Modified extended tanh-function method and nonlinear dynamics of microtubules |
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| Authors: | Slobodan Zdravković Louis Kavitha Miljko V. Satarić Slobodan Zeković Jovana Petrović |
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| Affiliation: | 1. Institut za nuklearne nauke Vin?a, Univerzitet u Beogradu, Po?tanski fah 522, 11001 Beograd, Serbia;2. Department of Physics, Periyar University, Salem 636 011, India;3. The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy;4. Fakultet tehni?kih nauka, Univerzitet u Novom Sadu, 21000 Novi Sad, Serbia;1. Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon;2. Institute of Theoretical and Computational Physics, Department of Physics, College of Sciences, Botswana International University of Science and Technology, P/Bag 16 Palapye, Botswana;3. Institute of Theoretical Physics, Department of Physics, Faculty of Science, University of Stellenbosch, Private Bag X1 Matieland, Stellenbosch 7602, South Africa;4. The African Institute for Mathematical Sciences, 6-8 Melrose Rd, Muizenberg 7945, South Africa;5. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon;1. AGH—University Science and Technology, Faculty of Geology, Geophysics and Environmental Protection, Krakow, Poland;2. AGH—University Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland;3. Rzeszow University of Technology, Faculty of Electrical and Computer Engineering, Rzeszow, Poland;4. Rzeszow University of Technology, Faculty of Mathematics and Applied Physics, Rzeszow, Poland;1. Instituto de Física, Universidade Federal de Alagoas, Maceió AL 57072-970, Brazil;2. Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970, Natal-RN, Brazil;1. Department of Mathematics, Malayer University, Malayer, Iran;2. Department of Mathematics, Razi University, Kermanshah 67149, Iran |
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| Abstract: | We here present a model of nonlinear dynamics of microtubules (MT) in the context of modified extended tanh-function (METHF) method. We rely on the ferroelectric model of MTs published earlier by Satari? et al. [1] where the motion of MT subunits is reduced to a single longitudinal degree of freedom per dimer. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. An analytical solution of the basic equation, describing MT dynamics, was compared with the numerical one and a perfect agreement was demonstrated. It is now clearer how the values of the basic parameters of the model, proportional to viscosity and internal electric field, impact MT dynamics. Finally, we offer a possible scenario of how living cells utilize these kinks as signaling tools for regulation of cellular traffic as well as MT depolymerisation. |
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