IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v605y2022ics0378437122005854.html
   My bibliography  Save this article

Detecting limit cycles in stochastic time series

Author

Listed:
  • Martiny, Emil S.
  • Jensen, Mogens H.
  • Heltberg, Mathias S.

Abstract

The emergence of oscillatory behaviour represents fundamental information about the interactions of the underlying system. In biological systems, oscillations have been observed in experimental data, but due to the significant level of noise, it is difficult to characterize whether observed dynamics based on time series, are truly limit cycles. Here, we present a simple three step method to identify the presence of limit cycles in stochastic systems. Considering input from one-dimensional time series, as are typically obtained in experiments, we propose statistical measures to detect the existence of limit cycles. This is tested on models from chemical networks, and we investigate how the underlying dynamics can be separated depending on the noise level and length of the series.

Suggested Citation

  • Martiny, Emil S. & Jensen, Mogens H. & Heltberg, Mathias S., 2022. "Detecting limit cycles in stochastic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    • Handle: RePEc:eee:phsmap:v:605:y:2022:i:c:s0378437122005854
    DOI: 10.1016/j.physa.2022.127917
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122005854
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.127917?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Mathias L. Heltberg & Sandeep Krishna & Mogens H. Jensen, 2019. "On chaotic dynamics in transcription factors and the associated effects in differential gene regulation," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    3. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    4. Leung, H.K., 1998. "Stochastic Hopf bifurcation in a biased van der Pol model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 146-155.
    5. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    6. Savaş Tay & Jacob J. Hughey & Timothy K. Lee & Tomasz Lipniacki & Stephen R. Quake & Markus W. Covert, 2010. "Single-cell NF-κB dynamics reveal digital activation and analogue information processing," Nature, Nature, vol. 466(7303), pages 267-271, July.
    Full references (including those not matched with items on IDEAS)

    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. Gabriele Micali & Gerardo Aquino & David M Richards & Robert G Endres, 2015. "Accurate Encoding and Decoding by Single Cells: Amplitude Versus Frequency Modulation," PLOS Computational Biology, Public Library of Science, vol. 11(6), pages 1-21, June.
    2. 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.
    3. Jung Hun Park & Gábor Holló & Yolanda Schaerli, 2024. "From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    4. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
    5. 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.
    6. 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.
    7. 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.
    8. Ankit Gupta & Mustafa Khammash, 2022. "Frequency spectra and the color of cellular noise," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    9. Bottani, Samuel & Grammaticos, Basile, 2008. "A simple model of genetic oscillations through regulated degradation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1468-1482.
    10. 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).
    11. Margherita Carletti & Malay Banerjee, 2019. "A Backward Technique for Demographic Noise in Biological Ordinary Differential Equation Models," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    12. 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.
    13. 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.
    14. Konstantinos I Papadimitriou & Guy-Bart V Stan & Emmanuel M Drakakis, 2013. "Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-24, February.
    15. Inés P Mariño & Alexey Zaikin & Joaquín Míguez, 2017. "A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-25, August.
    16. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    17. Dhiman, Aman & Poria, Swarup, 2018. "Allee effect induced diversity in evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 32-38.
    18. 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.
    19. Javier Santos-Moreno & Eve Tasiudi & Hadiastri Kusumawardhani & Joerg Stelling & Yolanda Schaerli, 2023. "Robustness and innovation in synthetic genotype networks," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    20. Chen Jia & Ramon Grima, 2024. "Holimap: an accurate and efficient method for solving stochastic gene network dynamics," Nature Communications, Nature, vol. 15(1), pages 1-14, December.

    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:eee:phsmap:v:605:y:2022:i:c:s0378437122005854. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.