability to utilize a much larger fraction of the data collected leading to more power for differential testing.If only data derived from the 3' most tagging site of each gene is analyzed so that i across two libraries, individual Monte Carlo samples from each library can be differenced, mi1 - mi2, and the distribution of these differences used for inference; see [[Monte-Carlo sampling mechanisms such as DPB can easily be applied to evaluate differential expression across groups of libraries. In the case of comparison for gene ce; see [, Sectionm. Importantly, our method requires no asymptotic conditions to be met in order to guarantee the validity of the results.The Monte-Carlo sampling nature of the algorithms presented here and their computational efficiency leads to several advantages over recent methods -16. FirsThis work focuses on a general biasing mechanism that may have a significant impact on the interpretation of libraries generated by SAGE and closely related methods. Beyond drawing attention to the consequences of incomplete digestion, two main contributions are presented. First, we derive and analyze three Bayesian algorithms that provide corrected posterior inference for relative proportions of genes or tags in the overall population. Second, through calculations we deduce the consequences of tag formation bias on testing of differential expression and discuss how the algorithms derived here can be used to correctly assess differential expression.This work compliments the earlier work in  by proviflat prior was effective over a wide range of categories but resulted in excessive shrinkage for the most abundant categories. For a fixed number of sampled tags, this shrinkage effect becomes more severe as one increases the number of categories. Hence, aggregating tags provides a second advantage since it greatly reduces the number of categories used in an analysis. The proposed tub prior provides little shrinkage and posterior intervals based on this prior are very accurate for abundant categories. In practice, both priors should be applied and inference should be based on the samples with the larger average.The proposed methods are appropriate when incomplete digestion is the main source of multiple tag generation. They may be applied to both tag level data and to inference at the gene level based on aggregated counts. If possible, aggregating tags will provide better inferences due to larger available counts. Of the three approaches, the DPB method provided the most accurate confidence intervals over the widest range of relative proportions and we recommend its exclusive use. In addition, the choice of prior also plays an important role in the effectiveness of the algorithm. Of the two priors tested, the We note that the sampling algorithms presented are independent of the model for tag formation probability and models other than the geometric model discussed can easily be substituted. It should also be possible to extend the proposed methods using a mixture methodology as suggested by .Correction of tag formation bias may play a significant role in improving power in differential expression studies based on SAGE or related tag libraries. To ensure valid testing, one must either include bias correction or eliminate non-3' tag counts from the analysis. Furthermore, the ability to effectively test for changes in groups of genes (gene networks) is now possible due to the multivariate nature of the posterior distribution. This advantage may become significantly more important as more elaborate studies and techniques are developed in the future.S. cerevisiae and other microorganisms. However, alternative splicing is widespread in most multicellular organisms [Due to the overall simplicity of genome architecture, alternative splicing is generally not a problem when analyzing gene expression in rganisms ,2 and grrganisms .Extending our model in such a way should allow us to make inferences about the distribution of mRNA isoforms produced by a gene based on the distribution of tags experimentally observed.Conceptually, the problems caused by alternative splicing are similar to those caused by tag ambiguity between different genes. For example, in the case of alternative splicing, the challenge is in determining the mRNA isoform from which each tag originates. Similarly, in the case of ambiguous tags, the challenge is in determining the gene from which each tag originates. Thus it is plausible that data interpretation problems caused by both alternative splicing and ambiguous tags could be overcome by extending our model to include multiple sources of a single tag.S. cerevisiae [We explicitly consider three strategies to simulate from the posterior distribution given by Eq. (5). The algorithms discussed are tested for inferential accuracy using simulated data as well as being applied to a published SAGE data set that analyzes a yeast organism revisiae . The pubrevisiae .R-environment (Version 2.6.2) on an 8 core, Intel Xeon 2.66 GHz desktop server running Linux Ubuntu 8.04. R-scripts that implement the Gibbs sampling algorithms described below are provided; see Additional file All simulations described below were computed using N exists within the sampled cells. The total size N is random across samples and follows a gamma distribution that is rounded down to the nearest integer. The choice of gamma here is convenient due to its role as a conjugate prior to the Poisson distribution. Given N, the relative proportions of the categories of mRNA, mi, are unknown and assumed to follow a Dirichlet distribution with prior α1, ..., αl). The αi will typically be identical resulting in objective inference.The DPB approach, inspired by Casella and George , assumesN and mi, that the actual number of mRNA's of a certain type gi, i = 1, ... l, extracted from the group of cells, satisfies a Poisson distribution with mean μ = N·mi. Finally, the restriction enzyme process generates a tag count ti for a particular mRNA transcript in a binomial fashion based upon the tag formation probability ϕi. Hence, the hierarchical data generating mechanism follows, Ti~Binomial, gi~Poisson(N * mi), m ~Dl). We refer to this model as the Dirichlet-Poisson-Binomial (DPB) model.Because cells contain mRNA transcripts from thousands of different genes, the probability of seeing any particular type is low. It is therefore logical to assume, given gi may not add up to the total counts N. However, this approach allows us to infer the total population size N. Together, the elements described above give a joint posterior distribution,A first weakness of this model is that the sum of all counts ∑¿From this expression, we can deduce the set of full conditional distributions,δ = . Gibbs sampling can be implemented by iteratively simulating from each conditional after replacing any unknown random quantities in the conditioning set with simulation values from the previous iteration; see [where ion; see .γ1, γ2) which effect the mode of the posterior distribution. One possibility for choosing values of these parameters is to minimize the distance between the approximate analytical mode discussed in [The hierarchical model considered here is not identical to Eq. (3), but depends upon prior parameters  = 16438.81. This was chosen intentionally to determine if the posterior would converge to a reasonable estimate of N.In our simulations we used a shape parameter N, the total number of mRNA in the sample is assumed to follow a Poisson distribution with mean λ. Given this mRNA population size, the vector g of counts for each category of mRNA prior to tag formation follows a multinomial distribution,The Dirichlet-Multinomial-Binomial (DMB) approach is arguably more faithful to the sampling mechanism inherent in SAGE than DPB. mi and are assumed to follow a Dirichlet distribution with parameter vector ϕ1, ϕ2, ..., ϕl) is the vector of tag formation probabilities and letting δ = , the full conditional distributions are derived to be,whose probabilities are the mRNA proportions m *.where N. One drawback is that the observed data provides no information for posterior inference about the population size N. Iterative maximization for mode calculation is not viable due to the discrete nature of the multinomial conditional distribution.This formulation is more natural in the sense that it restricts the pre-tagging counts to sum to the population total θi = (miϕi)/(∑miϕi) and basing inference on the posterior of Eq. (5), a more straightforward approach uses the concept of missing data which is often associated with the EM algorithm; see [t with an extra category that represents any cDNA that is not converted to a tag. This count, r, is not observed, but if a distribution such as the Poisson is proposed, we may consider a Bayesian approach. Given the value of r and assuming a Dirichlet prior on the unknown initial proportions m ~Dl, the resulting posterior distribution for m is,Instead of re-normalizing the probabilities thm; see . We augml + 1 categories compared with the l categories in the prior distribution. Exact computation of the conditional expectations E(mi|r) is now straightforward. Using the formula for the mean of a Dirichlet distributionThis resulting posterior distribution is a Dirichlet distribution with mi, which must sum to one, gives r. Hence, the marginal expectation of mi across values of r isSumming the expectation over r ~Poisson(μ) then the posterior distribution can be written,Gibbs sampling is also available for this problem and extends inference to Bayesian interval estimates. If The full conditional distributions arer, μ must be selected. A logical mean for the Poisson is ttot ∑imi(1 - ϕi)/∑imi ϕi since ∑mi(1 - ϕi) = 1 - ∑mi ϕi is the probability that an mRNA is not converted into a tag. Equation (4) provides a useful estimate of ∑mi ϕi in the case of a flat prior.In order to apply the Gibbs sampler a value for the prior mean of ti + αi - 1)/(∑i(αi + ti) + r - l) while the mode for the Poisson is the mean rounded down to the nearest smaller integer. For example, considering a flat prior for m along with a prior mean of μ = 10, 100 for r, the posterior mode of the missing data model is nearly identical to the exact analytical mode given in [Like the DPB algorithm above, the missing data algorithm also admits an iterative optimization procedure in order to compute the posterior mode. The mode of the Dirichlet conditional given by  is  =  to compute individual probabilities ϕi. The number of cleaving sites followed a Poisson distribution with mean 2 with 1 count added to each category. This ensured that each "gene" has at least one cleaving site. The cleavage probability was set at p = .55 based on estimates given in [Simulation of libraries was based upon the proportions estimated from the aggregated l, and prior, 1,000 libraries, tj, each containing n = 15, 000 tags were simulated. For each simulated library, each of the three proposed algorithms was used to generate 20,500 posterior sample vectors mjk, k ∈ 1, ...20, 500. Every 20th sample was collected after a burn in period of 500 samples resulting 1,000 Monte Carlo samples of m for each method. Samples were then used to generate mean, median and 95% marginal posterior intervals for each of the l gene categories. Coverage percentages for the ith gene category are computed by finding the proportion of times that the interval for category i from a particular method contains the true proportion mi across the 1,000 simulated libraries tj . Figure Using the above protocol, for each combination of library size, RLZ devised and implemented the algorithms, computed the experiments and wrote the majority of the manuscript. MAG developed the tag formation model, prepared the real data, wrote parts of the manuscript, and provided subject matter expertise and computational resources. WMB helped edit the manuscript and construct graphical displays. AA assisted in development of the algorithms. All authors have read and approved this manuscript.SAGEGibbs.R. File contains a script which implement the Gibbs Samplers described in the paper. The script is written in the R-environment.Click here for file


Extramedullary hematopoiesis (EMH) is defined as the presence of hematopoietic stem cells such as erythroid and myeloid lineage plus megakaryocytes in extramedullary sites like liver, spleen and lymph nodes and is usually associated with either bone marrow or hematological disorders. Mammary EMH is a rare condition either in human and veterinary medicine and can be associated with benign mixed mammary tumors, similarly to that described in this case.Hematopoietic stem cells were found in a benign mixed mammary tumor of a 7-year-old female mongrel dog that presents a nodule in the left inguinal mammary gland. The patient did not have any hematological abnormalities. Cytological evaluation demonstrated two distinct cell populations, composed of either epithelial or mesenchymal cells, sometimes associated with a fibrillar acidophilic matrix, apart from megakaryocytes, osteoclasts, metarubricytes, prorubricytes, rubricytes, rubriblasts, promyelocytes, myeloblasts. Histological examination confirmed the presence of an active hematopoietic bone marrow within the bone tissue of a benign mammary mixed tumor.EMH is a rare condition described in veterinary medicine that can be associated with mammary mixed tumors. It's detection can be associated with several neoplastic and non-neoplastic mammary lesions, i.e. osteosarcomas, mixed tumors and bone metaplasia. Hematopoiesis in the adult animal is restricted to the marrow cavity of flat bones and long bones epiphysis . Thus, eMammary EMH is a rare condition and it is generally associated with non-neoplastic hematopoietic masses in both woman and bitches. However, the presence of hematopoietic activity can also be seen as an incidental finding associated with mammary neoplasia ,4,9-12.Cytological examination has been used since the 60's to investigate mammary lesions in women, and it is nowadays largely accepted as a screening test for such lesions in veterinary medicine. It is a minimally invasive and low cost diagnostic method which allows differentiation between non-neoplastic and neoplastic mammary lesions. In addition, it can accurately predict the malignant potential of mammary tumors if performed by an experienced pathologist -18.Based upon prevailing cytological characteristics, canine mammary tumors can be classified as epithelial, mesenchymal, or mixed type according to its origin ,18.Proliferation of epithelial cells from ducts and/or lobes, myoepithelial, and mesenchymal cells, in addition to cartilaginous, bone or myxoid fibrous tissue are sometimes seen in a variety of mammary neoplasm in dogs. These compound tumors are classified under the designation of mixed tumors ,15,18-20Even though the tumor cytological examination may show considerable tissue heterogeneity , hematolA 7-year-old intact female non-pure breed dog weighing 8.0 kg was admitted at the School of Veterinary Medicine and Animal Science from the Univ. Estadual Paulista (UNESP), Botucatu, São Paulo, Brazil. On clinical examination it was noted a subcutaneous mass in the left inguinal mammary gland, measuring 0.7 × 0.9 cm, and with 24-week of clinical evolution. The lesion was also firm with a smooth surface, painless, and with no ulceration nor deep muscle adhesion.®, São Paulo, Brazil) and a 10 ml syringe . The collected material was spread on five histological slides, and then fixed with methanol P.A.  and ethanol 95% . Three slides were stained with Giemsa and two with Papanicolaou stain. Samples were examined under light microscopy and classified according to Allen et al. [Thoracic radiography, hematological and blood biochemistry analysis, and cytological evaluation of the lesion were performed in order to achieve a diagnosis. For cytological analysis, samples were obtained from 2 different areas using a fine needle . Then, the samples were analyzed under light microscopy.Hematological parameters and urea, creatinine, alkaline phosphatase, aspartate aminotransferase and alanine aminotransferase values were within reference interval considered normal for the specie Table . Thorax Cytological evaluation Figures  and 2 reHistopathology revealed Figure  an encapSpontaneous mammary tumors in bitches are very similar to those in women, which makes it a good model for comparative studies ,16 in teThe mixed type, either benign or malignant, is one of the most common mammary gland tumor in bitches ,21,22, uThe cytological examination usually shows that most of the pleomorphic adenomas present groups of epithelial, myoepithelial, and bone tissue cells, as well a chondromyxoid stroma . SimilarAccording to Allen et al. , during The presence of one of the three lineages of hematopoietic cells out of the bone marrow is sufficient to characterize EMH ,4. In thEMH is generally seen in patients with bone marrow and hematological diseases such as chronic anemia, hematopoietic neoplasia, medular hyperplasia, suppurative bacterial infections, or cardiorespiratory conditions ,3,4,8,25Several hypothesis has been suggested to explain mammary EMH. Functional disruptions of bone marrow, e.g. drug therapy or myelofibrosis, stimulates circulating stem cells to find a favorable environment and differentiate into hematopoietic cells . Focal lIn this case, no biochemical or hematologic changes that could characterize a functional failure of bone marrow were detected, which could result in the production of chemical mediators capable of promoting favorable environment for stem cell implantation. The patient didn't suffer from any other disease, and was not under current drug therapy. No previous surgical manipulation of the mass was attempted. Thus, the pathogenesis of this case shall probably be related to intrinsic factors of the neoplastic process.As far we know there are no reports in human medicine literature regarding the presence of erythrocytes, myeloids cells, and megakaryocytes in mixed or metaplastic breast tumors, and pleomorphic adenomas. In veterinary medicine there is only one report from Fernandes et al.  that repDespite the existence of one previous report, the importance of those findings relies on the possible relationship with advanced medullar disorders. Moreover, mammary EMH is generally asymptomatic and clinically mimics a neoplasia.Sampling multiple different sites of the same tumor mass increases its representativeness and possibility of an accurate diagnosis, since there is a heterogeneous tissue composition within the same tumor. Hence, the EMH cytological diagnosis is straightforward when hematopoietic cells are present. However it's important to emphasize that the simple fact of finding this cell types does not allow a final diagnosis, since other neoplastic and non-neoplastic condition, i.e. osteosarcomas and bone metaplasia, may present similarly. Despite all that, histopathological examination is always recommended.FG performed the analysis and interpretation of cytologic and histologic findings, photographed images and helped to write the manuscript. MMC participated in clinical research, sampling and helped to write the manuscript. LNM has contributed to the analysis and interpretation of cytology and histology and for the preparation of the manuscript. JRVPL conducted clinical research and was responsible for collecting samples. NSR is the supervisor responsible for the case report and the review of the manuscript. All authors read and approved the final manuscript.