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Abstract BackgroundMany approaches have been developed to overcome technical noise in single cell RNA-sequencing (scRNAseq). As researchers dig deeper into data—looking for rare cell types, subtleties of cell states, and details of gene regulatory networks—there is a growing need for algorithms with controllable accuracy and fewer ad hoc parameters and thresholds. Impeding this goal is the fact that an appropriate null distribution for scRNAseq cannot simply be extracted from data in which ground truth about biological variation is unknown (i.e., usually). ResultsWe approach this problem analytically, assuming that scRNAseq data reflect only cell heterogeneity (what we seek to characterize), transcriptional noise (temporal fluctuations randomly distributed across cells), and sampling error (i.e., Poisson noise). We analyze scRNAseq data without normalization—a step that skews distributions, particularly for sparse data—and calculatepvalues associated with key statistics. We develop an improved method for selecting features for cell clustering and identifying gene–gene correlations, both positive and negative. Using simulated data, we show that this method, which we call BigSur (Basic Informatics and Gene Statistics from Unnormalized Reads), captures even weak yet significant correlation structures in scRNAseq data. Applying BigSur to data from a clonal human melanoma cell line, we identify thousands of correlations that, when clustered without supervision into gene communities, align with known cellular components and biological processes, and highlight potentially novel cell biological relationships. ConclusionsNew insights into functionally relevant gene regulatory networks can be obtained using a statistically grounded approach to the identification of gene–gene correlations.