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Modulational instability analysis of neuronal microtubules under the influence of Toda potential

Author Affiliations

  • 1Department of Physics, Periyar University, Salem, India
  • 2Department of physics, School of Basic and Applied Sciences, Central University of Tamilnadu, Thiruvarur, India
  • 3Department of Physics, Periyar University, Salem, India
  • 4Department of chemistry, Periyar University, Salem, India

Res. J. Recent Sci., Volume 9, Issue (2), Pages 23-26, April,2 (2020)


The cytoskeleton of eukaryotic cells is composed of several classes of protein polymers among which neuronal microtubules (NMTs) are the most prominent. The radical control of cellular processes in NMT system, that are cell division, intracellular trafficking, cellular morphogenesis process and also energy moved from one cell to another cell with least loss of energy. We investigate the excitations of soliton with small perturbation along the protofilaments that are governed by Discrete Nonlinear Schrodinger (DNLS) equation. We study the modulational instability analysis on microtubulin system under the influence of electric field with Toda potential. We perform a complete investigation of aninfluence of Toda potential of tubulin dimers in the development of energy localization that has the form of breather-like soliton excitations in the neuronal microtubulinprotofilament. The evolution of the localized wave is expected to explore a very interesting physical phenomenon such as energy transfer mechanism in biological systems.


  1. Kapitein L.C. and Hoogenraad C.C. (2015)., Building the Neuronal Microtubule Cytoskeleton., Neuron, 87(3), 492-506.
  2. Dustin P. (1984)., Microtubule poisons., In Microtubules. Springer, Berlin, Heidelberg, 171-233.
  3. Dent E.W. and Baas P.W. (2014)., Microtubules in neurons as information carriers., J. Neurochem., 129, 235-239.
  4. Zeković S., Muniyappan A., Zdravković S. and Kavitha L. (2013)., Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules., Chinese Physics B, 23(2), 020504.
  5. Kavitha L., Parasuraman E., Muniyappan A. and Gopi D. (2017)., Localized discrete breather modes in neuronal microtubules., Nonlinear Dynamics, 88, 2013-2033.
  6. Kavitha L., Muniyappan A., Prabhu A., Zdravković S., Jayanthi S. and Gopi D. (2013)., Nano breathers and molecular dynamics simulations in hydrogen-bonded chains., Journal of biological physics, 39(1), 15-35.
  7. Kavitha L., Sathishkumar P. and Gopi D. (2009)., Shape changing soliton in a site-dependent ferromagnet using tanh-function method., Phys. Scri., 79, 015402
  8. Kavitha L., Akila N., Prabhu A., Kuzmanovska-Barandaska O. and Gopi D. (2011)., Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities., Mathematical and Computer modeling, 53, 1095-1110.
  9. Nimmo J.J.C. (1983)., Jacobi Structures of the N-Soliton Solutions of the Nonlinear Schrödinger, the Heisenberg Spin and the Cylindrical Heisenberg Spin Equations., Phys. Lett. A., 99, 279.
  10. Pelap F.B., Kofane T.C., Flytzanis N. and Remoissenet M. (2001)., Wave modulations in the nonlinear biinductance transmission line., Journal of the Physical Society of Japan, 70(9), 2568-2577.
  11. Hasegawa A. and Tappert F.D. (1973)., Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion., Appl. Phys. Lett., 23, 142.
  12. Agrawal G.P. (1989)., Nonlinear Fiber Optics., FL: Academic, Orlando.
  13. Whitham G.B. (1965)., A general approach to linear and non-linear dispersive waves using a Lagrangian., Journal of Fluid Mechanics, 22(2), 273-283.