Analyzing noisy, high-dimensional gene expression data

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Most of our knowledge about gene regulatory networks has been obtained largely from perturbation experiments that vary e.g. environmental conditions or genotype. We developed an alternative approach that harnesses the power of high-throughput gene expression measurements (RNAseq) to extract functional relationships from the standing expression variation 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 devised a novel, versatile clustering approach based on network theory and the statistical physics of percolation on random geometric graphs. 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.

Fig. 1. Principle of percolation-based discovery of functional gene modules. Data from high-through gene expression measurements consist of an expression-count matrix (left, top) of N genes (typically ~10⁴) across D samples (typically ~10¹-10⁴). Each of the N genes can thus be considered a point in a D-dimensional space, however strong noise in the measurements often preclude the identification of correlated gene sets by typical dimensionality reduction methods such as t-SNE (bottom left). Our gene clustering method exploits a percolation phase transition generically arising in such noisy, high-dimensional data, as a function of the correlation-distance threshold δ that defines the single-linkage cluster hierarchy (center). The generic behavior of cluster growth as a function of the threshold distance δ as it approaches the critical point δ^* allows us to identify statistically significant clusters (right).

References

Werner, S., Rozemuller, W.M., Ebbing, A., Alemany, A., Traets, J.J.H, van Zon, J.S., van Oudenaarden, A., Korswagen, H.C., Stephens, G.J. & Shimizu, T.S. (2020). Functional modules from variable genes: Leveraging percolation to analyze noisy, high-dimensional data. bioRxiv. https://doi.org/10.1101/2020.06.10.143743

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Analyzing noisy, high-dimensional gene expression data

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