TY  - JOUR
AU  - Zeković, Slobodan
AU  - Muniyappan, Annamalai
AU  - Zdravković, Slobodan
AU  - Kavitha, Louis
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5904
AB  - We show how Jacobian elliptic functions (JEFs) can be used to solve ordinary differential equations (ODEs) describing the nonlinear dynamics of microtubules (MTs). We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kink-type soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.
T2  - Chinese Physics B
T1  - Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules
VL  - 23
IS  - 2
DO  - 10.1088/1674-1056/23/2/020504
ER  - 

@article{
author = "Zeković, Slobodan and Muniyappan, Annamalai and Zdravković, Slobodan and Kavitha, Louis",
year = "2014",
abstract = "We show how Jacobian elliptic functions (JEFs) can be used to solve ordinary differential equations (ODEs) describing the nonlinear dynamics of microtubules (MTs). We demonstrate that only one of the JEFs can be used while the remaining two do not represent the solutions of the crucial differential equation. We show that a kink-type soliton moves along MTs. Besides this solution, we also discuss a few more solutions that may or may not have physical meanings. Finally, we show what kind of ODE can be solved by using JEFs.",
journal = "Chinese Physics B",
title = "Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules",
volume = "23",
number = "2",
doi = "10.1088/1674-1056/23/2/020504"
}

Zeković, S., Muniyappan, A., Zdravković, S.,& Kavitha, L.. (2014). Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. in Chinese Physics B, 23(2).
https://doi.org/10.1088/1674-1056/23/2/020504

Zeković S, Muniyappan A, Zdravković S, Kavitha L. Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules. in Chinese Physics B. 2014;23(2).
doi:10.1088/1674-1056/23/2/020504 .

Zeković, Slobodan, Muniyappan, Annamalai, Zdravković, Slobodan, Kavitha, Louis, "Employment of Jacobian elliptic functions for solving problems in nonlinear dynamics of microtubules" in Chinese Physics B, 23, no. 2 (2014),
https://doi.org/10.1088/1674-1056/23/2/020504 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Kavitha, Louis
AU  - Satarić, Miljko V.
AU  - Zeković, Slobodan
AU  - Petrović, Jovana S.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5157
AB  - 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 Sataric 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. (C) 2012 Elsevier Ltd. All rights reserved.
T2  - Chaos, Solitons and Fractals
T1  - Modified extended tanh-function method and nonlinear dynamics of microtubules
VL  - 45
IS  - 11
SP  - 1378
EP  - 1386
DO  - 10.1016/j.chaos.2012.07.009
ER  - 

@article{
author = "Zdravković, Slobodan and Kavitha, Louis and Satarić, Miljko V. and Zeković, Slobodan and Petrović, Jovana S.",
year = "2012",
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 Sataric 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. (C) 2012 Elsevier Ltd. All rights reserved.",
journal = "Chaos, Solitons and Fractals",
title = "Modified extended tanh-function method and nonlinear dynamics of microtubules",
volume = "45",
number = "11",
pages = "1378-1386",
doi = "10.1016/j.chaos.2012.07.009"
}

Zdravković, S., Kavitha, L., Satarić, M. V., Zeković, S.,& Petrović, J. S.. (2012). Modified extended tanh-function method and nonlinear dynamics of microtubules. in Chaos, Solitons and Fractals, 45(11), 1378-1386.
https://doi.org/10.1016/j.chaos.2012.07.009

Zdravković S, Kavitha L, Satarić MV, Zeković S, Petrović JS. Modified extended tanh-function method and nonlinear dynamics of microtubules. in Chaos, Solitons and Fractals. 2012;45(11):1378-1386.
doi:10.1016/j.chaos.2012.07.009 .

Zdravković, Slobodan, Kavitha, Louis, Satarić, Miljko V., Zeković, Slobodan, Petrović, Jovana S., "Modified extended tanh-function method and nonlinear dynamics of microtubules" in Chaos, Solitons and Fractals, 45, no. 11 (2012):1378-1386,
https://doi.org/10.1016/j.chaos.2012.07.009 . .