Fig. 5. MAP6 induces microtubule bending: The frustrated core-shell model.

(A) After GTP hydrolysis, the GDP-bound tubulin protofilaments can exist in two distinct states (a), with slightly differing elongations (see Supplementary Text): a long tubulin state (blue) and a short tubulin state (red). (b) The short state of the GDP-tubulin is energetically favored with respect to the long one. (B) For microtubules polymerized with tubulin alone, GTP-tubulin is incorporated into the lattice in its long state. After GTP hydrolysis, the short GDP-tubulin state is energetically dominant. The microtubule shortens but stays straight. To allow visualization of the lumen, only two protofilaments, one on each side of the microtubule, are shown. (C) For microtubules copolymerized with tubulin and MAP6 (a), MAP6 binds to the nonhydrolyzed, long GTP-tubulin state and forms an elastic network inside the microtubule, stabilizing the initial (long) state at the time point of binding. After hydrolysis, the GDP-tubulin tends to shorten but enters into conflict with the force exerted by the intraluminal MAP6 network to maintain the tubulin long state. The resulting frustration is minimized by a symmetry-breaking mechanism [i.e., compact tubulin dimers (red) on one side of the cylinder and elongated tubulin dimers (blue) on the opposite side], leading to a curved ground state and in which areas of high local stress form holes or apertures (not shown in the scheme; Fig. 4). The observed radius of curvature of the superhelix, about 2.5 μm, is theoretically realized for a length difference of about 0.6% between the short and long state of GDP-tubulin (see Supplementary Text for more details). (b) MAP6Δ4-35 mutant only binds outside the microtubule where it stabilizes the lattice without inducing microtubule curvature. Note that MAP6 also binds on the microtubule external surface (a). (D) Model validation: The table shows the agreements between data predicted from the model with those experimentally obtained.