IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007062.html
   My bibliography  Save this article

Two component model of microtubules and continuum approximation

Author

Listed:
  • Zdravković, S.
  • Zeković, S.
  • Bugay, A.N.
  • Petrović, J.

Abstract

In the present work, we study the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a two-component model describing tangential oscillations of dimers. A crucial nonlinear differential equation is solved using continuum approximation. We show that the dynamics of microtubules can be explained in terms of kink and antikink solitary waves. We used two mathematical procedures, that is the tangent hyperbolic function method and, more general, the simplest equation method. It is shown that both procedures bring about equal solutions.

Suggested Citation

  • Zdravković, S. & Zeković, S. & Bugay, A.N. & Petrović, J., 2021. "Two component model of microtubules and continuum approximation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007062
    DOI: 10.1016/j.chaos.2021.111352
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007062
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111352?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. Ali, Khalid K. & Cattani, Carlo & Gómez-Aguilar, J.F. & Baleanu, Dumitru & Osman, M.S., 2020. "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Kudryashov, Nikolai A., 2005. "Simplest equation method to look for exact solutions of nonlinear differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1217-1231.
    3. El-Wakil, S.A. & Abdou, M.A., 2007. "New exact travelling wave solutions using modified extended tanh-function method," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 840-852.
    4. Tabi, Conrad Bertrand & Tankou, Eric & Mohamadou, Alidou, 2017. "Nonlinear coupled mode excitations in microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 187-194.
    5. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
    6. Dai, Chaoqing & Zhang, Jiefang, 2006. "Jacobian elliptic function method for nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1042-1047.
    7. Zdravković, Slobodan & Kavitha, Louis & Satarić, Miljko V. & Zeković, Slobodan & Petrović, Jovana, 2012. "Modified extended tanh-function method and nonlinear dynamics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1378-1386.
    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. Ranković, Dragana & Zdravković, Slobodan, 2022. "Two component model of microtubules – subsonic and supersonic solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Ranković, Dragana & Sivčević, Vladimir & Batova, Anna & Zdravković, Slobodan, 2023. "Three kinds of W-potentials in nonlinear biophysics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 170(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. Ranković, Dragana & Sivčević, Vladimir & Batova, Anna & Zdravković, Slobodan, 2023. "Three kinds of W-potentials in nonlinear biophysics of microtubules," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Ranković, Dragana & Zdravković, Slobodan, 2022. "Two component model of microtubules – subsonic and supersonic solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Akbulut, Arzu & Taşcan, Filiz, 2017. "Application of conservation theorem and modified extended tanh-function method to (1+1)-dimensional nonlinear coupled Klein–Gordon–Zakharov equation," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 33-40.
    4. Bekir, Ahmet & Boz, Ahmet, 2009. "Application of Exp-function method for (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 458-465.
    5. Verma, Pallavi & Kaur, Lakhveer, 2019. "Integrability, bilinearization and analytic study of new form of (3+1)-dimensional B-type Kadomstev–Petviashvili (BKP)- Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 879-886.
    6. Fokas, A.S. & Cuevas-Maraver, J. & Kevrekidis, P.G., 2020. "A quantitative framework for exploring exit strategies from the COVID-19 lockdown," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Attia Rani & Muhammad Shakeel & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Prem Junsawang, 2022. "Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    8. Innocent Simbanefayi & Chaudry Masood Khalique, 2020. "Group Invariant Solutions and Conserved Quantities of a (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    9. Fahmy, E.S., 2008. "Travelling wave solutions for some time-delayed equations through factorizations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1209-1216.
    10. Yusufoğlu, E. & Bekir, A., 2008. "The tanh and the sine–cosine methods for exact solutions of the MBBM and the Vakhnenko equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1126-1133.
    11. Mustafa Inc & Rubayyi T. Alqahtani & Ravi P. Agarwal, 2023. "W-Shaped Bright Soliton of the (2 + 1)-Dimension Nonlinear Electrical Transmission Line," Mathematics, MDPI, vol. 11(7), pages 1-13, April.
    12. Bekir, Ahmet & Cevikel, Adem C., 2009. "New exact travelling wave solutions of nonlinear physical models," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1733-1739.
    13. Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Symmetry Methods and Conservation Laws for the Nonlinear Generalized 2D Equal-Width Partial Differential Equation of Engineering," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    14. Taghread Ghannam Alharbi & Abdulghani Alharbi, 2023. "A Study of Traveling Wave Structures and Numerical Investigations into the Coupled Nonlinear Schrödinger Equation Using Advanced Mathematical Techniques," Mathematics, MDPI, vol. 11(22), pages 1-16, November.
    15. Dubey, Shweta & Chakraverty, S., 2022. "Application of modified extended tanh method in solving fractional order coupled wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 509-520.
    16. Yang, Lijuan & Du, Xianyun & Yang, Qiongfen, 2016. "New variable separation solutions to the (2 + 1)-dimensional Burgers equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1271-1275.
    17. Zayed, E.M.E. & Alurrfi, K.A.E., 2016. "Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 111-131.
    18. GaziKarakoc, Seydi Battal & Ali, Khalid K., 2020. "Analytical and computational approaches on solitary wave solutions of the generalized equal width equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    19. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
    20. Ali, Karmina K. & Yokus, Asıf & Seadawy, Aly R. & Yilmazer, Resat, 2022. "The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

    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:chsofr:v:152:y:2021:i:c:s0960077921007062. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.