Microtubule Dynamics Depart from the Wormlike Chain Model

Thermal shape fluctuations of grafted microtubules were studied using high resolution particle tracking of attached fluorescent beads. First mode relaxation times were extracted from the mean square displacement in the transverse coordinate. For microtubules shorter than $\sim 10\mu \mathrm{m}$, the relaxation times were found to follow an $L^2$ dependence instead of $L^4$ as expected from the standard wormlike chain model. This length dependence is shown to result from a complex length dependence of the bending stiffness which can be understood as a result of the molecular architecture of microtubules. For microtubules shorter than $\sim 5\mu \mathrm{m}$, high drag coefficients indicate contributions from internal friction to the fluctuation dynamics.

Figure 1

Schematic of the assay. One end of the microtubule is covalently grafted on the gold substrate. Lengths are measured along the contour starting at the substrate, with $L$ denoting the free end and $L_{\mathrm{a}}\le L$ marking the position of the tracer bead. Different fluorescent labels for the microtubule and the bead allow for separate imaging of the two and prevent photobleaching.

Figure 2

Relaxation times extracted from MSD. Lines of slope 4 (solid line) and 2 (dashed line) are shown for comparison.

Figure 3

Persistence lengths obtained from the position variance. A plot of Eq. (5) using the parameters of $\lambda =21\mu \mathrm{m}$ and $l_{\mathrm{p}}^{\infty }=6300\mu \mathrm{m}$ obtained by Ref. 4 is shown for comparison (solid line). For short microtubules, the data deviate from the Timoshenko theory and level to a plateau (dashed line).

Figure 4

Drag coefficients $\zeta$ versus contour length $L$. For short microtubules, the experimental data lie significantly above the hydrodynamic estimate ${\zeta }_0$ of Eq. (2) (dashed line). The solid line shows a fit of Eq. (7) taking into account internal friction.