- Open Access
Reproducibility and reliability assays of the gene expression-measurements
© Darbani and Stewart; licensee BioMed Central Ltd. 2014
- Received: 9 November 2013
- Accepted: 7 March 2014
- Published: 13 May 2014
Reliability and reproducibility are key metrics for gene expression assays. This report assesses the utility of the correlation coefficient in the analysis of reproducibility and reliability of gene expression data.
The correlation coefficient alone is not sufficient to assess equality among sample replicates but when coupled with slope and scatter plots expression data equality can be better assessed. Narrow-intervals of scatter plots should be shown as a tool to inspect the actual level of noise within the data. Here we propose a method to examine expression data reproducibility, which is based on the ratios of both the means and the standard deviations for the inter-treatment expression ratios of genes. In addition, we introduce a fold-change threshold with an inter-replicate occurrence likelihood lower than 5% to perform analysis even when reproducibility is not acceptable. There is no possibility to find a perfect correlation between transcript and protein levels even when there is not any post-transcriptional regulatory mechanism. We therefore propose an adjustment for protein abundance with that of transcript abundance based on open reading frame length.
Here, we introduce a very efficient reproducibility approach. Our method detects very small changes in large datasets which was not possible through regular correlation analysis. We also introduce a correction on protein quantities which allows us to examine the post-transcriptional regulatory effects with a higher accuracy.
- Gene expression
Reliability or accuracy of data-to-reality, and reproducibility or inter-replicate variance, are typically assessed using the correlation coefficient. As a reliability assay, the agreement between transcript abundance and their encoded protein abundance has long been investigated [1–4]. RNA-Seq  has made the global profiling of gene expression achievable by covering comprehensive transcriptome data. As the most recent approach, reliability of the output has been examined by correlation analysis using microarray and/or Real Time RT-PCR [5–10]. In addition, the correlation between replicates has been used to judge the reproducibility of data [7, 10–15].
Correlation is the agreement level between two variables. The correlation coefficient varies between perfect agreement (r = ±1) and no agreement (r = 0). A perfect agreement implies equal change in one of the variables for a given fixed change of another variable. A negative correlation indicates an opposite direction in the agreement, i.e. reduction in one of the variables in response to positive changes in another, regardless of the agreement level. For example, we can find a perfect agreement but in the opposite direction between the dose of insecticides and the number of survived insects.
The inter-replicate variation of gene expression-quantities is of the utmost importance to biologists because lower variance means higher reproducibility. The correlation coefficient has been used to inspect the reproducibility of gene expression data [7, 10–15]. When the inter-replicate variance is low or zero, a higher or perfect correlation is expected but we can find the opposite, i.e. a low inter-replicate variance may be absent when there is a strong correlation. Thus, we cannot rely on the correlation digit as the sole criterion.
Since the correlation coefficient has been the main tool to assess agreement between replicates, technologies (microarray, Real Time RT-PCR, and RNA-Seq), and between protein and transcript abundance, this paper scrutinizes the power of correlation analysis for the biologist and introduces other alternatives. We introduce an alternative reproducibility assay approach. We advise that there should be an application of an inter-replicate based fold-change threshold to identify the most reliable variations among the significant intertreatment changes regardless of what the inter-replicate reproducibility may be. In addition, we introduce a correction step based upon the lengths of open reading frames (ORFs) for protein quantity before correlation analysis with the respective transcript abundance in order to assess post-transcriptional regulation.
The correlation coefficient is not sufficient as a reproducibility assay for expression data
Although the actual level of noise on the plots is not visible owing to the large dataset size, the inspection of very narrow intervals of the data range can be helpful (e.g., compare Figure 1A2 and B2 with A2α and B2α, respectively). By following this procedure we found > ±0.5× noise-level in the presented examples, which were not detectable when showing the whole dynamic range of expression. We advise that it would be helpful to include figures and supplements showing narrow-intervals of representations in the reports to provide readers with a useful overall picture.
Scatter plots using the logarithmic scale have been reported previously to represent expression data reproducibility [2, 4, 5, 11, 12, 15–17]. However, logarithmic transformation of data evokes changes in the variation between replicates, which affects slope and diminishes its usefulness. The similarity level between replicates and the percent of data which are 1 and lower than 1 have an impact on the direction, i.e. whether slope-deviation will be increased or decreased, and the rate of change of slope. We found considerable decreases in the deviation of the slope of inter-replicate regression line using uncorrected data where the inter-replicate similarity levels were low (compare Figure 1A1 and B1 with A1α and B1α, respectively). This artificially low slope-deviation could be incorrectly interpreted as high reproducibility. In conclusion, logarithmic scale slope is of little utility to reproducibility assays.
To examine the reliability of gene expression measurements, the agreement levels of expression data between technologies, i.e. RNA-Seq, microarray, and Real Time RT-PCR, have also been investigated [5–10]. These assays might have general agreement with each other but equality is not observed. Therefore, we should require a strong positive correlation but not equality among platforms, which could be represented by the slope of inter-replicate regression line. Aside from the evidence-free acceptance of one technology as the most reliable one, reliability assays suffer from the inefficiency of correlation coefficient when analyzing large sets of data. The acceptable threshold of correlation should be evaluated. Like for the reproducibility assay, we advise that the real level of noise should be examined on narrow-intervals of data ranges in scatter plots.
The mean and standard deviation of the inter-treatment gene expression ratios shed light on reproducibility
As an alternative to the correlation coefficient, we advise reporting the mean and standard deviation of the inter-treatment gene expression ratios to examine reproducibility. By calculating the ratios of each of the descriptive statistics for single replicates when compared to different replicates of another treatment, we should check the deviation of ratios from 1. The average of deviations and their standard deviation could be utilized as reproducibility coefficients. The higher deviation and higher standard deviation for the deviations indicate lower reproducibility.
Reproducibility of the microarray data
After quantile correction
Average number of genes with >50% inter-replicate variation
r (P) b
A.D d %
Average number of genes with >50% inter-replicate variation
r (P) b
A.D d %
E-GEOD-53990: Arabidopsis data with 6 treatments and 3 replicates
E-GEOD-27822: Barley data with 2 treatments and 3 replicates
E-GEOD-39950: Yeast data with 2 treatments and 3 replicates
E-GEOD-49918: E. coli data with 4 treatments and 3 replicates
E-GEOD-24524: E. coli data with 4 treatments and 2 replicates
It should be emphasized that the levels of reproducibility should not be compared among different experimental data. This is due to the data-dependency of the measured statistics. We found higher deviation values (15.3%, 14.2%, and 13.7%) for the yeast data when there were fewer genes with greater than 50% inter-replicate variance (4.4%, 4.3%, and 4.2%) compared to the rice data.
As indicated, we have included X/Y and Y/X as separate measurements of the genes between the treatments in order to fix the asymmetric aspect of the ratios around 1. We have not applied the well-known logarithmic transformation, i.e. log (X/Y) = log (X) – log (Y). The latter, can easily reduce the difference level between comparisons as we have already explained. Therefore, we will not see the actual difference at the reproducibility levels by applying the logarithmic transformation.
What can be done when reproducibility is low or not known?
The correlation coefficient or the alternative method introduced here shed light on general data reproducibility based on predefined thresholds. The main application of these approaches is in comparing different analytical methods such as correction measures with each other in order to use the most appropriate method. However, they do not provide detailed information as to which part of data has an acceptable reproducibility or what stringency level we should apply in our analysis to meet the low reproducibility levels in order to avoid making the data useless. Under the assumption of a similar natural variation of expression for all genes, i.e. since a gene with extreme inter-replicate variation for expression is assumed to be random, we advise applying a fold-change threshold to solve the problem. To be acceptable, the level of the statistically significant expression changes between the treatments should be not smaller than the predetermined threshold. This threshold should be determined by keeping the frequency of genes showing same or higher levels of inter-replicate changes lower than an acceptable likelihood of being false positive, i.e. 5% or 1%. Therefore, a significant inter-treatment foldchange of a gene should have an inter-replicate likelihood lower than either 1% or 5%. Applying this criterion keeps the usability gate open even when the reproducibility is low just by considering the reliable fold-changes. When analyzing the rice untreated root [GenBank ID: DRR000350 and DRR000354] and untreated shoot [GenBank ID: DRR000349 and DRR000353] samples, we found the fold-change thresholds of >3.7 and >2.0 at 1% and 5% levels, respectively. By comparing untreated shoot with untreated root, we found 5212 (48% of the significant differentially expressed genes) and 783 (7.3% of the significant differentially expressed genes) genes showing same or lower levels of fold-changes according to the 1% and 5% cut-offs, respectively. We can also apply a genegroup specific fold-change threshold when there is a bias towards specific genes, e.g., by gene-length or expression-quantity based clustering of the genes due to the higher variation of shortlength or low-abundant genes compared to the long or high abundant genes, respectively, in RNA-Seq.
ORF length-based correction on protein quantities is necessary before correlating them with their transcript abundance
No strong correlation has been found between protein and the RNA abundance [1–4]. One reason could be the multiple levels of regulatory mechanisms, from transcription to post-translation, that govern the expression of genes. By excluding all the technical and biological noise as well as experimental biases, different determinants including ribosomal occupancy (the fraction of a given gene’s transcripts engaged in translation at least by one ribosome) and ribosomal density (number of ribosomes per length-unit of transcripts) as translation activating factors, sequence features of translation initiation, elongation, and termination as ORF-specific translation-efficiency related factors, and amino acid availability as well as mRNA/protein half-life have been proposed to influence the mRNA-protein correlation [19–22]. Among these, ORF-specific translation-efficiency related factors explain 15-30% of the variation of mRNA-protein correlations [22–24]. The mRNA half-life does not show a considerable impact in contrast to the protein half-life, which explains ≈ 17% of the mRNA-protein correlation variations .
For many reasons, however, biologists most typically rely on transcript abundance as a gauge for gene expression. But, how reasonable is it to expect a high correlation between the transcript and the protein levels? To answer, let us assume the two expressed genes, A and B, are governed by post-transcriptional-free regulation mechanisms. This means that they have the same stability, half-life, and translation efficiency for the transcripts and same stability and half-life for the proteins of genes A and B. It is still possible to have different rates of induction or suppression between the protein levels of genes when there is a similar induction or repression rate at the transcript levels of the genes. Similar rates of change at the transcript levels of the genes A and B could result in different rates of change at the protein levels when the lengths of the coding sequences differ between the genes. It might be expected to find twice as much induction for the protein A compared to the protein B if the coding sequence of gene B is twice as long as that of the gene A. The longer protein B will take more time to be translated than the protein A. This can simply decrease the correlation between the protein and the RNA levels by uneven variation of the variables (the transcript level and the protein level). As an example, the induced protein levels for A and B were four and two times, respectively, if the transcript levels of the genes were induced two times. In this situation, there are uneven changes of two and four times at the protein levels (one of the variables) compared to a fixed two times change in transcript levels (another variable). Therefore, it is not reasonable to look at the agreement level between the RNA and their encoded protein quantities. Instead, we should consider the effects of treatments/tissues on the gene expression quantities regardless of gene expression assay. In conclusion, different levels of post-transcriptional regulations should not be interpreted as the sole reason for the medium-weak correlation between the protein and transcript levels due to the above-mentioned technical problem which could easily have a large impact on the issue, either positively or negatively.
To inspect the pure effects of post-transcriptional regulation we advise that protein quantities should be corrected for the length of coding sequences before correlating the protein and the transcript quantities with each other. We performed a length-based correction on the previously reported protein quantities before examining the correlation between protein and transcript quantities. For the 10 proteins of Plasmodium falciparum and their corresponding transcript abundance measured during six growth stages published in , the correlation showed a shift from −0.029 to 0.135 after the ORF length-based correction was applied for protein quantities (Additional file 1). We also examined two different expression datasets (Additional file 1): cell cycle with 173 genes and cell rescue with 115 genes in yeast where the expression quantities exist both at the protein and at transcript levels, reported by Greenbaum et al. . After the length-based correction on protein quantities the Pearson correlations were changed from 0.71 to 0.41 and from 0.45 to 0.29 in cell cycle and cell rescue datasets, respectively.
To further analyze the impact of ORF length-based bias in quantitative analysis of transcript and protein expressions, we looked at the correlation of mRNA changes with protein changes between human and chimpanzee reported by Fu et al. . We do not expect a negative correlation between changes of transcripts and of proteins. This is due to the fact that cells try to consume as little energy as possible. In addition, an overall trend of decreased mRNAs and increased proteins is not reasonable. However, we found a correlation of −0.37 between mRNAs (chimpanzee/human ratios) and proteins (chimpanzee/human ratios) of 143 genes. The averages of five and three biological replicates were applied to calculate the mRNAs changes and the proteins changes, respectively (Additional file 1). In contrast, a more reasonable correlation of −0.11 was obtained by using the ORF length-based corrected protein changes (Additional file 1).
Increased ribosomal occupancy means increased usage of minimum physical space on transcripts for ribosomal functionality. This can alleviate the effect of different ORF lengths on the deviations of fold-changes of protein quantities from the fold-changes of transcript quantities. In agreement with this, a higher protein transcript correlation was reported for the transcripts with high ribosomal occupancy . This indicates that the ORF length differences can easily affect the agreement between the transcripts and their coded protein quantities.
It is conceivable that the longer transcripts may be occupied by a higher number of ribosomes, which might alleviate the aforementioned effect of the ORF length on the correlation coefficient between protein and transcript abundance. However, the very weak correlation (r P = 0.22, r S = 0.34) between the ORF length and number of ribosomes on the transcripts and negativeweak correlation (r P = −0.39, r S = −0.56) between the ORF length and ribosomal occupancy, which we found (see Additional file 1) in the data published by Greenbaum et al. , introduce the number of ribosomes or the ribosomal occupancy of transcripts not as a random length-based event, but rather, as a post-transcriptional regulation mechanism. Not only there is no strong correlation between the transcript length and ribosome numbers but also longer transcripts show lower ribosomal density compared to shorter transcripts reported in . This could be explained by the fact that the first 40 codons of transcripts have over three-fold higher ribosomal density compared with any given 40 codons long fragment from the +40th codon downstream region of transcripts . In addition, trans-regulatory divergence and not ribosomal occupancy has recently been introduced as the force behind the differences in the yeast translational efficiency . Therefore, there should not be any concern about the alleviated effect of ORF length on the correlation coefficient. Correction for ORF length on protein quantity seems to be useful to extract much pure post-transcriptional regulation effects, at least based on the available data.
Although we introduce ORF length as a factor affecting the mRNA-protein correlation, it should be highlighted that our ORF length-based correction of protein quantities is too simplistic and cannot guarantee the purity of the variation of mRNA-protein correlation. Among the ORF-specific translation-efficiency factors, peptide elongation has been found as the major determinant to explain the variation of mRNA-protein correlation [22–24]. One conceivable reason could be the biological importance of the elongation process itself compared to the initiation and termination processes. However, the other key player could be the transcript/ORF length, which can easily influence the elongation process. Therefore, our introduced ORF length-based correction of protein quantities can be affected by the elongation-related regulatory variance and needs further development in order to extract the pure length-dependent variance from the variation of mRNA-protein correlation.
RNA-Seq data analyses
To evaluate the efficiency of correlation coefficient on real data, a publicly available rice RNA-Seq dataset was used in the analysis. The dataset included two replicates of root and shoot samples from plants before and after a one hour salinity stress treatment [GenBank ID: DRX000191, DRX000192, DRX000193, and DRX000194]. The software CLC Genomics Workbench (http://www.clcbio.com; Aarhus, Denmark) was used to map the reads on the rice Nipponbare reference genome to isolate different type of reads, i.e. total and uniexon and gene reads. The average of inter-replicate variations of selected reference genes were applied for the reference gene based data correction (data not shown). The differentially expressed genes were found as described by Robinson et al.  with a p-value cut-off of 0.01 and using the Benjamini & Hochberg method  for multiple testing correction.
Microarray data analysis
We also analysed four different microarray datasets which are publicly available in EMBL-EBI, ArrayExpress (http://www.ebi.ac.uk/arrayexpress/). The datasets studied included Arabidopsis data [E-GEOD-53990] with six treatments and three replicates, barley data [E-GEOD-27822] with two treatments and three replicates, yeast data [E-GEOD-39950] with two treatments and three replicates, and two Escherichia coli datasets [E-GEOD-49918 and E-GEOD-24524]. One E. coli dataset had four treatments and three replicates and another had four treatments and two replicates. We used the Affymetrix Expression Console build 220.127.116.11 to analyze the data; the 3 Expression Arrays-RMA was applied to extract the quantities both without any correction and together with quantile-based correction.
An alternative reproducibility test by measuring the mean and standard deviation statistics of intertreatment ratios of gene expression quantities
Measurement of the genes’ expression ratios between the treatments
T1iR(T1)/T2iR(T2), T1iR(T1)/T3iR(T3), T2iR(T2)/T3iR(T3), …, Tn-1iR(Tn-1)/TniR(Tn), and T2iR(T2)/T1iR(T1), T3iR(T3)/T1iR(T1), T3iR(T3)/T2iR(T2)…, TniR(Tn)/Tn-1iR(Tn-1)
Computing the mean (M) and standard deviation (S) for each population of ratios
MT1iR(T1)/T2iR(T2), …, MTn-1iR(Tn-1)/TniR(Tn), and T2iR(T2)/T1iR(T1), …, MTniR(Tn)/Tn-1iR(Tn-1)
Computing the ratios of the statistics between paired populations among which one of the replicates of one sample is compared to all the replicates in another sample.
For example, in case of MT1iR(T1)/T2iR(T2) we do as follows:
[MT1i1/T2i1]/[MT1i1/T2i2], [MT1i1/T2i1]/[MT1i1/T2i3], …, [MT1i2/T2i1]/[MT1i2/T2i2], [MT1i2/T2i1]/[MT1i2/T2i3],
Measuring the variation of the ratios
Measuring the average and standard deviation of the deviations of ratios
These parameters could be utilized as reproducibility coefficients. There will be no deviation when there is a perfect reproducibility. In addition, the standard deviation of the deviations is an indication of how constant the reproducibility is when considering all treatments. To facilitate all the steps of the analyses, an Excel file (Additional file 3) is prepared for users. It includes different sheets based on the number of treatments and replicates and it just need the data to be pasted in in order to calculate the reproducibility measurements. There is a manual sheet included as well. We analyzed the mentioned rice data including four treatments each with two replicates. Therefore, there were 48 populations of expression ratios for uncorrected data and the same for corrected data (see Additional file 1). To check the robustness of the method, we also applied the online-available yeast RNA-Seq dataset explained by Lipson et al. . This includes expression data of 6387 genes reported as transcript per million (t.p.m) and were found expressed in all the three technical replicates of the samples (see Additional file 1). Furthermore, we analyzed the mentioned five different microarray datasets from Arabidopsis, barley, yeast, and E. coli (see Additional file 2).
Protein quantity correction in order to assess the correlation between the protein and transcript abundance
Pure post-transcriptional regulation effects can be examined after correction of the protein quantities
ORF b (bp)
Here, we conclude to enhance the power of reproducibility assay of gene expression data by considering the slopes of inter-replicate linear regression lines and narrow-intervals of scatter plots as well as the correlation coefficient. We also introduce an efficient alternative approach which can detect small changes among large datasets. This works based on the means and standard deviations of the expression ratios of genes. As a reliability assay, it is advised not to rely on the correlation between the transcript and protein levels. This is due to the differences among the ORF-lengths of genes which can result in a weak correlation without post-transcriptional regulatory mechanisms. Finally, we advise an ORF-length based correction of protein quantities to examine a much pure effect of post-transcriptional regulatory mechanisms.
We thank Jennifer Hinds for formatting and line-editing work on the manuscript. We also thank Dr. Ilias Kappas from the editorial board of the journal and the anonymous reviewers for their useful comments. BD is supported by Aarhus University and University of Copenhagen. CNS is supported by University of Tennessee Ivan Racheff Endowment and AgResearch.
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