TY  - JOUR
AU  - Kavitha, L.
AU  - Parasuraman, E.
AU  - Muniyappan, A.
AU  - Gopi, D.
AU  - Zdravković, Slobodan
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1582
AB  - We made an attempt to provide a realistic picture of the localization of energy in microtubules (MTs), and we intend to model the nonlinear dynamics of MTs using the double-well form of the potential describing the dipole-dipole interactions. We investigate the modulational instability (MI) of the nonlinear plane wave solutions by considering both the wave vector (q) of the basic states and the wave vector (Q) of the perturbations as free parameters. A set of explicit criteria of MI is derived, and under the plane-wave perturbation, the constant amplitude solution becomes unstable and localized discrete breathers (DBs) solutions appear. We show numerically that MI is also an indicator of the presence of discrete breathers. We suggest that an electric field favourably leads the DB excitations towards the properly aligned end triggering a dissembly of the protofilament due to the energy release. These DBs could catalyse MT-associated proteins attachment/detachment and promote or inhibit the kinesin walk. We establish that the electromechanical vibrations in MTs can generate an electromagnetic field in the form of an electric pulse (breathers) which propagates along MT serving as signalling pathway in neuronal cells. The DBs in MT can be viewed as a bit of information whose propagation can be controlled by an electric filed. They might perform the role of elementary logic gates, thus implementing a subneuronal mode of computation. The generated DBs present us with novel possibilities for the direct interaction between the local electromagnetic field and the cytoskeletal structures in neurons. Thus, we emphasize that the effect of discreteness and electric field plays a significant role in MTs.
T2  - Nonlinear Dynamics
T1  - Localized discrete breather modes in neuronal microtubules
VL  - 88
IS  - 3
SP  - 2013
EP  - 2033
DO  - 10.1007/s11071-017-3359-7
ER  - 

@article{
author = "Kavitha, L. and Parasuraman, E. and Muniyappan, A. and Gopi, D. and Zdravković, Slobodan",
year = "2017",
abstract = "We made an attempt to provide a realistic picture of the localization of energy in microtubules (MTs), and we intend to model the nonlinear dynamics of MTs using the double-well form of the potential describing the dipole-dipole interactions. We investigate the modulational instability (MI) of the nonlinear plane wave solutions by considering both the wave vector (q) of the basic states and the wave vector (Q) of the perturbations as free parameters. A set of explicit criteria of MI is derived, and under the plane-wave perturbation, the constant amplitude solution becomes unstable and localized discrete breathers (DBs) solutions appear. We show numerically that MI is also an indicator of the presence of discrete breathers. We suggest that an electric field favourably leads the DB excitations towards the properly aligned end triggering a dissembly of the protofilament due to the energy release. These DBs could catalyse MT-associated proteins attachment/detachment and promote or inhibit the kinesin walk. We establish that the electromechanical vibrations in MTs can generate an electromagnetic field in the form of an electric pulse (breathers) which propagates along MT serving as signalling pathway in neuronal cells. The DBs in MT can be viewed as a bit of information whose propagation can be controlled by an electric filed. They might perform the role of elementary logic gates, thus implementing a subneuronal mode of computation. The generated DBs present us with novel possibilities for the direct interaction between the local electromagnetic field and the cytoskeletal structures in neurons. Thus, we emphasize that the effect of discreteness and electric field plays a significant role in MTs.",
journal = "Nonlinear Dynamics",
title = "Localized discrete breather modes in neuronal microtubules",
volume = "88",
number = "3",
pages = "2013-2033",
doi = "10.1007/s11071-017-3359-7"
}

Kavitha, L., Parasuraman, E., Muniyappan, A., Gopi, D.,& Zdravković, S.. (2017). Localized discrete breather modes in neuronal microtubules. in Nonlinear Dynamics, 88(3), 2013-2033.
https://doi.org/10.1007/s11071-017-3359-7

Kavitha L, Parasuraman E, Muniyappan A, Gopi D, Zdravković S. Localized discrete breather modes in neuronal microtubules. in Nonlinear Dynamics. 2017;88(3):2013-2033.
doi:10.1007/s11071-017-3359-7 .

Kavitha, L., Parasuraman, E., Muniyappan, A., Gopi, D., Zdravković, Slobodan, "Localized discrete breather modes in neuronal microtubules" in Nonlinear Dynamics, 88, no. 3 (2017):2013-2033,
https://doi.org/10.1007/s11071-017-3359-7 . .