TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Zeković, Slobodan
AU  - Bugay, Aleksandr Nikolaevich
AU  - Petrović, Jovana S.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9918
AB  - In the present work, we study the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a two-component model describing tangential oscillations of dimers. A crucial nonlinear differential equation is solved using continuum approximation. We show that the dynamics of microtubules can be explained in terms of kink and antikink solitary waves. We used two mathematical procedures, that is the tangent hyperbolic function method and, more general, the simplest equation method. It is shown that both procedures bring about equal solutions. © 2021
T2  - Chaos, Solitons and Fractals
T1  - Two component model of microtubules and continuum approximation
VL  - 152
SP  - 111352
DO  - 10.1016/j.chaos.2021.111352
ER  - 

@article{
author = "Zdravković, Slobodan and Zeković, Slobodan and Bugay, Aleksandr Nikolaevich and Petrović, Jovana S.",
year = "2021",
abstract = "In the present work, we study the nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. We introduce a two-component model describing tangential oscillations of dimers. A crucial nonlinear differential equation is solved using continuum approximation. We show that the dynamics of microtubules can be explained in terms of kink and antikink solitary waves. We used two mathematical procedures, that is the tangent hyperbolic function method and, more general, the simplest equation method. It is shown that both procedures bring about equal solutions. © 2021",
journal = "Chaos, Solitons and Fractals",
title = "Two component model of microtubules and continuum approximation",
volume = "152",
pages = "111352",
doi = "10.1016/j.chaos.2021.111352"
}

Zdravković, S., Zeković, S., Bugay, A. N.,& Petrović, J. S.. (2021). Two component model of microtubules and continuum approximation. in Chaos, Solitons and Fractals, 152, 111352.
https://doi.org/10.1016/j.chaos.2021.111352

Zdravković S, Zeković S, Bugay AN, Petrović JS. Two component model of microtubules and continuum approximation. in Chaos, Solitons and Fractals. 2021;152:111352.
doi:10.1016/j.chaos.2021.111352 .

Zdravković, Slobodan, Zeković, Slobodan, Bugay, Aleksandr Nikolaevich, Petrović, Jovana S., "Two component model of microtubules and continuum approximation" in Chaos, Solitons and Fractals, 152 (2021):111352,
https://doi.org/10.1016/j.chaos.2021.111352 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Čevizović, Dalibor
AU  - Bugay, Aleksandr N.
AU  - Maluckov, Aleksandra
PY  - 2019
UR  - http://aip.scitation.org/doi/10.1063/1.5090962
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8207
AB  - We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription. © 2019 Author(s).
T2  - Chaos
T1  - Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule
VL  - 29
IS  - 5
SP  - 053118
DO  - 10.1063/1.5090962
ER  - 

@article{
author = "Zdravković, Slobodan and Čevizović, Dalibor and Bugay, Aleksandr N. and Maluckov, Aleksandra",
year = "2019",
abstract = "We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription. © 2019 Author(s).",
journal = "Chaos",
title = "Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule",
volume = "29",
number = "5",
pages = "053118",
doi = "10.1063/1.5090962"
}

Zdravković, S., Čevizović, D., Bugay, A. N.,& Maluckov, A.. (2019). Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule. in Chaos, 29(5), 053118.
https://doi.org/10.1063/1.5090962

Zdravković S, Čevizović D, Bugay AN, Maluckov A. Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule. in Chaos. 2019;29(5):053118.
doi:10.1063/1.5090962 .

Zdravković, Slobodan, Čevizović, Dalibor, Bugay, Aleksandr N., Maluckov, Aleksandra, "Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule" in Chaos, 29, no. 5 (2019):053118,
https://doi.org/10.1063/1.5090962 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Parkhomenko, Aleksandr Yu.
AU  - Bugay, Aleksandr N.
PY  - 2018
UR  - http://aip.scitation.org/doi/10.1063/1.5046772
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7940
AB  - Nonlinear dynamics of DNA molecule at segments where DNA-RNA transcription occurs is studied. Our basic idea is that the solitary wave, moving along the chain, transforms into a demodulated one at these segments. The second idea is that the wave becomes a standing one due to interaction with DNA surrounding, e.g., RNA polymerase molecules. We explain why this is biologically convenient and show that our results match the experimental ones. In addition, we suggest how to experimentally determine crucial constant describing covalent bonds within DNA. © 2018 Author(s).
T2  - Chaos
T1  - Demodulated standing solitary wave and DNA-RNA transcription
VL  - 28
IS  - 11
SP  - 113103
DO  - 10.1063/1.5046772
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Parkhomenko, Aleksandr Yu. and Bugay, Aleksandr N.",
year = "2018",
abstract = "Nonlinear dynamics of DNA molecule at segments where DNA-RNA transcription occurs is studied. Our basic idea is that the solitary wave, moving along the chain, transforms into a demodulated one at these segments. The second idea is that the wave becomes a standing one due to interaction with DNA surrounding, e.g., RNA polymerase molecules. We explain why this is biologically convenient and show that our results match the experimental ones. In addition, we suggest how to experimentally determine crucial constant describing covalent bonds within DNA. © 2018 Author(s).",
journal = "Chaos",
title = "Demodulated standing solitary wave and DNA-RNA transcription",
volume = "28",
number = "11",
pages = "113103",
doi = "10.1063/1.5046772"
}

Zdravković, S., Satarić, M. V., Parkhomenko, A. Yu.,& Bugay, A. N.. (2018). Demodulated standing solitary wave and DNA-RNA transcription. in Chaos, 28(11), 113103.
https://doi.org/10.1063/1.5046772

Zdravković S, Satarić MV, Parkhomenko AY, Bugay AN. Demodulated standing solitary wave and DNA-RNA transcription. in Chaos. 2018;28(11):113103.
doi:10.1063/1.5046772 .

Zdravković, Slobodan, Satarić, Miljko V., Parkhomenko, Aleksandr Yu., Bugay, Aleksandr N., "Demodulated standing solitary wave and DNA-RNA transcription" in Chaos, 28, no. 11 (2018):113103,
https://doi.org/10.1063/1.5046772 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Bugay, Aleksandr N.
AU  - Parkhomenko, Aleksandr Yu.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1824
AB  - We here present a model of nonlinear dynamics of microtubules using modified extended tanh-function method as a mathematical tool. Interaction between neighbouring dimers belonging to a single protofilament is commonly modelled by a harmonic potential. In this paper, we introduce a more realistic Morse potential energy instead. We obtained three solitary waves as before, when the harmonic potential was used. However, the Morse potential allows transition from the state when elastic term in the expression for total energy is bigger than the inertial one to the state when the inertial potential is bigger. Also, three new solutions were obtained.
T2  - Nonlinear Dynamics
T1  - Application of Morse potential in nonlinear dynamics of microtubules
VL  - 90
IS  - 4
SP  - 2841
EP  - 2849
DO  - 10.1007/s11071-017-3845-y
ER  - 

@article{
author = "Zdravković, Slobodan and Bugay, Aleksandr N. and Parkhomenko, Aleksandr Yu.",
year = "2017",
abstract = "We here present a model of nonlinear dynamics of microtubules using modified extended tanh-function method as a mathematical tool. Interaction between neighbouring dimers belonging to a single protofilament is commonly modelled by a harmonic potential. In this paper, we introduce a more realistic Morse potential energy instead. We obtained three solitary waves as before, when the harmonic potential was used. However, the Morse potential allows transition from the state when elastic term in the expression for total energy is bigger than the inertial one to the state when the inertial potential is bigger. Also, three new solutions were obtained.",
journal = "Nonlinear Dynamics",
title = "Application of Morse potential in nonlinear dynamics of microtubules",
volume = "90",
number = "4",
pages = "2841-2849",
doi = "10.1007/s11071-017-3845-y"
}

Zdravković, S., Bugay, A. N.,& Parkhomenko, A. Yu.. (2017). Application of Morse potential in nonlinear dynamics of microtubules. in Nonlinear Dynamics, 90(4), 2841-2849.
https://doi.org/10.1007/s11071-017-3845-y

Zdravković S, Bugay AN, Parkhomenko AY. Application of Morse potential in nonlinear dynamics of microtubules. in Nonlinear Dynamics. 2017;90(4):2841-2849.
doi:10.1007/s11071-017-3845-y .

Zdravković, Slobodan, Bugay, Aleksandr N., Parkhomenko, Aleksandr Yu., "Application of Morse potential in nonlinear dynamics of microtubules" in Nonlinear Dynamics, 90, no. 4 (2017):2841-2849,
https://doi.org/10.1007/s11071-017-3845-y . .

TY  - JOUR
AU  - Sekulić, Dalibor L.
AU  - Satarić, Bogdan M.
AU  - Zdravković, Slobodan
AU  - Bugay, Aleksandr N.
AU  - Satarić, Miljko V.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1225
AB  - The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process. Published by AIP Publishing.
T2  - Chaos
T1  - Nonlinear dynamics of C-terminal tails in cellular microtubules
VL  - 26
IS  - 7
DO  - 10.1063/1.4959802
ER  - 

@article{
author = "Sekulić, Dalibor L. and Satarić, Bogdan M. and Zdravković, Slobodan and Bugay, Aleksandr N. and Satarić, Miljko V.",
year = "2016",
abstract = "The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process. Published by AIP Publishing.",
journal = "Chaos",
title = "Nonlinear dynamics of C-terminal tails in cellular microtubules",
volume = "26",
number = "7",
doi = "10.1063/1.4959802"
}

Sekulić, D. L., Satarić, B. M., Zdravković, S., Bugay, A. N.,& Satarić, M. V.. (2016). Nonlinear dynamics of C-terminal tails in cellular microtubules. in Chaos, 26(7).
https://doi.org/10.1063/1.4959802

Sekulić DL, Satarić BM, Zdravković S, Bugay AN, Satarić MV. Nonlinear dynamics of C-terminal tails in cellular microtubules. in Chaos. 2016;26(7).
doi:10.1063/1.4959802 .

Sekulić, Dalibor L., Satarić, Bogdan M., Zdravković, Slobodan, Bugay, Aleksandr N., Satarić, Miljko V., "Nonlinear dynamics of C-terminal tails in cellular microtubules" in Chaos, 26, no. 7 (2016),
https://doi.org/10.1063/1.4959802 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Zeković, Slobodan
AU  - Bugay, Aleksandr N.
AU  - Satarić, Miljko V.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1056
AB  - We here study nonlinear dynamics of microtubule (MT). A so-called u - model is explained in detail. A single longitudinal degree of freedom per MT subunits is assumed. It is known that a continuum approximation of a basic discrete dynamical equation of motion enables existence of kink and antikink solitons along MT. In this paper we use semi- discrete approximation for this equation and show that modulated solitonic waves could propagate as well. We suggest possible biological implications of these waves. Also, a detailed parameter analysis is performed. (C) 2016 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Localized modulated waves and longitudinal model of microtubules
VL  - 285
SP  - 248
EP  - 259
DO  - 10.1016/j.amc.2016.03.019
ER  - 

@article{
author = "Zdravković, Slobodan and Zeković, Slobodan and Bugay, Aleksandr N. and Satarić, Miljko V.",
year = "2016",
abstract = "We here study nonlinear dynamics of microtubule (MT). A so-called u - model is explained in detail. A single longitudinal degree of freedom per MT subunits is assumed. It is known that a continuum approximation of a basic discrete dynamical equation of motion enables existence of kink and antikink solitons along MT. In this paper we use semi- discrete approximation for this equation and show that modulated solitonic waves could propagate as well. We suggest possible biological implications of these waves. Also, a detailed parameter analysis is performed. (C) 2016 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Localized modulated waves and longitudinal model of microtubules",
volume = "285",
pages = "248-259",
doi = "10.1016/j.amc.2016.03.019"
}

Zdravković, S., Zeković, S., Bugay, A. N.,& Satarić, M. V.. (2016). Localized modulated waves and longitudinal model of microtubules. in Applied Mathematics and Computation, 285, 248-259.
https://doi.org/10.1016/j.amc.2016.03.019

Zdravković S, Zeković S, Bugay AN, Satarić MV. Localized modulated waves and longitudinal model of microtubules. in Applied Mathematics and Computation. 2016;285:248-259.
doi:10.1016/j.amc.2016.03.019 .

Zdravković, Slobodan, Zeković, Slobodan, Bugay, Aleksandr N., Satarić, Miljko V., "Localized modulated waves and longitudinal model of microtubules" in Applied Mathematics and Computation, 285 (2016):248-259,
https://doi.org/10.1016/j.amc.2016.03.019 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Bugay, Aleksandr N.
AU  - Aru, Guzel F.
AU  - Maluckov, Aleksandra
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6066
AB  - In the present paper, we study nonlinear dynamics of microtubules (MTs). As an analytical method, we use semi-discrete approximation and show that localized modulated solitonic waves move along MT. This is supported by numerical analysis. Both cases with and without viscosity effects are studied. (C) 2014 AIP Publishing LLC.
T2  - Chaos
T1  - Localized modulated waves in microtubules
VL  - 24
IS  - 2
DO  - 10.1063/1.4885777
ER  - 

@article{
author = "Zdravković, Slobodan and Bugay, Aleksandr N. and Aru, Guzel F. and Maluckov, Aleksandra",
year = "2014",
abstract = "In the present paper, we study nonlinear dynamics of microtubules (MTs). As an analytical method, we use semi-discrete approximation and show that localized modulated solitonic waves move along MT. This is supported by numerical analysis. Both cases with and without viscosity effects are studied. (C) 2014 AIP Publishing LLC.",
journal = "Chaos",
title = "Localized modulated waves in microtubules",
volume = "24",
number = "2",
doi = "10.1063/1.4885777"
}

Zdravković, S., Bugay, A. N., Aru, G. F.,& Maluckov, A.. (2014). Localized modulated waves in microtubules. in Chaos, 24(2).
https://doi.org/10.1063/1.4885777

Zdravković S, Bugay AN, Aru GF, Maluckov A. Localized modulated waves in microtubules. in Chaos. 2014;24(2).
doi:10.1063/1.4885777 .

Zdravković, Slobodan, Bugay, Aleksandr N., Aru, Guzel F., Maluckov, Aleksandra, "Localized modulated waves in microtubules" in Chaos, 24, no. 2 (2014),
https://doi.org/10.1063/1.4885777 . .