- Open Access
Microarray scanner calibration curves: characteristics and implications
© Shi et al; licensee BioMed Central Ltd. 2006
- Published: 15 July 2005
Microarray-based measurement of mRNA abundance assumes a linear relationship between the fluorescence intensity and the dye concentration. In reality, however, the calibration curve can be nonlinear.
By scanning a microarray scanner calibration slide containing known concentrations of fluorescent dyes under 18 PMT gains, we were able to evaluate the differences in calibration characteristics of Cy5 and Cy3. First, the calibration curve for the same dye under the same PMT gain is nonlinear at both the high and low intensity ends. Second, the degree of nonlinearity of the calibration curve depends on the PMT gain. Third, the two PMTs (for Cy5 and Cy3) behave differently even under the same gain. Fourth, the background intensity for the Cy3 channel is higher than that for the Cy5 channel. The impact of such characteristics on the accuracy and reproducibility of measured mRNA abundance and the calculated ratios was demonstrated. Combined with simulation results, we provided explanations to the existence of ratio underestimation, intensity-dependence of ratio bias, and anti-correlation of ratios in dye-swap replicates. We further demonstrated that although Lowess normalization effectively eliminates the intensity-dependence of ratio bias, the systematic deviation from true ratios largely remained. A method of calculating ratios based on concentrations estimated from the calibration curves was proposed for correcting ratio bias.
It is preferable to scan microarray slides at fixed, optimal gain settings under which the linearity between concentration and intensity is maximized. Although normalization methods improve reproducibility of microarray measurements, they appear less effective in improving accuracy.
- Linear Dynamic Range
- Microarray Scanner
- Ratio Bias
- Lowess Normalization
- Calibration Slide
The reliability of microarray data is dependent on many factors including the performance of the signal readout system [1–3]. Fluorescence is currently the predominant method for microarray signal detection not only for two-color systems but also for most one-color systems [4–6]. A critical component of a fluorescence scanner is the photomultiplier tube (PMT), in which fluorescent photons produce electrons that are amplified by the PMT voltage, also referred to as the PMT gain. For many microarray scanners, the PMT gain is an easily adjustable parameter, and the calibration curve (i.e., the curve showing the relationship between dye concentration and fluorescence intensity) depends on the gain setting [5–7].
DNA microarray measurements normally assume a linear relationship between detected fluorescent signal and the concentration of the fluorescent dye that is incorporated into the cDNA or cRNA molecules synthesized from the test sample. Each PMT has its own linear dynamic range within which signal intensity increases linearly with the increase of fluorescent dye concentration [5, 6]. However, due to the wide concentration range for genes expressed in a biological sample, the detected fluorescence intensity does not necessarily remain in the linear range for all genes tiled on a microarray. In addition, the background fluorescence intensity of the Cy3 channel is generally higher than that of the Cy5 channel [8–10]. Nonlinearity between fluorescence intensity and dye concentration can occur due to chemical saturation, dye quenching, signal bleaching, optical saturation, and instrument limitations. The impact of such nonlinearity on microarray data accuracy and reproducibility has been suggested and normalization methods have been proposed for correcting systematic and nonlinear bias. Lowess (locally weighted scatter plot smooth) is a locally weighted linear regression method that has been proposed and widely accepted as a normalization method for correcting intensity-dependent ratio bias [11–13].
Most studies dealing with nonlinearity in microarray data have been focusing on the intensity space, i.e., correcting the nonlinear relationship between intensity data from different PMT gains. For example, Dudley et al. applied a linear regression method on data acquired from the same slide under several PMT gains to extend the linear range of a scanner . Similar strategies of scanning the same slide at multiple PMT gains to extend the dynamic range of intensity have been reported by others [15–18].
In this study, we evaluate the characteristics and implications of the calibration curves for the two commonly used dyes (Cy5 and Cy3) under different PMT gains and offer explanations for several experimental observations commonly encountered in two-color microarray platforms. The effectiveness of Lowess and mean normalization methods on the accuracy and reproducibility of ratios estimated by microarray technology is assessed. A method of calculating ratios based on concentrations estimated from the calibration curves is proposed for correcting ratio bias. To our knowledge, the current work represents the most comprehensive study investigating the calibration characteristics and implications of the Cy5 and Cy3 under various PMT gain settings.
Microarray scanner calibration slide
Spotting oligonucleotide microarrays
Mouse 20 K oligonucleotides from MWG Biotech (High Point, North Carolina, USA) were spotted on glass slides as described elsewhere .
Microarray labeling and hybridization reactions
A slightly modified version of the indirect labeling protocol from The Institute of Genomic Research (TIGR, Rockville, Maryland, USA) was used for labeling with Cy5 and Cy3 dyes. The TIGR hybridization protocol was also slightly modified for the current study. Details have been described elsewhere .
Microarray scanning and image quantification
The scanner calibration slide was scanned from 150 V to 1000 V PMT gains at an interval of 50 V under the same laser power setting and at a resolution of 10 μm on a GenePix 4000 A scanner (Axon Instruments, Inc., Union City, California, USA), resulting in 18 scans of the same slide for each channel. A 16-bit TIFF image was acquired for each scan and quantified by using GenePix 4.0 software (Axon Instruments, Inc.) under the same procedures and parameter settings . Data from repeated scans under the same PMT gain before and after the whole scanning process showed minimal signal degradation.
Microarray data analysis
Microarray data were stored in ArrayTrack, a database and software system developed by the FDA's National Center for Toxicological Research for the management, analysis, and interpretation of DNA microarray data [20, 21]. Additional calculations were performed within S-Plus 6.1 (Insightful Corp., Seattle, Washington, USA), JMP 5.0.2 (The SAS Institute, Carry, North Carolina, USA), and DMVS 2.0 (Chipscreen Biosciences Ltd., Shenzhen, China).
Estimation of log ratios based on intensities
The fluorescence intensity data acquired from different PMT gains for the various concentration series allowed us to generate ratio data in a comprehensive way. First, Cy5 and Cy3 PMT gains are paired in 324 (18 times 18) ways. Second, each concentration series for one channel is paired with all concentration series of the other channel to generate many combinations of varying Cy5 and Cy3 concentrations, hence various ratios. To minimize the impact of saturated and undetectable spots on the accuracy of calculations, we have arbitrarily excluded the nine lowest concentration series for which the signal intensities were below the detection limit for most PMT gains. The five highest concentration series for which the signal intensities were saturated for most PMT gains were also excluded. Thus, 14 concentration series remained for each channel, resulting in 196 (14 times 14) possible combinations of Cy5 and Cy3 concentrations. Therefore, we obtained a log ratio matrix of 196 rows and 324 columns, corresponding to different combinations of concentrations and PMT gains, respectively.
Calculation of standard (true) log ratios
The standard (true) log ratios, StlgR, for the 196 concentration combinations discussed above were directly calculated from the spotted dye concentrations, instead of from measured fluorescence intensities.
Characteristics of the calibration curves of Cy5 and Cy3 channels
First, at any given PMT gain for the same dye, the fluorescence intensity increases as the dye concentration increases, and there is a range within which the signal increases linearly with dye concentration. This range is defined as the linear dynamic range, which can be expressed in terms of concentration range or intensity range. However, at higher concentrations, and well before the digital saturation at the intensity of 65535 (216-1) for a 16-bit scanner, the intensity no longer increases linearly with concentration. In addition, nonlinearity also occurs at lower concentrations and intensities.
Second, the linear dynamic range in terms of fluorescence intensity varies with PMT gain. For example, at lower PMT gains (e.g., 150 V–550 V), the linear range is narrower than that for higher PMT gains (e.g., 600 V–800 V). The linear range also narrows at high PMT gains (e.g., 850 V–1000 V) due to the saturation of spots with higher dye concentrations and a significant increase in background fluorescence intensity. Nonlinearity occurs at both higher and lower concentrations in a manner that heavily depends on the PMT gain setting.
Third, the slope of the linear part of the calibration curves varies for the same dye with different PMT gains; i.e., the slope is significantly lower when PMT gain is too low. For example, the slope for Cy3 is 0.90 at 700 V (Figure 2C) compared with 0.79 at 400 V (Figure 2D). It is worth noting that at lower PMT gains (e.g., <550 V for Cy5 and <500 V for Cy3), fluorescence intensity can hardly reach the level of digital saturation (65535) at the highest dye concentration on the calibration slide.
Fourth, there are inherent differences in the calibration curves for Cy5 and Cy3 at the same PMT gain setting. Generally, the slope for Cy5 is somewhat higher than that for Cy3 at the same PMT gain setting. For example, the slopes for Cy5 and Cy3 are 0.95 and 0.90, respectively, for a PMT gain of 700 V (Figure 2C), under which the inherent differences between Cy5 and Cy3 appear to be the smallest.
Fifth, the background fluorescence intensity differs significantly for Cy5 and Cy3 under the same PMT gain, and for the same dye under different PMT gains. We consider background as the fluorescence intensity level that does not change with dye concentration. The differences in background levels appear to be due to the inherent differences of the two photomultiplier tubes for the Cy5 and Cy3 dyes.
The nonlinearity in calibration curves, the differences in the spread and slope of the linear range of the calibration curves, and the differences in background level of the two dyes have important implications as to the reproducibility and accuracy of fluorescence intensities and the calculated gene expression ratios.
Reproducibility of log intensities
Reproducibility of log ratios
Accuracy and underestimation of log ratios
Intensity-dependence of anti-correlation
Simulation of a dye-swap experiment
Like many dose-response curves observed in biological sciences and the calibration curves of many analytical instruments, for a microarray scanner the calibration curves (Figure 2) that show the relationship between log fluorescence intensity (I) and log dye concentration (c) may be reasonably fitted into a Sigmoid function:
where θ defines the spread and slope of the linear range of a Sigmoid curve and the "background" level; D is the upper limit of the dynamic range and is set to 3 in this study. The simulated data with different θ values can be reasonably seen as fluorescence intensities obtained from different PMT gains for the same dye or from the same PMT gain setting for two different dyes.
Comparison of mean and Lowess normalization
When accuracy (i.e., the closeness between log estimated ratios and the log standard ratios) is considered (Figures 8D–I), the effectiveness of both mean and Lowess normalization appears questionable: ratio bias (underestimation) remains. Simulation results were also obtained by modeling more severe dye-bias with a larger difference in the θ parameter for the two dyes. The intensity-dependence of ratio bias and anti-correlation of the dye-swap pair became more dramatic (data not shown), and the effectiveness of the mean and Lowess normalization methods in correcting ratio bias remains minimal.
Concentration-based ratio calculation for correcting ratio bias
The intensity-dependent ratio bias and the anti-correlation appear to be a result of the nonlinearity of the calibration curves and the calculation of ratios from dividing the measured fluorescence intensities from the two channels. That is, the calculated fold changes obtained by directly dividing measured intensities do not accurately reflect the true fold difference in concentration.
We systematically assessed the characteristics of the calibration curves for Cy5 and Cy3 under 18 different PMT gain settings (Figures 2A–D) by using a scanner calibration slide spotted with pure fluorescent dyes. This approach enabled the separation of the effects of intrinsic characteristics of the two dyes (and the corresponding photomultiplier tubes for signal detection) from other experimental factors such as labeling and hybridization. The implications of the characteristics of the calibration curves have been demonstrated in terms of reproducibility and accuracy of log intensities and log ratios.
PMT gain setting
Our analysis of data from the scanner calibration slide and simulation revealed marked sensitivity of PMT gain setting on DNA microarray reproducibility and accuracy. The sensitivity strongly suggests an essential need to minimize the impact of nonlinearities for accurate measurement of differential gene expression. For example, the optimal PMT range and calibration behavior of the scanner should be well determined. Furthermore, all slides within the same study should always be scanned within the optimal PMT gain range (e.g., 600 V–800 V) where linearity is maximized. Preferably, slides in a study should be scanned at consistent PMT gain. For the scanner used in this study, a PMT gain at 700 V appears to be in the center of the optimal range, and small adjustment within a certain range (e.g., +/- 50 V) appeared to be acceptable. To minimize the difference between Cy5 and Cy3, PMT gains for the two channels should be set in a way so that the calibration curves for the two channels are as close as possible. A microarray experiment well performed in all early steps such as sample preparation, cDNA or cRNA synthesis, dye labeling, and hybridization could be compromised if the slides are scanned at non-optimal and different PMT gains. A practice of fixing PMT gain in the optimal range has not always been followed because the adjustment of PMT gains has been made very easy for the user  and sometimes encouraged by the vendor. Consequently, we reason that the scanners and theirs parameter settings might have significantly contributed to the lack of reliability of microarray data. The optimal range of the PMT gains for each channel of a scanner should be well-defined.
Possible causes of ratio underestimation
The accuracy of Affymetrix chips and customized cDNA microarrays have been assessed by comparing detected ratios to those from qRT-PCR ; both platforms consistently underestimate ratios. Hekstra et al. [27, 28] and Held et al.  addressed the problem of sequence-specific response of fluorescent signal as a function of concentration, and proposed ways to correct ratio underestimation for genes with high-fold changes observed in Affymetrix chips based on Langmuir adsorption and free-energy calculations, respectively.
Although ratio underestimation has become a commonly recognized feature of microarray technology, the exact causes have not been fully understood. Our results demonstrate that nonlinearity of the calibration curve is one of the causes of ratio underestimation, and the severity of ratio underestimation is closely related to the severity of the nonlinearity of the calibration curves under different PMT gains (Figures 5A–E). To minimize ratio underestimation, the linear dynamic range of the calibration curves of the scanner should be maximized and background intensity should be minimized. We noted that background-subtracted intensity improves the linear dynamic range of the calibration curve (data not shown).
Another important cause of ratio underestimation is non-specific binding, as explained by the following equation:
where R is ratio; I is the fluorescence intensity; and s and ns stand for specific and non-specific binding, respectively. When the intensity from both channels (1 and 2) are significantly contributed by non-specific binding, the calculated ratio will significantly deviate from the true ratio of I s 1 /I s 2 , based on a reasonable assumption that the contribution of the non-specific binding for the two channels (I ns 1 and I ns 2) are similar. For up-regulated genes (i.e., I s 1 > I s 2 ), the calculated ratio (a number > 1) will be smaller than I s 1 /I s 2 . For down-regulated genes (i.e., I s 1 <I s 2 ), the calculated ratio (a number < 1) will be greater than I s 1 /I s 2 . In both cases, there is an underestimation of the absolute log ratio. One extreme situation is that the contribution of non-specific binding is overwhelming compared to that of specific binding, thus leading to a ratio close to 1. This phenomenon has been experimentally observed in our laboratories when a non-optimized hybridization buffer from a commerical source was used (Han T et al., data not shown).
Intensity-dependence of anti-correlation and ratio bias
The main reason for anti-correlation between dye-swap replicates is the inherent differences in the calibration curves for the two dyes (Cy5 and Cy3). The nonlinearity of the calibration curves, in particular under a PMT gain setting at non-optimal range, is one cause for anti-correlation. A pronounced difference in Cy5 and Cy3 background has been observed [8–10] and can be another cause for ratio bias. What has been shown in our results is likely a combination of nonlinearity and background difference.
Gene-specific bias in binding affinity to the two dyes has been suggested to be a cause of ratio bias for some genes [24, 25]. Our data provide an alternative explanation to the phenomenon of intensity-dependence of ratio bias [11–13] as a result of the inherent differences in calibration curves of the two dyes where no labeling or hybridization steps are involved.
Correction of ratio bias
We demonstrate that normalization methods (including Lowess), while improving reproducibility, are not effective in reducing ratio bias from the truth. It appears that normalization methods and the averaging of dye-swap replicates effectively "hide" rather than reduce the problems related to ratio bias.
Strategies for correcting ratio bias by extending the dynamic range have been proposed [14–18], but such a procedure has not yet been adopted for routine use in microarray practice. Furthermore, ratio underestimation is still recognizable, e.g., after the Masliner correction (see Figure 2 of reference ). A perfect correlation in intensity (e.g., under the same PMT gain for the same dye) does not correct the intrinsic nonlinearity of the calibration curves (intensity versus concentration correlation). Rather, intensity correlation "hides" the nonlinearity of the calibration curves (Figure 7G versus Figures 7E and 7F). Therefore, the problems of nonlinearity observed in this study on the two-color platform largely apply to one-color platforms.
To effectively solve the problem of ratio bias due to nonlinearity in the calibration curves, we propose using concentration instead of intensity for ratio calculation. While this approach appears promising, a fundamental question is whether the calibration curves for different genes are similar enough for establishing a gene-independent calibration function, c = f(I); or whether it is feasible to obtain individual calibration curves for all the genes on a microarray. We are actively investigating this issue.
Standards for the calibration and validation of microarray scanners
The reliability of microarray data cannot be better than that of the microarray scanner. Universal standard (or reference) materials need to be established for calibrating and validating microarray scanners. The performance of a microarray scanner should be routinely checked by standard materials like the calibration slide used in the study. The user should be made aware of the implications of the changes of scanner settings (e.g., PMT gain and laser power) so that variability due to the scanner can be minimized and the true biological information can be reliably obtained by microarray technology. More studies on the calibration and validation of microarray scanners and the correction of the resulting data are warranted, as are guidelines on the proper use of microarray scanners.
Our results demonstrate the substantial impact of the PMT gain setting of a scanner on the reproducibility and accuracy of log ratios estimated by microarray technology resulting from the inherent characteristics of the two dyes under different PMT gains. Our data provide rational explanations to several experimental observations such as intensity-dependence of ratio bias, underestimation of ratio, and anti-correlation of dye-swap replicates. A concentration-based ratio calculation method is proposed for correcting ratio bias and underestimation. More studies on the effect of scanner settings on microarray data quality are warranted, and reference materials should be established for the calibration and validation of microarray scanners. Our results show that the effectiveness of normalization methods (including Lowess) in correcting ratio bias from the truth is very limited. The merits of various methods for the normalization, correction, and analysis of microarray data must be objectively assessed by using calibrated reference datasets so that not only reproducibility, but also accuracy, can be evaluated [3, 30].
We are grateful to Dr. Yaping Zong and Dr. Youxiang Wang of Full Moon Biosystems for stimulating discussions regarding the calibration and validation of microarray scanners. We thank Robert Delongchamp and Tucker Patterson for critical reading of the manuscript.
- Yue H, Eastman PS, Wang BB, Minor J, Doctolero MH, Nuttall RL, Stack R, Becker JW, Montgomery JR, Vainer M, et al.: An evaluation of the performance of cDNA microarrays for detecting changes in global mRNA expression. Nucleic Acids Res 2001, 29(8):E41–41. 10.1093/nar/29.8.e41PubMed CentralView ArticlePubMedGoogle Scholar
- Hoffman EP: Expression profiling – best practices for data generation and interpretation in clinical trials. Nat Rev Genet 2004, 5(3):229–237. 10.1038/nrg1297View ArticleGoogle Scholar
- Shi L, Tong W, Goodsaid F, Frueh FW, Fang H, Han T, Fuscoe JC, Casciano DA: QA/QC: challenges and pitfalls facing the microarray community and regulatory agencies. Expert Rev Mol Diagn 2004, 4(6):761–777. 10.1586/1473722.214.171.1241View ArticlePubMedGoogle Scholar
- Cheung VG, Morley M, Aguilar F, Massimi A, Kucherlapati R, Childs G: Making and reading microarrays. Nat Genet 1999, 21(1 Suppl):15–19. 10.1038/4439View ArticlePubMedGoogle Scholar
- Pickett S: Understanding and evaluating fluorescent microarray imaging instruments. IVT Technology 2003, 9(4):1–6.Google Scholar
- Zong Y, Wang Y, Zhang S, Shi Y: How to evaluate a microarray scanner. In Microarray Methods and Applications – Nuts & Bolts. Edited by: Hardiman G. Eagleville: DNA Press; 2003:99–114.Google Scholar
- Axon: GenePix Pro 4.0 User's Guide and Turtorial. Axon Instruments Inc 2001.Google Scholar
- Martinez MJ, Aragon AD, Rodriguez AL, Weber JM, Timlin JA, Sinclair MB, Haaland DM, Werner-Washburne M: Identification and removal of contaminating fluorescence from commercial and in-house printed DNA microarrays. Nucleic Acids Res 2003, 31(4):e18. 10.1093/nar/gng018PubMed CentralView ArticlePubMedGoogle Scholar
- Raghavachari N, Bao YP, Li G, Xie X, Muller UR: Reduction of autofluorescence on DNA microarrays and slide surfaces by treatment with sodium borohydride. Anal Biochem 2003, 312(2):101–105. 10.1016/S0003-2697(02)00440-2View ArticlePubMedGoogle Scholar
- Fuscoe J, Branham W, Melvin C, Desai V, Moland C, Han T, Shi L, Scully A, Delongchamp R: Technical issues involved in obtaining reliable data from microarray experiments. Regulatory Research Perspectives 2004.Google Scholar
- Quackenbush J: Microarray data normalization and transformation. Nat Genet 2002, 32(Suppl):496–501. 10.1038/ng1032View ArticlePubMedGoogle Scholar
- Yang YH, Dudoit S, Luu P, Lin DM, Peng V, Ngai J, Speed TP: Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Res 2002, 30(4):e15. 10.1093/nar/30.4.e15PubMed CentralView ArticlePubMedGoogle Scholar
- Yang IV, Chen E, Hasseman JP, Liang W, Frank BC, Wang S, Sharov V, Saeed AI, White J, Li J, et al.: Within the fold: assessing differential expression measures and reproducibility in microarray assays. Genome Biol 2002, 3(11):research0062.PubMed CentralPubMedGoogle Scholar
- Dudley AM, Aach J, Steffen MA, Church GM: Measuring absolute expression with microarrays with a calibrated reference sample and an extended signal intensity range. Proc Natl Acad Sci U S A 2002, 99(11):7554–7559. 10.1073/pnas.112683499PubMed CentralView ArticlePubMedGoogle Scholar
- Foster WR, Huber RM: Current themes in microarray experimental design and analysis. Drug Discov Today 2002, 7(5):290–292. 10.1016/S1359-6446(02)02184-0View ArticlePubMedGoogle Scholar
- Dodd LE, Korn EL, McShane LM, Chandramouli GV, Chuang EY: Correcting log ratios for signal saturation in cDNA microarrays. Bioinformatics 2004, 20(16):2685–2693. 10.1093/bioinformatics/bth309View ArticlePubMedGoogle Scholar
- Lyng H, Badiee A, Svendsrud DH, Hovig E, Myklebost O, Stokke T: Profound influence of microarray scanner characteristics on gene expression ratios: analysis and procedure for correction. BMC Genomics 2004, 5(1):10. 10.1186/1471-2164-5-10PubMed CentralView ArticlePubMedGoogle Scholar
- Bengtsson H, Jonsson G, Vallon-Christersson J: Calibration and assessment of channel-specific biases in microarray data with extended dynamical range. BMC Bioinformatics 2004, 5(1):177. 10.1186/1471-2105-5-177PubMed CentralView ArticlePubMedGoogle Scholar
- Desai VG, Moland CL, Branham WS, Delongchamp RR, Fang H, Duffy PH, Peterson CA, Beggs ML, Fuscoe JC: Changes in expression level of genes as a function of time of day in the liver of rats. Mutat Res 2004, 549(1–2):115–129.View ArticlePubMedGoogle Scholar
- Tong W, Cao X, Harris S, Sun H, Fang H, Fuscoe J, Harris A, Hong H, Xie Q, Perkins R, et al.: ArrayTrack – supporting toxicogenomic research at the U.S. Food and Drug Administration National Center for Toxicological Research. Environ Health Perspect 2003, 111(15):1819–1826.PubMed CentralView ArticlePubMedGoogle Scholar
- Tong W, Harris S, Cao X, Fang H, Shi L, Sun H, Fuscoe J, Harris A, Hong H, Xie Q, et al.: Development of public toxicogenomics software for microarray data management and analysis. Mutat Res 2004, 549(1–2):241–253.View ArticlePubMedGoogle Scholar
- Weinstein JN, Myers TG, O'Connor PM, Friend SH, Fornace AJ Jr, Kohn KW, Fojo T, Bates SE, Rubinstein LV, Anderson NL, et al.: An information-intensive approach to the molecular pharmacology of cancer. Science 1997, 275(5298):343–349. 10.1126/science.275.5298.343View ArticlePubMedGoogle Scholar
- Yuen T, Wurmbach E, Pfeffer RL, Ebersole BJ, Sealfon SC: Accuracy and calibration of commercial oligonucleotide and custom cDNA microarrays. Nucleic Acids Res 2002, 30(10):e48. 10.1093/nar/30.10.e48PubMed CentralView ArticlePubMedGoogle Scholar
- Dobbin K, Shih JH, Simon R: Statistical design of reverse dye microarrays. Bioinformatics 2003, 19(7):803–810. 10.1093/bioinformatics/btg076View ArticlePubMedGoogle Scholar
- Dobbin K, Shih JH, Simon R: Questions and answers on design of dual-label microarrays for identifying differentially expressed genes. J Natl Cancer Inst 2003, 95(18):1362–1369.View ArticlePubMedGoogle Scholar
- Rosenzweig BA, Pine PS, Domon OE, Morris SM, Chen JJ, Sistare FD: Dye bias correction in dual-labeled cDNA microarray gene expression measurements. Environ Health Perspect 2004, 112(4):480–487.PubMed CentralView ArticlePubMedGoogle Scholar
- Hekstra D, Taussig AR, Magnasco M, Naef F: Absolute mRNA concentrations from sequence-specific calibration of oligonucleotide arrays. Nucleic Acids Res 2003, 31(7):1962–1968. 10.1093/nar/gkg283PubMed CentralView ArticlePubMedGoogle Scholar
- Naef F, Socci ND, Magnasco M: A study of accuracy and precision in oligonucleotide arrays: extracting more signal at large concentrations. Bioinformatics 2003, 19(2):178–184. 10.1093/bioinformatics/19.2.178View ArticlePubMedGoogle Scholar
- Held GA, Grinstein G, Tu Y: Modeling of DNA microarray data by using physical properties of hybridization. Proc Natl Acad Sci U S A 2003, 100(13):7575–7580. 10.1073/pnas.0832500100PubMed CentralView ArticlePubMedGoogle Scholar
- Shi L, Tong W, Fang H, Scherf U, Han J, Puri RK, Frueh FW, Goodsaid FM, Guo L, Su Z, et al.: Cross-platform comparability of microarray technology: Intra-platform consistency and appropriate data analysis procedures are essential. BMC Bioinformatics 2005, 6(Suppl 2):S12. 10.1186/1471-2105-6-S2-S12PubMed CentralView ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.