Abstract

Microtubules are a filamenteous protein found inside cells, where they are the stiffest cytoskeletal polymer with a persistence length of several millimetres. In axons, the thin projections of nerve cells which wire the brain, well-organised parallel bundles of microtubules function as structural backbones and highways for intracellular transport by motor proteins.
However, in areas of neurodegeneration, highly curved microtubules are found, with radius of curvature on the order of 1µm. Similarly curved microtubules are sometimes seen in gliding assays, where microtubules are moved by the motor protein kinesin, rotating in a stable circular orbit amongst other microtubules translocating as rigid rods.
Recent evidence suggests that some microtubule-associated proteins such as kinesin are able to sense and alter MT curvature, and so we model MTs moving on gliding assays as inextensible rods with a preferred curvature, which is controlled by the differential binding of the kinesin. We find that there exist parameter regimes wherein metastable rings can form, and hence offer this differential binding as an explanation for these highly curved microtubules seen in vitro and in vivo.