Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory

• Published in: Journal of theoretical biology 2017-06, Vol.422, p.59-71
• Main Authors: Sahmani, S., Aghdam, M.M.
• Format: Article
• Language: English
• Subjects: Animals; Cell nanomechanics; Cytoplasm; Cytoplasm - metabolism; Humans; Microtubules; Microtubules - metabolism; Models, Biological; Nonlocal strain gradient elasticity; Size effects; Tubulin - metabolism
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2017.04.012

•Development an orthotropic size-dependent shell model for microtubules in a lining cell.•Prediction the size effects on axial instability of microtubules embedded in cytoplasm in a more comprehensive way.•Incorporating the both nonlocality and strain gradient size dependency simultaneously. Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them.