IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1004292.html
   My bibliography  Save this article

Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models

Author

Listed:
  • Niraj Kumar
  • Abhyudai Singh
  • Rahul V Kulkarni

Abstract

Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.Author Summary: One of the fundamental problems in biology is understanding how phenotypic variations arise among individuals in a population. Recent research has shown that phenotypic variations can arise due to probabilistic cell-fate decisions driven by inherent randomness (noise) in the process of gene expression. One of the manifestations of such stochasticity in gene expression is the production of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1 viral infections to cellular differentiation. Recent single-cell experiments provide evidence for complex arrival processes leading to bursting, however an analytical framework connecting such burst arrival processes with the corresponding higher moments of mRNA/protein distributions is currently lacking. We address this issue by invoking a mapping between general models of gene expression and systems studied in queueing theory. The framework developed and the results derived lead to new approaches for testing commonly used assumptions in modeling gene expression and for accurate estimation of burst parameters. Notably, the phenomenon of stochastic bursting has been observed in a wide range of disciplines ranging from neuroscience and finance to cell biology. The approaches developed and results obtained in this work will thus contribute towards quantitative characterization of burst processes in diverse systems of current interest.

Suggested Citation

  • Niraj Kumar & Abhyudai Singh & Rahul V Kulkarni, 2015. "Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models," PLOS Computational Biology, Public Library of Science, vol. 11(10), pages 1-22, October.
  • Handle: RePEc:plo:pcbi00:1004292
    DOI: 10.1371/journal.pcbi.1004292
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004292
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004292&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1004292?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Avigdor Eldar & Michael B. Elowitz, 2010. "Functional roles for noise in genetic circuits," Nature, Nature, vol. 467(7312), pages 167-173, September.
    2. John R. S. Newman & Sina Ghaemmaghami & Jan Ihmels & David K. Breslow & Matthew Noble & Joseph L. DeRisi & Jonathan S. Weissman, 2006. "Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise," Nature, Nature, vol. 441(7095), pages 840-846, June.
    3. Arjun Raj & Charles S Peskin & Daniel Tranchina & Diana Y Vargas & Sanjay Tyagi, 2006. "Stochastic mRNA Synthesis in Mammalian Cells," PLOS Biology, Public Library of Science, vol. 4(10), pages 1-13, September.
    4. Long Cai & Nir Friedman & X. Sunney Xie, 2006. "Stochastic protein expression in individual cells at the single molecule level," Nature, Nature, vol. 440(7082), pages 358-362, March.
    5. Mathias F. Wernet & Esteban O. Mazzoni & Arzu Çelik & Dianne M. Duncan & Ian Duncan & Claude Desplan, 2006. "Stochastic spineless expression creates the retinal mosaic for colour vision," Nature, Nature, vol. 440(7081), pages 174-180, March.
    6. Piers J Ingram & Michael P H Stumpf & Jaroslav Stark, 2008. "Nonidentifiability of the Source of Intrinsic Noise in Gene Expression from Single-Burst Data," PLOS Computational Biology, Public Library of Science, vol. 4(10), pages 1-10, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohammad Soltani & Cesar A Vargas-Garcia & Duarte Antunes & Abhyudai Singh, 2016. "Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-23, August.
    2. Youtao Lu & Jaehee Lee & Jifen Li & Srinivasa Rao Allu & Jinhui Wang & HyunBum Kim & Kevin L. Bullaughey & Stephen A. Fisher & C. Erik Nordgren & Jean G. Rosario & Stewart A. Anderson & Alexandra V. U, 2023. "CHEX-seq detects single-cell genomic single-stranded DNA with catalytical potential," Nature Communications, Nature, vol. 14(1), pages 1-19, December.
    3. Chen, Xiaoli & Wu, Fengyan & Duan, Jinqiao & Kurths, Jürgen & Li, Xiaofan, 2019. "Most probable dynamics of a genetic regulatory network under stable Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 425-436.
    4. Singh, Abhyudai & Vahdat, Zahra & Xu, Zikai, 2019. "Time-triggered stochastic hybrid systems with two timer-dependent resets," OSF Preprints u8fzg, Center for Open Science.
    5. Muir Morrison & Manuel Razo-Mejia & Rob Phillips, 2021. "Reconciling kinetic and thermodynamic models of bacterial transcription," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-30, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammad Soltani & Cesar A Vargas-Garcia & Duarte Antunes & Abhyudai Singh, 2016. "Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-23, August.
    2. Lee, Julian, 2023. "Poisson distributions in stochastic dynamics of gene expression: What events do they count?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    3. Marc S Sherman & Barak A Cohen, 2014. "A Computational Framework for Analyzing Stochasticity in Gene Expression," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-13, May.
    4. Abhyudai Singh & Mohammad Soltani, 2013. "Quantifying Intrinsic and Extrinsic Variability in Stochastic Gene Expression Models," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-12, December.
    5. Stuart Aitken & Marie-Cécile Robert & Ross D Alexander & Igor Goryanin & Edouard Bertrand & Jean D Beggs, 2010. "Processivity and Coupling in Messenger RNA Transcription," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-12, January.
    6. Singh, Abhyudai & Vahdat, Zahra & Xu, Zikai, 2019. "Time-triggered stochastic hybrid systems with two timer-dependent resets," OSF Preprints u8fzg, Center for Open Science.
    7. Ming Ni & Antoine L Decrulle & Fanette Fontaine & Alice Demarez & Francois Taddei & Ariel B Lindner, 2012. "Pre-Disposition and Epigenetics Govern Variation in Bacterial Survival upon Stress," PLOS Genetics, Public Library of Science, vol. 8(12), pages 1-11, December.
    8. Vera Bettenworth & Simon Vliet & Bartosz Turkowyd & Annika Bamberger & Heiko Wendt & Matthew McIntosh & Wieland Steinchen & Ulrike Endesfelder & Anke Becker, 2022. "Frequency modulation of a bacterial quorum sensing response," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    9. Jessica A Lee & Siavash Riazi & Shahla Nemati & Jannell V Bazurto & Andreas E Vasdekis & Benjamin J Ridenhour & Christopher H Remien & Christopher J Marx, 2019. "Microbial phenotypic heterogeneity in response to a metabolic toxin: Continuous, dynamically shifting distribution of formaldehyde tolerance in Methylobacterium extorquens populations," PLOS Genetics, Public Library of Science, vol. 15(11), pages 1-38, November.
    10. Chen, Aimin & Tian, Tianhai & Chen, Yiren & Zhou, Tianshou, 2022. "Stochastic analysis of a complex gene-expression model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    11. Jonathan Liu & Donald Hansen & Elizabeth Eck & Yang Joon Kim & Meghan Turner & Simon Alamos & Hernan Garcia, 2021. "Real-time single-cell characterization of the eukaryotic transcription cycle reveals correlations between RNA initiation, elongation, and cleavage," PLOS Computational Biology, Public Library of Science, vol. 17(5), pages 1-26, May.
    12. Hao Ge & Pingping Wu & Hong Qian & Xiaoliang Sunney Xie, 2018. "Relatively slow stochastic gene-state switching in the presence of positive feedback significantly broadens the region of bimodality through stabilizing the uninduced phenotypic state," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-24, March.
    13. Leighton T Izu & Tamás Bányász & Ye Chen-Izu, 2015. "Optimizing Population Variability to Maximize Benefit," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-17, December.
    14. Benjamin B Kaufmann & Qiong Yang & Jerome T Mettetal & Alexander van Oudenaarden, 2007. "Heritable Stochastic Switching Revealed by Single-Cell Genealogy," PLOS Biology, Public Library of Science, vol. 5(9), pages 1-8, September.
    15. Chanyoung Park & Kwadwo E. Owusu-Boaitey & Giselle M. Valdes & Peter W. Reddien, 2023. "Fate specification is spatially intermingled across planarian stem cells," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    16. Kazunari Iwamoto & Yuki Shindo & Koichi Takahashi, 2016. "Modeling Cellular Noise Underlying Heterogeneous Cell Responses in the Epidermal Growth Factor Signaling Pathway," PLOS Computational Biology, Public Library of Science, vol. 12(11), pages 1-18, November.
    17. Amy L. Hughes & Aleksander T. Szczurek & Jessica R. Kelley & Anna Lastuvkova & Anne H. Turberfield & Emilia Dimitrova & Neil P. Blackledge & Robert J. Klose, 2023. "A CpG island-encoded mechanism protects genes from premature transcription termination," Nature Communications, Nature, vol. 14(1), pages 1-19, December.
    18. Alistair N Boettiger & Peter L Ralph & Steven N Evans, 2011. "Transcriptional Regulation: Effects of Promoter Proximal Pausing on Speed, Synchrony and Reliability," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-14, May.
    19. Matthieu Wyart & David Botstein & Ned S Wingreen, 2010. "Evaluating Gene Expression Dynamics Using Pairwise RNA FISH Data," PLOS Computational Biology, Public Library of Science, vol. 6(11), pages 1-14, November.
    20. Lucy Ham & Megan A. Coomer & Kaan Öcal & Ramon Grima & Michael P. H. Stumpf, 2024. "A stochastic vs deterministic perspective on the timing of cellular events," Nature Communications, Nature, vol. 15(1), pages 1-10, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1004292. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.