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

Abstract

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, $\mu$=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 $K_w\mathrm{ }$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

Keywords:

• Dynamic stability responses
• MAPs
• MAP tau protein
• curved cantilevered microtubule
• viscoelastic properties

Disclosure statement

No potential conflict of interest was reported by the author(s).