Estimation and correction of non-specific binding in a large-scale spike-in experiment
© Schuster et al.; licensee BioMed Central Ltd. 2007
Received: 13 December 2006
Accepted: 26 June 2007
Published: 26 June 2007
The availability of a recently published large-scale spike-in microarray dataset helps us to understand the influence of probe sequence in non-specific binding (NSB) signal and enables the benchmarking of several models for the estimation of NSB. In a typical microarray experiment using Affymetrix whole genome chips, 30% to 50% of the probes will apparently have absent target transcripts and show only NSB signal, and these probes can have significant repercussions for normalization and the statistical analysis of the data if NSB is not estimated correctly.
We have found that the MAS5 perfect match-mismatch (PM-MM) model is a poor model for estimation of NSB, and that the Naef and Zhang sequence-based models can reasonably estimate NSB. In general, using the GC robust multi-array average, which uses Naef binding affinities, to calculate NSB (GC-NSB) outperforms other methods for detecting differential expression. However, there is an intensity dependence of the best performing methods for generating probeset expression values. At low intensity, methods using GC-NSB outperform other methods, but at medium intensity, MAS5 PM-MM methods perform best, and at high intensity, MAS5 PM-MM and Zhang's position-dependent nearest-neighbor (PDNN) methods perform best.
A combined statistical analysis using the MAS5 PM-MM, GC-NSB and PDNN methods to generate probeset values results in an improved ability to detect differential expression and estimates of false discovery rates compared with the individual methods. Additional improvements in detecting differential expression can be achieved by a strict elimination of empty probesets before normalization. However, there are still large gaps in our understanding of the Affymetrix GeneChip technology, and additional large-scale datasets, in which the concentration of each transcript is known, need to be produced before better models of specific binding can be created.
Despite the ubiquitous use of Affymetrix GeneChip arrays (Affymetrix has recorded more than 3,600 publications with data collected on this platform), we have a limited understanding of the technology. The physico-chemical details of hybridization of target mRNA on these arrays are still incomplete and models for specific and non-specific DNA-RNA interactions are continuously being refined (a recent example can be found in ). A deeper understanding of these processes is required to better separate experimental variation from biological variation. For example, it would allow for addressing the influence of the amount of labeled RNA on the intensity of the probes that do not specifically bind any transcript in the RNA sample. The removal of non-specific signal will lead to improvements in normalization, and it may also lead to more effective normalization methods, as normalization methods still suffer from some shortcomings .
The Affymetrix technology is remarkably simple and uniform throughout a large number of different array types: every feature on the chip contains millions of identical 25 nucleotide long DNA molecules covalently bound to the GeneChip array. Features are paired on the chip, the two members' sequences being identical except for the central (13th) nucleotide, which is changed to the complementary base in one of the members. The sequence exactly complementary to the target sequence is called PM for perfect match, while the other is called MM for mismatch. A MM probe is designed to measure the non-specific binding (NSB) of its partner PM probe. Feature pairs that probe a specific transcript are grouped into a reporter set. Depending on the GeneChip array type, reporter sets are made of 11 to 16 individual feature pairs, or reporters.
Processing raw Affymetrix expression data usually consists of three different operations on the data: the first operation is the separation of the signal due to specific hybridization of the target sequence to the probe from non-specific signal associated with a background signal from the chip surface and the non-specific binding of labeled cRNA. The second operation is the normalizing of this specific signal between experiments, and the third part is the summarizing of the signals from each probe into a synthetic expression value for the whole probeset. These different aspects of normalization may or may not be separate in the actual software implementation of the algorithm, and their order of application is not necessarily identical for different algorithms. An additional normalization at the probeset level may also improve the performance of a method.
In order to carry out a detailed analysis of the impact of the probe sequence on the observed intensity, one ideally needs a pool of mRNA where the concentration of every transcript is known. A large number of different target sequences is also required to sample the sequence space spanned by the probes. The influence of non-specific hybridization can also be studied, as various levels of target 'promiscuity' are inevitable as soon as the number of target sequences is large. Because of the huge effort required to generate such a controlled dataset, hybridization modeling and normalization calibration to date have been done on high-quality, but much smaller spike-in experiments. But recently, a larger scale dataset of known composition (the GoldenSpike dataset) has been made publicly available , consisting of six hybridizations, three replicates of two different cRNA compositions, hereafter called control (C) and spike-in (S), as the cRNA concentration in the latter samples are always equal to or higher than in the former samples.
Unlike other spike-in experiments in which transcripts are spiked into biological samples of unknown composition (for example, the Latin-square dataset ), all transcripts are known within the GoldenSpike dataset. All the cRNA samples are made of 3,859 clones of known sequence, 1,309 of which have a higher cRNA concentration in the S samples, while the cRNA concentrations of the remaining 2,550 clones are identical in all samples. The concentrations of the cRNA pools span slightly more than one order of magnitude, and the cRNA concentrations of the S samples are between one and four times larger than the corresponding clones' cRNA concentrations in the C sample.
This experimental setup represents a biological situation where roughly one-quarter of the genome is expressed, and among those expressed genes, about one-third are differentially expressed; however, compared to a 'normal' dataset, there are no 'down-regulated' clones, so the data are unusual and heavily imbalanced. This dataset provides a harsh test for normalization methods, as most of them assume a considerable degree of similarity between the mRNA concentration distribution within each experiment. The large differences in amounts of labeled cRNA in the GoldenSpike dataset violate this normalization assumption, and the effects are further increased by the absence of biological variability, as replicates are only technical.
The cRNA samples were generated from PCR products from the Drosophila Gene Collection (DGC release 1.0) . Plates of PCR products (13 separate plates in total) were mixed into 17 pools. Each pool was labeled and added to the final cRNA sample at specific concentrations and hybridized to the Affymetrix DrosGenome1 GeneChip array. This means that the absolute concentration of an individual cRNA transcript is not known, and the concentrations of transcripts within a pool will vary greatly depending on the quality of the PCR amplification for an individual clone. However, the relative concentration between C and S samples for individual transcripts will be known and the same for every transcript within a pool. Choe and colleagues  used the GoldenSpike dataset to compare several algorithms commonly used in microarray analysis and developed a 'best-route' method for the normalization and statistical testing of microarray data. To avoid the problems associated with the imbalance of transcript levels in C and S samples, they normalized the data using a subset of probesets that were known to be at the same concentration in each sample. In the GoldenSpike normalization method, non-specific binding is corrected by subtracting the MM signal from its partner PM signal using the MAS5 method [6, 7], and the PM-MM signals are normalized separately with the loess, quantiles , constant and invariantset  methods available in BioConductor  to create four separate expression measures at the probe level. The PM-MM signals within a probeset are then summarized into one expression value by both the tukey-biweight [6, 7] and the medianpolish  summary methods to create eight different expression measures. The final step of the GoldenSpike normalization is loess normalization of the probeset expression values for each expression measure .
Using receiver-operator characteristics (ROC) curves, the Cyber-T method was determined to be the most sensitive for detecting fold changes and reducing false positives (FPs) compared to a t-test or significance analysis of microarrays (SAM ) method . The Cyber-T method is based on the t-test method but uses a signal intensity-dependent standard deviation to reduce the significance of high fold changes in probesets with low signal intensity . To identify a 'robust' set of probesets that exhibit differential expression, Choe et al.  also recommended a method that combines the test statistics as calculated by Cyber-T of the eight expression values methods. For multiple hypothesis testing correction, the sample label permutation method (as used in SAM) was used to estimate the number of FPs [13–15] and generate q-values (analogous to false discovery rates (FDRs)).
It has been suggested that there are serious problems with the GoldenSpike dataset . Some of the problems are associated with using the dataset to evaluate statistical inference methods, as the distribution of P values for null probesets (that is, probesets with equal concentrations in C and S samples) is biased for low values and is not uniformly distributed between 0 and 1. For the GoldenSpike dataset, there is a bias for null probesets to have low P values, and the bias results in the calculated FDRs being much higher than the actual. We suggest that P value bias is partially due to the MAS5 PM-MM method to correct for non-specific binding.
Due to the high number of FPs at low intensity using MAS5 PM-MM, we were motivated to re-analyze the GoldenSpike dataset to assess the performance of the probe sequence-dependent models (the Naef  and Zhang  models). These empirical models adjust probe signal intensity based on probe sequence. For example, probes that contain many adenines tend to have lower intensity than probes with many cytosines, especially if the adenines and cytosines are in the center of the probe. We tested the ability of the models to estimate NSB of empty probesets and then used the publicly available implementations of the models to compare 300 different combinations of NSB correction/probe-level normalization/probe summary/probeset-level normalizations. Performance of each method was based mainly on the rates of finding true positives (TPs), and FPs and the estimation of FDRs. We also assessed the benefits of combining the statistical analysis of several methods.
Given that there are thousands of transcripts in the GoldenSpike dataset, we were able to expand the analysis of the data to include performance measures of methods at different intensities to detect any changes in performance for probesets with intensities dominated by NSB (empty or low intensity) and those dominated by specific-binding signal (medium and high intensity).
Results and discussion
Alignment of transcripts to probesets
The cRNA samples used in the GoldenSpike dataset were generated from 3,859 clones, and we were able to generate 'transcript' sequence information for 3,851 of the clones based on recent sequence information. From this information, we aligned the transcript sequences to the PM probes and found all the exact matches to PM probes. We were able to map the transcripts that had the same concentration in C and S samples, also referred to as having a fold change of 1 (FC = 1), to at least one probe within a probeset for 2,495 probesets. Spiked-in transcripts that had a higher concentration in S samples (FC > 1) were mapped to 1,284 probesets. Of the remaining probesets, 10,104 were unbound or 'empty' probesets, and 127 probesets could be mapped to multiple transcripts. For mixed probesets, 58 can be aligned to only FC = 1 transcripts and 69 can be aligned to at least one FC > 1 transcript (Additional data file 1). Choe and colleagues  found alignments to a similar number of probesets (2,535 FC = 1, 1,331 FC > 1, 13 mixed, and 10,131 empty).
Greater NSB signal in spike-in samples than control samples
The C and S samples in the GoldenSpike dataset have similar amounts of total RNA hybridized to the Affymetrix chips but have different amounts of labeled transcript. The S samples have almost twice the amount of labeled cRNA hybridized to each replicate chip as C samples (due to the 'spiked-in' transcripts). For the samples to have the same amount of total RNA hybridized, the C samples were supplemented with unlabeled poly(C) RNA. As the cRNA in the C and S samples are made from the same PCR amplification and labeling reaction, the difference in the total amount of labeled RNA hybridized to the chips is the most likely explanation for the empty and low intensity probesets in the S samples being significantly higher than in the C samples. Proper correction for NSB would result in empty and FC = 1 probesets having a log2 difference of zero between C and S replicates.
MAS5 PM-MM is a poor model for estimating NSB
False positives for differentially expressed genes
The most common model for the removal of non-specific binding signal is the MAS5 PM-MM model. In this model, the MM probe intensity is an estimate for the non-specific binding of its partner PM probe. However, this model does not seem to correct for non-specific binding as the intensities of empty S probesets are still roughly 50% greater than empty probesets in C samples (Figure 1b).
False positives using the GoldenSpike MAS5 PM-MM methods
Null subset normalization
FC = 1 subset normalization
FC = 1
FC > 1
Pvalue distributions of null probesets
The q-value of a probeset is defined as an estimate of the proportion of FPs among all probesets with equal or lower q-values. To calculate q-values, a test statistic is generated for the data and for permutations of the data. The permutations are based on randomly re-assigning the sample labels (for example, given the six GoldenSpike RNA samples and three C/S replicates, there are nine permutations of sample labels that do not match the 'correct' labeling), and for a particular test statistic cutoff, the mean number of probesets called significant after sample label permutation is an estimate of the number of FPs for that cutoff value and used to calculate q-values [11, 15]. At a given test statistic, if 100 probesets are significant when the sample labels are correct and on average 10 probesets are significant when the sample labels are permuted, then the estimate of FDR for that cutoff value (q-value) is 0.10.
While the differences in NSB signal in C and S samples account for a significant proportion of null probesets with low P values, there are other issues that will effect the P value distribution of null probesets. A single C and S sample was generated and an aliquot from each sample was used to create each replicate, and technical variation in the methods to generate each hybridization could result in subtle P values biases if not accounted for in the statistical analysis. For example, the mean raw PM values for FC = 1 probesets (1,898, 2,210 and 2,495 for C replicates, and 2,257, 1,803, and 2,466 for S replicates) suggests different sized aliquots and possible pairing between C and S replicates based on aliquot size. Also, most fluidics stations can only hybridize four samples at one time, and with six replicates, there might be two batches of hybridizations. It is beyond the scope of this manuscript to address all the possible sources of technical variation and account for it in statistical models, as we have concentrated on using the GoldenSpike dataset to infer the best methods to correct NSB and have not used the dataset to evaluate statistical methods. With only three replicates, it is also unlikely that technical variation can be properly taken into account. For example, analysis of the Latin Square spike-in experiment (3 replicates of 14 samples with 42 spiked-in transcripts)  revealed similar bias null probesets having low P values bias for null probesets, even when the set of TPs was expanded to include probesets that do not perfectly match the spiked-in transcripts .
Probe sequence-dependent models for NSB correction
Having shown that PM-MM is a poor model for estimating NSB signal, we tested if the non-specific binding signal could be better modeled with the Zhang and Naef probe sequence-dependent models for short oligonucleotide binding. To do this, we used the GoldenSpike dataset at the level of the probes rather than at the level of probesets and took great care to align the probe sequences on the clones' sequences when available. When there was no complete clone sequence, we used the Drosophila Genome Release 4.0  to pad the missing sequence. To reduce any effect of promiscuity, we used only empty probes that cannot be mapped to any clone, even when up to six alignment errors are considered.
We tried to evaluate the success of two models describing NSB of empty probes: a model based on Naef et al.  that assumes that the affinity of a probe can be described as the sum of the single nucleotide affinities across the probe. The second model is based on Zhang's position-dependent-nearest-neighbor (PDNN) model , in which the affinity of a probe can be described by the sum of all nearest-neighbor di-nucleotides within a probe, but the influence of each di-nucleotide is weighted depending on its position in the probe. Both models are described in Materials and methods.
Results of fits on empty probes
The Zhang model predicts that probes with many GC di-nucleotides would have a high signal especially if the GC di-nucleotides are in the middle of the probe, as shown in Figure 4b,c. The fitted binding energy parameters derived for each di-nucleotide in the six experiments are not as consistent as the parameters fitted in the Naef model, but the parameters fitted for the weights associated with each di-nucleotide position are more consistent and confirm the importance of the central part of the probe. Table 2 shows that the Zhang model seems to predict the observations better than the Naef model despite having fewer parameters, which apparently contradicts a previous observation that di-nucleotide binding was not the main effect in the binding . However, our fitted parameters for the Zhang model were significantly different from those publicly available for four human chips and three mouse chips.
We had also planned to use the GoldenSpike dataset to investigate the specific binding signal using models derived from the Zhang and Naef models described above, taking advantage of the fact that the clones' cRNA concentrations are approximately known. Unfortunately, a detailed inspection of the data suggested that there is a very high variability between clone concentrations within a single PCR pool and we were not able to use this dataset to model specific binding.
Comparing methods to generate probeset expression values
Similar to the analysis in , we have compared several methods to generate probeset expression values, but we have chosen to evaluate each method based on the following criteria: the estimation of fold changes for FC = 2 probesets, the ability to separate true fold changes from false fold changes, the rate of finding TPs versus the rate of finding FPs, and the difference between calculated q-values and true q-values. There are too many methods to discuss individually, and we have limited the discussion to groups of methods that have the same NSB correction method and/or same probe summary method, as the choice of NSB correction and probe summary method seem to have the biggest influence on performance.
Accuracy and precision
It has been previously observed that background correction "appears to improve accuracy but, in general, worsen precision" , and various methods have been put forward to measure accuracy and precision. As the concentration of each transcript is not known but the exact fold change is known in the GoldenSpike experiment, we have chosen the mean log2 fold change for the probesets that can be aligned to transcripts with a two-fold difference (FC = 2) between C and S samples to be a measure of accuracy (mean of 125 probesets with the lowest P values as calculated by Cyber-T). As a measure of precision, we have taken 1% of FC = 1 and 1% of empty probesets with the lowest P values. Ideally, the log2 fold changes of FC = 2 probesets would be 1 and easily distinguished from fold changes of null probesets, as empty and FC = 1 probesets are expected to have a log2 fold change of zero.
Performance measured by AUC
While differences between FC = 2 and null probeset fold changes are interesting, it is not a good measure of performance for separating truly differentially expressed genes from FPs. To measure the performance of each method, we calculated the area under the ROC (AUC) using Cyber-T P values as predictions. To allow a comparison of AUC measures based on the presence or absence of transcript, we also made two AUC calculations for each method, one using only probesets with 'present' transcripts (FC > 1, FC = 1, and mixed) and one using all probesets (FC > 1, FC = 1, mixed, and empty).
The use of empty probesets results in a drop of AUC performance, especially when only background correction and not NSB correction is used, and this suggests that empty probesets are a more significant source of FPs that bound FC = 1 probesets. The best performing methods for probesets with present transcripts use GC-NSB, affyPLM or medianpolish probe summary and variance stabilization normalization (vsn) probeset-level normalization, but there is little difference between MAS5 PM-MM and GC-NSB methods when the probesets are normalized with the loess method (Figure 6c).
It is also clear in Figure 6c that the GoldenSpike method (called GOLD in the Figures) for combining the statistical analysis of eight different normalization methods  does not result in performance gains compared to individual MAS5 PM-MM normalization methods. In fact, the combined statistical analysis tends to under-perform the four individual normalization methods that use medianpolish probe summary.
In general, methods that correct for NSB tend to have more accurate q-values when considering all probesets and only probesets with present transcripts, but the q-values generated with all probesets are very poor estimates of the true q-value. The method that gave the most accurate measure of q-values for probesets with present transcripts was the GoldenSpike method, suggesting that combining statistical analyses might be a method to extract more accurate estimates of q-values (Figure 6d).
The AUC performance and true q-value comparisons highlight how difficult it is to compare methods to find a 'best method', and it is best left to the user to determine which is the best method in the context of their experiment. However, it is very clear that empty probesets contribute a significant number of FPs and greatly distort q-value calculation in the GoldenSpike dataset, and users should gauge the contribution of probesets with absent transcripts to estimated FDRs.
Performance is dependent on probeset intensity
We have defined unbound probesets as probesets that are very unlikely to exhibit specific-binding signal (that is, empty probesets and probesets that are specific for transcripts that are too scarce to be detected). The default settings for the MAS5 present/absent algorithm [7, 25] are not stringent enough to identify these probesets, as more than 25% of the probesets classified as having present target transcripts are empty probesets (1,227 out of 4,767 probesets). In addition, there is a significant number of FC = 1 probesets that are not likely to report target transcript specific signal.
To select probesets that are likely to report only NSB signal, we defined unbound probesets as having a mean log2 probeset expression value below 4 for C and S replicates (after GC-NSB correction). There are 10,322 probesets (9,820 empty, 438 FC = 1, 51 FC > 1 and 13 mixed) classified as unbound probesets, and such a strict cutoff is likely to reflect a realistic level to detect true fold changes. Out of the 300 methods to generate expression values, the highest AUC score is 0.697 and reflects a high cost for finding TPs. A P value or q-value cutoff designed to find 5 out of the 51 FC > 1 probesets would result in 225 FPs, and 771 FPs to find 10. The unbound probesets are likely to contribute only to FPs, and any statistical significance associated with these probesets should be ignored or the probesets should be removed from any analysis.
Low intensity probesets
Medium intensity probesets
The AUC performance of medium intensity probesets is better than low intensity probesets, suggesting that the influence of NSB signal is diminished in medium intensity probesets, and when only medium intensity probesets are normalized, AUC performance for RMA background and MAS5 PM-MM methods improves. The best performance is achieved with MAS5 PM-MM/(affyPLM or medianpolish) probe summary/loess probeset-level normalization methods, and the best performing methods when considering all probesets (GC-NSB/(affyPLM or medianpolish probe summary)/loess probeset-level normalization) perform worse than the equivalent MAS5 PM-MM and RMA background correction methods (Figure 11c).
The q-value calculations are also more accurate than low intensity probesets, and MAS5 PM-MM/medianpolish probe summary/(loess or vsn) probeset-level normalization methods have the best combination of AUC and q-value performance, but the combined statistical analysis results in the most accurate FDR estimate (Figure 11d).
High intensity probesets
The AUC performance of high intensity probesets is less than medium intensity probesets, probably due to the chemical saturation of high intensity probesets. When considering normalization with only high intensity probesets, the PDNN and the MAS5 PM-MM/(affyPLM or medianpolish) probe summary/(loess or vsn) probeset-level normalization methods perform best. When considering normalization of all probesets, GC-NSB/(affyPLM or medianpolish) probe summary/vsn probeset-level normalization methods have the best AUC performance but very poor q-value calculations. In general, the q-value estimates are more accurate than low and medium intensity probesets, and for the PDNN methods and the combined statistical method, the estimates of 0.10 q-values are very accurate and have the best balance between AUC performance and q-value accuracy (Figure 11e,f).
Performance of high intensity MM probesets
The 'alchemy' method
It is not practical to subdivide a microarray dataset by probeset intensity and analyze each subset individually with the best performing methods (for example, GC-NSB methods for low intensity probesets, and MAS5 for medium intensity, MAS5 or PDNN for high intensity probesets, and MM probes for very high intensity probesets). Instead, we have chosen 10 methods that have complementary strengths and weaknesses for input into the GoldenSpike statistical method (the 'alchemy' method; see Additional data file 4 for scripts). The benefit of this method is that the combination of four MAS5, four GC-NSB and two PDNN methods to generate expression values outperforms the individual methods and the GoldenSpike method (combined analysis of eight MAS5 PM-MM methods) in AUC performance and true q-value tests. The alchemy method also outperforms the GoldenSpike method when only subsets of probesets are used in the statistical analysis (low, medium, and high intensity probesets and probesets that can be aligned to FC = 1 and FC > 1 transcripts). However, the new method does not solve the problem of FPs associated with the differences in NSB of empty and low intensity probesets and results in very poor FDR estimates when considering all probesets.
True positives and false positives
FC = 1
Mixed, FC = 1
Mixed, FC > 1
FC = 1.2
FC = 1.5
FC = 1.7
FC = 2
FC = 2.5
FC = 3
FC = 3.5
FC = 4
The knowledge of all transcripts in the GoldenSpike dataset makes it an invaluable resource for understanding the properties of Affymetrix short-oligonucleotide whole genome chips, even though the dataset is far from ideal, with major differences in the amount of labeled cRNA hybridized in C and S samples and the substantial imbalance of transcripts due to the spike-in.
Our analysis of the GoldenSpike dataset extends the performance analysis started by Choe et al.  to include empirical models and re-enforces the importance of considering probe sequence for NSB estimation. The empirical probe-sequence models have greatly improved our understanding of the Affymetrix GeneChip technology and indicate that we have a good understanding of NSB signal of empty probesets. The probe-sequence based models are significantly better at estimating and correcting NSB signal than the MAS5 PM-MM method, but the improvement in performance of the GC-NSB single-nucleotide model is only evident with empty and low intensity probesets. At medium and high intensity, where NSB signal contributes significantly less to probeset intensity, the MAS5 PM-MM method allows for better detection of spiked-in transcripts, and at high intensity, the PDNN model works well. This suggests that our understanding of the specific binding signal is poor, and any statistical analysis of an individual method is subject to the faults of that method. We suggest a method that combines the GC-NSB, PDNN and MAS5 PM-MM methods. The statistical analysis combining the methods may compensate for the shortcomings of the individual methods and result in better estimates of FDRs. However, a combined statistical analysis is far from ideal, and a better model of DNA-RNA interaction would be preferable.
Hopefully, the GoldenSpike dataset will result in improvements in both the Naef and Zhang models for separating NSB signal from specific binding signal. There are still big improvements needed, especially for modeling the specific binding signal and correcting for chemical saturation, which require additional large-scale datasets in which the concentration of every transcript is known.
Materials and methods
Mapping of clones to probes
To achieve a faithful picture of the binding between the clones and the microarray chip, we have mapped all probes' sequences onto the clones' sequences, allowing up to eight alignment errors, either with the PM sequence, or with the MM sequence. In order to perform these alignments, we had to have a careful look at the clone sequences. Out of the 3,870 clones used in the experiments, 3,859 are unique (11 are duplicated on two plates), 3,721 are fully sequenced, and 130 have partial sequence information (120 have 5' and 3' sequences, 7 only 5' sequence and 3 are not attached to any sequence, but are still connected to a known gene) and 8 do not have any kind of sequence information. The fly genome release 4.0  was used to fill the missing sequences for these 130 incomplete clones, against which the partial sequences were aligned to determine the missing parts. This padding was not possible for four clones that have 5' and 3' partial sequences, because the 5' and 3' sequences appeared on very distant genomic locations. Sequence completion was also impossible for one clone with only 5' sequence available, because the only match was on the reverse strand of a known gene. For the other 125 incomplete clones, the sequences were completed with genomic sequences, rather than transcribed sequences, since in most cases there was no known transcript compatible with the clone's partial sequence. In total, there were complete experimental sequences for 3,721 clones, the fly genome was used to complete the sequences of 125 clones, and for 13 clones, no sequence information at all was used, either because they did not have any sequence information in the first place, or because the partial sequence information was in contradiction with the fly genome. To this extent, we were able to get an almost exact picture of the cRNA contents in the samples.
We proceeded by considering all alignments with eight or fewer errors, and we were able to classify PM and MM probes according to the strength of their binding with potentially many different clone sequences. To perform NSB model refinements, we retained empty probes that do not bind any clone with less than seven alignment errors; 54,559 empty probes (25,780 PM and 28,779 MM) matching the criterion above were selected. Finally, 5% of probes at each end (most and least bright) were removed from all computations to reduce the influence of possible outliers, which may arise from contamination by the clones of unknown sequence.
B ≈ a + bexp(Ax)
B ≈ a + b/(1 + exp(w T Ae))
where B is the probe's observed brightness, a a constant background and b is proportional to the amount of NSB, which is assumed to be identical between all empty probes, but which may depend on the specific experiment, as is the 'optical background' a. The other parameters, the relative affinities x, the binding energies eand the weights w(necessary because the center of the probe contributes more to the brightness than either end) are assumed to be independent of a particular experiment, and perhaps even valid for different types of GeneChip arrays. The probe sequence is represented by the matrix A, which is such that A ij is 1 when the nucleotide at position i is of type j (j = 1, 2, 3 or 4 for A, C, G and T) and 0 otherwise.
We treated each chip independently and optimized the models' parameters by a least-squares fit against a subset of 30,000 empty probes, leaving the remaining 24,559 empty probes for cross-validation. The fits were based on log values, to reduce the dynamic range of the observations. This version of the Naef model contains 77 parameters (2 scaling parameters a and b, and affinities for A, C and G for each of the 25 nucleotide positions; the affinity for T is constrained by the three others). The Zhang model contains only 42 parameters (2 scaling parameters, 16 binding energies and 24 weights, 1 per di-nucleotide position). The ratio of observations to parameters is greater than 350 (Naef model) and 650 (Zhang model), taking into account the trimming of the 5% most and least bright probes for each experiment. The parameter optimization results are summarized in Figure 4.
We also tested the fitted parameters on the cross-validation probes, to ensure that the binding affinities x, or the binding energies eand their corresponding weights wwere equally able to reproduce intensities from another set of sequences. For this operation, we first put the xaffinities, binding energies eand weights won the same scale for the six experiments. We then used the mean values of those scaled parameters over the six experiments as fixed parameters for the 'scaling fits', allowing for a scaling parameter s in the exponent's argument in equations 1 and 2. Therefore, three variables (a, b and s) were optimized against the cross-validation probe intensities. The agreement between the cross-validation intensities and the corresponding modeled values obtained from those fits is very close to the agreements reached by the models where x, e, and wwere refined.
With the exception of PDNN calculations in Perfect Match , all of the analysis and graphics produced for this publication used the statistical program R version 2.3.1  and packages within BioConductor . When possible, we broke the process into background/NSB correction (RMA background , MAS5 PM-MM [6, 7] and GC-RMA ), probe-level normalization (loess, constant [6, 7], quantiles , vsn  and invariantset ), probe summary into probeset values (medianpolish , li-wong , tukey-biweight [6, 7], farms , affyPLM , and avgdiff) and probeset-level normalization (vsn and loess). In addition, we calculated probeset values with RMA , GC-RMA  and probe logarithmic intensity error (PLIER) estimation  within BioConductor and with the DNA-Chip Analyzer (dChip)  and Perfect Match  software. All probeset values were imported into R, and normalized using FC = 1 probesets as a subset.
Additional data files
The following additional data are available with the online version of this paper. Additional data file 1 is a table of the alignment of clones to probesets. Columns represent (in order): Affy, Affymetrix probeset identifier; Clone, the Drosophila Gene Collection clone that aligns to that probeset; C, the concentration pool of that clone in C samples; S, the concentration pool of the clone in S samples; fold, the fold change between S and C samples for the clone; score, alignment score indicating the quality of the alignment (14 = alignment to all 14 probes in probeset); pool, pool number; well, well position in PCR-plate; plate, plate number. Additional data file 2 is a figure showing performance measure for low intensity probesets with and without empty probesets. AUC performance and q-value estimates for low intensity probesets when empty probesets are (a, c) excluded from the analysis and (b, d) included. TPs are FC > 1 probesets and mixed probesets that can be aligned to spiked-in transcripts. True negatives are FC = 1 probesets, empty probesets and mixed probesets that can be aligned only to FC = 1 probesets. Expression values were generated by masking all probes that could not be mapped to the low intensity probesets, re-calculating the probeset expression values and calculating the AUC and q-values. AUC and q-values were also generated from FC = 1 normalizations using all probesets with present transcripts. See legend for coloring of symbols. Additional data file 3 includes modified GoldenSpike scripts for use in R with BioConductor. Additional data file 4 includes scripts to run the alchemy method in R with BioConductor (requires Additional data file 3)
This work was supported by a grant from the Wellcome Trust, Functional Genomic Analysis of Aging. We thank B Wertheim and the referees for helpful comments on the manuscript.
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