Hybridization interactions between probesets in short oligo microarrays lead to spurious correlations
© Okoniewski and Miller; licensee BioMed Central Ltd. 2006
Received: 23 January 2006
Accepted: 02 June 2006
Published: 02 June 2006
Microarrays measure the binding of nucleotide sequences to a set of sequence specific probes. This information is combined with annotation specifying the relationship between probes and targets and used to make inferences about transcript- and, ultimately, gene expression. In some situations, a probe is capable of hybridizing to more than one transcript, in others, multiple probes can target a single sequence. These 'multiply targeted' probes can result in non-independence between measured expression levels.
An analysis of these relationships for Affymetrix arrays considered both the extent and influence of exact matches between probe and transcript sequences. For the popular HGU133A array, approximately half of the probesets were found to interact in this way. Both real and simulated expression datasets were used to examine how these effects influenced the expression signal. It was found not only to lead to increased signal strength for the affected probesets, but the major effect is to significantly increase their correlation, even in situations when only a single probe from a probeset was involved. By building a network of probe-probeset-transcript relationships, it is possible to identify families of interacting probesets. More than 10% of the families contain members annotated to different genes or even different Unigene clusters. Within a family, a mixture of genuine biological and artefactual correlations can occur.
Multiple targeting is not only prevalent, but also significant. The ability of probesets to hybridize to more than one gene product can lead to false positives when analysing gene expression. Comprehensive annotation describing multiple targeting is required when interpreting array data.
Sources of noise in microarray experiments may be numerous [1, 2], thus most researchers try to minimize its influence or estimate it through various quality control, normalization and outlier filtering procedures . One source of variation is cross-hybridization (CH), which occurs when unintended sequences hybridize to a probe alongside the intended target. In the case of Affymetrix arrays, which use a set of short (typically 25-mer) oligonucleotide probes to target a transcript, hybridization conditions are carefully controlled with the aim of minimizing the effect of CH due to non-specific binding . In addition, each Perfect Match (PM) probe is accompanied by a Mismatch probe (MM), in which the middle residue has been changed. The intention is that this can be used to provide a measure of the level of CH associated with each PM probe. A more detailed discussion of CH in short oligo arrays may be found in . From October 2004, Affymetrix also started to display brief summaries of cross-hybridization within their own NetAffx service .
In some circumstances, probes may match exactly to more than one transcript. This is important because these probes can no longer be identified with a unique transcript, but are instead dependent on more than one gene product. The situation is rendered somewhat more complex by the fact that Affymetrix arrays use more than one probe (typically, 11 PM/MM pairs – together referred to as a "probeset") to target each transcript. Recently, several databases have been built to provide a mapping of Affymetrix probesets to known transcripts [7–10], to sequences from cDNA microarrays [11, 12], or for applying algorithmic approaches to cross-platform or cross-species comparisons . A recent paper  presents a global overview of the interpretation of GeneChip arrays, and the need to update annotation to match the continued evolution of genomic databases. The solution includes the redefinition of CDF files, similar to what was proposed initially in , which may be sufficient in many cases.
The issue of 'multiply targeted' probes is important because they have the potential to result in cross-talk between the probesets they are part of. If their effects are significant, and expression summarizing algorithms are unable to control for them, then one outcome of this will be that otherwise unrelated probesets will appear correlated, since they are being driven by a shared signal.
The ADAPT database  was used to investigate the extent and significance of multiply-targeted probesets in Affymetrix expression data (see methods). Use is made of the fact that the platform's combination of short oligos and strict hybridization conditions, which are designed to maximize binding to the PM probes whilst minimizing binding to the MM ones. This makes it viable to use in silico methods to identify which probes are likely to bind with 100% identity to which transcripts. We refer to cases of exact matches between probe and transcript as Multiple Targeting (MT), to distinguish from the more general case of cross-hybridization, in which matches with less than 100% identity may occur.
Particular attention is directed at the influence MT can have on the apparent correlation between probesets' expression measurements. Since Pearson correlation is scale independent, it is not influenced by the overall magnitude of either signal being compared, but rather on the similarity in their shapes. Although it may seem counter-intuitive, when two signals are superimposed, the amount of correlation found between each of the original signals and the combined one is driven by the relative variance of those two signals, not by their mean intensity (an example and further discussion of this can be found in the supplemental material). Many microarray data analysis techniques rely on correlation analysis, with the majority of methodologies aiming to draw a distinction between genes that are, in some way, co-occurring, co-expressed or correlated and those that do not follow a significant common pattern. Methodologies such as hierarchical clustering [14, 15] and relevance networks [16–18] make direct use of the Pearson correlation coefficient of expression values between probesets, whilst others (such as ANOVA and more general linear models), are ultimately based on correlation-like principles.
In this paper, we consider the extent and structure of these relationships, followed by an investigation of how much effect they have both on signal strength and on the correlation between probesets.
The prevalence of multiple targeting in oligo arrays
An analysis of the HG_U133A array reveals that many transcripts (Ensembl: 7,257; RefSeq: 6,702) are matched with multiple probesets (i.e. case a in Fig. 1) while almost half (10,223) of the total 22,215 probesets (excluding control probesets) show exact matches (with 1 or more PM probes) to more than one Ensembl (9,460) or RefSeq (9,666) transcript (i.e. case b in Fig. 1). For comparison, 18,722 probesets were found to match to at least one well-known transcript.
The effect of MM probes is minimal: the number of MM probes that can hybridize exactly to known transcripts is about 1,000 times smaller (Ensembl: 1,899 MM matches vs. over 1,956,000 PM matches, RefSeq: 1,962 MM vs. 1,922,000 PM) – most of them singleton matches to unrelated sequences. Thus we exclude MM probes from subsequent analyses. Since MM probes were not considered, and RMA makes no use of these probes in its computations, RMA processed data is used for all calculations presented here, although similar effects were also observed with MAS5 processing.
Affymetrix probeset names are supposed to identify probesets that are associated with multiple targeting. In particular, those marked "_x_at" are identified as being non-specific. Similarly, "_s_at" probesets are identified as potentially targeting different gene family members or splice variants. The analysis shows that many of the probesets associated with MT are not identified in this way and are simply annotated " _at" (2,189 according to Ensembl matches; 1,496 for RefSeq). These numbers are likely to be underestimates because ADAPT was built using only well characterized sequences. Thus, a significant number of the standard "_at" probesets are involved in MT.
Structures of multiple targeting in oligo arrays
The two basic building blocks of MT interaction networks are Probeset-Transcript-Probeset (PTP) motifs (Figure 1a), and Transcript-Probeset-Transcript (TPT) motifs (Figure 1b). Depending on the robustness of the analysis algorithms used to process array data, the presence of either motif can be expected to lead to non-independence between the expression profiles of the participating probesets.
Summarization of PTP and TPT motifs for various Affymetrix arrays
Families of related probesets
Probesets may be involved in multiple PTP and TPT motifs, resulting in an MT-network. This can be expressed as a graph in which nodes represent transcripts and probesets, while edges represent matches between transcripts and probesets, labelled with the number of matching probes involved in the interaction. Such graphs are informative because so many probesets have the potential to be involved in MT (almost half for HGU133A arrays). Since Affymetrix arrays measure the binding of cRNA sequences to sequence-specific probes, the searches used to define MT help catalogue which binding events are possible. Knowledge of MT interactions is important because it begins to describe what is actually being measured in a microarray experiment.
Figure 2 shows one such graph, laid out using LGL . Edges attached to RefSeq transcripts are painted red, Ensembl ones, green. Blue is used to mark the strength of MT, with intensity corresponding to the number of matching probes. The LGL graph, when magnified, shows a set of disconnected families -detached sub-graphs of various complexity. Thus, almost all of the MT relationships are local ones.
To build families, the database was queried to identify all PTP motifs. Then, a simple search algorithm used to identify the maximal graph that can be reached from a starting probeset using the identified motifs. Probesets that are not involved in any PTP motifs result in trivial families that consist of just a single probeset. An additional step is used to eliminate "hub probesets", as described below.
For HG_U133A arrays, this process results in the identification of 3,859 families containing at least 2 probesets (for examples – see Additional file 2). The mean number of probesets in the family is not high -about 2.56. Interestingly, 429 families (involving a total of 1,529 probesets), were found in which family members were annotated to different genes. Importantly, these families were not simply comprised of "_x_at" probesets: 456 were annotated "_at" and 497 – "_s_at".
A full list of MT families is included in the supplementary data (see Additional file 3), along with an applet that allows the exploration of these families, attached to exemplary expression data (see Additional file 4).
There is a group of probesets (not always annotated by Affymetrix as " _x_at") that match a large number of transcripts, usually with a small number of probes. They may be called "hub" probesets, because their expression combines signals from many available transcripts. In the network of probeset-transcript relationships, hub probesets often join together smaller families of probesets, often many at a time. A typical example of a hub probeset is "221992_at" which matches to 44 RefSeq or Ensembl transcripts, with an average 3.18 probes per match, or "210524_x_at" (127 matches, 1.5 probe on average).
Number of hub probesets and hub probesets not annotated x_at depending on the condition of the number of matching transcripts
Transcripts matched – more than:
Quantitation of the effect of multiple targeting
Probes found by the database searches to target multiple transcripts, generally have a higher measured signal than those that target unique transcripts. For example, the average measured expression level in the Gene Atlas data is 16% higher for multiply targeted PM probes and over 80% higher when the PM – MM difference for individual PM:MM probe pairs is considered.
These numbers refer to differences in the raw probe intensities, which are subsequently grouped into probesets and processed by an expression summary tool such as MAS5 or RMA. The following sections investigate whether these changes at the probe level are carried through to the MAS5 or RMA processed expression summaries, and the influence they have on Pearson correlation.
Real data, same transcript
Figure 1b shows a situation where the expression level of a probeset might be expected to be driven by two different transcripts. Since there is no independent estimate available for the expression levels of the individual transcripts involved in TPT motifs, simulation experiments were performed to mimic the effect by artificially spiking raw expression data.
Figure 5 shows the results of one such simulation, designed to consider the effects of the presence of an additional transcript in equal abundance to the intended target. It can be seen that as the number of spiked probes increases, the signal becomes more pronounced. As previously observed with real data, a single matching probe can have a significant influence on the computed expression level. Even when the expression level is relatively high the signal from only 2 probes can be sufficient to lead to apparent differential expression. Even so, the largest fold changes are generally restricted to the lower intensity probesets, indicating that both MAS5 and RMA do a good job at reducing the effects of outliers.
Intensity vs. correlation
Both real and artificial datasets demonstrate that MT can have a significant effect on correlation, even when only a small proportion of probesets are involved in the interaction. Algorithms such as RMA and MAS5 successfully employ robust averaging techniques (such as median polishing or a Tukey's biweight) to reduce the effect of outliers. Thus, when only a small number of probes in a probeset are involved in MT, changes in measured expression level are expected to be generally small. This is confirmed in both the real and simulation datasets.
However, even when overall changes in intensity are minimal, increase in Pearson correlation can still be high. This is because Pearson correlation is driven by similarity in profile shape, not intensity; small amounts of stray signal can lead to large increases in r, even if the overall mean between probesets are very different. Since Pearson correlation centers each variable about its mean, and scales it by its standard deviation, correlation is entirely dependent on the relative shape and variance of the two signals, not their overall intensity. When two signals, a and b are compared to their sum, s, the signal that is most correlated with s depends not on their relative sizes, but on their relative variance. This is counter-intuitive but important to recognize when considering the effects of interacting signals on correlation (see Additional file 9).
In situations where probesets are already strongly correlated, the addition of extra signal due to cross hybridization with another transcript might be expected to reduce correlation. Spiking experiments found this to be the case (data not shown). Interestingly, however, even though there are occasions where r is reduced by multiple targeting, the general tendency is towards significantly increased correlation (as shown in Figure 3; similar figure for simulation experiments – see Additional file 10).
False positive rates will also be raised because otherwise absent probesets with signals resulting only from background levels of non-specific hybridization can experience additional, structured, signal due to exact matches to transcripts other than the intended target.
Functional homogeneity and spurious correlations in families of probesets
Analysis of MT-families shows that out of the 3,859 shown in Figure 2, 395 contained probesets annotated (using the BioConductor annaffy package ) to 2 or more UniGene clusters. When gene symbols are considered, annotation becomes even more ambiguous: 429 families contained transcripts annotated to different genes. Thus, even though the majority of families are homogenous with respect to UniGene and gene symbols – some 10–15% (depending on size of the family and source of annotation) may be annotated to different genes. This translates to about 1000 probesets.
It is clear that multiple targeting is an important artefact within microarray data: nearly half of all probesets on the HG_U133A array are associated with MT. When real expression data are considered, it can be seen that these probesets are significantly more correlated than would be expected by chance. These results are also supported by simulation experiments, using datasets derived from real experimental data, that allow MT to be considered in a more controlled framework. MT can lead to increased correlation between associated probesets, even when only a small proportion of their probes are involved. Although expression summary algorithms are successful at reducing the effects of outlier probes, the do not remove them completely, and small amounts of stray signal can still have a significant influence on correlation. The reason for this apparent paradox is the scale-invariance of Pearson correlation; absolute signal is not important. What is important are the variance and (effectively) the relative similarity in shape of the expression profiles. For this reason, particular care must be taken when analysing expression data using correlation-based approaches. The situation is also further complicated by the fact that MT occurs at a probe level – adding additional signal to individual probes within a probeset – but correlation is calculated after normalization and expression summarization using an algorithm such as RMA or MAS5. This additional complexity makes it difficult to reliably predict what will happen when signals are combined. However, empirical data (Figure 6) show that influence on correlation is dependent on the relative variance of the two probesets being combined. As expected, high variance spiked probes generally have more of an effect than low variance spikes, but interestingly, adding low variance spikes to low variance data (the magenta line in Figure 6) has more of an effect than adding high variance spikes to low variance data (the cyan line). This is likely to be a consequence of the expression summarization and normalization that is imposed on the data.
One consequence of MT is that because it serves to add structure to otherwise random probesets with no genuine signal, it can lead to the detection of false positives unless the presence of cross-matching probesets is known. Analysis of the intensity distributions for MT and non-MT probesets shows a considerable degree of overlap (see Additional file 11). This means that MT probesets cannot be removed simply by filtering on intensity. In fact, because MT generally increases signal strength, such filtering might actually serve to enrich for MT probes.
MT is ultimately a sequence-based event; it occurs when two sequences show 100% identity across the 25bp targeted by a probe. At the level of a probeset, this is most likely to occur when transcripts show a high degree of sequence similarity. The relationships is troublesome, because a major use of expression data is to identify probesets (and, via annotation, genes) with correlated expression profiles, and to use these relationships to infer functional similarities. Since sequence similarity is itself often the basis by which common function is inferred , sequence similarity combined with MT has the potential to become a self-fulfilling prophecy.
A search of the database found that about 5% of family members contained probesets annotated to different genes. Thus, the chances of finding a spurious functional relationship due to MT between a pair of randomly selected genes is small. However, this is optimistic, because microarray analysis generally involves filtering to produce a set of significant probesets (either by magnitude of change, or by statistical confidence). The result of such filtering is to enrich the final 'hit list' not only for real biological effects, but also for anything else that is consistent, including biochemical or sequence based artefacts such as MT. This is illustrated by the heatmap in the Figure 8; MT families fall into separate clusters against a background of randomly selected probesets.
One possible solution to MT is to redefine probesets so that probes targeting the same transcript are placed into larger probesets representing the entire sequence, as proposed by . This is the approach taken also by , but authors conclude that "under many circumstances it is not possible to generate transcript-specific probe sets for genes with multiple transcripts based on probes available on the current generation of GeneChips". Thus they may be used to make distinction at the level of genes, but not at the level of transcripts or splice variants – MT with all its consequences, still exists. There is a compromise to be made between generalisation and maintaining the ability to resolve subtle differences between transcripts and, for example, splice variants.
The issue becomes more significant with the new generation of microarrays such as the Affymetrix exon array  that deliberately use multiple probesets to distinguish between individual transcripts from within a set of splice variants expressed by a particular gene. The result is a many-many relationship between gene, transcript and probeset.
Annotation schemes that attempt to compress these many-many relationships into a one-to-one mapping lose the complexities inherent in the system. Grouping together a probeset that targets more than one transcript with probesets that target one or more individual transcripts, results in MT occurring between the new probeset and all the other transcripts it shares probes with. From one perspective, many these issues are simply down to annotation. The apparent aretefacts in the data only exist because the probeset annotations do not accurately reflect the transcripts they bind to.
With all solutions, including those that attempt to solve the problem by aggregating probes into larger probesets, annotation is crucial, since inaccuracies will arise unless all the many-many relationships that occur within the data are represented explicitly.
Cross hybridization between probesets is a significant effect that has real consequences for the interpretation of microarray data. It may cause a variety of problems during analysis including false positives and negatives, and generally increased correlation between multiply-targeted probesets. Although the results presented here are for Affymetrix arrays, it is reasonable to expect similar effects to occur with other expression-based technologies. The use of short oligos and strict hybridization conditions makes it possible to perform the in silico searches required to identify MT within Affymetrix data. However, CH is not exclusive to any one platform, and similar behaviour is likely to be seen elsewhere. Expression summary algorithms must correct not only for variation across arrays, but also for variation between individual probes within a probeset. This is generally performed using some kind of robust averaging procedure, but even small amounts of stray signal can lead to high correlations between probesets. Although algorithms such as RMA and MAS5 do a very good job of significantly reducing the influence of outlier probes, they do not always remove it completely – and this is manifested by significantly increased correlation between probesets, even when only a small subset of probes are involved.
Many of the issues described above can be avoided with more detailed annotation. Often the terms 'gene', 'transcript' and 'probeset' are used interchangeably. This is dangerous, because the relationship is not one-one-one, and the existence of MT networks can lead to apparent biological relationships that are, in fact, artefactual. Expression data that is presented simply as a gene list is difficult to interpret properly, since the complexities of the interaction networks implicit within the data are lost. The community should ensure that the actual probeset IDs are always available alongside gene names or transcript accessions. This allows the graph structures associated with gene-transcript-probeset mappings to be explored where necessary and used to fully interpret the complexities of gene expression data.
MT networks and interaction graphs were produced by extracting data from ADAPT and redirecting the output for visualization to LGL , and our own visualization software. As global layouts of graphs such as LGL are static, thus not interactive, because the number of vertices is too big for efficient real-time rendering, an applet was developed for fast and flexible analyses of individual families. These small, local graphs within the applet were realized with the JUNG API .
Databases, experimental data sources and data processing
ADAPT  is a database of mappings between Affymetrix probesets, transcripts and genes. It is populated by searching all probe sequences for exact matches to transcript data taken from RefSeq (Release 11 at the time of writing)  and Ensembl (V30 at the time of writing) . For RefSeq, both "known" and "model" sequences are used; for Ensembl, ADAPT uses those assigned "known", "novel" or "pseudo" status. Both databases are used because they employ different methods to predict transcript/gene sequences.
The ADAPT database was queried (using SQL and RdbiPqSQL database link to R) to extract a set of tables describing all possible MT links between probesets and transcripts, excluding anti-sense strand matches. The probesets may match transcripts with anything from 1 to 16 matching probes. The tables implicitly define an unconnected graph (see Figure 2 and supplemental file 1), and form the basis for all subsequent explorations of MT. In order to consider the strength of the MT effect and its consequences on expression studies, data from ADAPT were combined with expression data from experiments generated using the HG-U133A array. Expression levels were produced using MAS5 and RMA, as implemented in Bioconductor (packages affy and simpleaffy [3, 29, 30]).
Results were analogous when experiments were repeated with MAS5. All plots presented were generated using the Novartis Gene Atlas  dataset. Similar results were seen with both leukaemia  and sarcoma  datasets – publicly available from ArrayExpress.
Pearson correlation was calculated for all the pairs of probesets found to be targeting the same transcript. The distribution of correlation coefficients was calculated for all probeset pairs and for all pairs where one of the probesets matches to a transcript with less than a specified number of probes.
A subset of 50 HG_U133A arrays from Gene Atlas V2 was used as the basis for simulation experiments designed to explore how the number of MT probes influences expression measurements from RMA processed data.
Spiking was conducted as follows: prior to expression summary generation using RMA, 500 probesets were selected at random to be spiked and 500 (at random) to act as a source of spiking data. No filtering was applied to these probesets. Probesets were randomly paired, and between 1 and 10 probe-pairs selected for each probeset (again at random). The signals from the spike-sources were added to the original signals for the spike-targets. In this way TPT motifs were simulated. The resulting simulated data were batch normalized using RMA and compared to the original un-spiked data (again batch normalized using RMA, separately from the first set). In all simulation experiments spiking for the selected probesets was carried out across the entire set of arrays.
In the second experiment, a set of 500 probesets was selected, as before. A second set with the same number of probesets was then chosen at random. These probesets were selected from a subset of the probesets available, generated by filtering the expression data on variance. In this way, both sets could be sampled from probesets with specifically high, average or low variance of expression. High and low variance are defined as the top or bottom 2000 probesets, sorted by of variance, excluding the 100 most extreme ones. Each probeset in the second list was used to supply data for the probeset in the first list; between 1 and 11 probes were chosen and the probe intensities from the second list added to the corresponding probes in the first list. Various levels of influence were applied, adding a specific proportion of one probeset signal to another: PM 11after= PM1before+ f f * PM2, where for f f ranging from 0.05 to 1. In this way, cross-hybridization between probesets in the first list, and the transcripts represented by the probesets in the second list, was simulated.
"A Database of Affymetrix Probesets and Transcripts"
Large Graph Layout
MicroArray Suite – Affymetrix algorithm (MAS 5.0)
perfect match probe
probeset-transcript-probeset network motif
Robust Multichip Average algorithm
transcript-probeset-transcript network motif
This work was funded by Cancer Research UK.
Zhi Cheng Wang and Tim Yates maintain and manage the ADAPT database. We thank Stuart Pepper, Francesca Buffa and Claire Wilson for useful discussions.
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