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PreprintCited by 117Single-cell and spatial transcriptomicsGene expression and cancer classificationGene Regulatory Network Analysis

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Discrete Distributional Differential Expression (D 3 E) - A Tool for Gene Expression Analysis of Single-cell RNA-seq Data

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Delmans, Mihails, Hemberg, Martin·2015·BMC Bioinformatics
DOI 10.1101/020735PMC PMC4772470

Preprint — published as 10.1186/s12859-016-0944-6 · Paper page

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Abstract

The advent of high throughput RNA-seq at the single-cell level has opened up new opportunities to elucidate the heterogeneity of gene expression. One of the most widespread applications of RNA-seq is to identify genes which are differentially expressed between two experimental conditions. Here, we present a discrete, distributional method for differential gene expression (D 3 E), a novel algorithm specifically designed for single-cell RNA-seq data. We use synthetic data to evaluate D 3 E, demonstrating that it can detect changes in expression, even when the mean level remains unchanged. Since D 3 E is based on an analytically tractable stochastic model, it provides additional biological insights by quantifying biologically meaningful properties, such as the average burst size and frequency. We use D 3 E to investigate experimental data, and with the help of the underlying model, we directly test hypotheses about the driving mechanism behind changes in gene expression.

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Fig. 1 Overview of D3E. a Graphical representation of the transcriptional bursting model. b Example of a realization of the transcriptional bursting model with parameters α=1,β=10, γ=100, and λ=1 [12]. In this regime, the gene exhibits a bursty behavior with a bimodal stationary distribution. c Derivation of the biologically-relevant parameters from the parameters of the transcriptional bursting model. d Flowchart of the D3E algorithm
Fig. 1 Overview of D3E. a Graphical representation of the transcriptional bursting model. b Example of a realization of the transcriptional bursting model with parameters α=1,β=10, γ=100, and λ=1 [12]. In this regime, the gene exhibits a bursty behavior with a bimodal stationary distribution. c Derivation of the biologically-relevant parameters from the parameters of the transcriptional bursting model. d Flowchart of the D3E algorithmCC BY · PubMed Central
Fig. 2 DE analysis for synthetic data. a Sensitivity to changes in parameters of the Poisson-Beta distribution for the Cramér-von Mises, KS and likelihood ratio tests. A lighter color denotes a low sensitivity to changes of a particular parameter. b Average sensititivity scores for the panels in a as well as the run-times. c An example of a matrix which was used to assign the colors in a. Here, parameters α=.22 and β=.28, while γ is varied from 1 to 100 on a log-scale. Each element in the matrix reflects a p-value of a KS test between two Poisson-Beta distributions with the corresponding parameters. We expect to find high values along the diagonal, where the changes are smaller. d DE analysis for the scenario where the mean is fixed but the variance is changed. D3E is able to reliably identify differentially expressed genes based on the change in the shape of distribution alone. Here, the color represents the p-value for the Cramér-von Mises test with dark colors indicating a low value
Fig. 2 DE analysis for synthetic data. a Sensitivity to changes in parameters of the Poisson-Beta distribution for the Cramér-von Mises, KS and likelihood ratio tests. A lighter color denotes a low sensitivity to changes of a particular parameter. b Average sensititivity scores for the panels in a as well as the run-times. c An example of a matrix which was used to assign the colors in a. Here, parameters α=.22 and β=.28, while γ is varied from 1 to 100 on a log-scale. Each element in the matrix reflects a p-value of a KS test between two Poisson-Beta distributions with the corresponding parameters. We expect to find high values along the diagonal, where the changes are smaller. d DE analysis for the scenario where the mean is fixed but the variance is changed. D3E is able to reliably identify differentially expressed genes based on the change in the shape of distribution alone. Here, the color represents the p-value for the Cramér-von Mises test with dark colors indicating a low valueCC BY · PubMed Central
Fig. 3 Comparison of DE methods for synthetic data. Each panel shows the receiver operator characteristics (ROC) calculated for synthetic data using five different DE algorithms. The numbers below each panel indicate the area under the curve. The rows correspond to different thresholds for when a gene is considered significantly changed. DESeq2 reports NA for many genes. Since the NA cannot be interpreted as either DE or not DE, we treat these calls as false, which explains the unusual shape of the ROC curve and the fact that the AUC value is below.5
Fig. 3 Comparison of DE methods for synthetic data. Each panel shows the receiver operator characteristics (ROC) calculated for synthetic data using five different DE algorithms. The numbers below each panel indicate the area under the curve. The rows correspond to different thresholds for when a gene is considered significantly changed. DESeq2 reports NA for many genes. Since the NA cannot be interpreted as either DE or not DE, we treat these calls as false, which explains the unusual shape of the ROC curve and the fact that the AUC value is below.5CC BY · PubMed Central
Fig. 4 Sensitivity to transcript dropout errors. a Errors for the estimates of the parameters for the synthetic data in Fig. 2 a using the Bayesian inference method. Each bar represents the geometric mean squared relative error for the parameter estimates b Errors for the estimates of the correlations between the estimated changes in parameters for the synthetic data in Fig. 2 a. Each bar represents the estimated Pearson correlation coefficient between the log-changes of the quantities
Fig. 4 Sensitivity to transcript dropout errors. a Errors for the estimates of the parameters for the synthetic data in Fig. 2 a using the Bayesian inference method. Each bar represents the geometric mean squared relative error for the parameter estimates b Errors for the estimates of the correlations between the estimated changes in parameters for the synthetic data in Fig. 2 a. Each bar represents the estimated Pearson correlation coefficient between the log-changes of the quantitiesCC BY · PubMed Central
Fig. 5 Analysis of experimental data. a Histogram showing the fold-changes for the genes which were considered significantly changed (blue) and not changed (gray) for D3E, DESeq2, limma, edgeR and SCDE. b Histograms showing the distribution of parameter values for all cells from [15]. From top to bottom, the panels represent the frequency, the burst size, the inferred rates for the transcriptional bursting model, and the duty cycle. c Examples of two genes, Cdc42bpb in the top panel and Hist1h2bb in the bottom panel, which were identified as DE by D3E. In both cases, the change in mean expression is less than 70 % whereas the variance increases by >10-fold. d Karnaugh table showing the number of genes identified as differentially expressed by D3E, SCDE, limma, edgeR, and DESeq2 for the two datasets collected by Islam et al. [15]. e Scatterplots showing the mean in mESCs, and the fold-change, as well as the fold-change of the mean compared to the change in degradation rate, burst frequency and burst size. In all panels, black dots represent genes which did not change, red dots represent genes which were deemed significant by D3E
Fig. 5 Analysis of experimental data. a Histogram showing the fold-changes for the genes which were considered significantly changed (blue) and not changed (gray) for D3E, DESeq2, limma, edgeR and SCDE. b Histograms showing the distribution of parameter values for all cells from [15]. From top to bottom, the panels represent the frequency, the burst size, the inferred rates for the transcriptional bursting model, and the duty cycle. c Examples of two genes, Cdc42bpb in the top panel and Hist1h2bb in the bottom panel, which were identified as DE by D3E. In both cases, the change in mean expression is less than 70 % whereas the variance increases by >10-fold. d Karnaugh table showing the number of genes identified as differentially expressed by D3E, SCDE, limma, edgeR, and DESeq2 for the two datasets collected by Islam et al. [15]. e Scatterplots showing the mean in mESCs, and the fold-change, as well as the fold-change of the mean compared to the change in degradation rate, burst frequency and burst size. In all panels, black dots represent genes which did not change, red dots represent genes which were deemed significant by D3ECC BY · PubMed Central

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Metadata

Authors
Delmans, M., & Hemberg, M.
Affiliations
  • University of Cambridge (GB)
  • Wellcome Sanger Institute (GB)
Corresponding author
  • Delmans, Mihails
  • Hemberg, Martin
ORCID
Venue
BMC Bioinformatics
Publisher
openRxiv
Published
2015-06-10
Volume
17
Issue
1
Pages
110-110
ISSN
1471-2105 (ISSN-L)
DOI
10.1101/020735
PMC
PMC4772470
OpenAlex
W2950583356
Cited by
111
References
48
Citations by year
2026: 3 · 2025: 3 · 2024: 9 · 2023: 15 · 2022: 17 · 2021: 25 · 2020: 10 · 2019: 7 · 2018: 12 · 2017: 8 · 2016: 2
FWCI
5.03
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Bioinformatics (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • Wellcome Trust
  • University of Cambridge
  • Biotechnology and Biological Sciences Research Council (1497818)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
Keywords
differential gene expression, single-cell RNA sequencing, stochastic gene expression models, gene expression heterogeneity, burst size, burst frequency, synthetic data evaluation
MeSH terms
Algorithms, Humans, RNA, Statistical Distributions, Sequence Analysis, RNA, Gene Expression Profiling, Single-Cell Analysis, High-Throughput Nucleotide Sequencing

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