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* Institute of Biophysics and Biochemistry, School of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China; and
National Laboratory of Biomacromolecules, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, People's Republic of China
Correspondence: Address reprint requests to Tao Xu, E-mail: txu{at}mail.hust.edu.cn; or Anlian Qu, E-mail: alqu{at}mail.hust.edu.cn.
| ABSTRACT |
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| INTRODUCTION |
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Two-dimensional (2-D) confocal microscopy has been used to explore granule movement in single optical section (Pouli et al., 1998
; Levitan, 1998
). The contribution from the missing z direction is ignored by assuming that observed granules move within the observation plane during the experimental time. Three-dimensional (3-D) single-particle tracking (SPT) in living cells has been difficult for confocal fluorescence microscopy. This probably is due to low time resolution inherited with the laser scanning, high photobleaching, and toxicity at the expense of low light collection efficiency. Recently developed total internal reflection fluorescence microscope (TIRFM) has proved very successful in studying the movement of single granules. The advantages of low background, high temporal resolution, minimal photobleaching, and phototoxicity have made TIRFM very popular in tracking the docking and fusion of granules (Steyer and Almers, 1999
; Oheim and Stühmer, 2000
; Ohara-Imaizumi et al., 2002
). However, as the penetration depth of the evanescent field is limited to several hundreds of nanometers, TIRFM can only be employed to study granules right underneath the plasma membrane close to the coverglass-solution interface, whereas granules residing deeper inside the cytosol are invisible under TIRFM. It is unclear whether the "unphysiological" adhesion of cell membrane to the coverglass will have an impact on the mobility and function of secretory granules. On the other hand, although TIRFM is generally used for 2-D tracking, z-mobility can be indirectly inferred from the changes in the intensity of fluorescence (Ölveczky et al., 1997
; Johns et al., 2001
). However, since TIRFM is extremely sensitive to the objects' vertical movement, fluctuation in fluorescence unrelated to changes in axial position (such as variation in excitation power, quenching, or dequenching of fluorescence due to pH change, etc.) will result in misinterpretation of the z-position.
To avoid the restriction of TIRFM in observing only the cell-glass interface and to expand our knowledge on 3-D movement of granules throughout living cells, we have constructed a system to combine deconvolution wide-field fluorescence microscopy (WFFM) and 3-D single-particle tracking technique. We have employed this method to study the 3-D mobility of single granules in living PC12 cells. Indeed, 3-D mobility of granules distant from the plasma membrane has yet to be demonstrated. We have compared the mobility of granules that are either close to the plasma membrane (GP) or located deep inside the cytosol (GC). Our data illustrated that the mobility of internal granules is greater than those near the plasma membrane. Whereas the majority of granules wander in random and caged fashion, stimulation increases significantly the percentage of granules that travel in a directed fashion. We also found that the mobility of GP is more prone to the disruption of F-actin, whereas that of GC is less affected. Our results demonstrate that combining deconvolution and 3-D SPT is useful in following the long-term 3-D movement of single granules within living cells.
| MATERIALS AND METHODS |
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60 min later. To verify our determination of the membrane contour, cells were first incubated in normal external solution containing 4 µM FM1-43 (Molecular Probes, Eugene, OR) for 510 min until we saw a stable fluorescence staining that was uniformly distributed along the plasma membrane. After locating the plasma membrane, FM1-43 was washed out from the membrane in dye-free buffer, which resulted in a rapid disappearing of the staining. Then, for the same cell we labeled its granules with AO as described above. To avoid unnecessary photobleaching, fluorescence excitation was turned on only during image acquisition. [K+]o was raised by local perfusion with a multi-channel perfusion system (MPS-1, YiBo Life Science Instrument, Wuhan, China). The stimulation buffer contained (in mM): 90.4 NaCl, 65 KCl, 2 MgCl2, 1.8 CaCl2, and 10 HEPES (pH 7.4). Sometimes, dense-core granules were labeled by transient transfection with human pro-neuropeptide Y (NPY) (plasmid kindly provided by W. Almers, Vollum Institute, Oregon Health and Science University, Portland, OR) fused to the N-terminal of DsRed, which would be used to compare with AO-labeled granules in size, but not used for successive 3-D imaging due to the longer exposure time required for imaging DsRed labeled granules. Actin cytoskeletons were disrupted by incubating the cells with 5 µM latrunculin B (ICN Biomedicals, Aurora, Ohio) for 2 min.
Image collection
Cells were grown on high refractive-index glass coverslips and viewed under an inverted microscope (IX70; Olympus America, Melville, NY) with a 1.65 numerical-aperture (NA) objective (APO x100 O HR, Olympus). Excitation light from a fiber optical-coupled monochromator (Polychrome IV; TILL Photonics, Bayern, Germany) was passed through a shutter that opened only during camera exposure. The wavelength selection and shutter were controlled by the image acquiring software (TILL vision 4.0, Till Photonics). Images were acquired with a cooled charge-coupled device (PCO SensiCam, Kelheim, Germany) with pixel size of 0.067 µm at the specimen plane. Appropriate dichroic mirror (505 DCLP from Chroma Technology, Brattleboro, VT) and emission filter (535LP from Chroma) were used for imaging. A series of 2-D images were collected via moving the focal plane through a cell with the piezoelectric z axis controller (E-662. LR, Physik Instrumente, Karlsruhe, Germany). The focal plane advanced
75% of the distance moved by the objective due to the discrepancy in refractive index between the immersion oil and cytosol. Accordingly, we reconstructed 3-D images of cells with those stacks of 2-D sections. For obtaining successive 3-D images of a cell, we selected the plane where the outmost edge of the cell appeared sharpest as the reference plane. Starting from the reference plane, we sampled sixteen 2-D sections with 0.2 µm stepping size to generate one 3-D image. An illustration of the imaged region is shown in Fig. 1 D between the dashed lines. As to the same imaged region, we successively recorded its 3-D images every 5 s for 70 s to generate a stack including fifteen 3-D images. In our imaging protocol, exposure time for each optical section was 5 ms, and the waiting interval for the next section was 170 ms. Occasionally, more sections were sampled to include the whole cell.
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The iterative expectation-maximum algorithm based on a maximum-likelihood approach (Conchello and McNally, 1996
) was used to deconvolve every recorded 3-D fluorescence image. The deconvolution algorithm used in our study was regularized with intensity regularization that can avoid the appearance of some artificial bright spots in deconvolved images (Conchello and McNally, 1996
; Markham and Conchello, 1997
). To verify the result of deconvolution, we employed a well-defined 3-D specimen, FocalCheck Fluorescent Microsphere from Molecular Probes. The bead is a spherical shell of fluorescence with a thickness of 0.50.7 µm as provided by Molecular Probes.
Evaluation of 3-D SPT with simulation
2-D SPT has been widely applied to monitor subpixel displacements of individual fluorescence particles between successive images, and some evaluation frameworks have been performed (Gosh and Webb, 1994
; Kues et al., 2001
; Cheezum et al., 2001
; Thompson et al., 2002
). The rationale of subpixel displacement detection is that fluorescence of single particles spreads over more than one pixel in recorded images, so the subpixel displacement can be tracked by weighting the fluorescence distribution from multiple pixels between successive time-lapse images. Here, we calculated centroids of successive images to estimate subpixel displacements in three dimensions. The centroid of a single axis is
![]() | (1) |
is the coordinates of a pixel on the x axis, and
denotes the fluorescence intensity of the corresponding pixel. A threshold was defined as the fraction of the maximum fluorescence intensity, and those normalized pixels below the threshold were appointed zero. We applied computer-generated granule trajectories and movement, based on the measured parameters, to assess the influences of different signal/noise ratios (SNRs) and thresholds on SPT performance. The simulated granule, with similar size with actual granules (120 nm in diameter, Tooze et al., 1991
The mean-square displacement (MSD) is of critical importance for assessing the parameters of granule's 3-D mobility, so we evaluated the performance of our SPT algorithm for estimating the MSD of the simulated granule at different SNR levels. The resemblance between SPT-estimated MSD and the actual one was assessed by the P-values given in the Kolmogorov-Smirnov (KS) test. For every given SNR, the optimized threshold for each simulated granule tracking was determined by maximizing the P-values (see Fig. 2). In addition, the bias and standard deviation (STD) was calculated and used as another indication of tracking accuracy for the selection of appropriate threshold:
![]() | (2) |
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The mobility of each granule can be analyzed by determining its MSD as a function of time interval n
t. MSD in three dimensions can be calculated as follows:
![]() | (3) |
t is the time interval between two successive 3-D images in a stack, x(j
t), y(j
t) and z(j
t) are the coordinates of the granule at time j
t, and x(j
t + n
t), y(j
t + n
t), and z(j
t + n
t) are the coordinates of the granule in another image taken n
t later.
For random diffusion, granules move with a single 3-D diffusion coefficient (D(3)):
![]() | (4) |
is superimposed on random diffusion:
![]() | (5) |
![]() | (6) |
2 value. The scope of movement of a granule is defined as the mean value of its displacements in three dimensions during the observation period.
Statistics
For normally distributed data, population averages were expressed as mean ± SE unless otherwise stated, and statistic significance was assessed by the Student's t-test. STD was used in Fig. 3 C. Skewed distribution was confirmed by Fisher equation (Becherer et al., 2003
). The median and median standard error (MSE) was used to describe skewed distributed data. Statistical significance of the difference between two skewed distributions was assessed with KS test,
2 value, or both. P < 0.05 and P < 0.01 were denoted as * and **, respectively.
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| RESULTS |
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Before applying deconvolution to live cell images, we assessed the algorithm using well-defined 15-µm diameter beads with a thin fluorescent shell of 0.50.7 µm in width. As would be expected, sections in unprocessed 3-D images of the bead were seriously blurred by out-of-focus light (inset in Fig. 1 C), and the width of shell was much larger than its actual size. Deconvolution computationally reduced the out-of-focus blurring, and gradually gave better estimates of the width of the shell with increasing iteration times (Fig. 1 C). Since low spatial frequency signal (<1/µm) contributes little to the analysis of the mobility of granules that are generally <1 µm in size (Steyer and Almers, 1999
; Oheim and Stühmer, 2000
), we first deconvolved time-lapse images with a small number of iterations (100 for this study), and then high-pass filtered them at a spatial frequency of 1/µm. As depicted in Fig. 1 C, deconvolution with 100 iterations followed by high-pass filtering at a spatial frequency of 1/µm gave similar estimate of the width of the shell as that of simple deconvolution with 1000 iterations. Thus, for the rest of the image processing, we routinely employed the 100-iteration deconvolution together with high-pass filtering at a spatial frequency of 1/µm. The recorded and processed images from an AO-loaded PC12 cell are displayed in Fig. 1 D for comparison.
Accuracy of SPT depends on the SNR and threshold level
Both the SNR of the object and the threshold level applied to the image are critical for the performance of centroid-dependent SPT. In this study, simulated granule trajectories and movement reconstructions, based on measured parameters, were used to evaluate the performance of SPT. We have generated sequential stacks of 3-D images containing single simulated granules at different SNR. Then, we used different SNRs as a parameter and identified the optimized threshold for each granule tracking according to its SNR. For a particular SNR, different threshold selection exerts significant impact on the SPT-estimated MSD as shown in Fig. 2 A. The reason is that as lower threshold is applied, too many background fluorescence remains around tracked granules, making the centroid-based SPT insensitive to granule movement and underestimate MSD throughout; whereas high threshold excludes too many pixels critical for the calculation of centroid and induces unexpected variability in the tracking as well as overestimation of MSD. Hence, we have examined the influence of different thresholds on the significance of difference (assayed by the P-value in KS test) and the bias between the real MSD and the one estimated from SPT (Fig. 2 B). Thus, appropriate threshold should be chosen to maximize the P-value and minimize the bias at given SNR. The relationship of optimized thresholds, corresponding P-values, and biases versus SNRs is revealed in Fig. 2 C. We notice that higher SNRs give better accuracy in SPT. This emphasizes the necessity to choose fluorescence spots with SNR equal to or above 6 for mobility tracking. Based on the SNR of each granule, we selected corresponding thresholds according to Fig. 2 C. For intermediate SNRs not simulated, thresholds were chosen by interpolation between the neighboring integer SNRs.
Identification of fluorescence spots
Most near-membrane fluorescence spots in PC12 cells labeled with AO have been identified as single large dense-core granules (Avery et al., 2000
). However, as AO tends to accumulate in acidic compartments, it is important to verify that the cytosolic fluorescence spots that we selected for analysis are actually granules. After deconvolving and high-pass filtering the images, we identified fluorescence spots with an SNR equal to or >6 (marked with arrows in Fig. 3 A) for further analysis. The lateral and axial fluorescence profiles of each selected AO spot were fitted with Gaussian functions, and the full width at half-maximum (FWHM) of the fitted Gaussian function was taken as a measure of the size of particles (one example is shown in Fig. 3 A, right). Fig. 3 B displays the size distributions of 188 fluorescent spots with the peak lateral and axial size at 0.35 ± 0.02 µm and 0.92 ± 0.05 µm (mean ± STD), respectively. The larger axial size is caused by the relatively lower axial resolution inherited in WFFM. We then compared the averaged size of these fluorescence spots with that of NPY-DsRed labeled large dense-core secretory granules (Lang et al., 2000
; Holroyd et al., 2002
) with similar SNR and found their sizes were nearly equivalent (Fig. 3 C). In fact, the lateral size of our selected fluorescent spots is close to the TIRFM observation of dense-core granules in PC12 cells (Lang et al., 2000
). Thus, we verified that the selection criteria seem to restrict most of the remaining fluorescence spots to large dense-core granules. We further selected those fluorescence spots with both lateral and axial size within the mean ± 2
of the Gaussian size distribution for further mobility analysis. Compared with NPY-DsRed labeled granules, larger SNR could be obtained for AO-loaded granules during much shorter exposure time (Fig. 3 C), so the employment of AO would provide us the ease of labeling, rapid sampling, and less photodamage for imaging live cells.
3-D tracking of single granules in resting cells
Previous studies have suggested that granules diminished in their mobility as they approached the plasma membrane (Steyer et al., 1997
; Johns et al., 2001
). Also, the dense cortical actin network underneath the plasma membrane might influence the mobility of granules (Oheim and Stühmer, 2000
; Lang et al., 2000
). To confirm the usefulness of our 3-D SPT in studying the mobility of granules at different locations inside the cell, we have separated total granules into two groups, GPs and GCs, according to their relative distances from the detected contour of plasma membrane. The membrane contour was detected using the edge-detecting algorithm of Canny (1986)
. Briefly, it calculates the intensity gradient of images with the derivative of a Gaussian filter and locates the edge by looking for local maximum of the gradient. This method is robust to noise and likely to detect even weak edges. We compared the contour detected from deconvolved AO-stained images with that obtained from FM1-43 staining in the same cell. FM1-43 is not fluorescent in solution, and becomes fluorescent when incorporated into the membrane lipids (Leung et al., 2002
; Angleson et al., 1999
). As shown in Fig. 4 A, the membrane contours recognized from AO- and FM1-43-stained images were quantitatively comparable. The mean absolute difference between the two contours was 0.29 ± 0.02 µm (estimated from four cells) with a maximum and minimum value of 0.42 µm and 0.1 µm, respectively. The same section as in Fig. 4 A was high-pass filtered and displayed in high magnification in Fig. 4 B. Granules that meet our selection criteria are marked with circles. One granule identified as GP is indicated with an arrow in Fig. 4 B. The time-lapse images of this GP in the x, y and x, z plane are displayed in Fig. 4 C. As shown in Fig. 4 C, the granule seems quite consistent in its size and shape. However, sometimes the rotation of the nonspherical granule may change its projection in the 2-D section. Thus, as further evidence that the deconvolution did not introduce severe artifacts in our study, we have calculated the averaged 3-D volume of granules and found little variation between successive images, as demonstrated in Fig. 4 D.
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10%) moving along a fixed direction as if transported by some already constructed tracks (Fig. 5 C). Their MSD plots resulted in a positive curvature because the V2 term of Eq. 5 would dominate the MSD for longer time (Fig. 5 C). Interestingly, the directed velocity of granule transportation for GC (15.4 ± 0.8 x 103 µm/s, median ± MSE, n = 15) is also larger than that of GP (8.5 ± 0.39 x 103 µm/s, median ± MSE, n = 13) (P < 0.05, KS test). For comparison, we recorded sequential 3-D images of immobilized 0.175-µm diameter beads under various imaging conditions. As an example, the averaged MSD plot from six beads under SNR = 6 is displayed in Fig. 5 A, wherein a D(3) of 0.087 x 104 µm2/s is calculated. This probably reflects our lower limit of detection under this imaging condition.
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0.4 µm (Lang et al., 2000| DISCUSSION |
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In classical 2-D time-resolved particle tracking, the contribution from the missing axial direction is usually ignored. TIRFM-based tracking attempts to resolve the z-mobility from the fluctuation in granule's fluorescence that is exponentially related to the change in axial position. However, small changes in the axial position will result in large changes in fluorescence measured with TIRFM. Also, fluctuation in fluorescence unrelated to axial position will result in misinterpretation of the z-position. Moreover, TIRFM can only be employed to study vesicles right underneath the plasma membrane, whereas vesicles residing deeper inside the cytosol are invisible under TIRFM. Despite the recent development in 3-D tracking of single particles (Kao and Verkman, 1994
; Speidel et al., 2003
; Levi et al., 2003
), the 3-D mobility of granules within living cells has not been demonstrated. In this study, we have employed a centroid-based 3-D SPT from time-resolved stacks of 3-D images, and the displacements of single granules in three dimensions could be directly obtained. We found that granules can be assumed to move the same way in z direction as they behave in lateral direction, suggesting the missing z direction information in 2-D tracking probably will not impose significant distortion in assessing the lateral mobility of granules. However, 3-D tracking does offer the advantage of following granules in a larger 3-D space, not restricting to a single optical plane.
We have demonstrated that appropriate threshold selection is very critical for the precision of granule tracking. Specific threshold should be selected for each given SNR to assure the best result in 3-D tracking. We have found that higher SNRs give better accuracy in SPT, thus improving SNR will help to get better precision in granule tracking. With our NA 1.65 objective, a theoretical resolution of 0.18 µm in x, y plane and 0.45 µm in z direction is expected. The evident discrepancy between lateral and axial resolution caused by diffraction limit leads to nonisotropic resolution and precision in 3-D particle tracking. In fact, we found that the threshold optimized (optimizing procedure, see Fig. 2) for lateral tracking performance was different from that optimized for axial tracking (data not shown) at a given SNR. Increases in resolutions along x, y directions and z direction, especially breaking the distortion occurred in z direction, will balance the tracking performance in different directions. The recently developed stimulated emission depletion technique (Klar et al., 2000
) and beam-scanning multifocal multiphoton 4Pi-confocal microscopy (Egner et al., 2002
) have finally broken the diffraction barrier and achieved a nearly spherical resolution of
100 nm. These techniques will find more application in the demand for more precise and isotropic 3-D particle tracking. However, the drawbacks of these techniques inherited with confocal microscopy, i.e., low time resolution, high photobleaching, and photodamage, will limit their use when long-term 3-D tracking in living cell is demanded.
3-D mobility of secretory granules in PC12 cells
AO accumulates within granules as well as nonvesicular compartments like lyso- or endosome. By choosing fluorescence spots with SNR
6 and by applying high-pass filtering, the selected fluorescence spots has single Gaussian profiles in fluorescence with lateral and axial FWHMs indistinguishable from those of NPY-DsRed labeled dense-core granules, suggesting we were mainly analyzing AO-labeled large dense-core granules in this study. AO-loaded granules are much brighter than NPY-DsRed labeled ones, as 5 ms exposure of AO-loaded granules gave similar SNR to that of NPY-DsRed labeled granules with 100 ms exposure time (Fig. 3 C). Thus, the advantage of AO is not only its ease of use, but also the less exposure time and hence less photodamage. PC12 cells are densely packed with secretory granules. Our selection criteria might exclude most of the weakly stained spots (i.e., small synaptic like vesicles) and large spots for analysis; however,
65% of the observed granules remained for analysis after selection. Moreover, although the density of our selected AO-labeled granules (0.12 ± 0.02/µm2) is lower than that of NPY-labeled granules observed under TIRFM (0.358/µm2, Taraska et al., 2003
) in PC12 cells, it is comparable with the density of cytosolic granules in chromaffin cells observed using electron microscopy (0.11/µm2, Steyer et al., 1997
).
The characterization of particle motion imposes demands on the temporal and spatial resolution required for the measurement. When there is only simple free diffusion, as indicated by the linear dependence of MSD on time, the time resolution of the measurement does not influence the determination of the diffusion coefficient from the slop of the plot of MSD(n
t). In contrast, when diffusion is constrained by a cage or tether, a characteristic time of observation is required together with a corresponding requirement for sufficient temporal resolution to resolve the dynamic motion (Qian et al., 1991
). Previous study has suggested that granules wander rapidly with a diffusion coefficient of 19 x 104 µm2/s within a cage that leaves
70 nm space around granules, whereas the cage itself diffuses in random 10-fold more slowly over longer distances (Steyer and Almers, 1999
). The slow effective sampling rate (0.2 Hz) used in this study due to 3-D stack generation will miss the fine movement of granules within the cage. However, it will accurately track the long range diffusion of granules, which presumably reflects the movement of the cage.
Imaging under TIRFM is restricted to a thin layer underneath the plasma membrane, which adheres unphysiologically to the coverglass. Whether the adhesion of plasma membrane to coverglass will affect the mobility of neighboring granules and their fusion remains to be examined. Interestingly, we found that GPs residing far away from the basal plasma membrane exhibit similar diffusion coefficient as that measured by TIRFM (Steyer and Almers, 1999
, Becherer et al., 2003
). GP in this study also traveled in a similar cage as that observed under TIRFM. Along with the fact that diffusion of fluorescent dyes could be observed as a "cloud" after fusion, it is likely the adhesion of basal membrane to coverglass does not exert significant effect on the surrounding granules.
Secretory granules have long been assumed to belong to distinct functional pools (Bratanova-Tochkova et al., 2002
; Duncan et al., 2003
). By simultaneously tracking near-membrane and cytosolic granules, we have found significant differences between these two groups of granules in their D(3), radius of cage, and scope of movement. The mobility of these two groups of granules is also differentially affected by disruption of F-actin. These results suggest that the motion of the two groups of granules is mediated by different mechanisms. However, we failed to distinguish subgroups within either GPs or GCs. The distributions of diffusion coefficient for either GP or GC did not exhibit multiple distinct peaks, suggesting granules are smoothly organized into one population, rather than into distinct pools, and most of them travel with lower mobility. This result is consistent with a recent study in the neurites of differentiated PC12 cells under TIRFM by Ng et al. (2003)
, who reported a broad and asymmetric distribution in diffusion coefficient without a separation of a distinct pool of granules. With the advantage of our method to study the mobility of granules deep inside the cytosol, we now extend this feature to cytosolic granules.
Correlation of granules with cortical actin cytoskeleton
Although some granules wandered with random diffusion, granule trafficking is likely to be mediated by different cytoskeleton systems along with a number of motor proteins (Hirokawa, 1998
; Kamal and Goldstein, 2002
). Thus, the motion of single granules might be influenced by expected or unexpected organelles on their way. The caged diffusion of granules much adjacent to the plasma membrane has been previously elucidated by TIRFM (Steyer and Almers, 1999
; Oheim and Stühmer, 2000
; Johns et al., 2001
), which is seen as the entrapment of granules inside the cortical actin cytoskeleton meshwork. In this study, we have found that besides near-membrane granules, a majority of cytosolic granules traveled in a caged fashion as well. Interestingly, lots of GCs are likely trapped in a larger cage than GPs, suggesting a relatively looser meshwork inside cytosol. In addition to its role in restricting the movement of granules, cytoskeleton meshwork has also been thought to actively participate in granule motion, as well as to supply directional tracks for granule transportation (Rogers and Gelfand, 2000
; Lang et al., 2000
). In this study, we did find a small fraction of granules traveling in a directed fashion. Stimulation with HK solution increased the number of granules in directed traveling as well as the velocity of directed traveling (data not shown), whereas the diffusion coefficients remained unchanged, indicating an increased impelling of granules in an active manner. The augmentation in directed traveling was significantly inhibited by disruption of actin cytoskeleton for GP, but not for GC (Fig. 7 A). Moreover, the D(3) and the scope of movement of GP were also more prone to the treatment of LB than those of GC (Fig. 7, B and C). Taking together, we propose that the movement of near-membrane granules are likely mediated as well as constrained by cortical actin network, whereas cytoskeleton other than cortical actin participates in the movement of cytosolic granules. Further experiments are demanded to identify the correlations between granule mobility and the underlying molecular mechanisms employing similar techniques used in this study.
| ACKNOWLEDGEMENTS |
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This work was supported by National Science Foundation of China Grants No. 60071030 to A. Qu, Nos. 30025023, 3000062, and 30130230 to T. Xu, and National Basic Research Program of China (973) Grant G1999054000 and 2001CCA04100 to T. Xu. We are grateful for the support from the Li Foundation and the Sinogerman Scientific Center. The laboratory of T. Xu belongs to a Partner Group Scheme of the Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
Submitted on March 19, 2004; accepted for publication May 25, 2004.
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