3.2. Assessing RNA Quantity
Before continuing the analysis of potential sources of batch effects, let us first introduce suitable metrics for the assessment of the amounts of RNA available for hybridization in a given sample. To this end, we computed so-called λ and β chip summary measures estimating the relative specific (λ) and non‑specific (β) transcript abundance levels in negative decadic logarithmic scale (see Methods Section) for all samples of the Gene Logic dilution experiment. In this experiment two distinct types of RNA samples, liver tissue and CNS cell line (SNB-19), have been hybridized to Affymetrix Human Genome U95A arrays at varying concentrations [35]. Multiple samples have been prepared from total RNA according to the manufacturers’ protocol and the resulting aRNA has been collected into one master solution for each of the two RNA types. The master solutions, whose RNA concentrations have been determined using an electropherometer (at 260 nm), were then diluted to generate solutions with nominal aRNA masses between 1.25 and 20 µg. Five technical replicates were processed for each concentration, leaving a total of 50 samples.
Panel a of Figure 2 displays the obtained λ parameters in dependence of RNA mass for the 50 microarray samples. λ increases with increasing RNA mass between 1 and 10 µg with Pearson correlation coefficients of r = 0.71 for liver tissue and r = 0.78 for SNB‑19. However, λ does not increase further for a RNA mass of 20 µg which can be explained by the up-down effect: increasing RNA concentrations result in a larger non-specific background accompanied by a smaller effective specific binding constant due to bulk dimerization [21]. The λ summary measure averages the ratio of specifically and non-specifically bound transcripts (see Equation (4)). It is not collinear with RNA mass, as the effect of bulk dimerization is not considered in the hybridization model. In summary, λ describes the amounts of aRNA of a particular microarray hybridization in a non-linear, yet for typical RNA ranges sensitive fashion.
The β parameter from Equation (5) characterizes the dynamic range of the specific hybridization signal (see [5] for a detailed discussion of this chip-specific parameter). As shown in Figure 2b the parameter β decreases with increasing RNA amount. The increasing concentration of RNA in the hybridization solution here results in an increased signal contribution due to non-specific binding and thus in a non-linear, negative effect on the measuring range β.
Figure 2  Chip-specific summary parameters λ and β in dependence of the amount of hybridized RNA. We computed both parameters for the samples of Gene Logic’s dilution data set where two types of RNA (liver and SNB-19) have been hybridized at varying concentrations with 5 replicate samples for each concentration. In Panel (a) λ increases roughly linear with increasing RNA mass between 1 and 10 µg (Pearson correlations of r > 0.7), but saturates at 20 µg; Panel (b) shows how β decreases with increasing RNA mass. An amount of 10 µg aRNA is recommended for the employed HG-U95A platform.

3