# Fluctuating Motor Forces Bend Growing Microtubules

- 261 Downloads
- 6 Citations

## Abstract

Despite their rigidity, microtubules in living cells bend significantly during polymerization resulting in greater curvature than can be explained by thermal forces alone. However, the source of the non-thermal forces that bend growing microtubules remains obscure. We analyzed the motion of microtubule tips in NIH-3T3 fibroblasts expressing EGFP-EB1, a fluorescent +TIP protein that specifically binds to the growing ends of microtubules. We found that dynein inhibition significantly reduced the deviation of the growing tip from its initial trajectory. Inhibiting myosin modestly reduced tip fluctuations, while simultaneous myosin and dynein inhibition caused no further decrease in fluctuations compared to dynein inhibition alone. Our results can be interpreted with a model in which dynein linkages play a key role in generating and transmitting fluctuating forces that bend growing microtubules.

### Keywords

Microtubule bending Dynein Myosin## Introduction

Microtubules play a central role in cell polarization,28 migration,8 intracellular trafficking,6 cell division,22 and nuclear positioning.26*In vitro* experiments show that microtubules subjected to thermal forces have a persistence length on the order of millimeters,10 yet *in vivo* they exhibit bends on micron length scales. These bends develop primarily by deflections from linear tip trajectories rather than subsequent bending of intact microtubules,5 although initial bends may be amplified by compressive forces once the tip reaches the cell periphery4 or by the activity of cytoplasmic molecular motors.32

Thermal forces are too small to explain the deflections of growing microtubules in living cells,5 and the causes of microtubule bending before the tips reach the cell periphery remain obscure. Growing microtubules can bend due to compressive stresses generated by polymerization against a barrier.2,4,7 Furthermore, the activity of myosin motors drives fluctuations in the cytomatrix, causing bending of existing microtubules *in vivo*3; myosin forces could bend growing microtubules by a similar mechanism. Processive microtubule motors such as dynein or kinesin can exert forces on the microtubule if they are anchored to the cytomatrix at the cargo-binding end.2,12,25,32 As the motor walks along the microtubule it pulls on the anchor point, resulting in a tensile force between the anchor and the point of attachment to the microtubule. Odde and coworkers2 have suggested that the anterograde motion of buckling microtubules (moving towards the cell periphery) can be explained by microtubule-bound motor activity. In laser severing experiments with single microtubules in endothelial cells, newly created minus-ended microtubules bend (instead of straightening) in a dynein dependent manner,32 consistent with a model for dynein pulling forces along the entire length of the microtubule. This model also explains amplified buckles at the cell periphery and how the centrosome can be centered by an astral array of microtubules.32

Given the athermal nature of forces that deflect growing microtubule tips,5 we reasoned that motor activity may also be responsible for bending growing microtubules. Using *in vivo* experiments, we show that bending of the trajectories of growing microtubule tips is significantly decreased in dynein-inhibited cells. Myosin-inhibition also decreases bends while kinesin-inhibition has no effect. Simultaneous inhibition of myosin and dynein in cells does not cause any additional reduction in bending beyond that by inhibition of dynein alone. We interpret these results with a mathematical model in which dynein linkages generate and transmit fluctuating forces that bend growing microtubules.

## Materials and Methods

### Cell Culture, Transfection, and Inhibition Experiments

NIH-3T3 fibroblasts were cultured in Dulbecco’s Modified Eagle Medium (DMEM) (Mediatech, Manassas, VA) with 10% Donor Bovine Serum (DBS) (Gibco, Grand Island, NY). The cells were maintained at 37 °C in humidified 5% CO_{2}. For microscopy the cells were plated on 35 mm glass-bottomed dishes (WPI, Sarasota, FL) and allowed to spread overnight at 37 °C and 5% CO_{2}. The glass-bottomed dishes were coated with 5 *μ*g/mL fibronection (BD Biocoat™, Franklin Lakes, NJ) and kept at 4 °C overnight before cell seeding.

In control experiments, cells were transiently co-transfected with pGFP-EB1 (Addgene plasmid 17234) and DsRed and were incubated for 18–24 h prior to plating. DsRed was expressed to allow comparisons with cells expressing fluorescently labeled proteins such as DsRed-CC1. In dynein inhibition experiments, cells were co-transfected with DsRed-CC1 (Fig. S1) and with mCherry-KHC in kinesin-1 inhibition experiments (Fig. S1). DsRed-CC1 renders dynein inactive by competitively binding to it and preventing dynein interactions with dynactin31,32 while mCherry-KHC can inhibit kinesin-1 by multiple mechanisms.23 Transient transfection of plasmids into cells was performed with Lipofectamine™ 2000 transfection reagent (Life Technologies, Invitrogen, Carlsbad, CA). Some cells were treated for 30 min with 10 *μ*M Y27632, which is a Rho-kinase (ROCK) inhibitor that causes substantial inhibition of non-muscle myosin.16,18

### Confocal Microscopy

The cells were imaged on a Leica SP5 DM6000 confocal microscope equipped with a 63X oil immersion objective. During microscopy, cells were maintained at 37 °C in a temperature, CO_{2}, and humidity controlled environmental chamber. In order to image EGFP-EB1, a 488 nm laser with 10% power and an appropriate GFP bandpass filter was used. Images were taken at a resolution of 1024 × 1024 and with a speed of 400 Hz, at a rate of 3 s/frame. The images were further analyzed using LAS AF Lite (Leica Systems) software. For dynein and kinesin-1 inhibition studies, expression of DsRed-CC1 and mCherry-KHC was confirmed using epifluorescence microscopy.

### Trajectory Analysis

Microtubule trajectories were constructed from an analysis of EB1 movies using plusTipTracker, a MATLAB based open source software package that combines automated tracking, data analysis, and visualization tools for analysis of movies of fluorescently labeled microtubule plus end binding proteins (+TIPs).1 The software detects EB1 comets by application of locally optimal thresholds using a watershed-based technique. The track reconstruction is described in more detail elsewhere.14

To test the accuracy of the software for our experiments, we first measured the positional error in the measurements. Fixed NIH-3T3 cells expressing EGFP-EB1 were imaged for 2 min at three-second intervals. Since the position of the tips is fixed, the variation in the +TIP detection by the software provides an estimate of the positional error. The deviation from the mean was calculated for about eight tips. Figure S2 shows the plot of the frequency vs. the deviation from the mean. Fitting a normal distribution to the data yielded a standard deviation of 0.06 *μ*m while the average distance travelled by the tips in between successive frames was 1.1 *μ*m. Thus there is a 6% error in the measurements, which was deemed to be small enough to enable reliable tracking of the tips.

*x*-axis by an angle that was determined by the slope of the fitted line. The rotated trajectories thus had the same initial direction. To quantitatively investigate microtubule curvature, we next performed a Fourier decomposition of the reconstructed trajectories,10 with a trajectory length of 8

*μ*m. The tangent angle, \( \theta = \tan^{ - 1} \left( {dy/dx} \right), \) was decomposed as a sum of sine waves,

We assume that the microtubules are clamped at the centrosome (i.e., a fixed orientation), so that the boundary condition at the origin, *θ*(0) = 0 is automatically imposed by the basis functions.

*N*coordinates (

*x*

_{k},

*y*

_{k}) making up a trajectory, the length ∆

*s*

_{k}and tangent angles

*θ*

_{k}of each of the (

*N*− 1) segments that connect the coordinates were calculated:

### Model for Dynein Force Generation

Motor forces are included as linkages distributed along the length of the microtubule, as illustrated in Fig. 3a. We imagine that a particular segment of the microtubule is occasionally captured by a cytoskeletal bound dynein motor and bound for times of the order of \( k_{\text{off}}^{ - 1} , \) where we take the dynein off rate to be of the order of 1 s^{−1}.32 A segment of length *h* will capture a dynein motor in a time step \( \delta t \) with a probability \( p = nhk_{\text{off}} \delta t, \) where *n* is the (linear) density of dynein motors per unit length of the microtubule, estimated at about two cytoskeletal-bound motors per micron.32 On average the binding and unbinding rates will balance at the desired motor density *n* if each bound motor unbinds with a probability \( k_{\text{off}} \delta t. \) Note that these formulas assume that the binding and unbinding probabilities are small, \( k_{\text{off}} \delta t \ll 1; \) more general formulas can be derived in cases where \( k_{\text{off}} \delta t \) is not small. The motor model resembles that proposed by Nedelec and Foethke24; the main difference is that in our implementation the motors only exist while bound to the microtubule instead of being permanently bound to random positions in the cytomatrix. It seems unlikely that this will cause any substantial difference in the simulations.

**b**

_{i}linking the point of attachment to the microtubule,

**x**

_{i}, with the anchor point in the cytomatrix,

**a**

_{i}. (2) The dynein motor walks towards the microtubule minus end, with a force-dependent speed, until the tangential force reaches the stall force

*f*

_{max}or the motor unbinds. The motor is displaced from its initial position both by walking along the microtubule and from the motion of the microtubule itself,

**v**is the velocity of the microtubule segment. The motor walks with a speed

*v*

_{m,i}in the direction of the local tangent to the microtubule

**t**, which is formed by assuming the filament is made up of straight segments connecting the nodes. We assume a linear force velocity relation varying from a maximum speed in the force-free state,

*v*

_{max}to zero at the stall force,

*f*

_{max}The coordinate

*s*

_{i}, which measures the position of the motor along the contour length of the microtubule, is incremented by \( v_{m,i} \delta t \) at each time step, and the motor position is then determined by interpolating from the neighboring nodes. The velocity of the segment is found by interpolating the nodal velocities. (3) The initial distribution of directions of the microtubule-cytomatrix linkage,

**b**, is isotropic with the anchor points initialized as

**a**

_{i}(0) =

**x**

_{i}(0) +

**b**

_{i}To model the action of the myosin network, the anchor points

**a**

_{i}are moved with random velocities, which represents the motor-induced motions of the cytomatrix. Each anchor point is assumed to move with a constant velocity

**r**

_{i}(

*t*) =

**a**

_{i}(

*t*) −

**x**

_{i}(

*t*), with a linear force along the linkage (Fig. 3a)

It is possible for the motor to exert a compressive force on the dynein–cytomatrix linkage if \( {\mathbf{r}}_{i}{\cdot} {\mathbf{t}} \)< 0. However this is always transient since eventually the motor will walk to a position such that \( {\mathbf{r}}_{i}{\cdot} {\mathbf{t}} \) > 0.

### Equation of Motion

*L*(free from external couples) can be written as a line integral of the mean-square curvature,17

*s*is the distance along the filament arc, and

*B*is the bending modulus. If we discretize the filament into

*N*segments of uniform length

*h*=

*L*/

*N*, then a second-order approximation to the strain energy is given by20,21

*C*

_{n}is related to the angle between adjacent segments, \( C_{n}^{2} = 2\left( {h^{2} - {\mathbf{r}}_{n,n - 1} \cdot{\mathbf{r}}_{n + 1,n} } \right)/h^{4} . \) The discrete approximation to

*H*can then be differentiated to find the elastic force on each node of the filament. In addition to the elastic forces, there is also a constraint force that is required to maintain the length of the individual segments, \( {\mathbf{r}}_{n,n - 1} \cdot{\mathbf{r}}_{n,n - 1} = h^{2} . \)20,21

**v**

_{n}are obtained from the force balance:

**f**

_{n}is the total force on node

*n*from the motors on neighboring segments. The friction coefficient

*y*is taken to represent the background friction of the cellular matrix; we take value of 10 Pa s, or 10 N m

^{−2}s, based on measurements of microtubule relaxation in dynein-inhibited cells.32

## Results

### Fluctuations in Growing Microtubule Tips

We tracked the position of EGFP-EB1 labeled microtubule tips in cells using plusTipTracker and microtubule trajectories were reconstructed from the measured tip positions. The tips were tracked in a region that encircled the centrosome, but not closer than 5 *μ*m to the cell periphery. This was done to exclude events where the growing tip might experience compressive loading as it grew against the membrane. To avoid spurious tracks, each trajectory was visually confirmed to be correctly detected and trajectories that weren’t reconstructions of the growth of a single tip were discarded. A minimum of 12–13 cells were imaged and 300–600 trajectories per condition were quantified.

*x*-axis, as described in “Materials and Methods” section. In control cells that expressed DsRed the trajectories were observed to spread out significantly over tens of seconds.

Model parameters

Symbol | Parameter | Range | Source | Value used |
---|---|---|---|---|

| Maximum dynein force | 5–8 pN | 8 pN | |

| Dynein speed (no force) | 0.8 | 0.8 | |

| Dynein spring constant | 0.1–1 pN nm | 1 pN nm | |

| Dynein-nucleus off-rate | No value | 1 s | |

| Dynein density | No value | 2 | |

| Number of microtubules | 200–500 | 100 | |

| MT polymerization speed | 0.1–0.2 | 0.1 | |

ξ | Effective friction | 10 Pa s | ||

| Myosin speed | 0.1–0.2 | 0.1 | |

| Bending modulus | 24–30 pN nm | 25 pN nm |

### Motor Activity Bends Growing Microtubules

We next over-expressed DsRed-CC1 in NIH-3T3 fibroblasts to competitively inhibit dynein.31,32 The spread in the trajectories was less in dynein-inhibited cells compared to control cells (compare Figs. 1a and 1b). When kinesin was inhibited by expressing mCherry-KHC,23 the spread was similar to the control cells (Fig. S3).

We next attempted to inhibit non-muscle myosin activity with blebbistatin, a specific myosin II inhibitor.15 However, at doses that inhibited myosin activity, blebbistatin treatment caused a significant rounding of cells making it difficult to track EB1 tips reliably in these cells. We therefore treated cells with Y27632, a ROCK inhibitor that has been shown to cause a large decrease in non-muscle myosin activity without causing cell rounding.16,18 The spread of the trajectories on Y27632 treatment is shown in Fig. 1c and appears to be decreased when compared to control cells, but to a lesser extent than in dynein-inhibited cells (Fig. 1b).

As all trajectories start at the origin and are initially oriented along the positive *x*-axis, any deviation of the trajectories in the *y*-direction is a measure of the spread. One method of quantifying the effects of motor inhibition on trajectory spread is to compare the variance of the *y* positions of the tips at different times. However, modest but statistically significant differences in tip speed were observed when dynein, kinesin, or ROCK was inhibited (Fig. S4). Owing to the differences in the polymerization velocity, we instead chose to examine the length-dependence of the variance at each condition (Fig. 1d). The variance in dynein-inhibited cells is decreased by a factor of two in comparison with control cells. There is a smaller decrease in variance in ROCK inhibited cells, but there is no statistically significant difference between kinesin-1 inhibited cells and control cells.

### Fourier Mode Analysis of Tip Trajectories

*p*< 0.05 for mode 1 by Student’s

*t*test), indicating that dynein linkages contribute significantly to the bending of microtubule trajectories (Fig. 2a). In contrast, trajectories in cells where only kinesin was inhibited showed no discernible differences from the control cells (Fig. 2b). Inhibition of myosin only reduced the mean-square amplitudes at some wavelengths, and to a lesser extent than inhibition of dynein (Fig. 2c). Inhibition of both myosin and dynein showed a similar reduction in mode amplitudes as inhibition of dynein alone (Fig. 2d).

These results suggest that both myosin and dynein contribute to bending the trajectories of microtubule tips. One possibility, consistent with these results, is that myosin motor-induced force fluctuations are transmitted primarily through dynein linkages between the microtubule and the actin cytoskeleton; blocking these linkages by CC1 would then be sufficient to block both myosin-induced forces and dynein-induced forces on the polymerizing microtubules.

### Simulations of Fluctuations in Growing Microtubules

A typical simulation of a growing microtubule is illustrated in Movie 1 and Fig. 3b for the case where dynein is anchored to a stationary cytomatrix (i.e., **v**_{a,i} = 0). The dynein motors pull along the direction of the motor-anchor vector, indicated by the red lines, and so exert lateral as well as tangential forces. The microtubule can be significantly diverted from a straight-line path as shown in Fig. 3c, which shows the final configurations of 100 fully-grown (8 *μ*m) microtubules. The variance of the tip position calculated from the simulated trajectories in Fig. 3c is about 0.8 *μ*m^{2} at 8 *μ*m length, which is somewhat less than that observed in experiments (1.3 *μ*m^{2} at 8 *μ*m, Fig. 1d). However in dynein-inhibited cells, there is still a significant variance in the tip position (0.47 *μ*m^{2} at 8 *μ*m, Fig. 1d) which is much larger than can be accounted for by thermal forces alone. Since there are no such background fluctuations in the simulations and microtubules grow straight in the absence of motor forces, it is to be expected that the fluctuations in the tip positions are less than those observed in the experiments. The simulated variance in the tip positions closely matches the observed *difference* between control cells and dynein-inhibited cells.

We next performed a Fourier decomposition on the simulated trajectories in Fig. 3c. The variance of the first bending mode, var(*a*_{1}) = 0.09 *μ*m is due entirely to dynein activity (no other effects are included in the simulation). This variance matches exactly to the reduction in variance of the first bending mode following dynein inhibition, from 0.144 *μ*m in control cells to 0.054 *μ*m in dynein inhibited (DI) cells (Fig. 2a), i.e., var(*a*_{1}^{CON}) − var(*a*_{1}^{DI}) = 0.09 *μ*m However, the observed effect of dynein on the second mode var(*a*_{2}^{CON}) − var(*a*_{2}^{DI}) = 0.045 *μ*m is not well reproduced by the simulation result, var(*a*_{2}) = 0.01 *μ*m.

Since myosin inhibition produced a measureable decrease in the variance of tip positions, we next investigated the influence of myosin forces on the microtubule tip trajectories. We used a simple model of myosin activity, where the anchor points of dynein on the cytomatrix move with a fixed velocity; here we choose **v**_{a} = 0.05 *μ*m s^{−1}, which is consistent with measurements of myosin motor speeds.30 A simulation showing the growth of a typical microtubule with moving anchor points is shown in Movie 2. It can be seen that there is more curvature in the growing filament, which is reflected in larger values for the variance of the first bending mode var(*a*_{1}) = 0.15 *μ*m. The larger deflections and curvatures can also be seen in the trajectory plots of 100 sample microtubules (Fig. 3d). The amplitude of the second mode, var(*a*_{2}) = 0.02 *μ*m, is larger than in the absence of cytoskeletal flow but still smaller than the experimental observations. Thus our models only account for the large scale fluctuations in microtubule shape, but not the detailed Fourier spectrum.

We found that the shapes of the microtubules were insensitive to variations in the dynein motor parameters. It is the mechanism of dynein pulling that tends to lead to deflected filaments rather than the exact motor parameters. On the other hand the shapes are sensitive to the motion of the anchor points, which we used to represent myosin-driven fluctuations in the cytomatrix. The speed of the anchor points (0.05 *μ*m s^{−1}) was less than typical myosin motor speeds (0.15–0.2 *μ*m s^{−1}), based on the assumption that the cytomatrix moves more slowly than the motors pulling it. In future the compliance of the cytomatrix could be taken into account with a force balance on the myosin-actin network instead of a prescribed motion of the anchor points.

## Discussion

Despite their rigidity, microtubules in living cells contain both short-wavelength bends at the periphery and long-wavelength bends in the cell interior.2,5,10,32 The action of minus-end directed motors, specifically dynein, provides an explanation for both the short wavelengths and the localization of these buckles near the periphery.32 While growth of microtubules along curved paths has been proposed as the reason for long wavelength bends in the cell interior,5 the forces that cause growing microtubule tips to deflect from a straight path have remained unclear. In this paper, we suggest that forces bending the growing microtubule are transmitted to it by dynein. These forces may be generated by dynein activity itself, or by myosin forces that cause motion of dynein anchors in the cytomatrix.

Our results show that dynein and myosin inhibition significantly decrease the spread in microtubule trajectories, but kinesin inhibition does not have any noticeable effect. However, even when both dynein and myosin activity is suppressed, microtubules still spread considerably more than would be expected from thermal forces alone. Thus, there appears to be no single cause for the observed microtubule shapes; both dynein, myosin, and some, as yet undetected, causes (organelles or other motors) all contribute to the observed deflections.

The dynein–cytomatrix linkage plays both an active and a passive role in determining microtubule shapes. Dynein generates bends by its own motor activity (active) and it transmits myosin forces *via* the motion of the cytomatrix in the region of its anchor point (passive). In this view, inhibiting the dynein–cytomatrix linkage by DsRed-CC1 prevents dynein from pulling on the microtubule but also inhibits transmission of myosin forces to the microtubule. Assuming that the contributions of dynein and myosin are additive, a comparison of the variance of the first mode amplitudes suggests that about 40% of the stored bending energy comes from as yet unidentified sources, 15% from myosin activity5 transmitted by stationary dynein linkages, and 45% from dynein motor activity as if pinned to a static cytomatrix.

An alternative explanation of the data is that myosin does not play a significant role in influencing filament shapes and that dynein accounts for about 60% of the filament bending energy. Myosin inhibition could reduce the effectiveness of dynein molecules that are pulling on the microtubules because the F-actin network is less dense in the absence of myosin crosslinking. Inhibiting myosin in cells where dynein activity is also inhibited would then be expected to have no further effect on the spread, while inhibiting myosin or dynein alone would decrease the deviation from straight paths.

Both these mechanisms are consistent with the experimental observations. To assess the plausibility of these different mechanisms, we carried out simulations of microtubule growth under the action of dynein and myosin motor forces. First, we investigated the possibility that cytoskeletal-bound dynein motors can produce bends in growing microtubules. We found that dynein motors produced significant deflections in the microtubule tips, as measured by the variance in the tip position for 100 microtubules (Fig. 3c). The variance in position for 8 *μ*m segments, ~0.8 *μ*m^{2} correlates well with the difference in variance in control cells (~1.2 *μ*m^{2}) and dynein-inhibited cells (~0.5 *μ*m^{2}). Moreover, simulations of the variance in the amplitude of the first mode match the experimentally measured change in mode amplitudes when dynein is inhibited. We next implemented a very simple model where the anchor points of the dynein motors move with randomly chosen velocities, mimicking the effect of myosin driven flow in the cytomatrix. Larger bends were observed when the fluctuations in cytomatrix were included, but these are too large to be consistent with the difference between control cells and those with dynein–cytomatrix linkages inhibited. Thus the simulations support the hypothesis that dynein is the key driver of fluctuations in microtubule shape, with myosin generated forces playing at most a secondary role.

## Notes

### Acknowledgments

The following grant supported this work: NSF CMMI 0954302, NSF CMMI 0927945, NIH GM102486, and NSF CTS-0505929. DsRed-CC1 and mCherry-KHC were gifts from Prof. Trina Schroer (Johns Hopkins University) and Prof. Kristen Verhey (University of Michigan). We thank the anonymous referee for pointing out the appropriateness of sine functions in the curvature analysis rather than a cosine basis.

## Supplementary material

### References

- 1.Applegate, K. T., S. Besson, A. Matov, M. H. Bagonis, K. Jaqaman, and G. Danuser. plusTipTracker: quantitative image analysis software for the measurement of microtubule dynamics.
*J. Struct. Biol.*176:168–184, 2011.CrossRefGoogle Scholar - 2.Bicek, A. D., E. Tuzel, A. Demtchouk, M. Uppalapati, W. O. Hancock, D. M. Kroll, and D. J. Odde. Anterograde microtubule transport drives microtubule bending in LLC-PK1 epithelial cells.
*Mol. Biol. Cell*20:2943–2953, 2009.CrossRefGoogle Scholar - 3.Brangwynne, C. P., G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz. Nonequilibrium microtubule fluctuations in a model cytoskeleton.
*Phys. Rev. Lett.*100:118104–118104, 2008.CrossRefGoogle Scholar - 4.Brangwynne, C. P., F. C. MacKintosh, S. Kumar, N. A. Geisse, J. Talbot, L. Mahadevan, K. K. Parker, D. E. Ingber, and D. A. Weitz. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement.
*J. Cell Biol.*173:733–741, 2006.CrossRefGoogle Scholar - 5.Brangwynne, C. P., F. C. MacKintosh, and D. A. Weitz. Force fluctuations and polymerization dynamics of intracellular microtubules.
*Proc. Natl. Acad. Sci. U.S.A.*104:16128–16133, 2007.CrossRefGoogle Scholar - 6.Caviston, J. P., and E. L. Holzbaur. Microtubule motors at the intersection of trafficking and transport.
*Trends Cell Biol.*16:530–537, 2006.CrossRefGoogle Scholar - 7.Dogterom, M., and B. Yurke. Measurement of the force–velocity relation for growing microtubules.
*Science*278:856–860, 1997.CrossRefGoogle Scholar - 8.Etienne-Manneville, S. Actin and microtubules in cell motility: which one is in control?
*Traffic*5:470–477, 2004.CrossRefGoogle Scholar - 9.Gennerich, A., and S. L. Reck-Peterson. Probing the force generation and stepping behavior of cytoplasmic dynein.
*Methods Mol. Biol.*783:63–80, 2011.CrossRefGoogle Scholar - 10.Gittes, F., B. Mickey, J. Nettleton, and J. Howard. Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape.
*J. Cell Biol.*120:923–934, 1993.CrossRefGoogle Scholar - 11.Gliksman, N. R., R. V. Skibbens, and E. D. Salmon. How the transition frequencies of microtubule dynamic instability (nucleation, catastrophe, and rescue) regulate microtubule dynamics in interphase and mitosis: analysis using a Monte Carlo computer simulation.
*Mol. Biol. Cell*4:1035–1050, 1993.Google Scholar - 12.Hamaguchi, M. S., and Y. Hiramoto. Analysis of the role of astral rays in pronuclear migration in sand dollar eggs by the Colcemid-UV method.
*Dev. Growth Differ.*28:143–156, 1986.CrossRefGoogle Scholar - 13.Howard, J. Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, MA: Sinauer, 2001.Google Scholar
- 14.Jaqaman, K., D. Loerke, M. Mettlen, H. Kuwata, S. Grinstein, S. L. Schmid, and G. Danuser. Robust single-particle tracking in live-cell time-lapse sequences.
*Nat. Methods*5:695–702, 2008.CrossRefGoogle Scholar - 15.Kovacs, M., J. Toth, C. Hetenyi, A. Malnasi-Csizmadia, and J. R. Sellers. Mechanism of blebbistatin inhibition of myosin II.
*J. Biol. Chem.*279:35557–35563, 2004.CrossRefGoogle Scholar - 16.Kumar, S., I. Z. Maxwell, A. Heisterkamp, T. R. Polte, T. P. Lele, M. Salanga, E. Mazur, and D. E. Ingber. Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics.
*Biophys. J.*90:3762–3773, 2006.CrossRefGoogle Scholar - 17.Landau, L. D., and E. M. Lifshitz. Theory of Elasticity. New York: Pergamon Press, 1981.Google Scholar
- 18.Lele, T. P., J. Pendse, S. Kumar, M. Salanga, J. Karavitis, and D. E. Ingber. Mechanical forces alter zyxin unbinding kinetics within focal adhesions of living cells.
*J. Cell. Physiol.*207:187–194, 2006.CrossRefGoogle Scholar - 19.Lindemann, C. B., and A. J. Hunt. Does axonemal dynein push, pull, or oscillate?
*Cell Motil. Cytoskeleton*56:237–244, 2003.CrossRefGoogle Scholar - 20.Llopis, I., M. C. Lagomarsino, I. Pagonabarraga, and C. P. Lowe. Cooperativity and hydrodynamic interactions in externally driven semiflexible filaments.
*Comput. Phys. Commun.*179:150–154, 2008.CrossRefGoogle Scholar - 21.Llopis, I., I. Pagonabarraga, M. C. Lagomarsino, and C. P. C. Lowe. Sedimentation of pairs of hydrodynamically interacting semiflexible filaments.
*Phys. Rev. E*76:061901, 2007.CrossRefGoogle Scholar - 22.Lodish, H. F., A. Berk, C. A. Kaiser, M. Krieger, M. P. Scott, A. Bretscher, H. Ploegh, and P. Matsudaira. Molecular Cell Biology. New York: W.H. Freeman, 2008.Google Scholar
- 23.Navone, F., J. Niclas, N. Hombooher, L. Sparks, H. D. Bernstein, G. McCaffrey, and R. D. Vale. Cloning and expression of a human kinesin heavy chain gene: interaction of the COOH-terminal domain with cytoplasmic microtubules in transfected CV-1 cells.
*J. Cell Biol.*117:1263–1275, 1992.CrossRefGoogle Scholar - 24.Nedelec, F., and D. C. Foethke. Collective Langevin dynamics of flexible cytoskeletal fibers.
*New J. Phys.*9:427, 2007.CrossRefGoogle Scholar - 25.O’Connell, C. B., and Y. L. Wang. Mammalian spindle orientation and position respond to changes in cell shape in a dynein-dependent fashion.
*Mol. Biol. Cell*11:1765–1774, 2000.Google Scholar - 26.Reinsch, S., and P. Gonczy. Mechanisms of nuclear positioning.
*J. Cell Sci.*111:2283–2295, 1998.Google Scholar - 27.Shelden, E., and P. Wadsworth. Observation and quantification of individual microtubule behavior in vivo: microtubule dynamics are cell-type specific.
*J. Cell Biol.*120:935–945, 1993.CrossRefGoogle Scholar - 28.Siegrist, S. E., and C. Q. Doe. Microtubule-induced cortical cell polarity.
*Genes Dev.*21:483–496, 2007.CrossRefGoogle Scholar - 29.Toba, S., T. M. Watanabe, L. Yamaguchi-Okimoto, Y. Y. Toyoshima, and H. Higuchi. Overlapping hand-over-hand mechanism of single molecular motility of cytoplasmic dynein.
*Proc. Natl. Acad. Sci. U.S.A.*103:5741–5745, 2006.CrossRefGoogle Scholar - 30.Umemoto, S., and J. R. Sellers. Characterization of in vitro motility assays using smooth muscle and cytoplasmic myosins.
*J. Biol. Chem.*265:14864–14869, 1990.Google Scholar - 31.Wu, J., K. C. Lee, R. B. Dickinson, and T. P. Lele. How dynein and microtubules rotate the nucleus.
*J. Cell. Physiol.*226:2666–2674, 2010.CrossRefGoogle Scholar - 32.Wu, J., G. Misra, R. J. Russell, A. J. C. Ladd, T. P. Lele, and R. B. Dickinson. Effects of dynein on microtubule mechanics and centrosome positioning.
*Mol. Biol. Cell*22:4834–4841, 2011.CrossRefGoogle Scholar