IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1005236.html
   My bibliography  Save this article

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Author

Listed:
  • James C Schaff
  • Fei Gao
  • Ye Li
  • Igor L Novak
  • Boris M Slepchenko

Abstract

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.Author Summary: Mechanisms of some cellular phenomena involve interactions of molecular systems of which one can be described deterministically, while the other is inherently stochastic. Calcium ‘sparks’ in cardiomyocytes is one such example, in which dynamics of calcium ions, which are usually present in large numbers, can be described deterministically, whereas the channels open and close stochastically. The calcium influx through the channels renders the entire system stochastic, but a fully stochastic treatment accounting for each calcium ion is computationally expensive. Fortunately, such systems can be efficiently solved by hybrid methods in which deterministic and stochastic algorithms are appropriately integrated. Here we describe fundamentals of a general-purpose deterministic-stochastic method for simulating spatially resolved systems. The internal workings of the method are explained and illustrated by applications to very different phenomena such as calcium ‘sparks’, stochastically gated reactions, and spontaneous cell polarization.

Suggested Citation

  • James C Schaff & Fei Gao & Ye Li & Igor L Novak & Boris M Slepchenko, 2016. "Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-23, December.
  • Handle: RePEc:plo:pcbi00:1005236
    DOI: 10.1371/journal.pcbi.1005236
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005236
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005236&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1005236?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. Steven J. Altschuler & Sigurd B. Angenent & Yanqin Wang & Lani F. Wu, 2008. "On the spontaneous emergence of cell polarity," Nature, Nature, vol. 454(7206), pages 886-889, August.
    2. Steven S Andrews & Nathan J Addy & Roger Brent & Adam P Arkin, 2010. "Detailed Simulations of Cell Biology with Smoldyn 2.1," PLOS Computational Biology, Public Library of Science, vol. 6(3), pages 1-10, March.
    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. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.

    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. Brian Drawert & Andreas Hellander & Ben Bales & Debjani Banerjee & Giovanni Bellesia & Bernie J Daigle Jr. & Geoffrey Douglas & Mengyuan Gu & Anand Gupta & Stefan Hellander & Chris Horuk & Dibyendu Na, 2016. "Stochastic Simulation Service: Bridging the Gap between the Computational Expert and the Biologist," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-15, December.
    2. Fridtjof Brauns & Leila Iñigo de la Cruz & Werner K.-G. Daalman & Ilse Bruin & Jacob Halatek & Liedewij Laan & Erwin Frey, 2023. "Redundancy and the role of protein copy numbers in the cell polarization machinery of budding yeast," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    3. Johannes Schöneberg & Frank Noé, 2013. "ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-14, September.
    4. Rory M Donovan & Jose-Juan Tapia & Devin P Sullivan & James R Faeder & Robert F Murphy & Markus Dittrich & Daniel M Zuckerman, 2016. "Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-25, February.
    5. Shi, Qingyan & Song, Yongli, 2022. "Spatiotemporal pattern formation in a pollen tube model with nonlocal effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:pcbi00:1005236. 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.