Persistence Length of Microtubules Based on a Continuum Anisotropic Shell Model

Motivated by seemingly contradictory experimental observations on whether the persistence length of a microtubule depends on its contour length, here we employ a continuum anisotropic shell model to study the flexural rigidity of flexible tubular structures under externally applied loads. The model shows that there indeed exists a range of tube lengths in which the persistence length strongly depends on the contour length. However, for sufficiently long tubes, the persistence length approaches a constant value which depends only on the material properties. These results provide feasible explanations for the seemingly contradictory experimental observations in the literature. The model further indicates that the persistence length of a slender tubular structure depends on not only its geometrical and material properties but also the frequency and spatial mode of applied loading. Closed form analytical solutions are derived for flexible tubes with simply supported boundaries and material symmetry about the tube axis, while a finite element analysis based on anisotropic shell theory and mean field Langevin dynamics are conducted to complement/generalize the analytical results. The predicted relation between the persistence length and contour length is quantitatively compared with existing experimental measurements on protein microtubules in eukaryotic cells.