Persistence Length of Microtubules Based on a Continuum Anisotropic Shell Model

Abstract

Division of Engineering, Box D, Brown University, Providence, RI 02912, USAMotivated by seemingly contradictory experimental observations on whether the persistence lengthof a microtubule depends on its contour length, here we employ a continuum anisotropic shellmodel to study the ”exural rigidity of ”exible tubular structures under externally applied loads. Themodel shows that there indeed exists a range of tube lengths in which the persistence lengthstrongly depends on the contour length. However, for suf“ciently long tubes, the persistence lengthapproaches a constant value which depends only on the material properties. These results providefeasible explanations for the seemingly contradictory experimental observations in the literature. Themodel further indicates that the persistence length of a slender tubular structure depends on not onlyits geometrical and material properties but also the frequency and spatial mode of applied loading.Closed form analytical solutions are derived for ”exible tubes with simply supported boundaries andmaterial symmetry about the tube axis, while a “nite element analysis based on anisotropic shelltheory and mean “eld Langevin dynamics are conducted to complement/generalize the analyticalresults. The predicted relation between the persistence length and contour length is quantitativelycompared with existing experimental measurements on protein microtubules in eukaryotic cells.