Mechanics of Microtubule Buckling Supported by Cytoplasm

The cytoskeleton provides the mechanical scaffold and maintains the integrity of cells. It is usually believed that one type of cytoskeleton biopolymer, microtubules, bears compressive force. In vitro experiments found that isolated microtubules may form an Euler buckling pattern with a long-wavelength for very small compressive force. This, however, does not agree with in vivo experiments where microtubules buckle with a short-wavelength. In order to understand the structural role of microtubules in vivo, we developed mechanics models that study microtubule buckling supported by cytoplasm. The microtubule is modeled as a linearly elastic cylindrical tube while the cytoplasm is characterized by different types of materials, namely, viscous, elastic, or viscoelastic. The dynamic evolution equations, the fastest growth rate, the critical wavelength, and compressive force, as well as equilibrium buckling configurations are obtained. The ability for a cell to sustain compressive force does not solely rely on microtubules but is also supported by the elasticity of cytoplasm. With the support of the cytoplasm, an individual microtubule can sustain a compressive force on the order of $100pN$⁠. The relatively stiff microtubules and compliant cytoplasm are combined to provide a scaffold for compressive force.