Beta-Poisson model for single-cell RNA-seq data analyses
Open accessAbstract
Motivation: Single-cell RNA-sequencing technology allows detection of gene expression at the single-cell level. One typical feature of the data is a bimodality in the cellular distribution even for highly expressed genes, primarily caused by a proportion of non-expressing cells. The standard and the over-dispersed gamma-Poisson models that are commonly used in bulk-cell RNA-sequencing are not able to capture this property. Results: We introduce a beta-Poisson mixture model that can capture the bimodality of the single-cell gene expression distribution. We further integrate the model into the generalized linear model framework in order to perform differential expression analyses. The whole analytical procedure is called BPSC. The results from several real single-cell RNA-seq datasets indicate that ∼90% of the transcripts are well characterized by the beta-Poisson model; the model-fit from BPSC is better than the fit of the standard gamma-Poisson model in > 80% of the transcripts. Moreover, in differential expression analyses of simulated and real datasets, BPSC performs well against edgeR, a conventional method widely used in bulk-cell RNA-sequencing data, and against scde and MAST, two recent methods specifically designed for single-cell RNA-seq data. Availability and Implementation: An R package BPSC for model fitting and differential expression analyses of single-cell RNA-seq data is available under GPL-3 license at https://github.com/nghiavtr/BPSC . Contact: yudi.pawitan@ki.se or mattias.rantalainen@ki.se Supplementary information: Supplementary data are available at Bioinformatics online.
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“Furthermore, papers evaluating the performance of single-cell-specific tools all compute the simulations as if cells were independent15–21.”
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What can we learn when fitting a simple telegraph model to a complex gene expression model?
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“Poisson-Beta model [48], our method considered the transcriptional bursting process characterized by burst size s/ko f f and burst frequency kon.”
Orrapin, S., Thongkumkoon, P., Udomruk, S., Moonmuang, S., Sutthitthasakul, S., Yongpitakwattana, P., Pruksakorn, D., & Chaiyawat, P. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms241512337 · Cited by 28 · see citing works
“To tackle these issues, a number of software packages that are specifically designed for single-cell data have been proposed, for instance, the beta-Poisson model for scRNA seq (BPSC) [82], model-based analysis of single-cell transcriptomics (MAST) [83], Monocle [84], and DEsingle [85].”
MethodBaumann, D. C., Wong, A., Akhaphong, B., Jo, S., Pritchard, S. K., Mohan, R., Chung, G., Zhang, Y., & Alejandro, E. U. (2020) · Development · doi:10.1242/dev.186643 · Cited by 26 · see citing works
“Subsequently, two methods were used to test for differential gene expression: the beta-Poisson model of analysis (Vu et al., 2016); and a method that grouped single cells into six”
MethodAnalysis of Single-Cell RNA-seq Data by Clustering Approaches
Zhu, X., Li, H., Guo, L., Wu, F., & Wang, J. (2018) · Current Bioinformatics · doi:10.2174/1574893614666181120095038 · Cited by 25 · see citing works
Differential analysis of binarized single-cell RNA sequencing data captures biological variation
Bouland, G. A., Mahfouz, A. E., & Reinders, M. J. T. (2021) · NAR Genomics and Bioinformatics · doi:10.1093/nargab/lqab118 · Cited by 22 · see citing works
Modeling group heteroscedasticity in single-cell RNA-seq pseudo-bulk data
You, Y., Dong, X., Wee, Y. K., Maxwell, M. J., Alhamdoosh, M., Smyth, G. K., Hickey, P. F., Ritchie, M. E., & Law, C. W. (2023) · Genome biology · doi:10.1186/s13059-023-02949-2 · Cited by 23 · see citing works
“…count matrix, which is a major point of difference between single-cell and bulk data [4, 5], other researchers modeled scRNA-seq data as either zero-inflated or multi-modal in distribution and developed tailored DE analysis methods for scRNA-seq data (e.g., MAST [4], BPSC [7], and DEsingle [8]).”
Method4D nucleome equation predicts gene expression controlled by long-range enhancer-promoter interaction
Wang, Z.-H., Luo, S.-H., Zhang, Z.-Q., Zhou, T.-S., & Zhang, J. (2023) · PLoS Comput. Biol. · doi:10.1371/journal.pcbi.1011722 · Cited by 12 · see citing works
“When focusing only on the downstream gene expression, that is, given a d S (or a frozen E-P topology), we find that the stationary probability distribution of mRNA abundance P mRNA ( x ) is a Poisson-Beta distribution (Fig 2C, [51]).”
BackgroundSukys, A., & Grima, R. (2025) · Nucleic Acids Research · doi:10.1093/nar/gkaf295 · Cited by 21 · see citing works
A generalized moment-based method for estimating parameters of stochastic gene transcription
Chen, L., Zhu, C., & Jiao, F. (2022) · Mathematical Biosciences · doi:10.1016/j.mbs.2022.108780 · Cited by 20 · see citing works
DREAMSeq: An Improved Method for Analyzing Differentially Expressed Genes in RNA-seq Data
Gao, Z., Zhao, Z., & Tang, W. (2018) · Frontiers in Genetics · doi:10.3389/fgene.2018.00588 · Cited by 20 · see citing works
“However, scRNA-seq data displays typical features of bimodality (the NB model cannot capture bimodality) (Vu et al., 2016), making such data less efficient for mining using common RNA-seq data-analysis methods.”
MethodPaplomatas, P., Krokidis, M. G., Vlamos, P., & Vrahatis, A. G. (2023) · Applied Sciences · doi:10.3390/app13042353 · Cited by 20 · see citing works
Transcriptional bursting dynamics in gene expression
Zhang, Q., Cao, W., Wang, J., Yin, Y., Sun, R., Tian, Z., Hu, Y., Tan, Y., & Zhang, B. (2024) · Frontiers in Genetics · doi:10.3389/fgene.2024.1451461 · Cited by 18 · see citing works
Zou, J., Deng, F., Wang, M., Zhang, Z., Liu, Z., Zhang, X., Hua, R., Chen, K., Zou, X., & Hao, J. (2022) · Briefings in Bioinformatics · doi:10.1093/bib/bbac180 · Cited by 20 · see citing works
Nguyen, H. T., Bryois, J., Kim, A., Dobbyn, A., Huckins, L. M., Muñoz‐Manchado, A. B., Ruderfer, D. M., Genovese, G., Fromer, M., Xu, X., et al. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/135293 · Cited by 19 · see citing works
Guo, X., Ning, J., Chen, Y., Liu, G., Zhao, L., Fan, Y., & Sun, S. (2023) · Briefings in Functional Genomics · doi:10.1093/bfgp/elad011 · Cited by 18 · see citing works
Enhancing mitochondrial proteolysis alleviates alpha-synuclein-mediated cellular toxicity
Zhang, X., Ruan, L., Wang, H., Zhu, J., Li, T., Sun, G. L., Dong, Y., Wang, Y., Berreby, G., Shay, A., et al. (2024) · npj Parkinson s Disease · doi:10.1038/s41531-024-00733-y · Cited by 18 · see citing works
scDEA: differential expression analysis in single-cell RNA-sequencing data via ensemble learning
Li, H.-S., Ou-Yang, L., Zhu, Y., Yan, H., & Zhang, X.-F. (2021) · Briefings in Bioinformatics · doi:10.1093/bib/bbab402 · Cited by 17 · see citing works
Penalized Latent Dirichlet Allocation Model in Single-Cell RNA Sequencing
Wu, X., Wu, H., & Wu, Z. J. (2021) · Statistics in Biosciences · doi:10.1007/s12561-021-09304-8 · Cited by 17 · see citing works
“…models and methods have been developed, either to address the challenges associated with scRNA-seq in answering familiar questions, such as identifying differential expression [11, 34, 37], or new questions, such as cell clustering [16, 19, 29, 30] and pseudo-time construction [1, 13, 21, 32, 33].”
MethodSingle-Cell RNA Sequencing of Plant-Associated Bacterial Communities
Ma, Q., Bücking, H., González-Hernández, J. L., & Subramanian, S. (2019) · Frontiers in Microbiology · doi:10.3389/fmicb.2019.02452 · Cited by 17 · see citing works
“BPSC (Vu et al., 2016) 2016 R beta-Poisson mixture model”
Chawla, S., Samydurai, S., Kong, S. L., Wu, Z., Wang, Z., Tam, W. L., Sengupta, D., & Kumar, V. (2020) · Nucleic Acids Research · doi:10.1093/nar/gkab018 · Cited by 20 · see citing works
“The statistical modelling of read-count of a gene (or genomic site) across multiple cells is a non-trivial task, especially for single-cell open-chromatin and scRNA-seq profiles due to variability in the dropout rate and sequencing depth among cells (8,11).”
BackgroundIsoform-level gene expression patterns in single-cell RNA-sequencing data
Vu, T. N., Wills, Q. F., Kalari, K. R., Niu, N., Wang, L., Yudi Pawitan, Y., & Rantalainen, M. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty100 · Cited by 16 · see citing works
Self-citationBayesian Framework for Detecting Gene Expression Outliers in Individual Samples
Vivian, J., Eizenga, J. M., Beale, H. C., Vaske, O. M., & Paten, B. (2020) · JCO Clinical Cancer Informatics · doi:10.1200/cci.19.00095 · Cited by 15 · see citing works
“model single-cell expression, such as a β-Poisson mixture model.(55) In conclusion, as clinicians have begun to demonstrate that RNA-seq analysis can produce actionable findings for patients with cancer, it is necessary to have informed and principled analytic tools for an individual patient.”
BackgroundDas, S., & Rai, S. N. (2021) · Genomics · doi:10.1016/j.ygeno.2021.02.014 · Cited by 15 · see citing works
Alternating EM algorithm for a bilinear model in isoform quantification from RNA-seq data
Deng, W., Mou, T., Kalari, K. R., Niu, N., Wang, L., Yudi Pawitan, Y., & Vu, T. N. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz640 · Cited by 15 · see citing works
Self-citationZhou, L., Peng, X., Chen, M., He, X., Tian, G., Yang, J., & Peng, L. (2025) · GigaScience · doi:10.1093/gigascience/giae103 · Cited by 15 · see citing works
“In STMSGAL, both the encoder and the decoder with the activation function of the exponential linear unit (ELU) [ 80 ] included neural networks with 2 graph attention la yers , where the number of neurons was 512 and 30, r espectiv el y.”
ZIAQ: a quantile regression method for differential expression analysis of single-cell RNA-seq data
Zhang, W., Wei, Y., Zhang, D., & Xu, E. (2020) · Bioinformatics · doi:10.1093/bioinformatics/btaa098 · Cited by 13 · see citing works
OSG-GEM: Gene Expression Matrix Construction Using the Open Science Grid
Poehlman, W. L., Rynge, M., Branton, C., Balamurugan, D., & Feltus, F. A. (2016) · Bioinformatics and Biology Insights · doi:10.4137/bbi.s38193 · Cited by 13 · see citing works
“1) and differential gene expression profiling 37 (DEG in Fig.”
BackgroundSCRIP: an accurate simulator for single-cell RNA sequencing data
Qin, F., Luo, X., Xiao, F., & Cai, G. (2021) · Bioinformatics · doi:10.1093/bioinformatics/btab824 · Cited by 12 · see citing works
Modeling expression ranks for noise-tolerant differential expression analysis of scRNA-seq dataPreprint
Gupta, K., Lalit, M., Biswas, A., Sanada, C. D., Greene, C., Hukari, K. W., Maulik, U., Bandyopadhyay, S., Ramalingam, N., Ahuja, G., et al. (2021) · Genome Research · doi:10.1101/gr.267070.120 · Cited by 13 · see citing works
BISC: accurate inference of transcriptional bursting kinetics from single-cell transcriptomic data
Luo, X., Qin, F., Xiao, F., & Cai, G. (2022) · Briefings in Bioinformatics · doi:10.1093/bib/bbac464 · Cited by 12 · see citing works
An in silico FSHD muscle fiber for modeling DUX4 dynamics and predicting the impact of therapy
Cowley, M. V., Prüller, J., Ganassi, M., Zammit, P. S., & Banerji, C. R. S. (2023) · eLife · doi:10.7554/elife.88345 · Cited by 12 · see citing works
Wang, X., Li, Y., & Jia, C. (2023) · Journal of The Royal Society Interface · doi:10.1098/rsif.2023.0467 · Cited by 12 · see citing works
“Interestingly, the discrete hypergeometric-type distribution and the continuous beta distribution are also linked by the Poisson representation, and this beautiful relation has been used in the parameter inference of the telegraph model [26].”
MethodInfluentialMulti-omics in exploring the pathophysiology of diabetic retinopathy
Li, X., Dong, X., Zhang, W., Shi, Z., Liu, Z., Sa, Y., Li, L., Ni, N., & Mei, Y. (2024) · Frontiers in Cell and Developmental Biology · doi:10.3389/fcell.2024.1500474 · Cited by 12 · see citing works
Niu, J., Xu, W. L., Wei, D., Qian, K., & Wang, Q. (2022) · Analytical Chemistry · doi:10.1021/acs.analchem.2c00601 · Cited by 13 · see citing works
Self-supervised deep learning of gene–gene interactions for improved gene expression recovery
Wei, Q., Islam, M. T., Zhou, Y., & Xing, L. (2024) · Briefings in Bioinformatics · doi:10.1093/bib/bbae031 · Cited by 10 · see citing works
“Wi j = 1 q q  k=1 Sk i S k j 1 q2 ( q  k=1 Sk i )( q  k=1 Sj), (2)”
M3S: a comprehensive model selection for multi-modal single-cell RNA sequencing data
Zhang, Y., Wan, C., Wang, P., Chang, W., Huo, Y., Chen, J., Ma, Q., Cao, S., & Zhang, C. (2019) · BMC Bioinformatics · doi:10.1186/s12859-019-3243-1 · Cited by 10 · see citing works
Variability of the innate immune response is globally constrained by transcriptional bursting
(2023) · doi:10.3389/fmolb.2023.1176107 · Cited by 8 · see citing works
“231 232 We first used a profile likelihood approach [17, 39] to fit the measured scRNA-seq count 233 distributions assuming steady state kinetics of the 2-state model (the so called Beta-Poisson 234 model) for the 1,551 high confidence genes, each across 20 treatment datasets (Table S3).”
MethodCanopy2: Tumor Phylogeny Inference by Bulk DNA and Single-Cell RNA Sequencing
Weideman, A. M., Wang, R., Ibrahim, J. G., & Jiang, Y. (2025) · Statistics in Biosciences · doi:10.1007/s12561-024-09466-1 · Cited by 7 · see citing works
“7 Estimates of bursting kinetics using BPSC [17] and SCALE [18].”
InfluentialSong, D., & Li, J. J. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.11.17.387779 · Cited by 7 · see citing works
Phase separation reduces cell-to-cell variability of transcriptional bursting
Hong, L. E., Wang, Z., Zhang, Z., Luo, S., Zhou, T., & Zhang, J. (2023) · Mathematical Biosciences · doi:10.1016/j.mbs.2023.109127 · Cited by 6 · see citing works
Zhu, B., Li, H., Zhang, L., Chandra, S. S., & Zhao, H. (2022) · Briefings in Bioinformatics · doi:10.1093/bib/bbac166 · Cited by 6 · see citing works
“…DESeq2 [6], edgeR [7] as well as limma-voom [8, 9], (ii) the ensemble method scDEA [15] and (iii) the individual single cell methods considered in scDEA, including BPSC [34], DEsingle [35], monocle [36], scDD [13], T-test [37], Wilcoxon test [38], SeuratBimod [39, 40] and zingeR.edgeR [41].”
Miao, Z., Kong, W., Vinayak, R. K., Sun, W., & Han, F. (2022) · Journal of the American Statistical Association · doi:10.1080/01621459.2022.2120401 · Cited by 6 · see citing works
“…Poisson model (Robinson, McCarthy, and Smyth 2010), Poisson-Gamma model (Love, Huber, and Anders 2014; Huang et al. 2018), Poisson-Beta model (Vu et al. 2016), Poisson-log normal model (Silva et al. 2019), Poisson mixture model with K-clusters (Rau et al. 2015), finite Poisson mixture models…”
MethodLu, Y., Oliva, M., Pierce, B. L., Liu, J., & Chen, L. S. (2024) · Nature Communications · doi:10.1038/s41467-024-46675-0 · Cited by 7 · see citing works
“Here we tested whether the expression of a gene in one layer differs from the other layers 46 .”
Imputation method for single-cell RNA-seq data using neural topic model
Qi, Y., Han, S., Tang, L., & Liu, L. (2022) · GigaScience · doi:10.1093/gigascience/giad098 · Cited by 4 · see citing works
“As a result, the observ ed zer o v alue does not r eflect the underl ying true ex-pr ession le v el [ 15 , 16 ].”
BackgroundZhang, C., & Jiao, F. (2024) · Biosystems · doi:10.1016/j.biosystems.2024.105128 · Cited by 5 · see citing works
Biswas, B., Kumar, N., Sugimoto, M., & Hoque, M. A. (2024) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2024.108769 · Cited by 5 · see citing works
- Authors
- Vu, T. N., Wills, Q. F., Kalari, K. R., Niu, N., Wang, L., Rantalainen, M., & Pawitan, Y.
- Affiliations
- Karolinska Institutet (SE)
- Centre for Human Genetics (GB)
- Mayo Clinic (US)
- 1 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, 17177 Stockholm, Sweden
- Corresponding author
- Rantalainen, Mattias
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2016-04-19
- Volume
- 32
- Issue
- 14
- Pages
- 2128-2135
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2339613031
- Cited by
- 157
- References
- 24
- Citations by year
- 2026: 8 · 2025: 9 · 2024: 15 · 2023: 20 · 2022: 19 · 2021: 26 · 2020: 10 · 2019: 12 · 2018: 19 · 2017: 13 · 2016: 5
- FWCI
- 8.49
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Bioinformatics (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Funders
- Swedish Science Council
- Swedish Cancer Foundation
- NIH
- 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 › Genomics and Phylogenetic Studies
- Keywords
- single-cell RNA sequencing, differential expression analysis, generalized linear models, overdispersed count data, MAST
- MeSH terms
- Models, Theoretical, RNA, Sequence Analysis, RNA, Computational Biology, Gene Expression Profiling, Single-Cell Analysis
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