{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T10:00:47Z","timestamp":1781863247960,"version":"3.54.5"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014014","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000}}],"reference-count":99,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T00:00:00Z","timestamp":1773619200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shanghai Action Plan for Technological Innovation Grant","award":["23S41900500"],"award-info":[{"award-number":["23S41900500"]}]},{"name":"Natural Science and Engineering Research Council of Canada Discovery Grant","award":["RGPIN-2024-06015"],"award-info":[{"award-number":["RGPIN-2024-06015"]}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["RPG-2024-082"],"award-info":[{"award-number":["RPG-2024-082"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>The Negative Binomial (NB) distribution is widely used to approximate transcript count distributions in single-cell RNA sequencing (scRNA-seq) data, yet the reason for its ubiquity is not fully understood. Here, we employ a computationally efficient model selection technique to map the relationship between the best-fit models \u2013 Beta-Poisson (Telegraph), NB, and Poisson \u2013 and the kinetic parameters that govern gene expression stochasticity. Our findings reveal that the NB distribution closely approximates simulated data (incorporating both biological and technical noise) within an intermediate range of the sum of the gene activation and inactivation rates normalized by the mRNA degradation rate. This range expands with decreasing mean expression, increasing technical noise, and larger sample sizes. The results imply that: (i) good NB fits occur in diverse parameter regimes without exclusively indicating transcriptional bursting; (ii) for small sample sizes, biological noise predominantly shapes the NB profile even when technical noise is present; (iii) under steady-state conditions, gene-specific parameters (burst size and frequency) estimated in regions where the NB model fits well, typically show large relative errors, even after corrections for technical noise, and (iv) gene ranking by burst frequency remains reliably accurate, suggesting that burst parameters are most informative in a relative sense. Finally, applying technical-noise\u2013corrected model fitting to scRNA-seq data confirms that a substantial fraction of mammalian genes fall within these NB-fitting regimes, despite lacking transcriptional bursting.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1014014","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:55:40Z","timestamp":1773683740000},"page":"e1014014","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":2,"title":["From noise to models to numbers: Evaluating negative binomial models and parameter estimations in single-cell RNA-seq"],"prefix":"10.1371","volume":"22","author":[{"given":"Yiling","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhanpeng","family":"Shu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2600-5806","authenticated-orcid":true,"given":"Zhixing","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1266-8169","authenticated-orcid":true,"given":"Ramon","family":"Grima","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,3,16]]},"reference":[{"issue":"5","key":"pcbi.1014014.ref001","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1038\/nmeth.1315","article-title":"mRNA-Seq whole-transcriptome analysis of a single cell","volume":"6","author":"F Tang","year":"2009","journal-title":"Nature Methods"},{"issue":"7","key":"pcbi.1014014.ref002","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1101\/gr.110882.110","article-title":"Characterization of the single-cell transcriptional landscape by highly multiplex RNA-seq","volume":"21","author":"S Islam","year":"2011","journal-title":"Genome Res"},{"issue":"8","key":"pcbi.1014014.ref003","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1038\/nbt.2282","article-title":"Full-length mRNA-Seq from single-cell levels of RNA and individual circulating tumor cells","volume":"30","author":"D Ramsk\u00f6ld","year":"2012","journal-title":"Nat Biotechnol"},{"issue":"6","key":"pcbi.1014014.ref004","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1038\/s41587-020-0497-0","article-title":"Single-cell RNA counting at allele and isoform resolution using Smart-seq3","volume":"38","author":"M Hagemann-Jensen","year":"2020","journal-title":"Nat Biotechnol"},{"issue":"1","key":"pcbi.1014014.ref005","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1038\/nmeth.1778","article-title":"Counting absolute numbers of molecules using unique molecular identifiers","volume":"9","author":"T Kivioja","year":"2011","journal-title":"Nat Methods"},{"issue":"7","key":"pcbi.1014014.ref006","doi-asserted-by":"crossref","DOI":"10.1093\/nar\/gkaf295","article-title":"Cell-cycle dependence of bursty gene expression: insights from fitting mechanistic models to single-cell RNA-seq data","volume":"53","author":"A Sukys","year":"2025","journal-title":"Nucleic Acids Res"},{"issue":"1","key":"pcbi.1014014.ref007","article-title":"Probabilistic outlier identification for RNA sequencing generalized linear models","volume":"3","author":"S Mangiola","year":"2021","journal-title":"NAR Genom Bioinform"},{"issue":"2","key":"pcbi.1014014.ref008","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1038\/s41587-019-0379-5","article-title":"Droplet scRNA-seq is not zero-inflated","volume":"38","author":"V Svensson","year":"2020","journal-title":"Nat Biotechnol"},{"issue":"21","key":"pcbi.1014014.ref009","doi-asserted-by":"crossref","first-page":"3486","DOI":"10.1093\/bioinformatics\/btx435","article-title":"powsimR: power analysis for bulk and single cell RNA-seq experiments","volume":"33","author":"B Vieth","year":"2017","journal-title":"Bioinformatics"},{"issue":"4","key":"pcbi.1014014.ref010","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1093\/bioinformatics\/btz726","article-title":"bayNorm: Bayesian gene expression recovery, imputation and normalization for single-cell RNA-sequencing data","volume":"36","author":"W Tang","year":"2020","journal-title":"Bioinformatics"},{"issue":"6","key":"pcbi.1014014.ref011","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1038\/nmeth.2930","article-title":"Validation of noise models for single-cell transcriptomics","volume":"11","author":"D Gr\u00fcn","year":"2014","journal-title":"Nat Methods"},{"issue":"6","key":"pcbi.1014014.ref012","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004333","article-title":"BASiCS: Bayesian analysis of single-cell sequencing data","volume":"11","author":"CA Vallejos","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1014014.ref013","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1038\/nmeth.4150","article-title":"Single-cell mRNA quantification and differential analysis with Census","volume":"14","author":"X Qiu","year":"2017","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1014014.ref014","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/s41467-018-07931-2","article-title":"Single-cell RNA-seq denoising using a deep count autoencoder","volume":"10","author":"G Eraslan","year":"2019","journal-title":"Nat Commun"},{"issue":"16","key":"pcbi.1014014.ref015","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1093\/bioinformatics\/bty1044","article-title":"M3Drop: dropout-based feature selection for scRNASeq","volume":"35","author":"TS Andrews","year":"2019","journal-title":"Bioinformatics"},{"issue":"7","key":"pcbi.1014014.ref016","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1038\/s41592-018-0033-z","article-title":"SAVER: gene expression recovery for single-cell RNA sequencing","volume":"15","author":"M Huang","year":"2018","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1014014.ref017","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1186\/s13059-019-1874-1","article-title":"Normalization and variance stabilization of single-cell RNA-seq data using regularized negative binomial regression","volume":"20","author":"C Hafemeister","year":"2019","journal-title":"Genome Biol"},{"issue":"12","key":"pcbi.1014014.ref018","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1038\/s41592-018-0229-2","article-title":"Deep generative modeling for single-cell transcriptomics","volume":"15","author":"R Lopez","year":"2018","journal-title":"Nat Methods"},{"issue":"7","key":"pcbi.1014014.ref019","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1038\/nmeth.2967","article-title":"Bayesian approach to single-cell differential expression analysis","volume":"11","author":"PV Kharchenko","year":"2014","journal-title":"Nat Methods"},{"issue":"2","key":"pcbi.1014014.ref020","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.molcel.2014.06.029","article-title":"Dynamic heterogeneity and DNA methylation in embryonic stem cells","volume":"55","author":"ZS Singer","year":"2014","journal-title":"Mol Cell"},{"key":"pcbi.1014014.ref021","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.12175","article-title":"Single-cell analysis of transcription kinetics across the cell cycle","volume":"5","author":"SO Skinner","year":"2016","journal-title":"Elife"},{"issue":"1","key":"pcbi.1014014.ref022","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.celrep.2014.05.053","article-title":"Transcription factors modulate c-Fos transcriptional bursts","volume":"8","author":"A Senecal","year":"2014","journal-title":"Cell Rep"},{"key":"pcbi.1014014.ref023","article-title":"Quantifying how post-transcriptional noise and gene copy number variation bias transcriptional parameter inference from mRNA distributions","volume":"11","author":"X Fu","year":"2022","journal-title":"Elife"},{"key":"pcbi.1014014.ref024","doi-asserted-by":"crossref","first-page":"7125","DOI":"10.1038\/srep07125","article-title":"Stochastic promoter activation affects Nanog expression variability in mouse embryonic stem cells","volume":"4","author":"H Ochiai","year":"2014","journal-title":"Sci Rep"},{"issue":"1","key":"pcbi.1014014.ref025","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.molcel.2015.01.027","article-title":"Bursty gene expression in the intact mammalian liver","volume":"58","author":"K Bahar Halpern","year":"2015","journal-title":"Mol Cell"},{"issue":"6","key":"pcbi.1014014.ref026","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.cell.2005.09.031","article-title":"Real-time kinetics of gene activity in individual bacteria","volume":"123","author":"I Golding","year":"2005","journal-title":"Cell"},{"issue":"4","key":"pcbi.1014014.ref027","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.tig.2020.01.003","article-title":"What is a transcriptional burst","volume":"36","author":"E Tunnacliffe","year":"2020","journal-title":"Trends in Genetics"},{"issue":"7","key":"pcbi.1014014.ref028","doi-asserted-by":"crossref","first-page":"823","DOI":"10.15252\/msb.20156257","article-title":"Structure of silent transcription intervals and noise characteristics of mammalian genes","volume":"11","author":"B Zoller","year":"2015","journal-title":"Mol Syst Biol"},{"issue":"6028","key":"pcbi.1014014.ref029","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1126\/science.1198817","article-title":"Mammalian genes are transcribed with widely different bursting kinetics","volume":"332","author":"DM Suter","year":"2011","journal-title":"Science"},{"issue":"3","key":"pcbi.1014014.ref030","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1137\/110852887","article-title":"Analytical results for a multistate gene model","volume":"72","author":"T Zhou","year":"2012","journal-title":"SIAM J Appl Math"},{"issue":"5","key":"pcbi.1014014.ref031","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1016\/j.bpj.2020.07.020","article-title":"A stochastic model of gene expression with polymerase recruitment and pause release","volume":"119","author":"Z Cao","year":"2020","journal-title":"Biophys J"},{"issue":"5","key":"pcbi.1014014.ref032","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1012118","article-title":"What can we learn when fitting a simple telegraph model to a complex gene expression model?","volume":"20","author":"F Jiao","year":"2024","journal-title":"PLOS Computational Biology"},{"issue":"1","key":"pcbi.1014014.ref033","doi-asserted-by":"crossref","first-page":"2833","DOI":"10.1038\/s41467-025-58127-4","article-title":"Transient power-law behaviour following induction distinguishes between competing models of stochastic gene expression","volume":"16","author":"AG Nicoll","year":"2025","journal-title":"Nat Commun"},{"issue":"2","key":"pcbi.1014014.ref034","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1006\/tpbi.1995.1027","article-title":"Markovian Modeling of Gene-Product Synthesis","volume":"48","author":"J Peccoud","year":"1995","journal-title":"Theoretical Population Biology"},{"issue":"1","key":"pcbi.1014014.ref035","article-title":"Inferring the kinetics of stochastic gene expression from single-cell RNA-sequencing data","volume":"14","author":"JK Kim","year":"2013","journal-title":"Genome Biol"},{"issue":"10","key":"pcbi.1014014.ref036","article-title":"Stochastic mRNA synthesis in mammalian cells","volume":"4","author":"A Raj","year":"2006","journal-title":"PLoS Biology"},{"issue":"7","key":"pcbi.1014014.ref037","doi-asserted-by":"crossref","DOI":"10.1093\/bioinformatics\/btad395","article-title":"Modelling capture efficiency of single-cell RNA-sequencing data improves inference of transcriptome-wide burst kinetics","volume":"39","author":"W Tang","year":"2023","journal-title":"Bioinformatics"},{"issue":"32","key":"pcbi.1014014.ref038","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.adl4893","article-title":"3D chromatin architecture, BRD4, and Mediator have distinct roles in regulating genome-wide transcriptional bursting and gene network","volume":"10","author":"P Trzaskoma","year":"2024","journal-title":"Sci Adv"},{"issue":"6","key":"pcbi.1014014.ref039","doi-asserted-by":"crossref","first-page":"2396","DOI":"10.1137\/151005567","article-title":"Distribution modes and their corresponding parameter regions in stochastic gene transcription","volume":"75","author":"F Jiao","year":"2015","journal-title":"SIAM J Appl Math"},{"issue":"12","key":"pcbi.1014014.ref040","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1038\/nsmb.1514","article-title":"Single-RNA counting reveals alternative modes of gene expression in yeast","volume":"15","author":"D Zenklusen","year":"2008","journal-title":"Nat Struct Mol Biol"},{"issue":"12","key":"pcbi.1014014.ref041","doi-asserted-by":"crossref","first-page":"2118","DOI":"10.1038\/s41564-019-0553-z","article-title":"Measuring transcription at a single gene copy reveals hidden drivers of bacterial individuality","volume":"4","author":"M Wang","year":"2019","journal-title":"Nat Microbiol"},{"issue":"6078","key":"pcbi.1014014.ref042","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1126\/science.1216379","article-title":"Using gene expression noise to understand gene regulation","volume":"336","author":"B Munsky","year":"2012","journal-title":"Science"},{"key":"pcbi.1014014.ref043","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.cbpa.2019.05.031","article-title":"Visualizing transcription: key to understanding gene expression dynamics","volume":"51","author":"I Brouwer","year":"2019","journal-title":"Curr Opin Chem Biol"},{"issue":"4","key":"pcbi.1014014.ref044","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1083\/jcb.201710038","article-title":"Visualizing transcription factor dynamics in living cells","volume":"217","author":"Z Liu","year":"2018","journal-title":"J Cell Biol"},{"issue":"2","key":"pcbi.1014014.ref045","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.molcel.2016.03.007","article-title":"Enhancer regulation of transcriptional bursting parameters revealed by forced chromatin looping","volume":"62","author":"CR Bartman","year":"2016","journal-title":"Mol Cell"},{"key":"pcbi.1014014.ref046","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/1741-7007-11-15","article-title":"Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts","volume":"11","author":"J Vi\u00f1uelas","year":"2013","journal-title":"BMC Biol"},{"issue":"9","key":"pcbi.1014014.ref047","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1038\/s41588-018-0175-z","article-title":"Dynamic interplay between enhancer-promoter topology and gene activity","volume":"50","author":"H Chen","year":"2018","journal-title":"Nat Genet"},{"key":"pcbi.1014014.ref048","article-title":"RNA Polymerase II cluster dynamics predict mRNA output in living cells","volume":"5","author":"W-K Cho","year":"2016","journal-title":"Elife"},{"issue":"9","key":"pcbi.1014014.ref049","doi-asserted-by":"crossref","first-page":"4682","DOI":"10.1073\/pnas.1910888117","article-title":"Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells","volume":"117","author":"Z Cao","year":"2020","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1014014.ref050","doi-asserted-by":"crossref","first-page":"14049","DOI":"10.1038\/ncomms14049","article-title":"Massively parallel digital transcriptional profiling of single cells","volume":"8","author":"GXY Zheng","year":"2017","journal-title":"Nat Commun"},{"issue":"5","key":"pcbi.1014014.ref051","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.cell.2015.05.002","article-title":"Highly parallel genome-wide expression profiling of individual cells using nanoliter droplets","volume":"161","author":"EZ Macosko","year":"2015","journal-title":"Cell"},{"issue":"1","key":"pcbi.1014014.ref052","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.bpj.2023.10.021","article-title":"Quantifying and correcting bias in transcriptional parameter inference from single-cell data","volume":"123","author":"R Grima","year":"2024","journal-title":"Biophys J"},{"issue":"45","key":"pcbi.1014014.ref053","doi-asserted-by":"crossref","first-page":"17256","DOI":"10.1073\/pnas.0803850105","article-title":"Analytical distributions for stochastic gene expression","volume":"105","author":"V Shahrezaei","year":"2008","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"16","key":"pcbi.1014014.ref054","doi-asserted-by":"crossref","first-page":"168302","DOI":"10.1103\/PhysRevLett.97.168302","article-title":"Linking stochastic dynamics to population distribution: an analytical framework of gene expression","volume":"97","author":"N Friedman","year":"2006","journal-title":"Phys Rev Lett"},{"key":"pcbi.1014014.ref055","doi-asserted-by":"crossref","first-page":"032402","DOI":"10.1103\/PhysRevE.96.032402","article-title":"Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts","volume":"96","author":"C Jia","year":"2017","journal-title":"Phys Rev E"},{"issue":"8","key":"pcbi.1014014.ref056","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1038\/nbt.2642","article-title":"Single-cell gene expression analysis reveals genetic associations masked in whole-tissue experiments","volume":"31","author":"QF Wills","year":"2013","journal-title":"Nat Biotechnol"},{"issue":"19","key":"pcbi.1014014.ref057","doi-asserted-by":"crossref","first-page":"6994","DOI":"10.1073\/pnas.1400049111","article-title":"Phenotypic switching in gene regulatory networks","volume":"111","author":"P Thomas","year":"2014","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"11","key":"pcbi.1014014.ref058","doi-asserted-by":"crossref","first-page":"114113","DOI":"10.1063\/5.0131445","article-title":"Model reduction for the Chemical Master Equation: An information-theoretic approach","volume":"158","author":"K \u00d6cal","year":"2023","journal-title":"J Chem Phys"},{"issue":"1","key":"pcbi.1014014.ref059","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1186\/s13059-022-02601-5","article-title":"Statistics or biology: the zero-inflation controversy about scRNA-seq data","volume":"23","author":"R Jiang","year":"2022","journal-title":"Genome Biol"},{"issue":"3","key":"pcbi.1014014.ref060","doi-asserted-by":"crossref","first-page":"1336","DOI":"10.1137\/19M1253198","article-title":"Kinetic Foundation of the Zero-Inflated Negative Binomial Model for Single-Cell RNA Sequencing Data","volume":"80","author":"C Jia","year":"2020","journal-title":"SIAM J Appl Math"},{"issue":"2","key":"pcbi.1014014.ref061","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1038\/s41587-020-00810-6","article-title":"UMI or not UMI, that is the question for scRNA-seq zero-inflation","volume":"39","author":"Y Cao","year":"2021","journal-title":"Nat Biotechnol"},{"issue":"5","key":"pcbi.1014014.ref062","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1016\/j.cell.2015.04.044","article-title":"Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells","volume":"161","author":"AM Klein","year":"2015","journal-title":"Cell"},{"issue":"4","key":"pcbi.1014014.ref063","doi-asserted-by":"crossref","DOI":"10.1016\/j.molcel.2017.01.023","article-title":"Comparative Analysis of Single-Cell RNA Sequencing Methods","volume":"65","author":"C Ziegenhain","year":"2017","journal-title":"Mol Cell"},{"issue":"10","key":"pcbi.1014014.ref064","doi-asserted-by":"crossref","first-page":"1706","DOI":"10.1039\/C8LC01239C","article-title":"Droplet-based single cell RNAseq tools: a practical guide","volume":"19","author":"R Salomon","year":"2019","journal-title":"Lab Chip"},{"key":"pcbi.1014014.ref065","unstructured":"10x Genomics. What fraction of mRNA transcripts are captured per cell?. 10x Genomics Knowledge Base. 2025. [cited 2025 April 2]. https:\/\/kb.10xgenomics.com\/hc\/en-us\/articles\/360001539051-What-fraction-of-mRNA-transcripts-are-captured-per-cell"},{"issue":"2","key":"pcbi.1014014.ref066","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.cell.2008.09.050","article-title":"Nature, nurture, or chance: stochastic gene expression and its consequences","volume":"135","author":"A Raj","year":"2008","journal-title":"Cell"},{"issue":"5678","key":"pcbi.1014014.ref067","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1126\/science.1098641","article-title":"Control of stochasticity in eukaryotic gene expression","volume":"304","author":"JM Raser","year":"2004","journal-title":"Science"},{"issue":"43","key":"pcbi.1014014.ref068","doi-asserted-by":"crossref","first-page":"17454","DOI":"10.1073\/pnas.1213530109","article-title":"Transcriptional burst frequency and burst size are equally modulated across the human genome","volume":"109","author":"RD Dar","year":"2012","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"13","key":"pcbi.1014014.ref069","doi-asserted-by":"crossref","first-page":"7148","DOI":"10.1073\/pnas.110057697","article-title":"Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation","volume":"97","author":"J Paulsson","year":"2000","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"29","key":"pcbi.1014014.ref070","doi-asserted-by":"crossref","first-page":"7533","DOI":"10.1073\/pnas.1804060115","article-title":"Distribution shapes govern the discovery of predictive models for gene regulation","volume":"115","author":"B Munsky","year":"2018","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"2","key":"pcbi.1014014.ref071","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.tig.2023.11.003","article-title":"Time will tell: comparing timescales to gain insight into transcriptional bursting","volume":"40","author":"JVW Meeussen","year":"2024","journal-title":"Trends Genet"},{"issue":"3","key":"pcbi.1014014.ref072","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1038\/s41588-022-01014-1","article-title":"Transcriptional kinetics and molecular functions of long noncoding RNAs","volume":"54","author":"P Johnsson","year":"2022","journal-title":"Nat Genet"},{"issue":"6","key":"pcbi.1014014.ref073","doi-asserted-by":"crossref","first-page":"068401","DOI":"10.1103\/q5sd-tpms","article-title":"Joint Distribution of Nuclear and Cytoplasmic mRNA Levels in Stochastic Models of Gene Expression: Analytical Results and Parameter Inference","volume":"135","author":"Y Wang","year":"2025","journal-title":"Phys Rev Lett"},{"key":"pcbi.1014014.ref074","article-title":"A mechanistic model for the negative binomial distribution of single-cell mRNA counts","author":"L Amrhein","year":"2019","journal-title":"bioRxiv"},{"issue":"5","key":"pcbi.1014014.ref075","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/j.bpj.2012.07.015","article-title":"Consequences of mRNA transport on stochastic variability in protein levels","volume":"103","author":"A Singh","year":"2012","journal-title":"Biophys J"},{"issue":"26","key":"pcbi.1014014.ref076","doi-asserted-by":"crossref","first-page":"268105","DOI":"10.1103\/PhysRevLett.113.268105","article-title":"Exact distributions for stochastic gene expression models with bursting and feedback","volume":"113","author":"N Kumar","year":"2014","journal-title":"Phys Rev Lett"},{"issue":"10","key":"pcbi.1014014.ref077","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004292","article-title":"Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models","volume":"11","author":"N Kumar","year":"2015","journal-title":"PLoS Comput Biol"},{"issue":"8","key":"pcbi.1014014.ref078","doi-asserted-by":"crossref","first-page":"084115","DOI":"10.1063\/1.5144578","article-title":"Small protein number effects in stochastic models of autoregulated bursty gene expression","volume":"152","author":"C Jia","year":"2020","journal-title":"J Chem Phys"},{"key":"pcbi.1014014.ref079","doi-asserted-by":"crossref","first-page":"022409","DOI":"10.1103\/PhysRevE.102.022409","article-title":"Special function methods for bursty models of transcription","volume":"102","author":"G Gorin","year":"2020","journal-title":"Phys Rev E"},{"issue":"2","key":"pcbi.1014014.ref080","article-title":"Frequency Domain Analysis of Fluctuations of mRNA and Protein Copy Numbers within a Cell Lineage: Theory and Experimental Validation","volume":"11","author":"C Jia","year":"2021","journal-title":"Phys Rev X"},{"issue":"6","key":"pcbi.1014014.ref081","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1016\/j.bpj.2022.02.004","article-title":"Modeling bursty transcription and splicing with the chemical master equation","volume":"121","author":"G Gorin","year":"2022","journal-title":"Biophys J"},{"issue":"7","key":"pcbi.1014014.ref082","doi-asserted-by":"crossref","first-page":"074105","DOI":"10.1063\/5.0188455","article-title":"Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition","volume":"160","author":"B Wu","year":"2024","journal-title":"J Chem Phys"},{"issue":"11","key":"pcbi.1014014.ref083","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s11538-023-01213-9","article-title":"Assessing Markovian and Delay Models for Single-Nucleus RNA Sequencing","volume":"85","author":"G Gorin","year":"2023","journal-title":"Bull Math Biol"},{"issue":"9","key":"pcbi.1014014.ref084","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1038\/s43588-024-00689-2","article-title":"Biophysically interpretable inference of cell types from multimodal sequencing data","volume":"4","author":"T Chari","year":"2024","journal-title":"Nat Comput Sci"},{"issue":"7738","key":"pcbi.1014014.ref085","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1038\/s41586-018-0836-1","article-title":"Genomic encoding of transcriptional burst kinetics","volume":"565","author":"AJM Larsson","year":"2019","journal-title":"Nature"},{"issue":"4","key":"pcbi.1014014.ref086","doi-asserted-by":"crossref","first-page":"221057","DOI":"10.1098\/rsos.221057","article-title":"Inferring transcriptional bursting kinetics from single-cell snapshot data using a generalized telegraph model","volume":"10","author":"S Luo","year":"2023","journal-title":"R Soc Open Sci"},{"issue":"1","key":"pcbi.1014014.ref087","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1093\/nar\/gkac1204","article-title":"Genome-wide inference reveals that feedback regulations constrain promoter-dependent transcriptional burst kinetics","volume":"51","author":"S Luo","year":"2023","journal-title":"Nucleic Acids Res"},{"issue":"10","key":"pcbi.1014014.ref088","doi-asserted-by":"crossref","first-page":"1725","DOI":"10.1038\/s41556-024-01486-9","article-title":"Single-cell new RNA sequencing reveals principles of transcription at the resolution of individual bursts","volume":"26","author":"D Ramsk\u00f6ld","year":"2024","journal-title":"Nat Cell Biol"},{"issue":"9","key":"pcbi.1014014.ref089","doi-asserted-by":"crossref","first-page":"093001","DOI":"10.1088\/1751-8121\/aa54d9","article-title":"Approximation and inference methods for stochastic biochemical kinetics\u2014a tutorial review","volume":"50","author":"D Schnoerr","year":"2017","journal-title":"J Phys A: Math Theor"},{"issue":"1","key":"pcbi.1014014.ref090","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1093\/dnares\/dsn030","article-title":"Database for mRNA half-life of 19 977 genes obtained by DNA microarray analysis of pluripotent and differentiating mouse embryonic stem cells","volume":"16","author":"LV Sharova","year":"2009","journal-title":"DNA Res"},{"issue":"1","key":"pcbi.1014014.ref091","doi-asserted-by":"crossref","first-page":"8051","DOI":"10.1038\/s41598-019-44537-0","article-title":"Cell cycle dynamics of mouse embryonic stem cells in the ground state and during transition to formative pluripotency","volume":"9","author":"A Waisman","year":"2019","journal-title":"Sci Rep"},{"issue":"1","key":"pcbi.1014014.ref092","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1038\/s41467-022-30545-8","article-title":"Cell cycle gene regulation dynamics revealed by RNA velocity and deep-learning","volume":"13","author":"A Riba","year":"2022","journal-title":"Nat Commun"},{"issue":"12","key":"pcbi.1014014.ref093","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1038\/s41592-024-02471-8","article-title":"Statistical inference with a manifold-constrained RNA velocity model uncovers cell cycle speed modulations","volume":"21","author":"AR Lederer","year":"2024","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1014014.ref094","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1012752","article-title":"Trajectory inference from single-cell genomics data with a process time model","volume":"21","author":"M Fang","year":"2025","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1014014.ref095","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1038\/s41592-023-02144-y","article-title":"scPerturb: harmonized single-cell perturbation data","volume":"21","author":"S Peidli","year":"2024","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1014014.ref096","first-page":"35","article-title":"Mixed poisson distributions","volume":"73","author":"D Karlis","year":"2005","journal-title":"International Statistical Review\/Revue Internationale de Statistique"},{"key":"pcbi.1014014.ref097","unstructured":"Zabaikina I, Grima R. Imperfect molecular detection renormalizes apparent kinetic rates in stochastic gene regulatory networks. arXiv preprint. 2025. https:\/\/arxiv.org\/abs\/251202908"},{"issue":"10","key":"pcbi.1014014.ref098","doi-asserted-by":"crossref","first-page":"108101","DOI":"10.1103\/PhysRevLett.124.108101","article-title":"Extrinsic Noise and Heavy-Tailed Laws in Gene Expression","volume":"124","author":"L Ham","year":"2020","journal-title":"Phys Rev Lett"},{"key":"pcbi.1014014.ref099","article-title":"Pathway dynamics can delineate the sources of transcriptional noise in gene expression","volume":"10","author":"L Ham","year":"2021","journal-title":"Elife"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1014014","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014014","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T17:55:31Z","timestamp":1775152531000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014014"}},"subtitle":[],"editor":[{"given":"Ilya","family":"Ioshikhes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,3,16]]},"references-count":99,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3,16]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014014","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,16]]}}}