Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory

Tounsi, Abdelouahed; Heireche, Houari; Benhassaini, Hachemi; Missouri, M.

doi:10.1016/j.jtbi.2010.06.037

Cited by 37 publications

(30 citation statements)

References 33 publications

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“…But as many reports conclude, the shear between heterodimers might be a key reason for the length dependence of bending rigidity [29,33,34,36]. It should be noticed that a MT features a highly anisotropic symmetry in its lattice.…”

Section: Twisting and Shear Modulusmentioning

confidence: 97%

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Mechanics of Microtubules from a Coarse-Grained Model

2011

BioNanoSci.

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We develop a coarse-grained model for the microtubule (MT) based on its α and β subunits and many-body interactions between them. Thermodynamic and mechanical properties of MTs are investigated using this model by performing molecular dynamics (MD) simulations, which is validated by reproducing basic mechanical properties of MTs in consistence with experiments. Based on simulations results, phenomena observed such as the length dependence of persistence length, mechanically induced disaggregation, and coupling between bending, shear, and twisting deformation are discussed. The simple model presented here lays the ground for further exploration of MTs mechanics and cellular energetics where MTs are involved.

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Section: Twisting and Shear Modulusmentioning

confidence: 97%

“…For long MTs, L p approaches a constant value [33]. Other continuum mechanics-based studies are further carried out by including a nonlocal anisotropic elastic shell model to calculate L p and predict the buckling behavior of MTs [34,35], or a high-order shear theory for the length dependence of D and Young's modulus Y [36].…”

Section: Introductionmentioning

confidence: 99%

Mechanics of Microtubules from a Coarse-Grained Model

2011

BioNanoSci.

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“…To reduce the general formulations given in (15)(16)(17) to a single governing equation in terms of a single unknown variable, we use the stream function ψ, where…”

Section: Dynamic Equations Of Cytosol Motionmentioning

confidence: 99%

“…After substituting the stream function ψ from (18) into (15)(16)(17), the following relation can be obtained,…”

Section: Dynamic Equations Of Cytosol Motionmentioning

confidence: 99%

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Coupled oscillations of a protein microtubule immersed in cytoplasm: an orthotropic elastic shell modeling

Daneshmand

Amabili

2012

J Biol Phys

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Revealing vibration characteristics of sub-cellular structural components such as membranes and microtubules has a principal role in obtaining a deeper understanding of their biological functions. Nevertheless, limitations and challenges in biological experiments at this scale necessitates the use of mathematical and computational models as an alternative solution. As one of the three major cytoskeletal filaments, microtubules are highly anisotropic structures built from tubulin heterodimers. They are hollow cylindrical shells with a ∼ 25 nm outer diameter and are tens of microns long. In this study, a mechanical model including the effects of the viscous cytosol and surrounding filaments is developed for predicting the coupled oscillations of a single microtubule immersed in cytoplasm. The first-order shear deformation shell theory for orthotropic materials is used to model the microtubule, whereas the motion of the cytosol is analyzed by considering the Stokes flow. The viscous cytosol and the microtubule are coupled through the continuity condition across the microtubule-cytosol interface. The stress and velocity fields in the cytosol induced by vibrating microtubule are analytically determined. Finally, the influences of the dynamic viscosity of the cytosol, filament network elasticity, microtubule shear modulus, and circumferential wave-number on longitudinal, radial, and torsional modes of microtubule vibration are elucidated.

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Multiscale FEM simulations of cross‐linked actin network embedded in cytosol with the focus on the filament orientation

Klinge

Aygün

Gilbert

et al. 2018

Numer Methods Biomed Eng

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The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill‐Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel‐Ogden β‐model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo‐Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

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Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory

Cited by 37 publications

References 33 publications

Mechanics of Microtubules from a Coarse-Grained Model

Mechanics of Microtubules from a Coarse-Grained Model

Coupled oscillations of a protein microtubule immersed in cytoplasm: an orthotropic elastic shell modeling

Multiscale FEM simulations of cross‐linked actin network embedded in cytosol with the focus on the filament orientation

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