TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Nemeš, Tomas
AU  - Zdravković, Slobodan
PY  - 2023
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/11445
AB  - Calcium is one of the most versatile messengers for intracellular signaling. In the case of cilia and flagella calcium has the central role in transfer of communications between extracellular stimuli and intracellular formation of frequency modulated signal and their deciphering by target proteins. In this paper, the diffusion of fluorescently or otherwise tagged and un-tagged Ca2＋ particles is analyzed by solving the system of pertaining reaction–diffusion equations. We used Fourier transform tools to get asymptotic eigenfunctions for tagged (un-tagged) free and buffered Ca2＋ ions. We made some numerical estimations for diffusion coefficients corroborating the fact that messages diffuse faster than Ca2＋ messengers. From the best of our knowledge, this is the first time that Ca2＋ signaling in living cells is biophysically elaborated within the framework of model presented here. We suggest the experimental assay on the basis of radioactive Ca2＋ as tagged probe.
T2  - Biosystems
T1  - Calcium messages in flagella are faster than messenger particles
VL  - 232
SP  - 105003
DO  - 10.1016/j.biosystems.2023.105003
ER  - 

@article{
author = "Satarić, Miljko V. and Nemeš, Tomas and Zdravković, Slobodan",
year = "2023",
abstract = "Calcium is one of the most versatile messengers for intracellular signaling. In the case of cilia and flagella calcium has the central role in transfer of communications between extracellular stimuli and intracellular formation of frequency modulated signal and their deciphering by target proteins. In this paper, the diffusion of fluorescently or otherwise tagged and un-tagged Ca2＋ particles is analyzed by solving the system of pertaining reaction–diffusion equations. We used Fourier transform tools to get asymptotic eigenfunctions for tagged (un-tagged) free and buffered Ca2＋ ions. We made some numerical estimations for diffusion coefficients corroborating the fact that messages diffuse faster than Ca2＋ messengers. From the best of our knowledge, this is the first time that Ca2＋ signaling in living cells is biophysically elaborated within the framework of model presented here. We suggest the experimental assay on the basis of radioactive Ca2＋ as tagged probe.",
journal = "Biosystems",
title = "Calcium messages in flagella are faster than messenger particles",
volume = "232",
pages = "105003",
doi = "10.1016/j.biosystems.2023.105003"
}

Satarić, M. V., Nemeš, T.,& Zdravković, S.. (2023). Calcium messages in flagella are faster than messenger particles. in Biosystems, 232, 105003.
https://doi.org/10.1016/j.biosystems.2023.105003

Satarić MV, Nemeš T, Zdravković S. Calcium messages in flagella are faster than messenger particles. in Biosystems. 2023;232:105003.
doi:10.1016/j.biosystems.2023.105003 .

Satarić, Miljko V., Nemeš, Tomas, Zdravković, Slobodan, "Calcium messages in flagella are faster than messenger particles" in Biosystems, 232 (2023):105003,
https://doi.org/10.1016/j.biosystems.2023.105003 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Nemeš, Tomas
AU  - Satarić, Bogdan
AU  - Sekulić, Dalibor
AU  - Zdravković, Slobodan
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9059
AB  - The cytoskeleton of cilia and flagella is so called axoneme a stable cylindrical architecture of nine microtubule doublets. Axoneme performs periodic bending motion by utilizing specific dynein motor family powered by ATP hydrolysis. It is still unclear how this highly organized “ciliary beat” is being initiated and strongly coordinated by the combined action of hundreds dynein motors. Based on the experimental evidences we here elaborate a plausible scenario in which actually calcium ions play the roles of catalytic activators and coordinators of dynein attachments doing it in superposition with already known mechanical control tools of “ciliary beat”. Polyelectrolyte properties of microtubules incorporated in axoneme doublets enable the formation and propagation of soliton-like “ionic clouds” of Ca2+ ions along these “coaxial nanocables”. The sliding speed of such Ca2+ “clouds” along microtubule doublets is comparable with the speed of propagation of “ciliary beat” itself. We elaborated the interplay between influx of Ca2+ ions in ciliary based body and the sliding of microtubule triplets therein. In second segment we considered how the dynein motors activated by Ca2+ ions contained within solitonic “ionic clouds” in competition with axoneme curvature regulate ciliary and flagellar beating.
T2  - Biosystems
T1  - Calcium ions tune the beats of cilia and flagella
VL  - 196
SP  - 104172
DO  - 10.1016/j.biosystems.2020.104172
ER  - 

@article{
author = "Satarić, Miljko V. and Nemeš, Tomas and Satarić, Bogdan and Sekulić, Dalibor and Zdravković, Slobodan",
year = "2020",
abstract = "The cytoskeleton of cilia and flagella is so called axoneme a stable cylindrical architecture of nine microtubule doublets. Axoneme performs periodic bending motion by utilizing specific dynein motor family powered by ATP hydrolysis. It is still unclear how this highly organized “ciliary beat” is being initiated and strongly coordinated by the combined action of hundreds dynein motors. Based on the experimental evidences we here elaborate a plausible scenario in which actually calcium ions play the roles of catalytic activators and coordinators of dynein attachments doing it in superposition with already known mechanical control tools of “ciliary beat”. Polyelectrolyte properties of microtubules incorporated in axoneme doublets enable the formation and propagation of soliton-like “ionic clouds” of Ca2+ ions along these “coaxial nanocables”. The sliding speed of such Ca2+ “clouds” along microtubule doublets is comparable with the speed of propagation of “ciliary beat” itself. We elaborated the interplay between influx of Ca2+ ions in ciliary based body and the sliding of microtubule triplets therein. In second segment we considered how the dynein motors activated by Ca2+ ions contained within solitonic “ionic clouds” in competition with axoneme curvature regulate ciliary and flagellar beating.",
journal = "Biosystems",
title = "Calcium ions tune the beats of cilia and flagella",
volume = "196",
pages = "104172",
doi = "10.1016/j.biosystems.2020.104172"
}

Satarić, M. V., Nemeš, T., Satarić, B., Sekulić, D.,& Zdravković, S.. (2020). Calcium ions tune the beats of cilia and flagella. in Biosystems, 196, 104172.
https://doi.org/10.1016/j.biosystems.2020.104172

Satarić MV, Nemeš T, Satarić B, Sekulić D, Zdravković S. Calcium ions tune the beats of cilia and flagella. in Biosystems. 2020;196:104172.
doi:10.1016/j.biosystems.2020.104172 .

Satarić, Miljko V., Nemeš, Tomas, Satarić, Bogdan, Sekulić, Dalibor, Zdravković, Slobodan, "Calcium ions tune the beats of cilia and flagella" in Biosystems, 196 (2020):104172,
https://doi.org/10.1016/j.biosystems.2020.104172 . .

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  - Satarić, Miljko V.
AU  - Sivčević, Vladimir
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7652
AB  - In the present work, we deal with nonlinear dynamics of microtubules. A new model, describing nonlinear dynamics of microtubules, is introduced. Its advantages over two existing models are demonstrated. We show that dynamics of microtubules can be explained in terms of kink solitons. Also, circumstances yielding to either subsonic or supersonic solitons are discussed.
T2  - Nonlinear Dynamics
T1  - General model of microtubules
VL  - 92
IS  - 2
SP  - 479
EP  - 486
DO  - 10.1007/s11071-018-4069-5
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Sivčević, Vladimir",
year = "2018",
abstract = "In the present work, we deal with nonlinear dynamics of microtubules. A new model, describing nonlinear dynamics of microtubules, is introduced. Its advantages over two existing models are demonstrated. We show that dynamics of microtubules can be explained in terms of kink solitons. Also, circumstances yielding to either subsonic or supersonic solitons are discussed.",
journal = "Nonlinear Dynamics",
title = "General model of microtubules",
volume = "92",
number = "2",
pages = "479-486",
doi = "10.1007/s11071-018-4069-5"
}

Zdravković, S., Satarić, M. V.,& Sivčević, V.. (2018). General model of microtubules. in Nonlinear Dynamics, 92(2), 479-486.
https://doi.org/10.1007/s11071-018-4069-5

Zdravković S, Satarić MV, Sivčević V. General model of microtubules. in Nonlinear Dynamics. 2018;92(2):479-486.
doi:10.1007/s11071-018-4069-5 .

Zdravković, Slobodan, Satarić, Miljko V., Sivčević, Vladimir, "General model of microtubules" in Nonlinear Dynamics, 92, no. 2 (2018):479-486,
https://doi.org/10.1007/s11071-018-4069-5 . .

TY  - JOUR
AU  - Tuszynski, Jack A.
AU  - Satarić, Miljko V.
AU  - Sekulić, Dalibor L.
AU  - Satarić, Bogdan M.
AU  - Zdravković, Slobodan
PY  - 2018
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8397
AB  - Calcium ions (Ca2+) tune and control numerous diverse aspects of cochlear and vestibular physiological processes. This paper is focused on the Ca2+ control of mechanotransduction in sensory hair cells in the context of polyelectrolyte properties of actin filaments within the hair–bundles of inner ear. These actin filaments appear to serve as efficient pathways for the flow of Ca2+ ions inside stereocilia. We showed how this can be utilized for tuning of force–generating myosin motors. In an established model, we unified the Ca2+ nonlinear dynamics involved in the control of myosin adaptation motors with mechanical displacements of hair–bundles. The model shows that the characteristic time scales fit reasonably well with the available experimental data for spontaneous oscillations in the inner ear. This scenario promises to fill a gap in our understanding of the role of Ca2+ ions in the regulation of processes in the auditory cells of the inner ear. © 2018 Elsevier B.V.
T2  - Biosystems
T1  - Nonlinear calcium ion waves along actin filaments control active hair–bundle motility
VL  - 173
SP  - 181
EP  - 190
DO  - 10.1016/j.biosystems.2018.08.006
ER  - 

@article{
author = "Tuszynski, Jack A. and Satarić, Miljko V. and Sekulić, Dalibor L. and Satarić, Bogdan M. and Zdravković, Slobodan",
year = "2018",
abstract = "Calcium ions (Ca2+) tune and control numerous diverse aspects of cochlear and vestibular physiological processes. This paper is focused on the Ca2+ control of mechanotransduction in sensory hair cells in the context of polyelectrolyte properties of actin filaments within the hair–bundles of inner ear. These actin filaments appear to serve as efficient pathways for the flow of Ca2+ ions inside stereocilia. We showed how this can be utilized for tuning of force–generating myosin motors. In an established model, we unified the Ca2+ nonlinear dynamics involved in the control of myosin adaptation motors with mechanical displacements of hair–bundles. The model shows that the characteristic time scales fit reasonably well with the available experimental data for spontaneous oscillations in the inner ear. This scenario promises to fill a gap in our understanding of the role of Ca2+ ions in the regulation of processes in the auditory cells of the inner ear. © 2018 Elsevier B.V.",
journal = "Biosystems",
title = "Nonlinear calcium ion waves along actin filaments control active hair–bundle motility",
volume = "173",
pages = "181-190",
doi = "10.1016/j.biosystems.2018.08.006"
}

Tuszynski, J. A., Satarić, M. V., Sekulić, D. L., Satarić, B. M.,& Zdravković, S.. (2018). Nonlinear calcium ion waves along actin filaments control active hair–bundle motility. in Biosystems, 173, 181-190.
https://doi.org/10.1016/j.biosystems.2018.08.006

Tuszynski JA, Satarić MV, Sekulić DL, Satarić BM, Zdravković S. Nonlinear calcium ion waves along actin filaments control active hair–bundle motility. in Biosystems. 2018;173:181-190.
doi:10.1016/j.biosystems.2018.08.006 .

Tuszynski, Jack A., Satarić, Miljko V., Sekulić, Dalibor L., Satarić, Bogdan M., Zdravković, Slobodan, "Nonlinear calcium ion waves along actin filaments control active hair–bundle motility" in Biosystems, 173 (2018):181-190,
https://doi.org/10.1016/j.biosystems.2018.08.006 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Sekulić, Dalibor L.
AU  - Zdravković, Slobodan
AU  - Ralević, Nebojša M.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1560
AB  - It appears that so called post translational modifications of tubulin heterodimers are mostly focussed at positions of amino acid sequences of carboxy terminal tails. These changes have very profound effects on microtubule functions especially in connection with cellular traffic in terms of motor proteins. In this study, we elaborated the biophysical model aimed to explain the strategy governing these subtle interplays between structural and functional properties of microtubules. We relied onto Langevin equations including fluctuation dissipation processes. In that context we found out that small interaction between a charged motor neck domain and oppositely charged carboxy terminal tail of the a tubulin plays the decisive role in tuning kinesin-1 motor processivity along microtubules.
T2  - Journal of Theoretical Biology
T1  - A biophysical model of how alpha-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule
VL  - 420
SP  - 152
EP  - 157
DO  - 10.1016/j.jtbi.2017.03.012
ER  - 

@article{
author = "Satarić, Miljko V. and Sekulić, Dalibor L. and Zdravković, Slobodan and Ralević, Nebojša M.",
year = "2017",
abstract = "It appears that so called post translational modifications of tubulin heterodimers are mostly focussed at positions of amino acid sequences of carboxy terminal tails. These changes have very profound effects on microtubule functions especially in connection with cellular traffic in terms of motor proteins. In this study, we elaborated the biophysical model aimed to explain the strategy governing these subtle interplays between structural and functional properties of microtubules. We relied onto Langevin equations including fluctuation dissipation processes. In that context we found out that small interaction between a charged motor neck domain and oppositely charged carboxy terminal tail of the a tubulin plays the decisive role in tuning kinesin-1 motor processivity along microtubules.",
journal = "Journal of Theoretical Biology",
title = "A biophysical model of how alpha-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule",
volume = "420",
pages = "152-157",
doi = "10.1016/j.jtbi.2017.03.012"
}

Satarić, M. V., Sekulić, D. L., Zdravković, S.,& Ralević, N. M.. (2017). A biophysical model of how alpha-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule. in Journal of Theoretical Biology, 420, 152-157.
https://doi.org/10.1016/j.jtbi.2017.03.012

Satarić MV, Sekulić DL, Zdravković S, Ralević NM. A biophysical model of how alpha-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule. in Journal of Theoretical Biology. 2017;420:152-157.
doi:10.1016/j.jtbi.2017.03.012 .

Satarić, Miljko V., Sekulić, Dalibor L., Zdravković, Slobodan, Ralević, Nebojša M., "A biophysical model of how alpha-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule" in Journal of Theoretical Biology, 420 (2017):152-157,
https://doi.org/10.1016/j.jtbi.2017.03.012 . .

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  - Satarić, Miljko V.
AU  - Sekulić, Dalibor L.
AU  - Satarić, Bogdan M.
AU  - Zdravković, Slobodan
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/782
AB  - This paper aims to provide an overview of the polyelectrolyte model and the current understanding of the creation and propagation of localized pulses of positive ions flowing along cellular microtubules. In that context, Ca2+ ions may move freely on the surface of microtubule along the protofilament axis, thus leading to signal transport. Special emphasis in this paper is placed on the possible role of this mechanism in the function of microtubule based kinocilium, a component of vestibular hair cells of the inner ear. We discuss how localized pulses of Ca2+ ions play a crucial role in tuning the activity of dynein motors, which are involved in mechano sensitivity of the kinocilium. A prevailing notion holds that the concentration of Ca2+ ions around the microtubules within the kinocilium represents the control parameter for Hopf bifurcation. Therefore, a key feature of this mechanism is that the velocities of these Ca2+ pulses be sufficiently high to exert control at acoustic frequencies. (C) 2015 Elsevier Ltd. All rights reserved.
T2  - Progress in Biophysics and Molecular Biology
T1  - Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells
VL  - 119
IS  - 2
SP  - 162
EP  - 174
DO  - 10.1016/j.pbiomolbio.2015.07.009
ER  - 

@article{
author = "Satarić, Miljko V. and Sekulić, Dalibor L. and Satarić, Bogdan M. and Zdravković, Slobodan",
year = "2015",
abstract = "This paper aims to provide an overview of the polyelectrolyte model and the current understanding of the creation and propagation of localized pulses of positive ions flowing along cellular microtubules. In that context, Ca2+ ions may move freely on the surface of microtubule along the protofilament axis, thus leading to signal transport. Special emphasis in this paper is placed on the possible role of this mechanism in the function of microtubule based kinocilium, a component of vestibular hair cells of the inner ear. We discuss how localized pulses of Ca2+ ions play a crucial role in tuning the activity of dynein motors, which are involved in mechano sensitivity of the kinocilium. A prevailing notion holds that the concentration of Ca2+ ions around the microtubules within the kinocilium represents the control parameter for Hopf bifurcation. Therefore, a key feature of this mechanism is that the velocities of these Ca2+ pulses be sufficiently high to exert control at acoustic frequencies. (C) 2015 Elsevier Ltd. All rights reserved.",
journal = "Progress in Biophysics and Molecular Biology",
title = "Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells",
volume = "119",
number = "2",
pages = "162-174",
doi = "10.1016/j.pbiomolbio.2015.07.009"
}

Satarić, M. V., Sekulić, D. L., Satarić, B. M.,& Zdravković, S.. (2015). Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells. in Progress in Biophysics and Molecular Biology, 119(2), 162-174.
https://doi.org/10.1016/j.pbiomolbio.2015.07.009

Satarić MV, Sekulić DL, Satarić BM, Zdravković S. Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells. in Progress in Biophysics and Molecular Biology. 2015;119(2):162-174.
doi:10.1016/j.pbiomolbio.2015.07.009 .

Satarić, Miljko V., Sekulić, Dalibor L., Satarić, Bogdan M., Zdravković, Slobodan, "Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells" in Progress in Biophysics and Molecular Biology, 119, no. 2 (2015):162-174,
https://doi.org/10.1016/j.pbiomolbio.2015.07.009 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Maluckov, Aleksandra
AU  - Dekić, Mirjana
AU  - Kuzmanović, Slavica
AU  - Satarić, Miljko V.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/68
AB  - In this paper we study nonlinear dynamics of microtubules (MTs) relying on so-called u-model. A crucial discrete differential equation is transformed into a partial differential equation using a continuum approximation. Both the continuum and the discrete equations are solved and an excellent agreement of the results shows that MTs can be viewed as continuum systems. Thus we proved that the continuum approximation is applicable in research of nonlinear dynamics of MTs. (C) 2014 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Are microtubules discrete or continuum systems?
VL  - 242
SP  - 353
EP  - 360
DO  - 10.1016/j.amc.2014.05.068
ER  - 

@article{
author = "Zdravković, Slobodan and Maluckov, Aleksandra and Dekić, Mirjana and Kuzmanović, Slavica and Satarić, Miljko V.",
year = "2014",
abstract = "In this paper we study nonlinear dynamics of microtubules (MTs) relying on so-called u-model. A crucial discrete differential equation is transformed into a partial differential equation using a continuum approximation. Both the continuum and the discrete equations are solved and an excellent agreement of the results shows that MTs can be viewed as continuum systems. Thus we proved that the continuum approximation is applicable in research of nonlinear dynamics of MTs. (C) 2014 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Are microtubules discrete or continuum systems?",
volume = "242",
pages = "353-360",
doi = "10.1016/j.amc.2014.05.068"
}

Zdravković, S., Maluckov, A., Dekić, M., Kuzmanović, S.,& Satarić, M. V.. (2014). Are microtubules discrete or continuum systems?. in Applied Mathematics and Computation, 242, 353-360.
https://doi.org/10.1016/j.amc.2014.05.068

Zdravković S, Maluckov A, Dekić M, Kuzmanović S, Satarić MV. Are microtubules discrete or continuum systems?. in Applied Mathematics and Computation. 2014;242:353-360.
doi:10.1016/j.amc.2014.05.068 .

Zdravković, Slobodan, Maluckov, Aleksandra, Dekić, Mirjana, Kuzmanović, Slavica, Satarić, Miljko V., "Are microtubules discrete or continuum systems?" in Applied Mathematics and Computation, 242 (2014):353-360,
https://doi.org/10.1016/j.amc.2014.05.068 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Maluckov, Aleksandra
AU  - Balaz, A.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5998
AB  - We have established a new dynamical model of microtubules based on their intrinsic dipolar character. The model assumes a single angular degree of freedom per dimer describing the conformational displacements of constituent dimers in radial direction. A corresponding nonlinear dynamical equation of motion is solved both analytically, using the simplest equation method, and numerically. It is shown by both approaches that kink solitons could be elicited and sustained to propagate along the microtubule. We suggest that this model could explain some dynamical functional properties of microtubules, including the triggering of the onset of their depolymerization. (C) 2014 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - A nonlinear model of the dynamics of radial dislocations in microtubules
VL  - 237
SP  - 227
EP  - 237
DO  - 10.1016/j.amc.2014.03.113
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Maluckov, Aleksandra and Balaz, A.",
year = "2014",
abstract = "We have established a new dynamical model of microtubules based on their intrinsic dipolar character. The model assumes a single angular degree of freedom per dimer describing the conformational displacements of constituent dimers in radial direction. A corresponding nonlinear dynamical equation of motion is solved both analytically, using the simplest equation method, and numerically. It is shown by both approaches that kink solitons could be elicited and sustained to propagate along the microtubule. We suggest that this model could explain some dynamical functional properties of microtubules, including the triggering of the onset of their depolymerization. (C) 2014 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "A nonlinear model of the dynamics of radial dislocations in microtubules",
volume = "237",
pages = "227-237",
doi = "10.1016/j.amc.2014.03.113"
}

Zdravković, S., Satarić, M. V., Maluckov, A.,& Balaz, A.. (2014). A nonlinear model of the dynamics of radial dislocations in microtubules. in Applied Mathematics and Computation, 237, 227-237.
https://doi.org/10.1016/j.amc.2014.03.113

Zdravković S, Satarić MV, Maluckov A, Balaz A. A nonlinear model of the dynamics of radial dislocations in microtubules. in Applied Mathematics and Computation. 2014;237:227-237.
doi:10.1016/j.amc.2014.03.113 .

Zdravković, Slobodan, Satarić, Miljko V., Maluckov, Aleksandra, Balaz, A., "A nonlinear model of the dynamics of radial dislocations in microtubules" in Applied Mathematics and Computation, 237 (2014):227-237,
https://doi.org/10.1016/j.amc.2014.03.113 . .

TY  - JOUR
AU  - Kavitha, L.
AU  - Muniyappan, A.
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Marlewski, A.
AU  - Dhamayanthi, S.
AU  - Gopi, D.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/182
AB  - Among many types of proteinaceous filaments, microtubules (MTs) constitute the most rigid components of the cellular cytoskeleton. Microtubule dynamics is essential for many vital cellular processes such as intracellular transport, metabolism, and cell division. We investigate the nonlinear dynamics of inhomogeneous microtubulin systems and the MT dynamics is found to be governed by a perturbed sine-Gordon equation. In the presence of various competing nonlinear inhomogeneities, it is shown that this nonlinear model can lead to the existence of kink and antikink solitons moving along MTs. We demonstrate kink-antikink pair collision in the framework of Hirotas bilinearization method. We conjecture that the collisions of the quanta of energy propagating in the form of kinks and antikinks may offer a new view of the mechanism of the retrograde and anterograde transport direction regulation of motor proteins in microtubulin systems.
T2  - Chinese Physics B
T1  - Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes
VL  - 23
IS  - 9
DO  - 10.1088/1674-1056/23/9/098703
ER  - 

@article{
author = "Kavitha, L. and Muniyappan, A. and Zdravković, Slobodan and Satarić, Miljko V. and Marlewski, A. and Dhamayanthi, S. and Gopi, D.",
year = "2014",
abstract = "Among many types of proteinaceous filaments, microtubules (MTs) constitute the most rigid components of the cellular cytoskeleton. Microtubule dynamics is essential for many vital cellular processes such as intracellular transport, metabolism, and cell division. We investigate the nonlinear dynamics of inhomogeneous microtubulin systems and the MT dynamics is found to be governed by a perturbed sine-Gordon equation. In the presence of various competing nonlinear inhomogeneities, it is shown that this nonlinear model can lead to the existence of kink and antikink solitons moving along MTs. We demonstrate kink-antikink pair collision in the framework of Hirotas bilinearization method. We conjecture that the collisions of the quanta of energy propagating in the form of kinks and antikinks may offer a new view of the mechanism of the retrograde and anterograde transport direction regulation of motor proteins in microtubulin systems.",
journal = "Chinese Physics B",
title = "Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes",
volume = "23",
number = "9",
doi = "10.1088/1674-1056/23/9/098703"
}

Kavitha, L., Muniyappan, A., Zdravković, S., Satarić, M. V., Marlewski, A., Dhamayanthi, S.,& Gopi, D.. (2014). Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes. in Chinese Physics B, 23(9).
https://doi.org/10.1088/1674-1056/23/9/098703

Kavitha L, Muniyappan A, Zdravković S, Satarić MV, Marlewski A, Dhamayanthi S, Gopi D. Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes. in Chinese Physics B. 2014;23(9).
doi:10.1088/1674-1056/23/9/098703 .

Kavitha, L., Muniyappan, A., Zdravković, Slobodan, Satarić, Miljko V., Marlewski, A., Dhamayanthi, S., Gopi, D., "Propagation of kink-antikink pair along microtubules as a control mechanism for polymerization and depolymerization processes" in Chinese Physics B, 23, no. 9 (2014),
https://doi.org/10.1088/1674-1056/23/9/098703 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Zeković, Slobodan
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5528
AB  - In the present letter we describe a model of nonlinear dynamics of microtubules (MTs) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimers dynamics within MT, is solved both analytically and numerically. It is shown that such a nonlinear model can lead to the existence of kink solitons moving along the MTs. The internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled the estimation of the total energy, kink velocity and kink width. To simplify the calculation of the total energy we stated and proved a useful auxiliary theorem. Copyright (C) EPLA, 2013
T2  - Europhysics Letters / EPL
T1  - Nonlinear dynamics of microtubules -A longitudinal model
VL  - 102
IS  - 3
DO  - 10.1209/0295-5075/102/38002
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Zeković, Slobodan",
year = "2013",
abstract = "In the present letter we describe a model of nonlinear dynamics of microtubules (MTs) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimers dynamics within MT, is solved both analytically and numerically. It is shown that such a nonlinear model can lead to the existence of kink solitons moving along the MTs. The internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled the estimation of the total energy, kink velocity and kink width. To simplify the calculation of the total energy we stated and proved a useful auxiliary theorem. Copyright (C) EPLA, 2013",
journal = "Europhysics Letters / EPL",
title = "Nonlinear dynamics of microtubules -A longitudinal model",
volume = "102",
number = "3",
doi = "10.1209/0295-5075/102/38002"
}

Zdravković, S., Satarić, M. V.,& Zeković, S.. (2013). Nonlinear dynamics of microtubules -A longitudinal model. in Europhysics Letters / EPL, 102(3).
https://doi.org/10.1209/0295-5075/102/38002

Zdravković S, Satarić MV, Zeković S. Nonlinear dynamics of microtubules -A longitudinal model. in Europhysics Letters / EPL. 2013;102(3).
doi:10.1209/0295-5075/102/38002 .

Zdravković, Slobodan, Satarić, Miljko V., Zeković, Slobodan, "Nonlinear dynamics of microtubules -A longitudinal model" in Europhysics Letters / EPL, 102, no. 3 (2013),
https://doi.org/10.1209/0295-5075/102/38002 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Daniel, Muthiah
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5774
AB  - We study DNA dynamics relying on the plane-base rotator model for DNA. It is shown that this dynamics can be represented by kink and antikink solitons. We demonstrate that two velocities are relevant and these are the velocities of both a double and a single stranded DNA. A key question is which one is bigger as this is related to a value of the ratio of two parameters describing the hydrogen and the covalent interactions in DNA. If the velocity of double stranded DNA is larger than one of the single stranded chain then the two ferromagnetic strands are coupled antiferromagnetically. Otherwise, the two DNA strands are coupled ferromagnetically. We discuss possible experiments based on micromanipulation techniques that should be carried out to determine these velocities and the solitonic width.
T2  - International Journal of Modern Physics B
T1  - Kink Solitons in DNA
VL  - 27
IS  - 31
DO  - 10.1142/S0217979213501841
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Daniel, Muthiah",
year = "2013",
abstract = "We study DNA dynamics relying on the plane-base rotator model for DNA. It is shown that this dynamics can be represented by kink and antikink solitons. We demonstrate that two velocities are relevant and these are the velocities of both a double and a single stranded DNA. A key question is which one is bigger as this is related to a value of the ratio of two parameters describing the hydrogen and the covalent interactions in DNA. If the velocity of double stranded DNA is larger than one of the single stranded chain then the two ferromagnetic strands are coupled antiferromagnetically. Otherwise, the two DNA strands are coupled ferromagnetically. We discuss possible experiments based on micromanipulation techniques that should be carried out to determine these velocities and the solitonic width.",
journal = "International Journal of Modern Physics B",
title = "Kink Solitons in DNA",
volume = "27",
number = "31",
doi = "10.1142/S0217979213501841"
}

Zdravković, S., Satarić, M. V.,& Daniel, M.. (2013). Kink Solitons in DNA. in International Journal of Modern Physics B, 27(31).
https://doi.org/10.1142/S0217979213501841

Zdravković S, Satarić MV, Daniel M. Kink Solitons in DNA. in International Journal of Modern Physics B. 2013;27(31).
doi:10.1142/S0217979213501841 .

Zdravković, Slobodan, Satarić, Miljko V., Daniel, Muthiah, "Kink Solitons in DNA" in International Journal of Modern Physics B, 27, no. 31 (2013),
https://doi.org/10.1142/S0217979213501841 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
PY  - 2013
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5775
AB  - In the present paper we study the impact of dispersion and nonlinearity on DNA dynamics. We rely on the helicoidal Peyrard-Bishop model and use the fact that nonlinear DNA dynamics represents an interplay between nonlinearity and dispersion. We state that a dispersion coefficient P and a coefficient of nonlinearity Q, existing in nonlinear Schrodinger equation, are mutually dependent and show how function Q(P) and P(Q) can be obtained. Also, we show how all this can be used to find a possible interval for the parameter describing helicoidal structure of DNA. (C) 2013 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Nonlinear DNA dynamics: Nonlinearity versus dispersion
VL  - 225
SP  - 401
EP  - 406
DO  - 10.1016/j.amc.2013.09.064
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V.",
year = "2013",
abstract = "In the present paper we study the impact of dispersion and nonlinearity on DNA dynamics. We rely on the helicoidal Peyrard-Bishop model and use the fact that nonlinear DNA dynamics represents an interplay between nonlinearity and dispersion. We state that a dispersion coefficient P and a coefficient of nonlinearity Q, existing in nonlinear Schrodinger equation, are mutually dependent and show how function Q(P) and P(Q) can be obtained. Also, we show how all this can be used to find a possible interval for the parameter describing helicoidal structure of DNA. (C) 2013 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Nonlinear DNA dynamics: Nonlinearity versus dispersion",
volume = "225",
pages = "401-406",
doi = "10.1016/j.amc.2013.09.064"
}

Zdravković, S.,& Satarić, M. V.. (2013). Nonlinear DNA dynamics: Nonlinearity versus dispersion. in Applied Mathematics and Computation, 225, 401-406.
https://doi.org/10.1016/j.amc.2013.09.064

Zdravković S, Satarić MV. Nonlinear DNA dynamics: Nonlinearity versus dispersion. in Applied Mathematics and Computation. 2013;225:401-406.
doi:10.1016/j.amc.2013.09.064 .

Zdravković, Slobodan, Satarić, Miljko V., "Nonlinear DNA dynamics: Nonlinearity versus dispersion" in Applied Mathematics and Computation, 225 (2013):401-406,
https://doi.org/10.1016/j.amc.2013.09.064 . .

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 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
PY  - 2012
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/5033
AB  - We rely on the helicoidal Peyrard-Bishop model for DNA dynamics. Interaction between nucleotides at a same site belonging to different strands is modelled by a Morse potential energy. This potential depends on two parameters that are different for AT and CG pairs, which is a possible source for inhomogeneity. It was shown recently (ZdravkoviA double dagger and SatariA double dagger 2011) that certain values of these parameters bring about a negligible influence of inhomogeneity on the solitonic dynamics. We propose an experiment that should be carried out in order to determine the values of both of these parameters.
T2  - Journal of Biosciences
T1  - Morse potential in DNA molecule - An experiment proposal
VL  - 37
IS  - 4
SP  - 613
EP  - 616
DO  - 10.1007/s12038-012-9232-4
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V.",
year = "2012",
abstract = "We rely on the helicoidal Peyrard-Bishop model for DNA dynamics. Interaction between nucleotides at a same site belonging to different strands is modelled by a Morse potential energy. This potential depends on two parameters that are different for AT and CG pairs, which is a possible source for inhomogeneity. It was shown recently (ZdravkoviA double dagger and SatariA double dagger 2011) that certain values of these parameters bring about a negligible influence of inhomogeneity on the solitonic dynamics. We propose an experiment that should be carried out in order to determine the values of both of these parameters.",
journal = "Journal of Biosciences",
title = "Morse potential in DNA molecule - An experiment proposal",
volume = "37",
number = "4",
pages = "613-616",
doi = "10.1007/s12038-012-9232-4"
}

Zdravković, S.,& Satarić, M. V.. (2012). Morse potential in DNA molecule - An experiment proposal. in Journal of Biosciences, 37(4), 613-616.
https://doi.org/10.1007/s12038-012-9232-4

Zdravković S, Satarić MV. Morse potential in DNA molecule - An experiment proposal. in Journal of Biosciences. 2012;37(4):613-616.
doi:10.1007/s12038-012-9232-4 .

Zdravković, Slobodan, Satarić, Miljko V., "Morse potential in DNA molecule - An experiment proposal" in Journal of Biosciences, 37, no. 4 (2012):613-616,
https://doi.org/10.1007/s12038-012-9232-4 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Zdravković, Slobodan
AU  - Tuszynski, Jack A.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4628
AB  - Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into the coordinated mechanical movement of the entire motor protein. In this paper, we propose two combined nonlinear mechanisms for this particular functional activity and suggest the application of neutron scattering assays to experimentally determine the incoherent dynamic structure factor S(q, omega). We argue that this type of experiment is not only feasible but it could offer significant insights into the mechanism of MP function at a molecular level.
T2  - Chaos
T1  - Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering
VL  - 21
IS  - 4
DO  - 10.1063/1.3665091
ER  - 

@article{
author = "Satarić, Miljko V. and Zdravković, Slobodan and Tuszynski, Jack A.",
year = "2011",
abstract = "Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into the coordinated mechanical movement of the entire motor protein. In this paper, we propose two combined nonlinear mechanisms for this particular functional activity and suggest the application of neutron scattering assays to experimentally determine the incoherent dynamic structure factor S(q, omega). We argue that this type of experiment is not only feasible but it could offer significant insights into the mechanism of MP function at a molecular level.",
journal = "Chaos",
title = "Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering",
volume = "21",
number = "4",
doi = "10.1063/1.3665091"
}

Satarić, M. V., Zdravković, S.,& Tuszynski, J. A.. (2011). Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering. in Chaos, 21(4).
https://doi.org/10.1063/1.3665091

Satarić MV, Zdravković S, Tuszynski JA. Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering. in Chaos. 2011;21(4).
doi:10.1063/1.3665091 .

Satarić, Miljko V., Zdravković, Slobodan, Tuszynski, Jack A., "Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering" in Chaos, 21, no. 4 (2011),
https://doi.org/10.1063/1.3665091 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
PY  - 2011
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4417
AB  - Interaction between nucleotides at a same site belonging to different strands is studied. This interaction is modelled by a Morse potential which depends on two parameters. We study a relationship between the parameters characterizing AT and CG pairs. We show that certain circumstances, i.e. certain values of these parameters, bring about a negligible influence of inhomogeneity on the solitonic dynamics. (C) 2011 Elsevier Ireland Ltd. All rights reserved.
T2  - Biosystems
T1  - Transverse interaction in DNA molecule
VL  - 105
IS  - 1
SP  - 10
EP  - 13
DO  - 10.1016/j.biosystems.2011.02.005
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V.",
year = "2011",
abstract = "Interaction between nucleotides at a same site belonging to different strands is studied. This interaction is modelled by a Morse potential which depends on two parameters. We study a relationship between the parameters characterizing AT and CG pairs. We show that certain circumstances, i.e. certain values of these parameters, bring about a negligible influence of inhomogeneity on the solitonic dynamics. (C) 2011 Elsevier Ireland Ltd. All rights reserved.",
journal = "Biosystems",
title = "Transverse interaction in DNA molecule",
volume = "105",
number = "1",
pages = "10-13",
doi = "10.1016/j.biosystems.2011.02.005"
}

Zdravković, S.,& Satarić, M. V.. (2011). Transverse interaction in DNA molecule. in Biosystems, 105(1), 10-13.
https://doi.org/10.1016/j.biosystems.2011.02.005

Zdravković S, Satarić MV. Transverse interaction in DNA molecule. in Biosystems. 2011;105(1):10-13.
doi:10.1016/j.biosystems.2011.02.005 .

Zdravković, Slobodan, Satarić, Miljko V., "Transverse interaction in DNA molecule" in Biosystems, 105, no. 1 (2011):10-13,
https://doi.org/10.1016/j.biosystems.2011.02.005 . .

TY  - JOUR
AU  - Zdravković, Slobodan
AU  - Satarić, Miljko V.
AU  - Hadžievski, Ljupčo
PY  - 2010
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/4182
AB  - The impact of viscosity on DNA dynamics is studied both analytically and numerically. It is assumed that the viscosity exists at the segments where DNA molecule is surrounded by RNA polymerase. We demonstrate that the frictional forces destroy the modulation of the incoming solitonic wave. We show that viscosity, crucial for demodulation, is essential for DNA-RNA transcription. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3529360]
T2  - Chaos
T1  - DNA-RNA transcription as an impact of viscosity
VL  - 20
IS  - 4
DO  - 10.1063/1.3529360
ER  - 

@article{
author = "Zdravković, Slobodan and Satarić, Miljko V. and Hadžievski, Ljupčo",
year = "2010",
abstract = "The impact of viscosity on DNA dynamics is studied both analytically and numerically. It is assumed that the viscosity exists at the segments where DNA molecule is surrounded by RNA polymerase. We demonstrate that the frictional forces destroy the modulation of the incoming solitonic wave. We show that viscosity, crucial for demodulation, is essential for DNA-RNA transcription. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3529360]",
journal = "Chaos",
title = "DNA-RNA transcription as an impact of viscosity",
volume = "20",
number = "4",
doi = "10.1063/1.3529360"
}

Zdravković, S., Satarić, M. V.,& Hadžievski, L.. (2010). DNA-RNA transcription as an impact of viscosity. in Chaos, 20(4).
https://doi.org/10.1063/1.3529360

Zdravković S, Satarić MV, Hadžievski L. DNA-RNA transcription as an impact of viscosity. in Chaos. 2010;20(4).
doi:10.1063/1.3529360 .

Zdravković, Slobodan, Satarić, Miljko V., Hadžievski, Ljupčo, "DNA-RNA transcription as an impact of viscosity" in Chaos, 20, no. 4 (2010),
https://doi.org/10.1063/1.3529360 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Zeković, Slobodan
AU  - Tuszynski, Jack A.
AU  - Pokorny, J
PY  - 1998
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2207
AB  - We investigate the electronic degrees of freedom in cytoskeletal microtubules in the continuum approximation. The equations of motion of the propagating local conformational state are solved in the low temperature regime. The solution, which is a kink excitation, is coupled to the motion of the mobile electron of the constituent tubulin. We calculate the influence of kink excitations on the probability of the Mossbauer emission of gamma-active nuclei. A discussion follows on this potentially useful experimental tool for the detection of nonlinear excitations in a microtubule. [S1063-651X(98)14810-9].
T2  - Physical Review E
T1  - Mossbauer effect as a possible tool in detecting nonlinear excitations in microtubules
VL  - 58
IS  - 5
SP  - 6333
EP  - 6339
DO  - 10.1103/PhysRevE.58.6333
ER  - 

@article{
author = "Satarić, Miljko V. and Zeković, Slobodan and Tuszynski, Jack A. and Pokorny, J",
year = "1998",
abstract = "We investigate the electronic degrees of freedom in cytoskeletal microtubules in the continuum approximation. The equations of motion of the propagating local conformational state are solved in the low temperature regime. The solution, which is a kink excitation, is coupled to the motion of the mobile electron of the constituent tubulin. We calculate the influence of kink excitations on the probability of the Mossbauer emission of gamma-active nuclei. A discussion follows on this potentially useful experimental tool for the detection of nonlinear excitations in a microtubule. [S1063-651X(98)14810-9].",
journal = "Physical Review E",
title = "Mossbauer effect as a possible tool in detecting nonlinear excitations in microtubules",
volume = "58",
number = "5",
pages = "6333-6339",
doi = "10.1103/PhysRevE.58.6333"
}

Satarić, M. V., Zeković, S., Tuszynski, J. A.,& Pokorny, J.. (1998). Mossbauer effect as a possible tool in detecting nonlinear excitations in microtubules. in Physical Review E, 58(5), 6333-6339.
https://doi.org/10.1103/PhysRevE.58.6333

Satarić MV, Zeković S, Tuszynski JA, Pokorny J. Mossbauer effect as a possible tool in detecting nonlinear excitations in microtubules. in Physical Review E. 1998;58(5):6333-6339.
doi:10.1103/PhysRevE.58.6333 .

Satarić, Miljko V., Zeković, Slobodan, Tuszynski, Jack A., Pokorny, J, "Mossbauer effect as a possible tool in detecting nonlinear excitations in microtubules" in Physical Review E, 58, no. 5 (1998):6333-6339,
https://doi.org/10.1103/PhysRevE.58.6333 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Žakula, R. B.
AU  - Zeković, Slobodan
AU  - Pokorny, J
AU  - Fiala, J
PY  - 1996
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/2010
AB  - In this paper we investigate the change of microtubule cylinders length in the presence of endogenous AC fields generated by the cell itself. The dynamics of microtubule is described on the basis of classical u(4) model. The average stretching is calculated by using Kubos formalism for linear response of system.
T2  - Biosystems
T1  - The change of microtubule length caused by endogenous AC fields in cell
VL  - 39
IS  - 2
SP  - 127
EP  - 133
DO  - 10.1016/0303-2647(96)01610-3
ER  - 

@article{
author = "Satarić, Miljko V. and Žakula, R. B. and Zeković, Slobodan and Pokorny, J and Fiala, J",
year = "1996",
abstract = "In this paper we investigate the change of microtubule cylinders length in the presence of endogenous AC fields generated by the cell itself. The dynamics of microtubule is described on the basis of classical u(4) model. The average stretching is calculated by using Kubos formalism for linear response of system.",
journal = "Biosystems",
title = "The change of microtubule length caused by endogenous AC fields in cell",
volume = "39",
number = "2",
pages = "127-133",
doi = "10.1016/0303-2647(96)01610-3"
}

Satarić, M. V., Žakula, R. B., Zeković, S., Pokorny, J.,& Fiala, J.. (1996). The change of microtubule length caused by endogenous AC fields in cell. in Biosystems, 39(2), 127-133.
https://doi.org/10.1016/0303-2647(96)01610-3

Satarić MV, Žakula RB, Zeković S, Pokorny J, Fiala J. The change of microtubule length caused by endogenous AC fields in cell. in Biosystems. 1996;39(2):127-133.
doi:10.1016/0303-2647(96)01610-3 .

Satarić, Miljko V., Žakula, R. B., Zeković, Slobodan, Pokorny, J, Fiala, J, "The change of microtubule length caused by endogenous AC fields in cell" in Biosystems, 39, no. 2 (1996):127-133,
https://doi.org/10.1016/0303-2647(96)01610-3 . .

TY  - JOUR
AU  - Satarić, Miljko V.
AU  - Pokorny, J
AU  - Fiala, J
AU  - Žakula, R. B.
AU  - Zeković, Slobodan
PY  - 1996
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/7224
AB  - In this paper, we investigate the influence of endogenous d.c. and a.c. fields on the dynamics of microtubules in living cells. The dynamics of microtubules can be described by the adapted classical non-linear u(4) model convenient for systems with dipole-dipole interaction. It is demonstrated that, on the basis of this model, several properties of the dynamics of microtubules can be clarified.
T2  - Bioelectrochemistry and Bioenergetics
T1  - Microtubules in interactions with endogenous dc and ac fields in living cells
VL  - 41
IS  - 1
SP  - 53
EP  - 58
DO  - 10.1016/0302-4598(96)01928-9
ER  - 

@article{
author = "Satarić, Miljko V. and Pokorny, J and Fiala, J and Žakula, R. B. and Zeković, Slobodan",
year = "1996",
abstract = "In this paper, we investigate the influence of endogenous d.c. and a.c. fields on the dynamics of microtubules in living cells. The dynamics of microtubules can be described by the adapted classical non-linear u(4) model convenient for systems with dipole-dipole interaction. It is demonstrated that, on the basis of this model, several properties of the dynamics of microtubules can be clarified.",
journal = "Bioelectrochemistry and Bioenergetics",
title = "Microtubules in interactions with endogenous dc and ac fields in living cells",
volume = "41",
number = "1",
pages = "53-58",
doi = "10.1016/0302-4598(96)01928-9"
}

Satarić, M. V., Pokorny, J., Fiala, J., Žakula, R. B.,& Zeković, S.. (1996). Microtubules in interactions with endogenous dc and ac fields in living cells. in Bioelectrochemistry and Bioenergetics, 41(1), 53-58.
https://doi.org/10.1016/0302-4598(96)01928-9

Satarić MV, Pokorny J, Fiala J, Žakula RB, Zeković S. Microtubules in interactions with endogenous dc and ac fields in living cells. in Bioelectrochemistry and Bioenergetics. 1996;41(1):53-58.
doi:10.1016/0302-4598(96)01928-9 .

Satarić, Miljko V., Pokorny, J, Fiala, J, Žakula, R. B., Zeković, Slobodan, "Microtubules in interactions with endogenous dc and ac fields in living cells" in Bioelectrochemistry and Bioenergetics, 41, no. 1 (1996):53-58,
https://doi.org/10.1016/0302-4598(96)01928-9 . .