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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 calculate p values 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.

The origins of complex, heritable traits -- such as familial risk for cancer, diabetes, and neuropsychiatric illness -- are poorly understood. For the past decade, genome-wide association studies (GWAS) have been used to search for sites of genetic variation associated with such traits, but the alleles thus discovered account, according to the statistical methods used, for only a small fraction of the probability of displaying the trait. One hypotheses put forth to explain this apparent failure concerns the nature of genetic interaction: If genes often interact synergistically, so that small-effect variants have a much greater than additive effect when combined, such genes will be difficult to discover by GWAS. This hypothesis is often rejected based on empirical evidence that natural genetic variants mostly tend to interact additively. Here I provide evidence that, for deleterious traits, the force of natural selection can alter this situation dramatically, producing inadvertent selection for synergistic interactions among small-effect alleles. To first demonstrate this, I created a variety of dynamical models of real and fictitious biological processes that are required to perform a series of tasks and, to mimic one likely effect of natural selection, optimized their parameters so that their outputs would be more robust to the values of their parameters (considered one at a time). In models of suitable complexity, I observed that optimization drove most parameter combinations (pairs, triples, etc.) toward additive interaction, but invariably drove a subset toward very high synergy (epistasis). Next, I used a simple model of non-additive gene-gene interaction to simulate populations evolving in the presence of “phenotypic noise” (i.e., intrinsic and environmental variability in the relationship between phenotype and genotype) to show the occurrence of common diseases (i.e., unfit phenotypes with frequencies on the order of 1%) can, under the right circumsta

The origins of complex, heritable traits -- such as familial risk for cancer, diabetes, and neuropsychiatric illness -- are poorly understood. For the past decade, genome-wide association studies (GWAS) have been used to search for sites of genetic variation associated with such traits, but the alleles thus discovered account, according to the statistical methods used, for only a small fraction of the probability of displaying the trait. One hypotheses put forth to explain this apparent failure concerns the nature of genetic interaction: If genes often interact synergistically, so that small-effect variants have a much greater than additive effect when combined, such genes will be difficult to discover by GWAS. This hypothesis is often rejected based on empirical evidence that natural genetic variants mostly tend to interact additively. Here I provide evidence that, for deleterious traits, the force of natural selection can alter this situation dramatically, producing inadvertent selection for synergistic interactions among small-effect alleles. To first demonstrate this, I created a variety of dynamical models of real and fictitious biological processes that are required to perform a series of tasks and, to mimic one likely effect of natural selection, optimized their parameters so that their outputs would be more robust to the values of their parameters (considered one at a time). In models of suitable complexity, I observed that optimization drove most parameter combinations (pairs, triples, etc.) toward additive interaction, but invariably drove a subset toward very high synergy (epistasis). Next, I used a simple model of non-additive gene-gene interaction to simulate populations evolving in the presence of “phenotypic noise” (i.e., intrinsic and environmental variability in the relationship between phenotype and genotype) to show the occurrence of common diseases (i.e., unfit phenotypes with frequencies on the order of 1%) can, under the right circumsta

A major goal of human genetics is to elucidate the genetic architecture of human disease, with the goal of fueling improvements in diagnosis and the understanding of disease pathogenesis. The degree to which epistasis, or non-additive effects of risk alleles at different loci, accounts for common disease traits is hotly debated, in part because the conditions under which epistasis evolves are not well understood. Using both theory and evolutionary simulation, we show that the occurrence of common diseases (i.e. unfit phenotypes with frequencies on the order of 1%) can, under the right circumstances, be expected to be driven primarily by synergistic epistatic interactions. Conditions that are necessary, collectively, for this outcome include a strongly non-linear phenotypic landscape, strong (but not too strong) selection against the disease phenotype, and "noise" in the genotype-phenotype map that is both environmental (extrinsic, time-correlated) and developmental (intrinsic, uncorrelated) and, in both cases, neither too little nor too great. These results suggest ways in which geneticists might identify, a priori, those disease traits for which an "epistatic explanation" should be sought, and in the process better focus ongoing searches for risk alleles.

A major goal of human genetics is to elucidate the genetic architecture of human disease, with the goal of fueling improvements in diagnosis and the understanding of disease pathogenesis. The degree to which epistasis, or non-additive effects of risk alleles at different loci, accounts for common disease traits is hotly debated, in part because the conditions under which epistasis evolves are not well understood. Using both theory and evolutionary simulation, we show that the occurrence of common diseases (i.e. unfit phenotypes with frequencies on the order of 1%) can, under the right circumstances, be expected to be driven primarily by synergistic epistatic interactions. Conditions that are necessary, collectively, for this outcome include a strongly non-linear phenotypic landscape, strong (but not too strong) selection against the disease phenotype, and "noise" in the genotype-phenotype map that is both environmental (extrinsic, time-correlated) and developmental (intrinsic, uncorrelated) and, in both cases, neither too little nor too great. These results suggest ways in which geneticists might identify, a priori, those disease traits for which an "epistatic explanation" should be sought, and in the process better focus ongoing searches for risk alleles.