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 (