Are microtubules discrete or continuum systems?

Zdravković, Slobodan; Maluckov, Aleksandra; Dekić, Milovan; Kuzmanović, S.; Satarić, M. V.

doi:10.1016/j.amc.2014.05.068

Cited by 12 publications

(10 citation statements)

References 17 publications

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“…A key question in nonlinear biophysics is either an essentially discrete system can be considered as a continuum one. As for the MTs this question was answered recently [12]. Namely, the initial discrete equation 7was solved numerically and the result excellently matches the one shown here, based on the continuum approximation.…”

supporting

confidence: 70%

Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Djekic¹

2014

Kragujevac J Sci

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supporting

confidence: 70%

Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Djekic¹

2014

Kragujevac J Sci

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“…A key question in the studyng of the MT's dynamics is a possibility of use a continuum approximation. Recently has been shown [23] that for the non-linear model introduced in [2] the results obtained in the continuum approximation are in an excellent agreement with the results of the corresponding discrete model. The findings show that MT can be treated as the continuum system.…”

Section: A Continuum Approximationsupporting

confidence: 56%

“…To simplify the Lagrangian, we will make the following approximation (23). Taking into account that h 23 , |h 33 − h 22 | ≪ 1, we neglect by contributions of these terms and keep only terms with h 33 .…”

Section: A Continuum Approximationmentioning

confidence: 99%

Nonlinear dynamics of dipoles in microtubules: Pseudospin model

et al. 2016

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We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.

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“…A question if MTs are discrete or continuum systems was studied in Ref. [31], where it was shown that the continuum approximation is valid. The continuum approximation means a transition u n t ðÞ!ux ; t ðÞ , which allows a series expansion of the terms u nAE1 ,t h a ti s ,…”

Section: U-modelmentioning

confidence: 99%

“…(4) has already been solved using different mathematical procedures like standard procedure [23,27,29,30] and method of factorization [31,32]. There exists a group of procedures where the function Ψ is represented as a serious expansion over other known function like…”

Section: U-modelmentioning

confidence: 99%

Mechanical Models of Microtubules

Zdravković¹

2018

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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Microtubules are the major part of the cytoskeleton. They are involved in nuclear and cell division and serve as a network for motor proteins. The first model that describes nonlinear dynamics of microtubules was introduced in 1993. Three nonlinear models are described in this chapter. They are longitudinal U-model, representing an improved version of the first model, radial φ-model and new general model. Also, two mathematical procedures are explained. These are continuum and semi-discrete approximations. Continuum approximation yields to either kink-type or bell-type solitons, while semidiscrete one predicts localized modulated waves moving along microtubules. Some possible improvements and suggestions for future research are discussed.

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Are microtubules discrete or continuum systems?

Cited by 12 publications

References 17 publications

Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Employment of the method of factorization for solving problems in nonlinear dynamics of microtubules

Nonlinear dynamics of dipoles in microtubules: Pseudospin model

Mechanical Models of Microtubules

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