Functional modules from variable genes: Leveraging percolation to analyze noisy, high-dimensional data

While measurement advances now allow extensive surveys of gene activity (large numbers of genes across many samples), interpretation of these data is often confounded by noise — expression counts can differ strongly across samples due to variation of both biological and experimental origin. Complimentary to perturbation approaches, we extract functionally related groups of genes by analyzing the standing variation within a sampled population. To distinguish biologically meaningful patterns from uninterpretable noise, we focus on correlated variation and develop a novel density-based clustering approach that takes advantage of a percolation transition generically arising in random, uncorrelated data. We apply our approach to two contrasting RNA sequencing data sets that sample individual variation — across single cells of fission yeast and whole animals of C. elegans worms — and demonstrate robust applicability and versatility in revealing correlated gene clusters of diverse biological origin, including cell cycle phase, development/reproduction, tissue-specific functions, and feeding history. Our technique exploits generic features of noisy high-dimensional data and is applicable, beyond gene expression, to feature-rich data that sample population-level variability in the presence of noise. Significance Statement Gene expression largely determines the fate of each cell and ultimately the development and behavior of the whole organism. Whereas most of our knowledge on gene regulatory networks has been obtained from perturbation experiments (e.g. manipulating environmental conditions, genotype, or other physiological variables), here we develop an alternative approach based on the analysis of naturally occurring variations across individuals within a population. Using both single-cell and whole-animal RNA sequencing data, we demonstrate how a rich set of co-regulated gene modules can be uncovered from transcriptomic variability of individuals within unperturbed populations. To robustly extract interpretable clusters from the strong noise background, we devise a novel, versatile clustering approach based on network theory. With a foundation in the generic behavior of random networks near their percolation critical point, our method is broadly applicable, beyond gene expression, to any noisy, high-dimensional data that sample variation across individuals within a population.