IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0005131.html
   My bibliography  Save this article

A Mathematical Model for the Detection Mechanism of DNA Double-Strand Breaks Depending on Autophosphorylation of ATM

Author

Listed:
  • Kazunari Mouri
  • Jose C Nacher
  • Tatsuya Akutsu

Abstract

Background: After IR stress, DNA double-strand breaks (DSBs) occur and repair proteins (RPs) bind to them, generating DSB-RP complexes (DSBCs), which results in repaired DSBs (RDSBs). In recent experimental studies, it is suggested that the ATM proteins detect these DNA lesions depending on the autophosphorylation of ATM which exists as a dimer before phosphorylation. Interestingly, the ATM proteins can work as a sensor for a small number of DSBs (approximately 18 DSBs in a cell after exposure to IR). Thus the ATM proteins amplify the small input signals based on the phosphorylation of the ATM dimer proteins. The true DSB-detection mechanism depending on ATM autophosphorylation has yet to be clarified. Methodology/Principal Findings: We propose a mathematical model for the detection mechanism of DSBs by ATM. Our model includes both a DSB-repair mechanism and an ATM-phosphorylation mechanism. We model the former mechanism as a stochastic process, and obtain theoretical mean values of DSBs and DSBCs. In the latter mechanism, it is known that ATM autophosphorylates itself, and we find that the autophosphorylation induces bifurcation of the phosphorylated ATM (ATM*). The bifurcation diagram depends on the total concentration of ATM, which makes three types of steady state diagrams of ATM*: monostable, reversible bistable, and irreversible bistable. Bistability exists depending on the Hill coefficient in the equation of ATM autophosphorylation, and it emerges as the total concentration of ATM increases. Combining these two mechanisms, we find that ATM* exhibits switch-like behaviour in the presence of bistability, and the detection time after DNA damage decreases when the total concentration of ATM increases. Conclusions/Significance: This work provides a mathematical model that explains the DSB-detection mechanism depending on ATM autophosphorylation. These results indicate that positive auto-regulation works both as a sensor and amplifier of small input signals.

Suggested Citation

  • Kazunari Mouri & Jose C Nacher & Tatsuya Akutsu, 2009. "A Mathematical Model for the Detection Mechanism of DNA Double-Strand Breaks Depending on Autophosphorylation of ATM," PLOS ONE, Public Library of Science, vol. 4(4), pages 1-14, April.
  • Handle: RePEc:plo:pone00:0005131
    DOI: 10.1371/journal.pone.0005131
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0005131
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0005131&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0005131?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. Ertugrul M. Ozbudak & Mukund Thattai & Han N. Lim & Boris I. Shraiman & Alexander van Oudenaarden, 2004. "Multistability in the lactose utilization network of Escherichia coli," Nature, Nature, vol. 427(6976), pages 737-740, February.
    2. Timothy S. Gardner & Charles R. Cantor & James J. Collins, 2000. "Construction of a genetic toggle switch in Escherichia coli," Nature, Nature, vol. 403(6767), pages 339-342, January.
    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. Rajesh Ramaswamy & Ivo F Sbalzarini & Nélido González-Segredo, 2011. "Noise-Induced Modulation of the Relaxation Kinetics around a Non-Equilibrium Steady State of Non-Linear Chemical Reaction Networks," PLOS ONE, Public Library of Science, vol. 6(1), pages 1-10, 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. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    2. Tomas Tokar & Jozef Ulicny, 2013. "The Mathematical Model of the Bcl-2 Family Mediated MOMP Regulation Can Perform a Non-Trivial Pattern Recognition," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    3. Tobias May & Lee Eccleston & Sabrina Herrmann & Hansjörg Hauser & Jorge Goncalves & Dagmar Wirth, 2008. "Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-7, June.
    4. Zhou, Peipei & Cai, Shuiming & Liu, Zengrong & Chen, Luonan & Wang, Ruiqi, 2013. "Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 115-126.
    5. Carl Song & Hilary Phenix & Vida Abedi & Matthew Scott & Brian P Ingalls & Mads Kærn & Theodore J Perkins, 2010. "Estimating the Stochastic Bifurcation Structure of Cellular Networks," PLOS Computational Biology, Public Library of Science, vol. 6(3), pages 1-11, March.
    6. Shintaro Nagata & Macoto Kikuchi, 2020. "Emergence of cooperative bistability and robustness of gene regulatory networks," PLOS Computational Biology, Public Library of Science, vol. 16(6), pages 1-24, June.
    7. Xu, Yong & Zhu, Ya-nan & Shen, Jianwei & Su, Jianbin, 2014. "Switch dynamics for stochastic model of genetic toggle switch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 461-466.
    8. Marc Weber & Javier Buceta, 2013. "Stochastic Stabilization of Phenotypic States: The Genetic Bistable Switch as a Case Study," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-8, September.
    9. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    10. Paul Miller & Anatol M Zhabotinsky & John E Lisman & Xiao-Jing Wang, 2005. "The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover," PLOS Biology, Public Library of Science, vol. 3(4), pages 1-1, March.
    11. 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.
    12. Weiyue Ji & Handuo Shi & Haoqian Zhang & Rui Sun & Jingyi Xi & Dingqiao Wen & Jingchen Feng & Yiwei Chen & Xiao Qin & Yanrong Ma & Wenhan Luo & Linna Deng & Hanchi Lin & Ruofan Yu & Qi Ouyang, 2013. "A Formalized Design Process for Bacterial Consortia That Perform Logic Computing," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    13. Georg Fritz & Judith A Megerle & Sonja A Westermayer & Delia Brick & Ralf Heermann & Kirsten Jung & Joachim O Rädler & Ulrich Gerland, 2014. "Single Cell Kinetics of Phenotypic Switching in the Arabinose Utilization System of E. coli," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-12, February.
    14. T. Ochiai & J. C. Nacher, 2007. "Stochastic analysis of autoregulatory gene expression dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 14(4), pages 377-388, November.
    15. Shivang Hina-Nilesh Joshi & Chentao Yong & Andras Gyorgy, 2022. "Inducible plasmid copy number control for synthetic biology in commonly used E. coli strains," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    16. Thomas B. Kepler & Timothy C. Elston, 2001. "Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations," Working Papers 01-06-033, Santa Fe Institute.
    17. Luis Mier-y-Terán-Romero & Mary Silber & Vassily Hatzimanikatis, 2010. "The Origins of Time-Delay in Template Biopolymerization Processes," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-15, April.
    18. Bonassi Fernando V. & You Lingchong & West Mike, 2011. "Bayesian Learning from Marginal Data in Bionetwork Models," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, October.
    19. Zhdanov, Vladimir P., 2011. "Periodic perturbation of the bistable kinetics of gene expression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 57-64.
    20. Najme Khorasani & Mehdi Sadeghi & Abbas Nowzari-Dalini, 2020. "A computational model of stem cell molecular mechanism to maintain tissue homeostasis," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.

    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:pone00:0005131. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.