Buckling and force propagation along intracellular microtubules

Motivated by recent experiments showing the compressive buckling of microtubules in cells, we study theoretically the mechanical response of and force propagation along elastic filaments embedded in a non-linear elastic medium. We find that embedded microtubules buckle when their compressive load exceeds a critical value fc, and that the resulting deformation is restricted to a penetration depth that depends on both the non-linear material properties of the surrounding cytoskeleton, as well as the direct coupling of the microtubule to the cytoskeleton. The deformation amplitude depends on the applied load f>fc as (f-fc)1/2. This work shows how the range of compressive force transmission by microtubules can be tens of microns and is governed by the mechanical coupling to the surrounding cytoskeleton.