Six samples can be hybridized to the Illumina HumanWG-6 V3 chip, each sample on two array-sections of approximately 1, 000, 000 beads that are distributed amongst approximately 50, 000 bead-types. We treat the two sections as separate arrays for the purposes of analysis, due to previously observed inter-section differences [14, 15]. This also has the effect of making our results comparable to those one might expect from the Illumina HT-12 array which takes 12 samples, allocated one section each.
We have used two reference RNA samples, previously employed in the MAQC study , which have subsequently become a standard for microarray  and next-generation sequencing  studies. These are the Stratagene Universal Human Reference RNA (hereafter "UHRR"), and the Ambion Human Brain Reference RNA (hereafter "Brain"). Nine levels of mixture, including the four employed in the first MAQC study, were then created. These are 100:0, 99:1, 95:5, 90:10, 75:25, 50:50, 25:75, 10:90 and 0:100, where mixtures are presented as UHRR:Brain.
These nine levels allow for investigation of broad trends, and for the detection of subtle differences. Combined with the four levels of starting material that we are investigating, this leads to 36 samples to be arranged across six Illumina HumanWG6 V3 BeadChips. Clearly it would not be desirable to confound levels of starting material with BeadChips as we would be unable to distinguish our comparison of interest from technical variation. However it is desirable that our data resemble data from a 'real-world' experiment else they have no external validity and, in general, experiments are conducted on BeadChips using only one level of starting material.
Our design was chosen to address this tension between internal and external validity. Each BeadChip was run with samples from two starting quantities of RNA (three samples from both chosen starting quantities), and each possible combination of the two starting quantities was run once and only once amongst the six BeadChips. Full details of the design are given in Section 1 of Additional File 1.
Stock UHRR tubes were prepared following manufacturer's recommendation and pooled to create a stock of 1 mg/ml; Brain RNA was received at 1 mg/ml. The quality was checked using the Agilent Bioanalyser. The RNA was accurately diluted to a working stock of 100 ng/μ l and the dilution series was created to the specifications given above. The minimum pipetting volume used was 10 μ l.
The Illumina TotalPrep-96 Kit (4397949) was used to process the samples using the range of input concentrations in question. For the 50 ng and 10 ng input quantities a 1:10 dilution of working RNA was used. Quality and quantity of the cRNA was checked before proceeding with hybridisation to Human WG-6 V3 BeadArray. The Illumina WGGX DirectHyb Assay Guide (11286331 RevA) protocol was followed for hybridisation, washing and scanning of the BeadArray, with the scanner set to return bead-level data (Additional File 1, Section 2). Quality assessment was achieved via examination of metrics files (Additional File 1, Section 3), agreement with previous MAQC data sets (Additional File 1, Section 4), and performance of housekeeping controls (Additional File 1, Section 5).
Preprocessing and statistical analysis
Illumina BeadScan files were processed and analysed using the beadarray package  from Bioconductor. Arrays were pre-processed on the log2-scale on a per-array-section basis. BASH  was used to remove high-frequency spatial artefacts, followed by outlier removal (outliers being defined as observations more than three median absolute deviations from the median), and expression detection score calculation. The detection score is a standard measure for Illumina expression experiments, and can be viewed as an empirical estimate of the p-value for the null hypothesis that there is no expression. Between-array-section quantile-normalization was performed within each starting material level, and a non-linear regression model fitted across dilution levels within each starting RNA level.
Our approach demands reporting of raw, bead-level, Illumina data, which exceeds the MIAME requirements. As popular repositories are not designed for the storage of raw (bead-level) data from random arrays, the files are available to download from our website at http://www.compbio.group.cam.ac.uk/Resources/Dilution/Dilution.html.
A previously proposed [20
] non-linear model was used as the theoretical model for the dilution curve:
is the observed (normalized) log-intensity for probe p at starting RNA quantity r in mixture level m, c
is the proportion of the mixture that is UHRR, U
is the intensity associated with probe p at starting RNA level r in the UHRR sample, and B
is similarly defined for the Brain sample. The ϵ
are independent measurement errors with mean zero and standard deviation σ
This model implicitly assumes a linear relationship between quantity of RNA and measured intensity. This assumption is known not to hold over the full range of observed intensities for microarrays , and specifically for Illumina BeadArrays . While some models allow for non-linearity , they do not relate it to the known physico-chemical causes. To do so would be difficult and, in any case, would not obviously be advantageous in our situation.
The model can be rewritten in terms of Δ
and we fit this model in R using the nls() function, weighting each observation by the number of beads that contributed to the observation. Under this formulation, it is clear that the test of Δ = 0 from the summary.nls() function in R provides an approximate and quick test of a difference in log-intensities.
Restricting the analysis-group of bead-types
We have re-annotated the bead-types on the array , and have identified 23, 562 "perfect" bead-types (using the August 2009 annotation). These are bead-types that have a full 50 mer match to a reliable transcript, and do not possess additional undesirable properties (e.g. mapping to transcripts masked by repeat regions, having a non-unique transcriptomic match, mapping to transcripts that do not align well to the reference genome, etc.). Additionally, we define an 'analysis-group' of bead-types as a subset of these perfect bead-types that possess two further properties: 1) That their GC content is conducive to hybridization (i.e. in the range of 20-35 bases), which excludes a further 506 bead-types, and 2) That they occur at least six times on each array-section (see Additional File 1, Section 6). All analyses will be restricted to this 'analysis-group' unless otherwise stated.