Modified extended tanh-function method and nonlinear dynamics of microtubules
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2012
Authors
Zdravković, SlobodanKavitha, Louis
Satarić, Miljko V.
Zeković, Slobodan
Petrović, Jovana S.
Article (Published version)
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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.
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Chaos, Solitons and Fractals, 2012, 45, 11, 1378-1386Funding / projects:
- Photonics of micro and nano structured materials (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
- The influence of elementary excitations and conformations to physical properties of the new materials based on strongly correlated low-dimensional systems (RS-MESTD-Basic Research (BR or ON)-171009)
- UGC, BRNS, India, ICTP, Italy
DOI: 10.1016/j.chaos.2012.07.009
ISSN: 0960-0779
WoS: 000311018800011
Scopus: 2-s2.0-84866491463
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VinčaTY - 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 . .