Measuring the number and spacing of molecular motors propelling a gliding microtubule

The molecular motor gliding assay, in which a microtubule or other filament moves across a surface coated with motors, has provided much insight into how molecular motors work. The kinesin-microtubule system is also a strong candidate for the job of nanoparticle transporter in nanotechnology devices. In most cases, several motors transport each filament. Each motor serves both to bind the microtubule to a stationary surface and to propel the microtubule along the surface. By applying a uniform transverse force of 4–19 pN to a superparamagnetic bead attached to the trailing end of the microtubule, we have measured the distance $d$ between binding points (motors). The average value of $d$ was determined as a function of motor surface density $\mathit{\sigma }$. The measurements agree well with the scaling model of Duke, Holy, and Liebler, which predicts that $\langle d\rangle ~{\mathit{\sigma }}^{-2/5}$ if $0.05⩽\mathit{\sigma }⩽20\hspace{0.5em}\mu {\mathrm{m}}^{-2}$ [Phys. Rev. Lett. 74, 330 (1995)]. The distribution of $d$ fits an extension of the model. The radius of curvature of a microtubule bent at a binding point by the force of the magnetic bead was ≈1 μm, 5000-fold smaller than the radius of curvature of microtubules subjected only to thermal forces. This is evidence that at these points of high bending stress, generated by the force on the magnetic bead, the microtubule is in the more flexible state of a two-state model of microtubule bending proposed by Heussinger, Schüller, and Frey [Phys. Rev. E 81, 021904 (2010)].

Figure 1

The three regimes of the DHL model. Although we have set the boundaries between the regimes at 1 and 4 μm, these actually depend on $\mathit{\sigma }$.

Figure 2

Image sequence during a gliding assay showing two anchor points and one detachment event. The microtubule was gliding to the right throughout the sequence. The magnetic field was off in frames 1–3. After frame 3, a 1.4-A current was applied to the magnet. The resultant magnetic field applied a 4-pN force to the magnetic bead [24]. The direction of the force on the magnetic bead is shown in frame 9. The first anchor point is visible in frame 9 and is marked with an arrow. Between frames 9 and 27, attached kinesin motors continue to pull the microtubule to the right. This pulls the attached bead upward toward the first binding point. During frame 29, the microtubule detaches from the first anchor point and begins to show the location of the second anchor point. The two arrows in frame 29 mark the locations of the first and second anchor points. The distance between the anchor points is $d$. The bead diameter, 2.8 μm, serves as an internal length scale in all frames. The images in this figure are part of Popoff_movie_1.avi, which can be seen on EPAPS [31].

Figure 3

(a) Overlay of five frames from Fig. 2 to show the distance $d$ between two anchor points. (b) Schematic of frames 1, 9, 27, and 31. The position of the leading end of the microtubule is marked by the frame number in the upper right side of the diagram.

Figure 4

The average distance between anchor points plotted against ${\mathit{\sigma }}_{\mathrm{nom}}$. Also shown are best-fit curves for $\langle d\rangle ~{\mathit{\sigma }}^{-1}$ and $\langle d\rangle ~{\mathit{\sigma }}^{-2/5}$, corresponding to regimes (i) and (ii).

Figure 5

Measured and modeled distributions of the distance d. The experimental data are shown as normalized histogram frequencies $f$ for a bin width of 0.5 μm. The curves (red online) show the normalized probability distribution $R$ calculated by our extension of the DHL model [Eq. (9)]. The number of experimental observations in the histograms was 33, 154, and 20 for kinesin heavy chain concentrations of 1.5, 3.9, and 8.3 μg/mL, respectively.

Figure 6

A microtubule with a 180° bend caused by a 4-pN force acting on the bead. This force is directed toward the bottom of the image. The scale bar is $5\hspace{0.5em}\mu \mathrm{m}$.

Figure 7

Diagram of the motion of a bead after detachment. The force F on the bead provides an initial bending moment $\mathit{rF}$. As the bead moves down, the microtubule sweeps through an angle $\mathit{\theta }$. At $\mathit{\theta }=\pi /2$, the bending moment goes to zero. The deformation of the microtubule is localized near the anchor point, in contrast to the deformation of a simple cantilever with a small load applied to its tip.