InterOpt: Improved gene expression quantification in qPCR experiments using weighted aggregation of reference genes

Abstract

Quantification of gene expression is a crucial task in biomedical studies. Although high-throughput methods enable rapid and simultaneous expression quantification of coding or non-coding regions, qPCR is still vastly used due to its high availability, sensitivity, specificity, reproducibility, low cost, and ease of use. A limitation of qPCR has been the need of internal controls or reference genes (RGs) with stable expression in different conditions, to normalize the expression level of the other target genes. So far, several stability criteria and numerous methods for selecting a group of RGs have been proposed, however, important challenges must be addressed. Here we introduce a mathematical basis for precise modeling of qPCR expression normalization and justify widely used stability measures of RGs. We then propose a family of scale-invariant functions, as an alternative to the geometric mean, to optimize aggregated expression of RGs. We provide closed-form optimizations for several scale-invariant aggregation functions. Among them, we show the superiority of weighted geometric mean, whose parameters optimize standard deviation as the stability measure of aggregated RGs expression. We provide experimental support for this finding using real data of solid tumors and liquid biopsies of different sample sizes. The proposed methods can be easily integrated in the existing qPCR expression normalization pipelines of genes and non-coding RNAs. We also provide an implementation of the proposed methods as an R package, with GPU acceleration. Availability and implementationhttps://github.com/asalimih/InterOpt Contactasalimih@gmail.com