Generalization of DNA microarray dispersion properties: microarray equivalent of <it>t</it>-distribution

1745-6150-1-27 1745-6150 Research Generalization of DNA microarray dispersion properties: microarray equivalent of <it>t</it>-distribution Novak P Jaroslav jaroslav.novak@mail.mcgill.ca Kim Seon-Young kimsy@kribb.re.kr Xu Jun jun.xu@cshs.org Modlich Olga omodlich@onkochemie.uni-duesseldorf.de Volsky J David djv4@columbia.edu Honys David david.honys@gmail.com Slonczewski L Joan slonczewski@kenyon.edu Bell A Douglas bell1@niehs.nih.gov Blattner R Fred fred@genome.wisc.edu Blumwald Eduardo eblumwald@ucdavis.edu Boerma Marjan mboerma@uams.edu Cosio Manuel manuel.cosio@mcgill.ca Gatalica Zoran zorangatalica@creighton.edu Hajduch Marian marian.hajduch@fnol.cz Hidalgo Juan juan.hidalgo@uab.es McInnes R Roderick mcinnes@sickkids.ca Miller III C Merrill miller9418@yahoo.com Penkowa Milena m.penkowa@mai.ku.dk Rolph S Michael m.rolph@garvan.org.au Sottosanto Jordan jbso@ucdavis.edu St-Arnaud Rene rst-arnaud@shriners.mcgill.ca Szego J Michael michael.szego@utoronto.ca Twell David twe@leicester.ac.uk Wang Charles charles.wang@cshs.org

McGill University and Genome Québec Innovation Centre, 740 Docteur Penfield Avenue, Montreal, Québec, H3A 1A4, Canada

Human Genomics Laboratory, Genome Research Center, 52 Eoeun-dong, Yuseong-gu, Daejon, 305-333, Korea

Transcriptional Genomics Core, Cedars-Sinai Medical Center, Los Angeles, CA 90048, USA

Institut fur Onkologische Chemie, Heinrich Heine Universitat Dusseldorf, Moorenstr. 5, D-40225 Dusseldorf, Germany

St. Luke's-Roosevelt Hospital Center and Columbia University, Molecular Virology Division, 432 West 58th Street, Antenucci Building, Room 709, New York, NY 10019, USA

Institute of Experimental Botany AS CR, Rozvojová 135, CZ-165 02, Praha 6, Czech Republic and Charles University in Prague, Department of Plant Physiology, Viničná 5, 12844, Praha 2, Czech Republic

Department of Biology, Higley Hall, 202 N. College Dr., Kenyon College, Gambier, OH 43022, USA

Environmental Genomics Section, C3-03, PO Box 12233, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, USA

Department of Genetics, 425 Henry Mall, University of Wisconsin, Madison, WI 53706, USA

Department of Plant Sciences, University of California, One Shields Ave, Davis, CA 95616, USA

Department of Pharmaceutical Sciences, University of Arkansas for Medical Sciences, 4301 West Markham, Slot 522-3, Little Rock AR 72205, USA

Respiratory Division, Department of Medicine, McGill University, Montreal, Quebec, Canada

Department of Pathology, Creighton University School of Medicine, 601 North 30th Street, Omaha, NE, 68131-2197, USA

Laboratory of Experimental Medicine, Department of Pediatrics, Faculty of Medicine and Dentistry, Palacky University in Olomouc, Puskinova 6, 775 20 Olomouc, Czech Republic

Institute of Neurosciences and Department of Cellular Biology, Physiology and Immunology, Animal Physiology unit, Faculty of Sciences, Autonomous University of Barcelona, Bellaterra, Barcelona, 08193, Spain

Programs in Genetics and Developmental Biology, The Research Institute, The Hospital for Sick Children, Toronto, Canada M5G 1X8; Departments of Molecular and Medical Genetics and Pediatrics, University of Toronto, Toronto, M5S 1A1, Canada

Environmental Genomics Section, C3-03, PO Box 12233, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, USA

Section of Neuroprotection, Centre of Inflammation and Metabolism, The Faculty of Health Sciences, University of Copenhagen, Blegdamsvej 3, DK-2200, Copenhagen Denmark

Arthritis and Inflammation Research Program, Garvan Institute of Medical Research, 384 Victoria St, Darlinghurst NSW 2010, Australia

Department of Plant Sciences, University of California, One Shields Ave, Davis, CA 95616, USA

Genetics Unit, Shriners Hospital for Children and Departments of Surgery and Human Genetics, McGill University, Montréal H3A 2T5, Québec, Canada

Department of Biology, University of Leicester, LE1 7RH Leicester, UK

Department of Medicine, Cedars-Sinai Medical Center, David Geffen School of Medicine, UCLA, Los Angeles, CA 90048, USA

Biology Direct 1745-6150 2006 1 1 27 http://www.biology-direct.com/content/1/1/27 16959036 10.1186/1745-6150-1-27 01 9 2006 07 9 2006 07 9 2006 2006 Novak et al; licensee 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.

Abstract

Background

DNA microarrays are a powerful technology that can provide a wealth of gene expression data for disease studies, drug development, and a wide scope of other investigations. Because of the large volume and inherent variability of DNA microarray data, many new statistical methods have been developed for evaluating the significance of the observed differences in gene expression. However, until now little attention has been given to the characterization of dispersion of DNA microarray data.

Results

Here we examine the expression data obtained from 682 Affymetrix GeneChips^®with 22 different types and we demonstrate that the Gaussian (normal) frequency distribution is characteristic for the variability of gene expression values. However, typically 5 to 15% of the samples deviate from normality. Furthermore, it is shown that the frequency distributions of the difference of expression in subsets of ordered, consecutive pairs of genes (consecutive samples) in pair-wise comparisons of replicate experiments are also normal. We describe a consecutive sampling method, which is employed to calculate the characteristic function approximating standard deviation and show that the standard deviation derived from the consecutive samples is equivalent to the standard deviation obtained from individual genes. Finally, we determine the boundaries of probability intervals and demonstrate that the coefficients defining the intervals are independent of sample characteristics, variability of data, laboratory conditions and type of chips. These coefficients are very closely correlated with Student's t-distribution.

Conclusion

In this study we ascertained that the non-systematic variations possess Gaussian distribution, determined the probability intervals and demonstrated that the K_αcoefficients defining these intervals are invariant; these coefficients offer a convenient universal measure of dispersion of data. The fact that the K_αdistributions are so close to t-distribution and independent of conditions and type of arrays suggests that the quantitative data provided by Affymetrix technology give "true" representation of physical processes, involved in measurement of RNA abundance.

Reviewers

This article was reviewed by Yoav Gilad (nominated by Doron Lancet), Sach Mukherjee (nominated by Sandrine Dudoit) and Amir Niknejad and Shmuel Friedland (nominated by Neil Smalheiser).

Open peer review

Reviewed by Yoav Gilad (nominated by Doron Lancet), Sach Mukherjee (nominated by Sandrine Dudoit) and Amir Niknejad and Shmuel Friedland (nominated by Neil Smalheiser). For the full reviews, please go to the Reviewers' comments section.

Background

DNA microarrays provide large quantities of data for the study of diseases and biological processes in various organisms. However, microarray studies are subject to potential variations including biological and technical variability. Usually, the existence of a large dispersion makes it very difficult to draw any meaningful conclusions from the differences between the experimental and control groups 12. Alison et al. 1 give the most recent general evaluation of the approaches and methods, summarizing the items where consensus has been established as well as outstanding questions; they underline the need for replicates and the usefulness of drawing information from neighboring genes ("shrinkage"), which is discussed at length here, provide the overview of clustering methods, etc. Many methods have been developed to deal with the problem of separation of systematic and random or pseudorandom components of the signal. For example, in the case of arrays using multi-probe sets, such as Affymetrix GeneChips^®, we first have to derive a representative value of gene expression from the signals of individual probes ("low-level" analysis). The Affymetrix MAS 5 and GCOS use Tukey's biweight algorithm and yield an absolute expression value for each probe set (Affymetrix, 2005, GeneChip Expression Analysis Algorithm Tutorial, Part Number 700285, Rev. 1). The method of low-level analysis, developed by Li and Wong (dChip; 34) is designed to assess the observed differences in expressions of genes on the arrays under comparison. It is based on fitting data to a simplified model, assuming that the noise variable is independent of the signal. A different model, called Robust Multiarray Analysis (RMA), was proposed by Speed, Bolstad, Irizarry and co-workers 567 (see also Bolstad, B.M., 2004, PhD Thesis, University of California, Berkeley). It uses a log-transform of the data implicitly assuming that the error is proportional to the signal intensity. In reality, the error variable has both, constant and proportional components. Once the representative value of the gene expression is known, standard statistical methods of comparison can be used for "high level" analysis of the observed differences. Nonparametric methods, such as the Mann-Whitney U-test (Wilcoxon test) or analysis of variance on ranks, are generally preferable, although the parametric t-test and ANOVA are also frequently used. It should be pointed out that the statistical methods can only separate the systematic variations from the random or pseudo-random component. Random errors are recognizable because they conform to some known frequency distribution, usually Gaussian distribution. However, occasionally, one or several samples exhibit spurious differences from the rest of the data, due to changes in the biological state of the examined cells, quality of RNA etc. Such undesirable effects are often significant and can be detected only by detailed comparisons of the individual replicate samples.

So far, very little attention has been given to the general properties of the dispersion of gene expression levels. With respect to applicability of various statistical methods it is useful to know how the standard deviation behaves across the expression range and whether this behavior is consistent from one assay to another and among the different types of arrays. Verification of normality of the frequency distribution of random fluctuations is particularly relevant. All parametric methods are based on concordance of the observed frequency distribution with the normal (Gaussian) distribution. Most physical and chemical systems, where random variations result mainly from collective interactions of large ensembles of particles, exhibit frequency distributions close to the Gaussian. The underlying mechanisms of microarray data variability are certainly of the same nature as the collective phenomena in physical systems but the ensemble of the processes involved is so complex that one would expect some compound distribution, far from the simple form expressed by the Gaussian prototype.

The object of the present study is to examine the frequency distributions, general properties of the standard deviations and coefficients of the probability intervals. It was found that the general characteristics of dispersion are useful for quality control, reduction of a system dimension and other purposes. Firstly an overview of the frequency distributions is given for both replicate arrays (five or more replicates) and consecutive sampling of the expression difference in the ordered pairs of genes in two-array comparisons. Subsequently, we describe the consecutive sampling analysis and evaluation of the linear characteristic function, approximating the standard deviation of the data variability across the arrays. The standard deviation function is then employed to define the probability intervals encompassing specific percentages of the observed values. The boundaries of these intervals are defined by probability coefficients K_α. It was found that the values of K_αcoefficients obtained using various arrays are, at least in the first approximation, invariant. Finally, we compare the probability of coefficients K_αwith the corresponding values of inverse t-distribution.

Results

In the present investigation we analyzed 682 Affymetrix microarrays of 22 different types. Our main objective was to study the microarray data derived from particular biological investigations, generated in many different microarray core laboratories, rather than the sets of arrays produced in the context of technology development or testing methods of analysis. Only a few "testing" sets were included. We evaluated the CEL files using MAS 4 (Affymetrix, 2002, Statistical Algorithm Description Document. Part Number 701137, Rev. 3.) and employed the "Average Difference" as expression signal value. Because MAS 5 and GCOS distort the frequency distributions in the near-zero region by ignoring the negative values, MAS 5 and GCOS outputs are not suitable. Prior to the analysis, we verified the linearity and quality of the data, in particular, the absence of clusters with significantly different expressions. All data on each array were normalized to 100% of the array mean; all Affymetrix control genes were excluded.

Frequency distributions

In the case of experiments with five or more replicates, we tested the distributions of the expressions of individual genes. In addition, in all pair-wise comparisons we performed the Kolmogorov-Smirnov normality test on consecutive samples (Table 1). Based on our several thousands of tests, it was found that the Gaussian distribution was characteristic of the expression data obtained using the Affymetrix GeneChips^®. Typically, for good-quality data, between 85 and 95 percent of samples passed the test. Moreover, a limited number of tests using the data obtained from fiberoptic bead-based oligonucleotide microarrays by Illumina led to the same conclusion 8.

Table 1

Illustration of the consecutive sampling procedure

Rank

Probe set

Sample Y1

Sample Y2

Y2-Y1

(Y2+Y1)/2

Sample Mean

SD (Y2-Y1)

SD(Y1)+ SD(Y2)

...

251

J03040_at

628

614

-14

621

614.4

71.1

71.8

252

M26880_at

657

583

-74

620

253

HG384-HT384_at

577

662

619

254

X04654_s_at

633

604

-29

619

255

J04046_s_at

554

680

126

617

256

X69908_rna1_at

593

640

617

257

D85758_at

672

555

-117

614

258

L12168_at

633

592

-41

612

259

HG1614-HT1614_at

590

633

611

260

X71428_at

571

649

610

261

S75463_at

602

615

608

262

X69910_at

579

630

604

263

X57346_at

597

610

603

590.1

136.2

137.0

264

U01691_s_at

576

630

603

265

X17620_at

605

594

-11

600

266

U10323_at

562

617

590

267

AJ001421_at

413

766

354

589

268

X62654_rna1_at

576

602

589

269

D64142_at

666

510

-156

588

270

D21063_at

562

613

588

271

X16560_at

588

580

-8

584

272

D26600_at

580

586

583

273

M19267_s_at

599

566

-33

583

274

J02621_s_at

688

475

-213

582

...

Rank shows the rank from the highest mean expression. The columns "Sample Y1 and Y2" give the expression values, Y₂ - Y₁is the expressions difference and (Y2+Y1)/2 the mean expression of the probe sets Y1 and Y2. Sample Mean is the mean expression of the sample, "D(Y2-Y1)" is the standard deviation obtained from the difference of expressions and SD(Y1)+SD(Y2) is the sum of the standard deviations calculated from the values Y1 and Y2, respectively. The first 250 probe pairs are excluded to keep variation of the mean expression within the sample small.

For illustration, Table 2 shows the results of the Kolmogorov-Smirnov test for six studies using Affymetrix GeneChips^®with five to 11 replicates and two studies using Illumina arrays with four replicates each. The mean percentage of probe sets across the arrays failing the Kolmogorov-Smirnov test was 6.9 using the algorithm of Sokal and Rohlf 9 (intrinsic hypothesis, P = 0.05). Usually, but not always, it was found that larger percentages of failures occur in the near-zero region. We did not examine systematically reasons for the failures, but it was often noted that there were outliers and, occasionally, a change of the slope or a discontinuity, noticeable in the quantile-quantile plots. Generally, we performed our analysis in the positive range of values above a small, arbitrary threshold. However, in the several tests, the percentage of failures above and below the threshold was practically identical. Figure 1 illustrates the similarity of the normal distribution and distribution of the expressions measured by typical probe sets in the human cell line IMR90 (11 replicates) in the high range (from 1000 to maximum of 6681, panel A), near-zero range (from -0.4 to 0.4, panel B) and negative range (from a minimum of -923 to -20, panel C; data Ref. 10). A "typical" probe set is defined as a probe set with the Kolmogorov-Smirnov distance D at or close to the mean D in a given range. The figures show quantile-quantile plots (Q-Q plots), comparing the observed expression values to the corresponding values of the inverse normal cumulative distribution. The last panel D shows one sample that failed the test.

Table 2

Percentage of samples failing the Kolmogorov-Smirnov normality test

Array

Materials

No. of arrays

No. of probe sets

Threshold

% failure (total)

% failure (above)

% failure (below)

Affy. HuGeneFL

human cell line SKBR [a]

7070

2.7

7.2

6.9

7.8

Affy. HuGeneFL

human cell line IMR90 [a]

7070

4.1

6.3

6.5

5.9

Affy. U74Av2

murine lung tissue [b]

12422

10.0

6.1

6.6

5.5

Affy. U74Av2

murine lung tissue [c]

12422

13.6

7.6

8.3

6.4

Affy. U74Av2

murine lung tissue [d]

12422

14.2

10.6

10.7

Affy. Focus

human blood cell line [e]

8746

5.0

6.14

Illumina 1

human cell line GM10469 [f]

633

2.1

4.6

3.9

6.2

Illumina 2

human cell line GM10469 [f]

633

3.6

6.5

6.6

6.2

Average

---

6.9

Percentage of samples failing the Kolmogorov-Smirnov normality test at the level P = 0.05. All arrays are normalized to 100% of the mean value. The columns %failure (above) and %failure (below) give percentage of failures above and below the specified threshold.

[a] data Ref. [10].

[b] C57BL/6 (B6) WT mice, data Ref. [15].

[c] C57BL/6-Cftr-/- KO inbred mice, data Ref. [15].

[d] data M. Cosio.

[e] data O. Modlich and S. Raschke.

[f] lymphoblast cell line GM10469 [8].

Table 3

Comparison of the coefficients of standard deviation function derived from the consecutive sampling and individual probe sets

Array

No. of samples

Pair-wise a1

Individual genes a1

Difference %

Pair-wise a2

Individual genes a2

Difference %

HuGene FL (IMR90)

6.0

5.9

1.8

0.082

0.076

7.3

Focus

2.9

1.7

0.153

0.154

-0.6

MG-U74Av2

5.1

4.4

12.8

0.161

0.136

15.6

Illumina 1

2.7

2.4

12.2

0.092

0.085

7.7

Illumina 2

2.2

2.1

2.6

0.096

0.082

14.7

mean difference %

---

6.2

---

9.0

Columns pair-wise a1 and pair-wise a2 are the coefficients of the standard deviation characteristic function derived from the consecutive sampling. Columns individual genes a1 and a2 show the values derived from the individual probe sets and difference is the difference in % between the two methods.

Figure 1

Comparison of the observed frequency distribution to the inverse normal cumulative distribution

Comparison of the observed frequency distribution to the inverse normal cumulative distribution. Quantile-quantile plots show on y-axis the observed expression and on x-axis value of the corresponding inverse normal cumulative distribution. Microarray data are derived from HuGeneFL, using IMR90 cell line with 11 samples. Panels show the probe sets with the Kolmogorov-Smirnov maximum distance D equal or close to the mean value in the specified average expression rage. Inserts provide the Affymetrix probe set identification, average expression for a given gene and standard deviation. A: probe set HG2279-HT2375_at, rank 43, expression range from 1000 to 6681 (high range, maximum), average D in the range is 0.176, sample D is 0.176; B: probe set Z23091_rna1_at, rank 5484, expression range from -0.4 to 0.4 (near-zero range), average D in the rang is 0.181, sample D is 0.182; C: probe set X95876_at, rank 7003, expression range from -20 to -923 (negative range, minimum), average D in the range is 0.183, sample D is 0.182; D: example of the probe set that failed the test – probe set M14199_s_at, rank 25, sample D is 0.204 (data Novak et al., IMR90 [10]).

Furthermore, we observed that the probe sets with the mean expressions within a "reasonably small" range had, on average, a similar variance. Figure 2A shows pooled data of the 62 probe sets in the expression range from -0.1 to 0.1 (cell line IMR90, 11 replicates, Ref. 10) in Q-Q plot in comparison to the inverse normal cumulative distribution with good agreement except for about six outliers. The picture changes when we scan probe sets with a wide range of mean expressions. Figure 2B shows the Q-Q plot of 185 probes sets in the range of means from 500 to 1000; the lower part of the graph deviates substantially from the straight line. When we plotted the relative expression (i.e. expressions of the individual probe sets divided by the mean of 11 arrays; Figure 2C), we got all the points, except for about ten outliers, back on the 45° line. This implies that the standard deviation is linearly proportional to the mean expression level.

Figure 2

Comparison of the observed frequency distribution to the inverse normal cumulative distribution, pooled data

Comparison of the observed frequency distribution to the inverse normal cumulative distribution, pooled data. Quantile-quantile plots show on y-axis the observed expression and on x-axis value of the corresponding inverse normal cumulative distribution. Microarray data are derived from HuGeneFL, using the cell line IMR90 with 11 samples, pooled data. A: expression range from -0.1 to 0.1, 62 probe sets; B: expression range from 500 to 1000, 185 probe sets; C: expression range from 500 to 1000, 185 probe sets, relative expression values (sample expression divided by the mean of 11 samples; data Novak et al. [10]).

Based on the evidence of Figure 2, we hypothesize that approximately the same standard deviation can be obtained by scanning the data vertically, i.e. looking at expressions of the neighboring probe sets, or horizontally, i.e. looking at the series of arrays for each probe set. In other words, the probability that we will observe a difference d between the measurements M₁and M₂of the probe set Pr₁on the arrays A₁and A₂is, at least in the first approximation, about the same as the probability that we will observe such difference between the measurement M₃of the probe set Pr₁on the array A₁and the measurement M₄of the probe set Pr₂on the array A₂, provided that the mean expression of both populations is the same. It further follows that an estimate of mean standard deviation of a group of genes with approximately same mean expression can be obtained from comparison of two arrays. We need to rank the probe sets according to the mean expression and evaluate the standard deviation from the differences in gene expressions in samples of k consecutive genes; the range of the means within a sample must be small. Furthermore, in this arrangement we can also obtain the standard deviation by using the ranked probe sets of each individual array (Ref. 10, Supplementary Material). Note that the standard deviation derived from the difference converges to √2σ, where σ is a standard deviation of a given population. Figure 3 shows a comparison of the frequency distribution of the difference in expression of two consecutive samples with the corresponding inverse normal cumulative distribution (cell line IMR90).

Figure 3

Comparison of the observed frequency distribution of consecutive samples to the inverse normal cumulative distribution

Comparison of the observed frequency distribution of consecutive samples to the inverse normal cumulative distribution. Quantile-quantile plots show on y-axis the difference of expression of two microarrays and on x-axis value of the corresponding inverse normal cumulative distribution. Microarray data are derived from HuGeneFL, using cell line IMR90 [10]. Probe sets of the microarrays 1 and 3 are ordered according to the mean expression and statistical samples of 12 probe sets are taken in the range of ranks from 250 to 4800. Panels show the samples with the Kolmogorov-Smirnov maximum distance equal or close to the mean value in the specified average expression rage. Inserts provide the average mean expression (range avg.), mean of the differences (s. avg.) and standard deviation (s. SD). A: expression range from 400 to 620, average D in the range is 0.142, sample D is 0.142; B: expression range from 10 to 20, average D in the range is 0.204, sample D is 0.204.

Consecutive sampling analysis

Assume, as a working hypothesis, that we can estimate the standard deviation of the gene expression variability of series replicate arrays from two-array comparisons. Since the evidence derived from the frequency distribution suggests that the standard deviation is linearly proportional to the expression level (at least in the first approximation), we assume that a representative estimate of the standard deviation can be obtained in the form of a linear function of the mean expression. A similar model was proposed on a basis of theoretical considerations by Rocke and coworkers 11121314. The consecutive sampling program (see Methods) takes k pairs of expression values Y_1iand Y_2iranked according to the mean (Y_1i, Y_2i) and calculates the standard deviation from the difference Y_2i-Y_1i, where the subscripts 1 and 2 denote the array number and i signifies the probe set rank; typically we set k = 12, 25 or 50, depending on the size of the array. The standard deviation function is then determined by fitting the logarithmically transformed values to the logarithm of the linear function of the mean expression (see the Methods section). For illustration, Figure 4A shows the dispersion plot and boundaries of the 0.8 and 0.95 probability intervals for the murine array MG U74Av2 (lung tissue, AKR mice; Table 4), whereas Figure 4B shows standard deviations of the consecutive samples consisting of 12 ordered pairs of probe sets and the regression curve, representing the standard deviation function.

Table 4

Summary of values of the coefficients of standard deviation function and K_αcoefficients

GeneChip/average/SD/CV

No. of probe sets

Cons. samp. size

No. of arrays

No. of comp.

Coefficient. of st. dev. function

Average Kalpha values in given probability intervals

0.500

0.600

0.700

0.800

0.900

0.950

0.990

0.995

Total average [sum]

[682]

[900]

9.66

0.266

0.642

0.808

1.009

1.275

1.711

2.145

3.226

3.741

Total SD

9.99

0.146

0.033

0.039

0.043

0.045

0.052

0.080

0.270

0.390

Total CV

1.03

0.550

0.052

0.049

0.043

0.035

0.030

0.037

0.084

0.104

HuGeneFL [a1]

7070

8.61

0.115

0.64

0.81

1.01

1.27

1.71

2.16

3.41

4.09

HuGeneFL [b]

7070

8.09

0.418

0.61

0.77

0.97

1.24

1.73

2.24

3.58

4.18

HuGeneFL [c]

7070

34.58

0.435

0.61

0.76

0.94

1.20

1.60

2.03

3.39

4.10

HuGeneFL [c]

7070

28.93

0.393

0.59

0.73

0.92

1.18

1.60

2.07

3.42

4.07

HuGeneFL avg [sum]

[34]

[152]

20.05

0.34

0.61

0.77

0.96

1.22

1.66

2.13

3.45

4.11

HuGeneFL SD

13.71

0.15

0.02

0.03

0.04

0.07

0.10

0.09

0.05

HuGeneFL CV

0.68

0.44

0.04

0.05

0.03

0.01

HG-U95Av2 [d]

12559

6.30

0.688

0.61

0.78

1.00

1.30

1.83

2.32

2.98

3.26

HG-U95Av2 [e1]

12559

10.49

0.199

0.65

0.82

1.01

1.27

1.68

2.07

3.05

3.55

HG-U95Av2 [e2]

12559

10.59

0.200

0.64

0.81

1.01

1.26

1.67

2.07

3.07

3.56

HG-U95Av2 [e3]

12559

10.41

0.189

0.63

0.80

1.00

1.25

1.66

2.07

3.06

3.55

HG-U95Av2 [e4]

12559

10.91

0.185

0.63

0.79

0.99

1.24

1.66

2.04

3.02

3.50

HG-U95Av2 [e5]

12559

6.50

0.394

0.65

0.82

1.01

1.26

1.65

2.05

3.05

3.62

HG-U95Av2 [f]

12559

5.64

0.155

0.64

0.81

1.00

1.25

1.66

2.04

2.92

3.31

HG-U95Av2 [g1]

12559

4.79

0.479

0.61

0.76

0.95

1.20

1.64

2.10

3.22

3.71

HG-U95Av2 [g1]

12559

3.31

0.500

0.64

0.80

1.00

1.26

1.69

2.09

2.98

3.29

HG-U95Av2 avg [sum]

[77]

[82]

7.66

0.33

0.63

0.80

1.00

1.26

1.68

2.09

3.04

3.48

HG-U95Av2 SD

2.94

0.19

0.02

0.03

0.06

0.09

0.08

0.16

HG-U95Av2 CV

0.38

0.57

0.02

0.04

0.03

0.05

HG-U95B [d]

12563

16.26

0.636

0.63

0.80

1.01

1.30

1.80

2.28

3.18

3.68

HG-U95B [e5]

12563

17.95

0.167

0.64

0.80

0.99

1.24

1.65

2.02

3.08

3.54

HG-U95C [d]

12587

20.57

0.603

0.64

0.81

1.02

1.30

1.77

2.25

3.39

3.98

HG-U95C [e5]

12587

16.42

0.178

0.63

0.79

0.99

1.23

1.62

2.00

3.06

3.61

HG-U95D [d]

12587

39.79

0.501

0.62

0.78

0.99

1.28

1.77

2.33

3.80

4.42

HG-U95D [e5]

12587

54.45

0.240

0.63

0.79

0.99

1.23

1.62

2.05

2.98

3.48

HG-U95E [d]

12582

31.84

0.534

0.60

0.76

0.97

1.27

1.78

2.29

3.53

4.08

HG-U95E [e5]

12582

45.64

0.215

0.63

0.79

1.00

1.25

1.64

2.02

2.88

3.31

HG-U95B to E avg [sum]

[28]

[44]

30.37

0.38

0.63

0.79

0.99

1.26

1.71

2.16

3.24

3.76

HG-U95B to E SD

14.87

0.20

0.01

0.02

0.03

0.08

0.14

0.31

0.37

HG-U95B to E CV

0.49

0.53

0.02

0.05

0.07

0.10

HG-U133A 2.0 [e6]

22225

4.55

0.091

0.65

0.82

1.02

1.28

1.72

2.14

3.14

3.62

HG-U133A 2.0 [e7]

22225

4.50

0.106

0.66

0.84

1.04

1.31

1.75

2.17

3.18

3.63

HG-U133A 2.0 [e8]

22225

4.10

0.108

0.67

0.84

1.05

1.32

1.77

2.21

3.26

3.75

HG-U133A 2.0 [h1]

22225

3.91

0.288

0.64

0.80

1.00

1.26

1.67

2.08

3.05

3.54

HG-U133A 2.0 [i1]

22225

6.25

0.210

0.65

0.82

1.01

1.27

1.68

2.08

3.04

3.48

HG-U133A 2.0 [j]

22225

6.54

0.390

0.62

0.79

0.98

1.25

1.68

2.10

3.13

3.62

HG-U133A 2.0 [j]

22225

5.54

0.393

0.62

0.79

0.98

1.25

1.66

2.08

3.10

3.64

HG-U133A 2.0 [k1]

22225

3.68

0.672

0.63

0.80

1.00

1.27

1.71

2.11

2.84

3.16

HG-U133A 2.0 [k1]

22225

4.95

0.435

0.59

0.74

0.93

1.19

1.65

2.15

3.37

3.79

HG-U133A 2.0 [l1]

22225

6.45

0.151

0.64

0.81

1.01

1.27

1.68

2.08

3.06

3.55

HG-U133A 2.0 [l2]

22225

6.78

0.148

0.65

0.82

1.02

1.27

1.67

2.06

2.93

3.33

HG-U133A 2.0 avg [sum]

[91]

[99]

5.21

0.27

0.64

0.80

1.00

1.27

1.69

2.11

3.10

3.56

HG-U133A 2.0 SD

1.15

0.18

0.02

0.03

0.04

0.05

0.15

0.18

HG-U133A 2.0 CV

0.22

0.67

0.03

0.02

0.05

HG-U133 Plus 2 [i2]

54000

3.94

0.188

0.68

0.85

1.06

1.33

1.76

2.17

3.11

3.55

HG-U133 Plus 2 [l3]

54000

4.03

0.086

0.65

0.82

1.02

1.28

1.69

2.07

2.95

3.34

HG-U133 Plus 2 avg [sum]

[28]

[37]

3.99

0.14

0.67

0.83

1.04

1.30

1.72

2.12

3.03

3.44

HG-Focus [k2]

8756

4.13

0.216

0.70

0.87

1.08

1.35

1.76

2.15

3.06

3.47

HG-Focus [k2]

8756

4.13

0.181

0.68

0.86

1.07

1.33

1.76

2.18

3.08

3.56

HG-Focus [k2]

8756

3.90

0.198

0.70

0.87

1.08

1.36

1.81

2.22

3.15

3.55

HG-Focus [k2]

8756

3.69

0.176

0.68

0.86

1.07

1.35

1.79

2.19

3.17

3.64

HG-Focus [k2]

8756

3.46

0.183

0.67

0.85

1.05

1.33

1.77

2.19

3.12

3.49

HG-Focus [k2]

8756

4.01

0.205

0.71

0.89

1.10

1.38

1.81

2.19

3.11

3.53

HG-Focus [k2]

8756

3.98

0.174

0.68

0.85

1.06

1.32

1.74

2.14

3.06

3.43

HG-Focus avg [sum]

[34]

[76]

3.90

0.19

0.69

0.86

1.07

1.35

1.78

2.18

3.11

3.52

HG-Focus SD

0.24

0.02

0.01

0.02

0.03

0.04

0.07

HG-Focus CV

0.06

0.08

0.02

0.01

0.02

MG-Mu11kSubA, SubB [a]

13069

9.98

0.121

0.59

0.75

0.95

1.22

1.70

2.20

3.65

4.48

MG-Mu11kSubA, SubB [a]

13069

8.03

0.170

0.59

0.74

0.94

1.20

1.68

2.19

3.78

4.66

MG-Mu11kSubA, SubB [a]

13069

8.21

0.145

0.60

0.76

0.96

1.23

1.70

2.21

3.70

4.52

MG-Mu11kSubA, SubB [a]

13069

5.32

0.139

0.56

0.71

0.91

1.19

1.71

2.30

4.03

4.84

MG-Mu11kSubA, SubB [m1]

13069

13.86

0.321

0.64

0.81

1.01

1.28

1.73

2.22

3.62

4.24

MG Mu11kSubA, SubB [n1]

13069

11.84

0.420

0.66

0.82

1.01

1.26

1.71

2.21

3.61

4.32

MG-Mu11kSubA, SubB avg [sum]

[68]

[94]

9.54

0.219

0.61

0.77

0.96

1.23

1.70

2.22

3.73

4.51

MG-Mu11kSubA, SubB SD

3.03

0.122

0.04

0.02

0.04

0.16

0.22

MG-Mu11kSubA, SubB CV

0.32

0.557

0.06

0.05

0.04

0.03

0.01

0.02

0.04

0.05

Mu19kSubA, B, C [m2]

12420

15.41

0.314

0.63

0.79

0.99

1.25

1.73

2.26

3.95

4.56

MG-U74Av2 [o]

12588

8.72

0.180

0.59

0.75

0.95

1.23

1.70

2.20

3.56

4.30