THERMAL SCIENCE

International Scientific Journal

Jing Li

,

Yuyang Qiu

,

Dianchen Lu

,

Raghda A. M. Attia

,

Mostafa M. A. Khater

STUDY ON THE SOLITARY WAVE SOLUTIONS OF THE IONIC CURRENTS ON MICROTUBULES EQUATION BY USING THE MODIFIED KHATER METHOD

ABSTRACT
In this survey, the ionic current along microtubules equation is handled by applying the modified Khater method to get the solitary wave solutions that describe the ionic transport throughout the intracellular environment which describes the behavior of many applications in a biological nonlinear dispatch line for ionic currents. The obtained solutions support many researchers who are concerned with the discussion of the physical properties of the ionic currents along microtubules. Microtubules are one of the main components of the cytoskeleton, and function in many operations, comprehensive constitutional backing, intracellular transmit, and DNA division. Moreover, we also study the stability property of our obtained solutions. All obtained solutions are verified by backing them into the original equation by using Maple 18 and Mathematica 11.2. These solutions show the power and effective of the used method and its ability for applying to many other different forms of nonlinear partial differential equations.
KEYWORDS
Longitudinal wave equation, Modified Khater method, stability property, solitary wave solutions
PAPER SUBMITTED: 2019-07-22
PAPER REVISED: 2019-09-08
PAPER ACCEPTED: 2019-09-10
PUBLISHED ONLINE: 2019-10-06
DOI REFERENCE: https://doi.org/10.2298/TSCI190722370L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S2053 - S2062]
REFERENCES
  1. Hepler, P. K., & Palevitz, B. A. Microtubules and microfilaments. Annual Review of Plant Physiology, 25(1) (1974) 309-362.
  2. Burnside, B. Microtubules and microfilaments in amphibian neurulation. American Zoologist, 13(4) (1973) 989-1006.
  3. Burnside, B. Microtubules and microfilaments in newt neurulation. Developmental biology, 26(3) (1971) 416-441.
  4. Taylor, A. et al. Vasopressin: possible role of microtubules and microfilaments in its action. Science, 181 (1973) 347-350.
  5. Takeuchi, M. et al. Single microfilaments mediate the early steps of microtubule bundling during preprophase band formation in onion cotyledon epidermal cells. Molecular biology of the cell, 27(11) (2016) 1809-1820.
  6. Zhang, L. J. et al. A "driver switchover" mechanism of influenza virus transport from microfilaments to microtubules. ACS nano, 12(1) (2017) 474-484.
  7. Nejedla, M. et al. Profilin connects actin assembly with microtubule dynamics. Molecular biology of the cell, 27(15) (2016) 2381-2393.
  8. Fernandez, J. et al. Microtubule-associated proteins 1 (MAP1) promote human immunodeficiency virus type I (HIV-1) intracytoplasmic routing to the nucleus. Journal of Biological Chemistry, 290(8) (2015) 4631-4646.
  9. Li, G. et al. Interaction between microfilament and microtubule-dependent tensions and ischemia/hypoxic-induced alteration of structural tension in neuronal cells. Brain Research Bulletin, 149 (2015) 222-230.
  10. Angelini, G. Protein Phosphatase 2A Influences Cortical Microtubule Organization in Response to Salt Stress (Doctoral dissertation, University of New Hampshire) (2017).
  11. Miao, Z. et al. Microtubule actin cross‐linking factor 1, a novel potential target in cancer. Cancer Science, 108(10) (2017) 1953-1958.
  12. Wang, J. et al. Microtubule polymerization functions in hypersensitive response and accumulation of H2O2 in wheat induced by the stripe rust. BioMed Research International, 2016.
  13. Zhu, L. et al. High glucose upregulates myosin light chain kinase to induce microfilament cytoskeleton rearrangement in hippocampal neurons. Molecular Medicine Reports, 18(1) (2018) 216-222.
  14. Bergman, Z. et al. Microtubules are necessary for proper Reticulon localization during mitosis. BioRxiv, (2019) 516773.
  15. Takeuchi, M., Staehelin, A., and Mineyuki, Y. Actin-microtubule interaction in plants. Cytoskeleton-Structure, Dynamics, Function and Disease. InTechOpen, (2017) 33-54.
  16. Liu, F. et al. One-step synthesis of magnetic hollow mesoporous silica (MHMS) nanospheres for drug delivery nanosystems via electrostatic self-assembly templated approach. Chemical Communications, 51(12) (2015) 2357-2360.
  17. Harris, R. C., Boschitsch, A. H. and Fenley, M. O. Numerical Difficulties Computing Electrostatic Potentials Near Interfaces with the Poisson-Boltzmann Equation. Journal of chemical theory and computation, 13(8) (2017) 3945-3951.
  18. Liu, Y. et al. Protein‐Framed Multi‐Porphyrin Micelles for a Hybrid Natural-Artificial Light‐ Harvesting Nanosystem Angewandte Chemie International Edition, 55(28) (2017) 7952-7957.
  19. Chen, C. et al. Dynamic equilibria of short-range electrostatic interactions at molecular interfaces of protein-DNA complexes. The journal of physical chemistry letters, 6(14) (2015) 2733-2737.
  20. Arancibia, S. et al. Modeling of the Binding of Octopamine and Dopamine in Insect Monoamine Transporters Reveals Structural and Electrostatic Differences. ACS Chemical Neuroscience, 10(5) (2019) 2310-2317.
  21. Inc, M. et al. Time-fractional Cahn-Allen and time-fractional Klein-Gordon equations: Lie symmetry analysis, explicit solutions and convergence analysis. Physica A: Statistical Mechanics and its Applications, 493 (2018) 94-106.
  22. Rezazadeh, H. New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik, 167 (2018) 218-227.
  23. Inc, M. et al. Lie symmetry analysis, explicit solutions and conservation laws for the space- time fractional nonlinear evolution equations. Physica A: Statistical Mechanics and its Applications, 496 (2018) 371-383.
  24. Inc, M. et al. Optical solitary waves, conservation laws and modulation instability analysis to the nonlinear Schrödinger's equation in compressional dispersive Alvèn waves. Optik 155 (2018) 257-266.
  25. Korkmaz, A. et al. Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class. Journal of King Saud University-Science. (2018) in press.
  26. Ak, T. et al. Computational analysis of shallow water waves with Korteweg-de Vries equation. Scientia Iranica B, 25(5) (2018) 2582-2597.
  27. Liu, J. G. et al. Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev-Petviashvili equation. Nonlinear Dynamics, 95(2) (2019) 1027-1033.
  28. Ak, T., Triki, H., Dhawan, S., and Erduran, K. S. Theoretical and numerical investigations on solitary wave solutions of Gardner equation. The European Physical Journal Plus, 133(9) (2018) 382.
  29. Raza, N., Aslam, M. R., and Rezazadeh, H. Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media. Optical and Quantum Electronics, 51(2) (2019) 59.
  30. Ak, T., Aydemir, T., Saha, A., & Kara, A. H. (2018). Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation. Pramana, 90(6) (2018) 78.
  31. Khater, M., Attia, R. A., and Lu, D. Explicit Lump Solitary Wave of Certain Interesting (3+ 1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods. Entropy, 21(4) (2019) 397.
  32. Khater, M. M., Lu, D., and Attia, R. A. Dispersive long wave of nonlinear fractional Wu- Zhang system via a modified auxiliary equation method. AIP Advances, 9(2) (2019) 025003.
  33. Khater, M. M., Lu, D., and Attia, R. A. Lump soliton wave solutions for the (2+1)- dimensional Konopelchenko-Dubrovsky equation and KdV equation. Modern Physics Letters B, (2019) 1950199.
  34. Attia, R. A., Lu, D., and MA Khater, M. Chaos and relativistic energy-momentum of the nonlinear time fractional Duffing equation. Mathematical and Computational Applications, 24(1) (2019) 10.
  35. Khater, M., Attia, R., and Lu, D. Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions. Mathematical and Computational Applications, 24(1) (2019) 1.
  36. Raza, N., Murtaza, I. G., Sial, S., and Younis, M. On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients. Waves in Random and Complex Media, 28(3) (2018) 553-569.
  37. Yüzbaşı, Z. K., and Aslan, E.C. (2018). Exact Solutions with Lie Symmetry Analysis for Nano-Ionic Currents along Microtubules. In ITM Web of Conferences (Vol. 22, p. 01017). EDP Sciences.
  38. Celik, E., Bulut, H., & Baskonus, H. M. (2018). Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules. Indian Journal of Physics, 92(9), 1137-1143.
  39. Akram, G., and Mahak, N. Analytical solution of the Korteweg-de Vries equation and microtubule equation using the first integral method. Optical and Quantum Electronics, 50(3) (2018) 145.
  40. Md. Nur A. and Md. Mahbub A. An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules, Journal of Taibah University for Science, 11 (2017) 939-948.
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Study on the solitary wave solutions of the ionic currents on microtubules equation by using the modified Khater method

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