Making sense of microarray data distributions

Motivation: Typical analysis of microarray data has focused on spot by spot comparisons within a single organism. Less analysis has been done on the comparison of the entire distribution of spot intensities between experiments and between organisms. Results: Here we show that mRNA transcription data from a wide range of organisms and measured with a range of experimental platforms show close agreement with Benford's law (Benford, Proc. Am. Phil. Soc., 78, 551-572, 1938) and Zipf's law (Zipf, The Psycho-biology of Language: an Introduction to Dynamic Philology, 1936 and Human Behaviour and the Principle of Least Effort, 1949). The distribution of the bulk of microarray spot intensities is well approximated by a log-normal with the tail of the distribution being closer to power law. The variance, σ2, of log spot intensity shows a positive correlation with genome size (in terms of number of genes) and is therefore relatively fixed within some range for a given organism. The measured value of σ2 can be significantly smaller than the expected value if the mRNA is extracted from a sample of mixed cell types. Our research demonstrates that useful biological findings may result from analyzing microarray data at the level of entire intensity distributions.