Abstract
BackgroundNormalization is the process of removing non-biological sources of variation between array experiments. Recent investigations of data in gene expression databases for varying organisms and tissues have shown that the majority of expressed genes exhibit a power-law distribution with an exponent close to -1 (i.e. obey Zipf's law). Based on the observation that our single channel and two channel microarray data sets also followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. A computationally simple and intuitively appealing technique based on this observation is presented.ResultsUsing pairwise comparisons using MA plots (log ratio vs. log intensity), we compared this novel method to previously published normalization techniques, namely global normalization to the mean, the quantile method, and a variation on the loess normalization method designed specifically for boutique microarrays. Results indicated that, for single channel microarrays, the quantile method was superior with regard to eliminating intensity-dependent effects (banana curves), but Zipf's law normalization does minimize this effect by rotating the data distribution such that the maximal number of data points lie on the zero of the log ratio axis. For two channel boutique microarrays, the Zipf's law normalizations performed as well as, or better than existing techniques.ConclusionZipf's law normalization is a useful tool where the Quantile method cannot be applied, as is the case with microarrays containing functionally specific gene sets (boutique arrays).
Highlights
Normalization is the process of removing non-biological sources of variation between array experiments
Normalization results – single channel microarrays A comparison of the Zipf's normalization using controls (Zipfs)'s law normalization method to the simple method of setting all arrays to a global mean and to the quantile method was conducted on the single channel microarray data sets
Normalization to a global mean (Figure 1c) yielded data sets that displayed a higher variability in the coefficient c of the Zipf's power function than that observed after normalization by the Zipf's law method (Figure 1e) or the quantile method (Figure 1d)
Summary
Normalization is the process of removing non-biological sources of variation between array experiments. Based on the observation that our single channel and two channel microarray data sets followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. The purpose of all normalization techniques is to transform the data to eliminate sources of variability stemming from experimental conditions, leaving only biologically relevant differences in gene expression for subsequent analysis. Intra-array normalization deals with variability within a single array caused by factors such as differences in print-tip (page number not for citation purposes). This paper assumes intra-array normalization has been performed and presents an inter-array normalization method for comparison of gene intensity levels between multiple microarrays to deal with variation caused by such factors as differences in RNA isolation efficiency, labeling efficiency, hybridization conditions, exposure times, and detection efficiencies
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