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.
Keywords: Time-dependent properties; dynamic stability; fourth-order Runge Kutta approach; modified strain gradient theory; tubulin–labeled microtubules.