Detection of fractional steps in cargo movement by the collective operation of kinesin-1 motors

One-Motor Case.

The swiveling of a MT around the point where it is attached to an individual kinesin molecule was used as the main criterion for single-motor movement (Fig. 2A) (5, 13, 26). The precise position of the kinesin molecule (cross in Fig. 2A) was determined from a circular fit of the QD positions during a time interval where the MT movement was negligible (SI Appendix). The relative distance of the tracked QD from this kinesin position was calculated as a function of time, and several intervals of this data are represented in Fig. 2B (red curve). Clear steps can be observed by eye and were analyzed with a step-finding algorithm (27) (black curve and numbers). The histogram of pair-wise distances (Fig. 2C), which represents the distribution of distances between any two points along the displacement trace in Fig. 2B, shows a periodicity of 8 nm. This periodicity is in good agreement with the data obtained from the step-finding algorithm.

Fig. 3A shows the histogram of extracted step sizes obtained from 11 individual QDs (382 steps) bound to 11 swiveling MTs. The first peak of a double-Gaussian fit (continuous line) of this histogram yielded a central value of d₁ = 8.1 ± 0.2 nm. The second peak was constrained to be centered at twice the step size of the first peak to account for fast consecutive steps that could not be resolved with our time resolution. The histogram of the corresponding dwell times is presented in Fig. 3B. The distribution is well fit by a single-exponential rate constant of k₁ = 0.49 ± 0.03 s⁻¹. This rate constant corresponds to a second order association rate k_on ≈ 0.49/0.3 μM⁻¹ s⁻¹ = 1.6 μM⁻¹ s⁻¹ in good agreement with previously published values (28) for a kinesin-1 motor that takes one step upon hydrolysis of one ATP molecule (28, 29) with a Poisson-distributed stepping rate at limiting ATP concentrations (30).

Two-Motor Case.

MT swiveling could also be used to unambiguously determine when two motors moved a MT. The x-y trajectory of the QD shown in Fig. 2D contains two linear parts linked together by a swiveling part. Although the swiveling part is again indicative of only one motor interacting with the MT, we believe that exactly two kinesins carried the MT in the linear parts before and after the swiveling. Indeed, from fluorescence measurements, we estimated a kinesin density of ≈2 molecules per μm². Thus, it was very unlikely that a MT with a length of only a few microns would have interacted with more than two motors during the linear parts. Fig. 2E shows three different parts of the projected walked distance along the linear pathway of the QD (see Methods) as a function of time (Fig. 2E, red curve) during the two-motor regimes. Again, steps can be observed by eye and were analyzed with the step-finding algorithm (Fig. 2E, black curve and numbers). When multiple QDs bound to the same MT were tracked, coincidental stepping in time and step width were detected for a large number of steps. The histogram of pair-wise distances (Fig. 2F) reveals a structure with a periodicity of ≈4 nm, in agreement with the data obtained from the step-finding algorithm.

Fig. 3C shows the histogram of step sizes extracted by the step-finding algorithm obtained from 17 individual QDs (749 steps) bound to 16 MTs carried by two kinesins. As in the one-motor case, a double-Gaussian fit (Fig. 3C, continuous line) of this histogram was performed and yielded a central value of d₂ = 4.2 ± 0.1 nm for the first peak. The histogram of the corresponding dwell times (Fig. 3D) was best fit by a single-exponential decay with k₂ = 1.00 ± 0.04 s^−1.

For a Poisson stepper, the ratio of the velocity and the stepping rate should provide a second estimate of the step size. The average MT velocities were v₁ = 4.3 ± 0.5 nm/s (mean ± SEM, n = 11), and v₂ = 4.5 ± 0.4 nm/s (n = 17) in the one- and two-motor cases, respectively. Dividing by the respective stepping rates yields v₁/k₁ = 8.8 ± 1.7 nm, and v₂/k₂ = 4.5 ± 0.9 nm, in good agreement with our direct measurements of the step sizes.

Multimotor Case.

To test whether distinct steps would still be observable in cases where a large number of motors interacted with the MT, we performed control experiments at a 100-fold increased kinesin concentration (see Fig. 2 G–I). In the traces of the walked distance (data from 20 MTs), no steps were detectable. Moreover, in the histogram of pair-wise distances, neither a periodic structure nor a peak at 0 nm was observed, confirming the absence of steps.

Fluctuation Analysis.

To estimate the underlying step sizes without relying on any step-finding algorithm, we evaluated the statistical properties of our tracked data and compared them with the expected values for a Poisson stepper (see details in SI Appendix). An estimator of the step size d is given by:

where x(t) is the walked distance of a Poisson stepper at time t during a total time interval of T. y(t) is the deviation from the linearized movement where the speed of the stepper is estimated by: x(T)/T

Using the same data as used for the histograms of Fig. 3, we calculated step sizes of d₁^calc = 8.8 ± 0.8 nm in the one-motor case, and d₂^calc = 4.1 ± 0.3 nm in the two-motor case. The same analysis for the many-motor case resulted in d_many^calc = 0.73 ± 0.02 nm, confirming once again the absence of measurable steps. These findings provide a third independent check of the step sizes.

Irregular Cargo Jumps.

During gliding motility assays with kinesin concentrations similar to the two-motor case, a number of longer MTs did not show any periods of one-motor swiveling. When analyzing the walked distance as a function of time (see Fig. 4) no uniform steps of any step size were detected. Instead, we noticed occasional irregular and distinct jumps with sizes on the order of 10 nm that were never present when the MTs were driven by one or two motors. From fluorescence imaging of the kinesin molecules in overlap with the MTs, we conclude that three motors were involved in active transport. To further characterize the nature of the irregular jumps, we analyzed the “sideways” movement of the QDs perpendicular to the direction of MT motion. Although we found the extent of the sideways motion to be a function of the density of transporting motors and the position of the QD along the MT (SI Appendix), we did not observe any pronounced irregularities associated with the jumps. We interpret the absence of large sideways motion as indicating that the MT moved on a straight path over the motors and that the jumps are associated with readjustments of the strain within the motors in the direction of the path of the MTs. In contrast, when a MT bent outwards (“buckled”) between two transporting motors, a pronounced sideways motion was detected (SI Appendix). Intriguingly, the irregular jumps occurred in both forward and backward directions (Fig. 4B).

Gliding Assays with GFP-Kinesin and QD-Coated MTs.

We used truncated, GFP-labeled kinesin-1 constructs (rkin430_GFP), which contained the first 430 aa of kinesin-1 fused to a GFP and a His-tag at the tail domain (39). Rhodamine-labeled MTs were polymerized from 5 μl of bovine brain tubulin (4 mg/ml, mix of 1 biotin labeled/10 rhodamine labeled/189 unlabeled tubulin units; Cytoskeleton, Denver, CO) in BRB80 buffer [Pipes (pH 6.9)/1 mM EGTA/1 mM MgCl₂) with 4 mM MgCl₂, 1 mM Mg-GTP, and 5% DMSO at 37°C. After 5 min, MTs were stabilized and 100-fold diluted into room-temperature BRB80 containing 10 μM taxol and sheared four times to get short MTs (length <5 μm). Gliding motility assays were performed at room temperature in flow cells (final volume of ≈10 μl) made of two silanized (dichlorodimethylsilane; Sigma, Taufkizchen, Germany) glass coverslips and heated Parafilm for sealing. The flow sequence was as follows (all of the chemicals except where specifically mentioned were purchased from Sigma): (i) the flow cell was filled with a solution of TetraSpeck microspheres (0.2 μm diameter from Mo Bi Tec) diluted 10-fold in BRB80. (ii) After 2 min, the solution was exchanged with a BRB80 solution containing penta-His antibodies (Qiagen, Hilden, Germany) at 20 μg/ml for high-kinesin-concentration assays and 0.2 μg/ml for low-kinesin-concentration assays. (iii) After 5 min, the surface was blocked with a solution of casein (from bovine milk, 0.5 mg/ml in BRB80) for 5 min to prevent nonspecific protein binding. (iv) GFP-labeled kinesin (10 μg/ml rkin430_GFP, 0.2 mg/ml casein, and 10 μM Mg-ATP in BRB80) was incubated for 5 min to bind the motors specifically to the antibodies by their His-tags. (v) QDs [1 μl of streptavidin-coated QDs, 655 nm emission; Quantum Dot Corporation (Hayward, CA), diluted 80-fold in BRB80] were first incubated for 5 min with 2 μl of biotinylated MTs (labeling each of the MTs with ≈1 QD) and then mixed with 47 μl of motility solution containing 10 μM Taxol, 0.2 mg/ml casein, 1 mM Mg-ATP, and an oxygen-scavenger system (40 mM d-glucose, 0.040 mg/ml glucose oxidase, 0.016 mg/ml catalase, and 20 mM DTT). The resulting MT–QD solution was injected into the flow cell, and unhindered gliding motility was verified. For that, each recording was preceded by an experiment at 1 mM ATP (saturating ATP), when the gliding velocity was fast enough to be measured within less than 1 min. We found average velocities of MTs with and without QDs of v_with = 0.68 ± 0.06 μm/s (mean ± SD, n = 15) and v_without = 0.68 ± 0.07 μm/s (n = 15) at 1 mM ATP, indicating a negligible impact of the QDs. (vi) The flow cell was rinsed with a motility solution containing 0.3 μM ATP and an ATP-regenerating system (2 mM creatine phosphate, 2 units/ml creatine kinase) and sealed with Vitrex.

Image Acquisition by TIRF Microscopy.

Images were acquired on an Axiovert 200M microscope (Zeiss, Oberkochen, Germany) with a 100x (NA 1.45) oil-immersion objective, a Zeiss-TIRF slider, and a Micromax BFT 512 back-illuminated frame-transfer CCD camera (Photometrics, Tucson, AZ) or an Andor Ixon DV 897 (Andor, Belfast, U.K.). The pixel size in the acquired images was 130 nm (Micromax) or 160 nm (Andor). In some experiments a ×1.6 magnifying optovar, which reduced the pixel size was used. Fluorescence excitation was provided by a mixed gas argon-krypton laser (Innova 70C Spectra; Coherent, Santa Clara, CA) or Hg-arc lamp. The following filter sets (Chroma Technology, Rockingham, VT) were used: TRITC (exc 535/50, em 610/75, dc 565 LP) for the rhodamine-labeled MTs, GFP (exc 488/10, em 515/30, dc 505 LP) for the GFP-kinesin and QD-655 (exc 488/10, em 660/50, dc 505 LP) for the QDs. A MetaMorph imaging system (Universal Imaging, Downingtown, PA) was used for data acquisition and primary data processing. First, the positions of the slowly moving MTs were recorded by using epi-fluorescence microscopy (epi-TRITC in Fig. 1B). Second, the kinesin molecules (laser-GFP, arrows point to the individual motors in Fig. 1B) were localized by TIRF imaging without any previous illumination to avoid bleaching of the GFP molecules. Consequently, the positions of MT-attached QDs were recorded as a function of time in TIRF mode (laser-QD655, streams of 1,000 frames, 100-ms exposure time each under continuous laser illumination). Because the reference beads were fluorescent in all three channels, it was possible to superimpose precisely the images of the rhodamine-labeled MTs, the GFP-labeled kinesins, and the QDs (merged). As the emission wavelength of the QDs was in the far red (655 nm), the contribution of the fluorescence coming from the dimly rhodamine-labeled MT was negligible.

Nanometer Tracking of QDs.

The QD positions were tracked with nanometer accuracy by using a home-developed tracking software based on MatLab (MathWorks, Natick, MA) and two-dimensional Gaussian fits. For analysis, we used all tracked QD positions where the fluorescence intensity collected on the CDD chip corresponded to a flux of at least 500 photons per 100 ms at the centroid pixel, i.e., where photon shot noise was the principal source of noise. Thereby, we disregarded the data points of QDs in low-emission phases because of blinking in the analyzed trajectories. The theoretical tracking accuracy is then given by (s²/N)^0.5, where s² is the variance obtained from the Gaussian fit and N the number of collected photons (40). In our experiments, we found the Gaussian width s to be ≈140 nm and the average number of collected photons originating from one QD to be 4,500 per 100-ms exposure. The resulting calculated accuracy then yields 2.1 nm per frame in good agreement with the width of the Gaussian distribution determined from tracking a surface-immobilized QD (SI Appendix). The tracking accuracy of QDs bound to gliding MTs was slightly reduced to ≈3 nm mainly because of Brownian motion of the MT-QD complex (SI Appendix).

Step Analysis.

By using IGOR PRO 5.0 (WaveMetrics, Portland, OR): (i) the average position of five TetraSpeck beads was subtracted from the tracked positions of the QDs for drift correction, (ii) the pathways of the QDs were determined in the x–y plane after linear fits of the x position vs. time and the y position vs. time, and (iii) the QD positions were projected along the pathway to deduce the projected walked distance and the sideways motion. For swiveling MTs, bound to single motor molecules, the walked distance was calculated as the distance from the central kinesin position. Step analysis was performed by using an algorithm written in MatLab kindly provided by J. Kerssemakers and described in ref. 27. This algorithm assumes that the steps are hidden in Gaussian-distributed noise but makes no assumption on either step size or dwell time. The overall accuracy in step finding was tested by using piezo-based control measurements and allowed us to reliably discriminate steps as small as 4 nm (see SI Appendix).