Detecting boolean asymmetric relationships with a loop counting technique and its implications for analyzing heterogeneity within gene expression datasets

Abstract

AbstractMany traditional methods for analyzing gene-gene relationships focus on positive and negative correlations, both of which are a kind of ‘symmetric’ relationship. However, genes can also exhibit ‘asymmetric’ relationships, such as ‘if-then’ relationships used in boolean circuits. In this paper we develop a very general method that can be used to detect biclusters within gene-expression data that involve subsets of genes which are enriched for these ‘boolean-asymmetric’ relationships (BARs). These BAR-biclusters can correspond to heterogeneity that is driven by asymmetric gene-gene interactions, rather than more standard symmetric interactions. We apply our method to a single-cell RNA-sequencing data-set, demonstrating that the statistically-significant BAR-biclusters indeed contain additional information not present within more traditional ‘boolean-symmetric’-biclusters. For example, the BAR-biclusters involve different subsets of cells, and highlight different gene-pathways within the data-set. Moreover, by combining the boolean-asymmetric- and boolean-symmetric-signals, one can build linear classifiers which outperform those built using only traditional boolean-symmetric signals.Author summaryOne important step when analyzing large data-sets is to search for ‘heterogeneity’, i.e., subsets of the data that exhibit special characteristics. In the context of gene-expression data, this heterogeneity can take the form of a ‘bicluster’: a subset of samples across which certain genes interact in a special way. Traditionally, strategies for detecting biclusters have focused on gene-gene relationships such as correlations and anti-correlations; that is to say, gene-subsets that act in concert. In this paper we discuss a simple strategy for detecting biclusters that exhibit more general gene-gene relationships, such as one gene serving as a prerequisite for the expression of another, or a pair of genes which mutually exclude one another. Using a data-set from a study of Alzheimer’s disease, we demonstrate that these more general biclusters can be quite statistically significant, and can contain novel information not readily found in more traditional biclusters.