Single-cell genomics has transformed our ability to examine cell fate choice. Examining cells along a computationally ordered ‘pseudotime’ offers the potential to unpick subtle changes in variability and covariation among key genes. We describe an approach, scHOT—single-cell higher-order testing—which provides a flexible and statistically robust framework for identifying changes in higher-order interactions among genes. scHOT can be applied for cells along a continuous trajectory or across space and accommodates various higher-order measurements including variability or correlation. We demonstrate the use of scHOT by studying coordinated changes in higher-order interactions during embryonic development of the mouse liver. Additionally, scHOT identifies subtle changes in gene–gene correlations across space using spatially resolved transcriptomics data from the mouse olfactory bulb. scHOT meaningfully adds to first-order differential expression testing and provides a framework for interrogating higher-order interactions using single-cell data.
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All data analysis was performed on publicly available data. The liver developmental dataset is described at https://sydneybiox.github.io/scMerge/articles/case_study/Mouse_Liver_Data.html and instructions to download the data are available in the analysis scripts at https://github.com/MarioniLab/scHOT2019.
The MOB data was downloaded from the Spatial Research website https://www.spatialresearch.org/resources-published-datasets/doi-10-1126science-aaf2403/ and count matrix data and H&E stained brightfield image related to MOB replicate 11 was downloaded. Source data are provided with this paper.
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We thank all our colleagues, particularly at Cancer Research UK Cambridge Institute and The University of Sydney School of Mathematics and Statistics for their support and intellectual engagement. In particular, we acknowledge P. Yang and M. Morgan for their helpful discussion. We acknowledge the following sources of funding: Royal Society Newton International Fellowship (NIF\R1\181950) and funding from the Judith and Coffey Life Laboratory at the Charles Perkins Centre to S.G.; Australia NHMRC Career Developmental Fellowship (APP1111338) to J.Y.H.Y.; Research Training Program Tuition Fee Offset and Stipend Scholarship and Chen Family Research Scholarship to Y.L.; Australian Research Council Discovery Early Career Researcher Award (DE200100944) funded by the Australian Government to E.P.; NIH grant (R21DC015107) to D.M.L.; SJTU-USYD Translate Medicine Fund-Systems Biomedicine (AF6260003) to J.Y.H.Y., X.S. and Z.G.H.; National Natural Science Foundation of China (81802806) to X.S.; and Core funding from EMBL and Cancer Research UK (award no. 17197) to J.C.M. The funding source had no role in the study design; in the collection, analysis and interpretation of data, in the writing of the manuscript and in the decision to submit the manuscript for publication.
The authors declare no competing interests.
Peer review information Lin Tang was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.
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a, Scatter and ribbon plot of all significant genes showing loss of variability along hepatoblast branch (176 cells), ribbon width corresponding to adding and subtracting the weighted standard deviation from the weighted mean. b, Scatter and ribbon plot of all significant genes showing gain of variability along hepatoblast branch, with ribbon width as in Panel A. Source data
a, Line plots of clustered significant scHOT gene-pairs with FDR adjusted P-value < 0.2 for full cholangiocyte branch (308 cells). Vertical dashed line indicates trajectory branchpoint. b, Gene ontology functional enrichment using one-sided Fisher’s Exact Test barplots for all scHOT cholangiocyte clusters, grey bar color corresponds to FDR adjusted P-value < 0.05. Gene sample sizes indicated in each plot title. c, Gene ontology functional enrichment using one-sided Fisher’s Exact Test barplots for all scHOT hepatocyte clusters, with color as in panel B. Gene sample sizes indicated in each plot title. Source data
a, Spatial expression plots (262 spatially resolved positions) of two gene-pairs Arrb1 and Uchl1 as well as Arrb1 and Dnm3 which are not significantly differentially expressed across space using scHOT, but are significantly differentially correlated across space using scHOT with FDR adjusted P-value < 0.2. The third plot shows the local spatial correlation estimated for these two genes, recapitulating the layered pattern of the olfactory bulb. b, Spatial maps of mean local correlation and Gene Ontology functional enrichment using one-sided Fisher’s Exact Test barplots for all MOB scHOT clusters, gray bar color corresponds to FDR adjusted P-value < 0.05. Gene sample sizes indicated in each plot title. Source data
a, HVG selection for Developmental Liver Data. b, HVG selection for Spatial Transcriptomics analysis. c, Global correlation and null scHOT correlation test statistics for sampled gene pairs in both hepatocyte and cholangiocyte branches (268 and 265 gene pairs respectively). d, Global correlation and null scHOT correlation test statistics for sampled gene pairs (172 gene pairs) for spatial MOB data. e, Scatterplot of -log10(P-values) for differential correlation testing (22,155 gene pairs) of the liver hepatocyte branch, calculated using 10,000 permutations for each gene-pair (x-axis), and estimated using borrowed permutations over a subset of gene-pairs (y-axis). Black solid line corresponds to y = x, grey dashed lines correspond to unadjusted P-values of 0.05, and the solid red curve corresponds to the fitted loess curve. Source data
a, Illustrative example showing testing for correlation differences in three distinct groups. A set of local higher order statistics are calculated, and significance is compared by repeatedly permuting samples (grey boxplots). Illustrative example shows the set of local estimates of higher order statistics are combined using the sample standard deviation to assess how variable they are between groups. b, Possible schemes for the testing scaffold using gene networks, including: i) a gene-gene network; ii) a gene set scaffold where all pairwise combinations within a gene set are included; and iii) selected genes of interest versus all others. c, Examples of weighted higher order functions including weighted Pearson correlation, weighted Spearman correlation, weighted variance. Note that any user defined function can be used.
a, Spearman correlation map of -log10(P-values) of scHOT differential correlation testing (22,155 gene pairs) in hepatocyte branch with different choices of triangular span, from 0.05 to 0.70 in steps of 0.05. b, UpSet plot of 509 significant gene-pairs (FDR adjusted P-value < 0.2) from each scHOT testing scheme as in panel a. c, Spearman correlation map of -log10(P-values) of scHOT differential correlation testing ( 903 gene pairs) in MOB with different choice of spatial span. d, UpSet plot of 181 significant gene-pairs from each testing scheme as in panel c. e, Density plot of slopes of local correlation patterns of gene-pairs selected with low span (0.35 and below, colored blue) and high span (0.35 and above, colored red), dotted line shows the density over all slopes. f, Spearman correlation map of -log10(P-values) of scHOT differential correlation testing (22,155 gene pairs) in hepatocyte branch with different choices of higher order statistic, MIC—maximal information criterion, BDC—Brownian distance correlation, Pearson_block and Spearman_block refer to Pearson and Spearman correlation respectively, applied in a block-weighted context. g, UpSet plot of 367 significant gene pairs from each testing scheme as in panel f. Source data
a, Scatterplots of -log10(P-values) for hepatoblast to hepatocyte correlation scHOT testing (22,155 gene pairs) against the inclusion frequency of gene-pairs with FDR adjusted P-values < 0.2 for repeated subsampling without replacement of 90%, 80%, 70%, 60%, and 50% of the cells from the trajectory. Red points correspond to those selected as FDR adjusted P-value < 0.2 criteria for the full dataset. b, Spearman correlation map of -log10(P-values) of each subsampling strategy. c, Quantile-quantile line plots of -log10(P-values) for the full data (x-axis) and -log10(P-values) for each subsampling scenario (y-axis), split by subsampling percentage. Red lines correspond to y = x. Source data
Supplementary Table 1 , Significantly differentially variable genes using scHOT for the hepatoblast to branchpoint trajectory analysis (176 cells), with columns for the gene, the observed scHOT test statistic, unadjusted P value, FDR adjusted P value, gain or loss of variability and local variability and the start and end of the trajectory. b, Significantly differentially correlated gene pairs using scHOT for the hepatoblast to hepatocyte trajectory analysis (408 cells), with columns for the gene pair, the observed scHOT test statistic, the global Spearman correlation value, unadjusted P value, number of permutations used for P value estimation, minimum and maximum values of global correlation for which P value estimation was used, FDR adjusted P value, cluster number and local correlation at the start, branchpoint and end of the trajectory.
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Ghazanfar, S., Lin, Y., Su, X. et al. Investigating higher-order interactions in single-cell data with scHOT. Nat Methods 17, 799–806 (2020). https://doi.org/10.1038/s41592-020-0885-x