3.3. Amounts of Hybridized RNA
Ideally sufficiently large amounts of aRNA transcripts at constant levels should be used for hybridization to the surface-attached microarray probes to obtain good quality data. In practice this ideal is hard to archive, e.g., due to the considerable variation in the amount of available source RNA. Too high amounts of aRNA can reduce the dynamic range of the fluorescence signals whereas too low amounts increase the signal-to-noise ratio. Consequently, varying RNA amounts can affect gene expression estimates and reduce data quality.
The density distribution of the λ parameter is separately shown for the qc-included/qc-excluded sample sets (Figure 3a). For most good quality samples λ ranges between 1.0 and 1.5 with the peak at λ = 1.2. Interestingly, the peak of the distribution is significantly shifted to the left to λ = 1.05 for samples excluded by quality control, showing that low quality samples tend to have decreased relative specific transcript levels (see below).
Virtually none (<0.1%) of the samples that passed stringent quality control exhibit values smaller than λ = 0.95, which we consequently consider a conservative threshold for samples of critically low quality due to decreased specific RNA amounts. We find that 133 (1.6%) of all samples exhibit λ values below this threshold. This equals a fraction of 4.6% from the qc-excluded samples.
The parameter λ describes the average logged specific transcript level in units of the non-specific one. Low expression levels of some genes can have other origins than low RNA amounts, for example local surface deficiencies appearing as weakly shining blurs. Low RNA amounts can also be a result of degradation due to the overlap between the effects of RNA quality and RNA quantity.
The density distribution of the β parameters describing the measurement range of the microarray hybridization is shown in Figure 3b. Low RNA amounts are associated with a larger β values whereas high RNA amounts increase the non-specific background with negative consequences for the measuring range, and thus the signal calibration [5]. For qc-included samples the summary values are distributed closely around the peak at β = 2.25 ± 0.3 whereas for qc-excluded samples the β values spread much broader with a second peak for smaller measuring ranges. Selecting a threshold of β < 1.8, we find that 344 samples (4.2%) have a critically low measurement range.
Figure 3  Distribution of the λ and β parameters characterizing the amount of hybridized RNA for qc included/qc-excluded samples (panels (a) and (b)). The inset shows the hook curves for two selected samples and the corresponding λ and β values (red and blue dots in the same color as the curves). Panel (c) shows the principal components two and four of the HumanExpressionAtlas expression space where points are colored according to the value of λ.   We also assessed the impact of λ and β by relating them with the first five principal components of the expression space of the HumanExpressionAtlas data set. We obtained a correlation of r = −0.61 of λ with the fourth principal component (see Figure 3c). Furthermore, a correlation of r = −0.33 with the second principal component, which we previously showed to relate with RNA quality, was found. The other three components show only low correlations of −0.16 < r < 0.21. With coefficients of −0.04 < r < 0.01, the β parameter exhibits no correlation with the first five principal components. In summary, the relative specific signal shows significant systematic effects on the expression measures whereas the amount of non-specific hybridization does essentially not.