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.

Size-Dependent Free Vibration and Buckling of Three-Dimensional Graphene Foam Microshells Based on Modified Couple Stress Theory

In this research, the vibration and buckling of three-dimensional graphene foam (3D-GrF) microshells are investigated for the first time. In the microshells, three-dimensional graphene foams can distribute uniformly or non-uniformly through the thickness direction. Based on Love's thin shell theory and the modified couple stress theory (MCST), size-dependent governing equations and corresponding boundary conditions are established through Hamilton's principle. Then, vibration and axial buckling of 3D-GrF microshells are analyzed by employing the Navier method and Galerkin method. Results show that the graphene foam distribution type, size effect, the foam coefficient, the radius-to-thickness ratio, and the length-to-radius ratio play important roles in the mechanical characteristics of 3D-GrF microshells.

Optomechanical proposal for monitoring microtubule mechanical vibrations

Microtubules provide the mechanical force required for chromosome separation during mitosis. However, little is known about the dynamic (high-frequency) mechanical properties of microtubules. Here, we theoretically propose to control the vibrations of a doubly clamped microtubule by tip electrodes and to detect its motion via the optomechanical coupling between the vibrational modes of the microtubule and an optical cavity. In the presence of a red-detuned strong pump laser, this coupling leads to optomechanical-induced transparency of an optical probe field, which can be detected with state-of-the art technology. The center frequency and line width of the transparency peak give the resonance frequency and damping rate of the microtubule, respectively, while the height of the peak reveals information about the microtubule-cavity field coupling. Our method opens the new possibilities to gain information about the physical properties of microtubules, which will enhance our capability to design physical cancer treatment protocols as alternatives to chemotherapeutic drugs.