IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i22p5644-5662.html
   My bibliography  Save this article

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

Author

Listed:
  • Leyva, J. Francisco
  • Málaga, Carlos
  • Plaza, Ramón G.

Abstract

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.

Suggested Citation

  • Leyva, J. Francisco & Málaga, Carlos & Plaza, Ramón G., 2013. "The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5644-5662.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:22:p:5644-5662
    DOI: 10.1016/j.physa.2013.07.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113006328
    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.2013.07.022?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. Mimura, Masayasu & Sakaguchi, Hideo & Matsushita, Mitsugu, 2000. "Reaction–diffusion modelling of bacterial colony patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 283-303.
    2. Golding, Ido & Kozlovsky, Yonathan & Cohen, Inon & Ben-Jacob, Eshel, 1998. "Studies of bacterial branching growth using reaction–diffusion models for colonial development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(3), pages 510-554.
    3. David A. Kessler & Herbert Levine, 1998. "Fluctuation-induced diffusive instabilities," Nature, Nature, vol. 394(6693), pages 556-558, August.
    4. Ben-Jacob, Eshel & Cohen, Inon & Golding, Ido & Gutnick, David L. & Tcherpakov, Marianna & Helbing, Dirk & Ron, Ilan G., 2000. "Bacterial cooperative organization under antibiotic stress," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 247-282.
    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. Ma, Tinghuai & Li, Lu & Ji, Sai & Wang, Xin & Tian, Yuan & Al-Dhelaan, Abdullah & Al-Rodhaan, Mznah, 2014. "Optimized Laplacian image sharpening algorithm based on graphic processing unit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 400-410.
    2. Cruz-García, S. & Martínez-Farías, F. & Santillán-Hernández, A.S. & Rangel, E., 2021. "Mathematical home burglary model with stochastic long crime trips and patrolling: Applied to Mexico City," Applied Mathematics and Computation, Elsevier, vol. 396(C).

    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. Banitz, Thomas & Fetzer, Ingo & Johst, Karin & Wick, Lukas Y. & Harms, Hauke & Frank, Karin, 2011. "Assessing biodegradation benefits from dispersal networks," Ecological Modelling, Elsevier, vol. 222(14), pages 2552-2560.
    2. Mansour, M.B.A., 2007. "Traveling wave solutions of a reaction–diffusion model for bacterial growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 466-472.
    3. Samvel Sarukhanian & Anna Maslovskaya & Christina Kuttler, 2023. "Three-Dimensional Cellular Automaton for Modeling of Self-Similar Evolution in Biofilm-Forming Bacterial Populations," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    4. Lin Chen & Javad Noorbakhsh & Rhys M Adams & Joseph Samaniego-Evans & Germaine Agollah & Dmitry Nevozhay & Jennie Kuzdzal-Fick & Pankaj Mehta & Gábor Balázsi, 2014. "Two-Dimensionality of Yeast Colony Expansion Accompanied by Pattern Formation," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-14, December.
    5. Ron, Ilan G. & Golding, Ido & Lifsitz-Mercer, Beatrice & Ben-Jacob, Eshel, 2003. "Bursts of sectors in expanding bacterial colonies as a possible model for tumor growth and metastases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 485-496.
    6. Cohen, Inon & Ron, Ilan G & Ben-Jacob, Eshel, 2000. "From branching to nebula patterning during colonial development of the Paenibacillus alvei bacteria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(1), pages 321-336.
    7. Chapwanya, Michael & Dumani, Phindile, 2023. "Stationary and oscillatory patterns in microbial population under environmental stress," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 370-383.
    8. Gafiychuk, V.V. & Datsko, B.Yo., 2006. "Pattern formation in a fractional reaction–diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 300-306.
    9. Badoual, M. & Derbez, P. & Aubert, M. & Grammaticos, B., 2009. "Simulating the migration and growth patterns of Bacillus subtilis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 549-559.
    10. Golding, Ido & Kozlovsky, Yonathan & Cohen, Inon & Ben-Jacob, Eshel, 1998. "Studies of bacterial branching growth using reaction–diffusion models for colonial development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(3), pages 510-554.
    11. Kaoru Sugimura & Kohei Shimono & Tadashi Uemura & Atsushi Mochizuki, 2007. "Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites," PLOS Computational Biology, Public Library of Science, vol. 3(11), pages 1-12, November.
    12. Ben-Jacob, Eshel & Cohen, Inon & Golding, Ido & Gutnick, David L. & Tcherpakov, Marianna & Helbing, Dirk & Ron, Ilan G., 2000. "Bacterial cooperative organization under antibiotic stress," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 247-282.
    13. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.

    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:392:y:2013:i:22:p:5644-5662. 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.