Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano–sensitivity of hair cells

Satarić, M. V.; Sekulić, Dalibor L.; Satarić, Bogdan M.; Zdravković, Slobodan

doi:10.1016/j.pbiomolbio.2015.07.009

Cited by 9 publications

(2 citation statements)

References 59 publications

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“…[18] A new NLTL model has also been introduced to investigate the creation and propagation of localized pulses of positive ions flowing along cellular MTs. [19] Recently, Ndjomatchoua et al demonstrated that the electrical wave propagation in an MT could be modeled by a discrete NLTL including a cubic negative nonlinear resistance. [20] More recently, using an electrical model with strongly nonlinear resistive elements, Ghomsi et al studied the capability of the inner part of an MT.…”

Section: Introductionmentioning

confidence: 99%

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

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In this paper, the control of dissipation and amplification of solitary waves in an electrical model of microtubule is demonstrated. This model is consisted of a shunt nonlinear resistance-capacitance ($J(V)-C(V)$) circuit and a series resistance-inductance $(R-L$) circuit. Through the linear dispersion analysis, two characters of the network are found, that is low band pass and bandpass characters. The effects of the conductance's parameter $\lambda$ on the linear dispersion curve are also analyzed. It appears that the increase of $\lambda$ induces a decrease (an increase) of the width of the bandpass filter for positive (negative) values of $\lambda$. By applying the reductive perturbation method, we derive the equation governing the dynamics of the modulated waves in the system. This obtained equation is the well-known nonlinear Schrödinger equation extended by a linear term proportional to an hybrid parameter $\sigma$, i.e. dissipation or amplification coefficient. Based on this parameter, we successfully demonstrate the hybrid behavior (dissipation and amplification) of the system. The exact and approximate solitary wave solutions of the obtained equation are derived and the effects of the coefficient $\sigma$ on the characteristic parameters of these waves are investigated. Using the found analytical solutions, we show numerically that the waves that are propagated throughout the system can be dissipated, amplified, or remained stable depending on the network parameters. These results are not only in agreement with the analytical predictions, but also with the existing experimental results in the literature.

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Section: Introductionmentioning

confidence: 99%

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

et al. 2023

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“…The objective of this paper is to apply the latter method, namely the expp´Φpξqq-Expansion Method, to construct the exact solutions for the following two NPDEs modeling MT dynamics, [51][52][53][54][55][56][57][58][59]. In particular, in presenting the questions to be solved, for comparison purposes, we follow the initial set up established by Zayed and Alurrfi [56], solving the extended Riccatti equations (see Equations (1) and (2)).…”

Section: Introductionmentioning

confidence: 99%

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

Alam

Belgacem

2016

Mathematics

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Abstract:In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs) describing microtubules, by implementing the expp´Φpξqq-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the expp´Φpξqq-Expansion Method not disappointing in the least, is found and declared highly efficient.

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Nonlinear Dynamics of Microtubules

Zdravković

2022

Nonlinear Dynamics of Nanobiophysics

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Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano–sensitivity of hair cells

Cited by 9 publications

References 59 publications

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Dissipation and amplification management in an electrical model of microtubules: Hybrid behavior network

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

Nonlinear Dynamics of Microtubules

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