Free vibration analysis of microtubules based on the molecular mechanics and continuum beam theory

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Dynamic information of the time-dependent tobullian biomolecular structure using a high-accuracy size-dependent theory

As the most rigid cytoskeletal filaments, tubulin-labeled microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. The current structure is often under several environmental conditions as well as various dynamic or static loads that can decrease the stability of the viscoelastic tubulin-labeled microtubules. For this issue, the dynamic stability analysis of size-dependent viscoelastic tubulin-labeled microtubules using modified strain gradient theory by considering the exact three-length scale parameter. Viscoelastic properties are modeled using Kelvin-Voight model to study the time-dependent tubulin-labeled microtubules structure. By applying energy methods (known as Hamilton's principle), the motion equations of the tubulin-labeled microtubules are developed. The dynamic equations are based on first-order shear deformation theory (FSDT), and generalized differential quadrature and fourth-order Runge-Kutta methods are employed to find the model for the natural frequencies. The novelty of the current study is to consider the effects of viscoelastic properties, and exact values of size-dependent parameters on dynamic behaviors of the tubulin-labeled microtubules. Considering three-length scale parameters (l₀ = h, l₁ = h, l₂ = h) in this size-dependent theory leads to a better agreement with molecular dynamic (MD) simulation in comparison with other theories. The results show that when the rigidity of the edges is improved by changing the simply supported to clamped supported boundary conditions, the maximum deflection and stability of the living part would be damped much more quickly.Communicated by Ramaswamy H. Sarma.

Size-dependent dynamic stability analysis of the cantilevered curved microtubule-associated proteins (MAPs)

A pathway to the design of even more effective versions of the powerful anti-cancer drug Taxol is opened with the most detailed look ever at the dynamic and static behaviors of MAPs. Regarding this issue, the dynamic stability analysis of cantilevered microtubules in axons with attention to different size effect parameters based on the generalized differential quadrature method is presented. Supporting the effects of MAP Tau proteins and surrounding cytoplasm are considered as an elastic foundation. The better understanding modeled as a moderately thick curved cylindrical nanoshell. The real property of the living biological cells is presented as the Kelvin-Voight viscoelastic properties. Hamilton's principle is employed to establish the Clamped-Free boundary conditions and governing equations, which is finally solved by the Fourier-expansion based generalized differential quadrature method (FGDQM). Considering length scale and nonlocal parameters (l = 3h, μ=h/2) in nonlocal strain gradient theory (NSGT) leads to a better agreement with experimental results in comparison by other theories that in the results section is presented, in details. Based on presented semi-numerical results, for a specific value of the cantilevered microtubule length, the influence of the Kw parameter on the amplitude of MAPs is much more considerable, that should be attention to this value. Another important consequence is that when the property of the MAPs is not considered viscoelastic, the relation between axial load and frequency of the living structure is nonlinear but by considering the time-dependent viscoelastic property the relation could be linear.Communicated by Ramaswamy H. Sarma.

On the dynamics of a curved microtubule-associated proteins by considering viscoelastic properties of the living biological cells

Over the last few years, some novel researches in the field of medical science made a tendency to have therapy without any complications or side-effects of the disease with the aid of prognosis about the behaviors of the microtubules. Regarding this issue, the stability/instability analysis of curved microtubule-associated protein in axons with attention to different size effect parameters based on an exact continuum method is presented. The real property of the living biological cells is presented as the Kelvin-Voight viscoelastic properties. Considering length scale parameter (l/R = 0.2) in modified couple stress theory (MCST) leads to a better agreement with experimental results in comparison by other theories that in the results section is presented, in detail. Based on presented exact results, the effect of R1/R parameter on the relative frequency changes of the microtubules is hardly depended to the value of the external forced load that should be attention to this value. Another important consequence is that the influence of the microtubule curvature parameter on the relative frequency changes of the living substructure is hardly depended on the value of the time-dependent viscoelastic property, that researchers in the analysis of the microtubule should be attention to this important issue.Communicated by Ramaswamy H. Sarma.

Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory

Over the last few years, some novel researches in the field of medical science made a tendency to have a therapy without any complications or side-effects of the disease with the aid of prognosis about the behaviors of the substructure living biological cell. Regarding this issue, nonlinear frequency characteristics of substructure living biological cell in axons with attention to different size effect parameters based on generalized differential quadrature method is presented. Supporting the effects of surrounding cytoplasm and MAP Tau proteins are considered as nonlinear elastic foundation. The Substructure living biological cell are modeled as a moderately thick curved cylindrical nanoshell. The displacement- strain of nonlinearity via Von Karman nonlinear shell theory is obtained. Extended Hamilton's principle is used for obtaining nonlinear equations of the living biological cells and finally, GDQM and PA are presented to obtain large amplitude and nonlinear frequency information of the substructure living biological cell. Based on presented numerical results, increasing the nonlinear MAP tau protein parameter causes to improve the hardening behavior and increase the maximum amplitudes of resonant vibration of the microtubule. The crucial consequence is when the fixed boundary conditions in the microstructure switch to cantilevered, the living part of the cells could manage to have irrational feedback at the broad field of the excitation frequency. The current study has been made into the influences of the NSG parameters, geometrical and physical parameters on the instability of the curved microtubule employing continuum mechanics model.Communicated by Ramaswamy H. Sarma.

Electromechanical vibration of microtubules and its application in biosensors

An electric field (EF) has the potential to excite the vibration of polarized microtubules (MTs) and thus enable their use as a biosensor for the biophysical properties of MTs or cells. To facilitate the development, this paper aims to capture the EF-induced vibration modes and the associated frequency for MTs. The analyses were carried out based on a molecular structural mechanics model accounting for the structural details of MTs. Transverse vibration, radial breathing vibration and axial vibration were achieved for MTs subject to a transverse or an axial EF. The frequency shift and stiffness alteration of MTs were also examined due to the possible changes of the tubulin interactions in physiological or pathological processes. The strong correlation achieved between the tubulin interaction and MT vibration excited by EF provides a new avenue to a non-contacting technique for the structural or property changes in MTs, where frequency shift is used as a biomarker. This technique can be used for individual MTs and is possible for those in cells when the cytosol damping on MT vibrations is largely reduced by the unique features of MT-cytosol interface.

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene and hBN) and multiplanar (such as stanene and MoS₂) configurations. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently, a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for different classes of nanostructures (graphene, hBN, stanene and MoS₂) and nano-heterostructures (graphene-hBN, graphene-MoS₂, graphene-stanene and stanene-MoS₂), which are categorized on the basis of fundamental structural configurations. The numerical values of shear modulus are compared with the results from the scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of a wide range of nanostructures and nanoheterostructures.

Structure-property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

Effect of amino acid mutations on intra-dimer tubulin–tubulin binding strength of microtubules

Binding strength inside αβ-tubulin dimers of a microtubule (MT) with atomic resolutions are of importance in determining the structural stability of the MT as well as designing self-assembled functional structures from it. Through simulations, this study proposes a new strategy to tune the binding strength inside microtubules through point mutations of amino acids on the intra-dimer interface.