Higher-Order Continuum Model and Mesh-Free Simulation for Microtubules Under Hydrostatic Presssure

The mechanical properties and structural transitions of microtubules under hydrostatic pressure are studied in the theoretical scheme of the higher-order gradient continuum. A microtubule is treated as a higher-order continuum cylindrical tube with a thin wall, and the higher-order constitutive relationship is derived by virtue of the higher-order Cauchy-Born rule. The representative cell is chosen as a triangle unit that contains two tublin monomers and one guanosine triphosphate or guanosine diphosphate molecule. The tublin, guanosine triphosphate and guanosine diphosphate molecule are modeled as rigid balls, and the appropriate potential functions are used to desribe the interactions between different rigid balls. The higher-order constitutive model that can display nonlinear bahavior of microtubules is established by minimizing the energy of a representative cell. Mesh-free method is employed to implement the numerical computation, and the developed numeircal method can achieve the global simulation of microtubules. The structural transition of microtubules under hydrostatic pressure is studied, and the obtained critical pressure is very close to the reported value in literature.