Transcript levels of mmu21 genes were measured by qPCR in the cerebellum, midbrain, and cortex of eight Ts65Dn and eight control adult mice. Fifty mmu21 genes were tested, of which 33 are triplicated and 17 are disomic in Ts65Dn. Experiments were done in triplicate using two non-mmu21 reference genes that were previously tested for stability in each tissue. For each gene, we calculated a normalized expression value relative to the two reference genes (Additional data file 1).

A large majority of the mmu21 transcripts was found to be active in brain. Forty-two genes (31 trisomic and 11 disomic) were expressed in all three of the brain regions tested. Whereas some of those genes were expressed at high levels in all brain regions (for example, App, Son, S100b, Itsn, and Dyrk1a), others were differentially expressed (for instance, higher expression of Sh3bgr, Col18a1, Tiam1, Pde9a, and S100b in cerebellum, and lower expression of Ncam2 in cerebellum; data not shown). Eight genes (Prss7, Cryaa, Kcne1, Fam3b, Tff3, Tff2, Tmprss3, and C21orf56) were excluded from further analysis because they had very low or undetectable levels of expression (for example, Ct > 34 cycles).

For each mmu21 gene, we estimated the gene dosage effect in a given tissue by comparing the ratio of the arithmetic mean of the normalized expression values obtained for the eight Ts65Dn mice with that of the mean of the eight euploids. This value is referred to here as 'electronic' pool (e-pool). We confirmed a trend of 1.5-fold over-expression for the trisomic genes (Figure 1), as reported previously for pooled RNAs from Ts65Dn and controls using arrays or real-time PCR 19. Assuming that the ratio for diploid genes in trisomic mice versus euploid should be close to 1, the level of over-expression was corrected by the value of slope obtained for the duplicated genes. The global over-expression level of triplicated genes in Ts65Dn was 1.44-fold in cerebellum, 1.37-fold in cortex, and 1.39-fold in midbrain (Figure 1). We also performed a direct measurement of expression levels for RNAs pooled from the eight Ts65Dn and euploid mice, respectively (biologic pools referred as b-pools). We observed a nearly perfect correlation of the b-pools with the e-pools, suggesting that experimental measurement errors are minimal (Figures 2b, 3b, and 4b and Additional data file 2).

Data presented here compare well with previously published findings in Ts65Dn, in which investigations were performed in an independent set of mice and with different chemistry (TaqMan versus SYBR green or cDNA arrays) 19. Indeed, we observed a global correlation of 80% between the two studies comparing the Ts65Dn/euploid ratios for pooled RNAs using binned value ranges (see Materials and Methods). A direct comparison could not be made with the study of Lyle and coworkers 18 because they measured expression profiles in whole brain of RNAs from Ts65Dn mice at a different age. However, they also reported an overall over-expression close to 1.5-fold for the trisomic genes in Ts65Dn.

We used pooling schemes with eight individual Ts65Dn and control mice as a prerequisite to assess the robustness of our measurements comparing e-pools and b-pools. We validated the 1.5-fold over-expression of trisomic genes in Ts65Dn. However, this value represents a global trend that does not exhibit potential variations in gene expression between individuals. In the next step, we investigated the variation of expression levels for the mmu21 genes in the eight trisomic and control mice.

Analysis of individual samples allows recovery of important information that cannot be determined from pooled samples. We estimated the variation of gene expression between individual mice by using the coefficient of variation (CV). We then assessed whether the two populations (Ts65Dn and euploid) differ significantly in terms of this variance by using the F-test, and we applied the Wilcoxon test to judge whether the differences in expression levels between Ts65Dn and euploid animals were significant. Data are summarized in Additional data file 3.

It was first important to evaluate the potential influence of technical variation as compared with that of biological variation. We calculated technical variance based on the experimental replicates and biological variance measured between individuals in each group (Ts65Dn or euploid; see Materials and methods [below] and Additional data file 3), similar to analysis of variance estimations. We considered the percentage of technical variance over the total variance (technical + biologic variance) as a quality measure. The inter-individual variation in gene expression observed here can be attributed mostly to biologic differences because for most genes the biological variance contributes to more than 90% of the total variance (Additional data file 3). We could reliably detect expression differences as small as 1.3-fold for nearly all of the assays, because the average standard error of the mean for the relative expression measurements was 0.14 in the 95% confidence intervals.

We used the CV (see Materials and methods [below] and Additional data file 3) as an indicator of the variation in gene expression among individual mice in each group (Ts65Dn or euploid). The CV, in contrast to the variance, is independent of the gene expression level and thus enables inter-gene comparison. To group the CVs, we set arbitrary cut-offs defined as a very low (CV < 0.1), low (CV < 0.2), moderate (CV between 0.2 and 0.5), and high (CV > 0.5) variation in gene expression. In control mice six genes exhibited a CV < 0.1, suggesting that they are tightly regulated (Jam2 in cerebellum; App, in midbrain; and App, Wdr4, S100b, Gabpa, and Mrps6 in cortex). App was previously reported to exhibit highly variable expression in lymphoblastoid cell lines 26, but it appears here to be tightly regulated, with a CV of 0.18 in cerebellum, 0.1 in cortex, and 0.09 in midbrain. Few genes (three, five, and nine genes in cortex, midbrain, and cerebellum, respectively) exhibit highly variable expression levels (CV > 0.5). In Ts65Dn mice, 24 out of the 31 triplicated genes have CVs below 0.2, suggesting that although their expression is elevated, it remains relatively tightly regulated. None of the triplicated genes had CVs below 0.1. Only four triplicated genes (Kcne2, C21orf7, Cldn8, and Sh3bgr) exhibit a systematic high fluctuation in expression levels (CV > 0.5) across individuals and tissues. Among the disomic genes, two were tightly regulated (CV < 0.1) in cortex (Wdr4 and Lss) and one in the midbrain (Cstb). One disomic gene (Col18a1) exhibited high variation in expression levels (CV > 0.5) among all brain regions and in both groups (Ts65Dn and euploid).

For all of the trisomic genes, we plotted CVs for the Ts65Dn population against the CVs for the euploid population (Additional data file 4). For most of the tested genes there is no significant difference in the variation of expression levels between trisomic and euploid mice, because 85 out of 93 data points do not differ by more than 20% in CVs between the two groups. On average, 90% of the trisomic genes exhibit low or moderate variation in expression among groups. A few outliers, such as Kcne2 and C21orf7, exhibit dramatic variations in expression among mice. Kcne2, for example, was found to be highly variable in all three brain tissues and in both groups (Ts65Dn and euploid).

The variance in expression levels increases as gene expression increases. This obscures the fact that, in proportion, the level of variation is not greater. To determine statistically whether the presence of an extra copy of a gene influences its variation in expression level, we used the CV calculated with the F-test to circumvent this artefact. We observed that, overall, the amplitude of variation of gene expression did not differ significantly (P > 0.05) between euploid and Ts65Dn mice (Additional data file 3). The basal level of expression of a given gene follows a Gaussian distribution of similar width in trisomic and in euploid mice. This result confirms earlier findings in fetal cortex of human trisomy 21 24, at least as far as mmu21 genes are concerned. Three trisomic genes appeared to exhibit variation that was significantly greater (P < 0.05) in Ts65Dn than in euploid mice (Gabpa and Ifnar2 in the cortex, B3galt5 in the cerebellum). Contrary to our expectations, however, the CV was significantly smaller (P < 0.05) in trisomic mice for five trisomic genes (Ifnar2 and Kcne2 in cerebellum, Ets2 in cortex, and Usp16 and Cldn8 in midbrain). Moreover, we see few disomic genes with significant differences in CV (P < 0.05) between the two groups in the cerebellum; for S100b and Ncam2 the CV increases in Ts65Dn mice, whereas it decreases for Lss.

The expression levels of mmu21 genes in individual mice are shown in Figures 2a, 3a and 4a, where we plotted for each tissue the log ratios of the individual normalized gene expression values over the mean expression across all of the eight mice. For the purposes of direct comparison, the corresponding Ts65Dn/euploid gene expression ratios obtained from e-pools and b-pools are indicated on the same figure for each tissue (Figures 2b, 3b, and 4b). The figures enable identification of the genes with expression that varies substantially from those that are tightly regulated, and they demonstrate whether the corresponding mean ratio reflects the variability in gene expression in each tissue.

Finally, we evaluated the significance of the differences in expression levels between Ts65Dn and euploid mice by applying the nonparametric Wilcoxon test, which is robust against outlier values (Additional data file 3). For instance, in the midbrain the Ts65Dn/euploid ratio values of two trisomic genes are downregulated; these genes are C21orf7 (e-pool: ×0.68; b-pool: ×0.37) and Cldn8 (e-pool: ×0.55; b-pool: ×0.35; Figure 4). However, the distribution of the expression levels among single mice is broadly dispersed. In these particular cases, the high CV values in each group (Additional data file 3) and the nonsignificant P values of the Wilcoxon test (P > 0.05) confirmed that pooled Ts65Dn/euploid ratios did not reflect a genuine trend toward down-regulation at the level of individual mice. However, it should be noted that this gene, like Cldn8, is expressed at very low levels in brain. Similar effects are observed for these genes in cerebellum and cortex.

Three trisomic genes that were previously reported not to conform to the 1.5× rule, namely Bace2 in the cortex (×2.15), Kcne2 (×3.39), and Sh3bgr (×0.55) in midbrain 19, fall into the 1.5-fold range when analyzed as either b-pool or e-pool (Figures 2b, 3b, and 4b). Interestingly, these genes are among those that exhibit high variability in expression levels among groups in at least one tissue (Figures 2a, 3a, and 4a). The most extreme case of inter-individual variation in expression was observed for Kcne2, for which the CV values where always above 0.5 in all groups and all tissues. Both b-pool and e-pool ratios for Kcne2 are in the 1.5-fold range in the midbrain, whereas the apparent higher order upregulation in the cortex (e-pool: ×2.71; b-pool: ×3.34), does not reflect the individual expression levels spanning the largest range (Figures 2, 3, and 4). We observed that genes for which Ts65Dn/euploid ratios are skewed in pooled RNAs are most often those with high expression variation differences between mice. We conclude from this that the pool value is at best indicative of high variation in gene expression level across mice, but that it does not necessarily reflect a genuine upregulation or downregulation.

Two of the mmu21 disomic genes exhibited altered expression in our analysis. As in our previous study 19, Cbs RNA levels were reduced in cerebellum (e-pool: ×0.54; b-pool: ×0.58), midbrain (e-pool: ×0.62; b-pool: ×0.58), and cortex (e-pool: ×0.66; b-pool: ×0.59). For Cbs, a consistent and significant trend toward downregulation (Figures 2, 3, and 4) can be observed in all three brain tissues in individual mice. Cbs is involved in the transsulfuration pathway and converts homocysteine to cystathionine. Cbs deficiency can cause homocysteinuria, which affects the central nervous system among many other organs. Our data strongly suggest that Cbs is downregulated in response to trisomy in Ts65Dn, although we cannot determine whether it is directly or indirectly regulated by other mmu21 genes.

Pool data indicated that Col18a1 was reduced in cerebellum (e-pool: ×0.64; b-pool: ×0.50) and in midbrain (e-pool: ×0.68; b-pool: ×0.77). However, individual gene expression levels for Col18A1 were broadly dispersed in these tissues, and the two groups (Ts65Dn and euploid) are not clearly distinguishable (P > 0.05).

Three main categories of trisomic genes can be distinguished from the normalized expression levels: genes whose expression levels in the eight Ts65Dn mice are clearly above those in their euploid littermates (for instance, App in cortex or Mrlp39 in midbrain), enabling a clear distinction between the two populations; genes whose expression levels partially overlap between the two populations of mice (for example, Runx1 or C21orf5 in cerebellum); and genes with intermingled expression between the two populations (for instance, Bace2 or Kcne2 in cerebellum), which do not distinguish Ts65Dn from euploid animals. As expected, all of the 11 disomic genes tested here were found to be in the latter category except Cbs (see above).

Based on the distribution of expression levels in the brain, the three categories of mmu21 genes at dosage imbalance are presented in Figure 5. The first category contains genes whose expression in an individual trisomic mouse was always significantly higher than in any euploid animal tested (P < 0.01). It should be noted that in this first category we observed that, for some genes, one individual out of the trisomic or control group exhibited a slight overlap in its transcript level with that of the second genetic group, although it was still associated with consistent and significantly elevated expression levels in one group of mice as compared with the other (P < 0.01; for example, Jam2 in cerebellum; Figure 2). Across the three brain tissues, 20 genes exhibit expression levels significantly higher in trisomic than in euploid mice. We speculate that genes in this first category may have a greater penetrance in the cerebellar phenotypes observed in mouse models of DS 272829 and may also be important candidates in structural and functional deficits in the DS brain. Notably, three genes (App, Cbr1, and Mrps6) belong to this highly differentiated category for all three brain regions. Furthermore, many genes in this category (for instance, Jam2, App, Cbr1, Cct8, Itsn, Mrps6, and C21orf5) are conserved at least in Caenorhabditis elegans and Drosophila melanogaster, and are tightly regulated with a CV below 20% in trisomic or euploid, or both, indicating that these genes are important for development of the organism. Two genes that are good candidates for neurodegenerative pathologies associated with DS are App, which is mutated in some forms of Alzheimer's disease 30 and of which the upregulation contributes substantially to degeneration of cholinergic neurons 31 and Itsn (Intersectin), which is involved in clathrin-mediated endocytosis 32. Jam2 is associated with cell adhesion processes and Cct8 with protein folding and degradation. C21orf5 is a new member of the Dopey family and exhibits restricted regional brain expression 33.

The second category is populated by trisomic genes for which expression levels are partially or totally intermingled between the two populations of mice (P values between 0.01 and 0.05). Overall, 22 genes are included in this category. However, of these only two genes are found in all three brain tissues (C21orf51 and Dscr2). In general, genes in this category exhibit moderate variation in expression based on the CV. We hypothesize that genes whose expression is more variable are more likely to contribute to those pathogenic outcomes in DS that exhibit variable expressivity.

The third class includes genes for which the expression levels are intermingled between the two populations of mice (P > 0.05). Overall, 15 genes are included in this last category, and among these five were found in the three tissues (Bace2, C21orf7, Dyrk1a, Kcne2, and Sh3bgr). They all have moderate to high expression variation based on the CV. Thus, those genes may be less likely to contribute to constant trisomy-related phenotypes. Genes whose expression levels vary widely among individuals are more likely to reach a critical threshold of over-expression in a subset of individuals, and thus they might be more likely to be involved in phenotypes that occur in some but not all individuals with trisomy 21. We also observed notable behaviour differences between tissues. Four genes (Ets2, Gabpa, Il10rb, and Tiam1) were found in the first category for cortex, but were allocated to the third category for cerebellum. Notably, in midbrain Ets2 was also found in the first category whereas Gabpa, Il10rb, and Tiam1 were found in the second category. Either these genes are tightly controlled in a tissue specific manner or more samples must be analysed to assign them to one or the other group with certainty.

Total RNA was extracted from frozen tissues of Ts65Dn males and their euploid male littermates using Trizol reagent (Invitrogen, San Diego, CA, USA), following the manufacturer's instructions. Animals were between 13 and 16 weeks old. RNA was treated with RNase-free Dnase I, quantified by UV spectrophotometry, and its integrity was verified by gel electrophoresis. To create the sample pools, equal amounts of RNAs from four euploid or four trisomic animals for each brain tissue were pooled. RNA was transcribed into cDNA using random hexamers and SuperscriptII reverse transcriptase (Invitrogen). In total, 8 μg total RNA for each sample was converted into cDNA in 8 × 1 μg reactions, pooled, and diluted to 12.5 ng/μl equivalent total RNA.

For quantitative gene expression studies, we used pre-designed, gene-specific TaqMan^® probe and primer sets provided by Applied Biosystems (Foster City, CA, USA) (references for each assay are given in Additional data file 1). All assays met the amplification efficiency criteria of 100% ± 10% (ApplicationNote 127AP05-02 36) and were comparable to each other. For normalization purposes, 18 non-mmu21 control genes were tested on sample cDNA. We identified the most stable genes across samples using the geNorm method 37. Thus, two genes (Hprt and Hmbs; Additional data file 1) were selected and data were normalized to their geometric mean. All assays were performed in triplicate. To minimize intra-assay variation, the sample cDNA was premixed with the PCR mastermix and distributed equally into each reaction. For a given target gene all tissue samples were run on the same reaction plate. This increases the accuracy of inter-individual comparison, because the mRNA of interest is amplified under the same PCR conditions in all tissue samples. To validate the reproducibility of our system, one experiment including two cDNA samples was duplicated. The correlation between the two independent experiments was in excess of 99% (data not shown).

All reactions were set up in 10 μl volumes and used the TaqMan Universal PCR Master Mix (Applied Biosystems, Foster City, CA, USA). Assays were processed with the ABI Prism 7900HT Sequence detection System (Applied Biosystems, Foster City, CA, USA) under the following conditions: 50°C for 2 min, 95°C for 10 min, and 40 cycles of 95°C for 15 s/60°C for 1 min. Amplification plot and predicted threshold cycle (Ct) values were obtained with the sequence Detection Software (SDS 2.1; PE Applied Biosystems). Further calculations and graphical representations were done using Excel 2000. We verified that no correlation could be found between threshold cycles (Ct) and expression ratios (Ts65Dn/euploid), indicating that there was no systematic biases within our real-time PCR results. Nonetheless, It should be noted that when the Ct value increases above about 32, the standard error also increases, indicating a loss of precision of the replicate measurements.

A common threshold value was chosen for all genes and the baseline was set manually for individual genes. The relative expression calculation method relies on the principle of the comparative Ct method (User Bulletin #2; Applied Biosystems). Ct values were first normalized (ΔCt) to a geometric mean of the two normalization genes and converted to a relative expression quantity (NE) using the formula NE = 2^-ΔCt. A given Ts65Dn/euploid ratio was calculated by dividing their respective NE values. For electronic pool (e-pool) calculation, the NE values for all individuals in a given group (Ts65Dn or euploid) were averaged. For the analysis presented here, we considered binned ratios of 0.8 to 1.2 to be neutral (no change in expression), whereas binned values from 1.2 to 2.0 were considered equivalent to 1.5-fold expression change.

In order to compute variation across a sample, we calculated the coefficient of variation:

CV = σ NE ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaqGdbGaaeOvaiabg2da9maalaaabaaccaGae83WdmhabaWaa0aaaeaacaqGobGaaeyraaaaaaaaaa@3954@

Here, NE¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaadaqdaaqaaiaab6eacaqGfbaaaaaa@34D7@ is the mean expression and σ is the standard deviation of eight samples in a group.

In order to estimate the technical variance (TechVar) and the biological variance (BioVar) for each gene across the different individuals and the different technical replicate measurements, we used an analysis of variance-like approach:

TechVar = ∑ i = 1 I ∑ j = 1 J ( NE ij − NE ¯ i . ) 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaqGubGaaeyzaiaabogacaqGObGaaeOvaiaabggacaqGYbGaeyypa0ZaaabCaeaadaaeWbqaaiaacIcacaqGobGaaeyramaaBaaaleaacaqGPbGaaeOAaaqabaGccqGHsisldaqdaaqaaiaab6eacaqGfbaaamaaBaaaleaacaqGPbaabeaakiaac6caaSqaaiaabQgacqGH9aqpcaaIXaaabaGaaeOsaaqdcqGHris5aOGaaiykamaaCaaaleqabaGaaGOmaaaaaeaacaqGPbGaeyypa0JaaGymaaqaaiaabMeaa0GaeyyeIuoaaaa@5041@

BioVar = J ∑ i = 1 I ( NEi ¯ . − NE ¯ ) 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaqGcbGaaeyAaiaab+gacaqGwbGaaeyyaiaabkhacqGH9aqpcaqGkbWaaabCaeaacaGGOaWaa0aaaeaacaqGobGaaeyraiaabMgaaaGaaeOlaiabgkHiTmaanaaabaGaaeOtaiaabweaaaGaaiykamaaCaaaleqabaGaaGOmaaaaaeaacaqGPbGaeyypa0JaaGymaaqaaiaabMeaa0GaeyyeIuoaaaa@4825@

Where I is 8 (the size of the samples group), J is 3 (the technical replicate number), NE_ij is the j-th replicate measurement in the i-th individual, NE¯i. MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaadaqdaaqaaiaab6eacaqGfbaaaiaabMgacaqGUaaaaa@3674@ = mean NE for the ij-th individual, and NE¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaadaqdaaqaaiaab6eacaqGfbaaaaaa@34D7@ is the overall mean NE for all samples and technical replicates.

The total variance (TotVar) is defined by the following equations:

TotVar = ∑ i = 1 I ∑ j = 1 J ( NE ij − NE ¯ i ) 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8tuQ8FMI8Gi=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciGacaGaaeqabaqadeqadaaakeaacaqGubGaae4BaiaabshacaqGwbGaaeyyaiaabkhacqGH9aqpdaaeWbqaamaaqahabaGaaiikaiaab6eacaqGfbWaaSbaaSqaaiaabMgacaqGQbaabeaakiabgkHiTmaanaaabaGaaeOtaiaabweaaaGaaeyAaiaacMcadaahaaWcbeqaaiaaikdaaaaabaGaaeOAaiabg2da9iaaigdaaeaacaqGkbaaniabggHiLdaaleaacaqGPbGaeyypa0JaaGymaaqaaiaabMeaa0GaeyyeIuoaaaa@4E7F@

TotVar = TechVar + BioVar

For judging variance differences in the trisomic and euploid samples, we applied an F-test for each gene. This test requires the two samples to have a Gaussian distribution with the same mean value. Therefore, we divided each individual observation from a sample by the mean value of that sample group prior to analysis. Small P values in the F-test indicate whether there is a significant difference in expression variation.

For each gene we performed statistical tests based on the replicate signals in experiments with trisomic and euploid samples. Three standard tests were used in parallel: Student's t-test, the Welch test, and Wilcoxon's rank-sum test. To evaluate differential expression of the genes, P values of Wilcoxon's rank-sum test were preferred as a reference because this test does not depend for its validity on a specific distribution (for example, Gaussian). Furthermore, this test is robust against outlier values in the sample. A recursive function was implemented to calculate the precise P values 38.