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* Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California;
University of Connecticut Health Center, Department of Cell Biology and Center for Biomedical Imaging Technology, Farmington, Connecticut; and
University of Pennsylvania, School of Veterinary Medicine, Philadelphia, Pennsylvania
Correspondence: Address reprint requests to Vladimir Rodionov, University of Connecticut Health Center, Dept. of Cell Biology and Center for Biomedical Imaging Technology, 263 Farmington Ave., Farmington, CT 06032-1507. Tel.: 860-679-1850; Fax: 860-679-1039; E-mail: rodionov{at}nso.uchc.edu.
| ABSTRACT |
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| INTRODUCTION |
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Opposite-polarity MT motors are bound to the surface of the same cargo organelles (Lane and Allan, 1998
). As a result, MT-based transport is discontinuous and involves transitions between the three statesdisplacements to MT plus or minus ends and pauses (Gross et al., 2002
; Morris and Hollenbeck, 1993
; Welte et al., 1998
). Net direction of the movement is regulated by second messengers such as cAMP or Ca2+ ions (reviewed in Reilein et al., 2001
). Changes in the movement parameters that are induced by variations in the second-messenger levels are cell type-specific. Global regulation of the transport direction in some cells involves control over the runs of organelles only to MT plus or minus ends (Kamal and Goldstein, 2002
; Karcher et al., 2002
; Lane and Allan, 1998
; Vale, 2003
), whereas in others uninterrupted runs in both directions are affected (Rodionov et al., 2003
). Information about the changes in the movement parameters in response to intracellular signals is therefore essential for the identification of MT motors subjected to regulation. The measurement of the movement parameters involves recording of living cells at a high temporal and spatial resolution, tracking of moving organelles, and decomposition of the resulting trajectories into periods of runs and pauses (Morris and Hollenbeck, 1993
; Welte et al., 1998
).
Decomposition of the movement trajectories has proved to be a difficult task because of the random fluctuations in the positions of organelles in the cytoplasm as well as self-similar scale-free structure of typical trajectories. Here we introduce an algorithm for automatic detection of runs and pauses within organelle trajectories. The algorithm is based on the multiscale trend analysis (MTA) that extracts "trends"piecewise linear approximations of particle trajectories. The proposed algorithm is automatic and self-adapted to the characteristic durations and velocities of runs. We apply the algorithm to MT-dependent movement of pigment particles in melanophores and pigment cells of fish and amphibia, which provide a remarkable example of regulated MT-based transport (reviewed in Nascimento et al., 2003
).
The major function of melanophores is fast and synchronous redistribution of thousands of membrane-bounded organelles, pigment granules, which serves the purpose of chromatic adaptation of the animal. The granules either aggregate at the cell center or redisperse uniformly throughout the cytoplasm. Aggregation involves movement of granules along MTs by means of minus-end-directed MT motor cytoplasmic dynein (Nilsson and Wallin, 1997
). Dispersion combines transport of granules to the MT plus ends by a kinesin family motor (Rodionov et al., 1991
; Tuma et al., 1998
) and movement along actin filaments powered by a myosin (Rodionov et al., 1998
; Rogers and Gelfand, 1998
). Regulation of pigment transport involves changes in the levels of cAMP, which regulates the activity of MT and actin motors (reviewed in Nascimento et al., 2003
).
Previous analysis of the movement of pigment granules in melanophores has shown that aggregation and dispersion stimuli do not induce significant changes in the movement velocities, but have a profound effect on the length of uninterrupted runs (Gross et al., 2002
; Rodionov et al., 2003
). In fish melanophores, dispersion signal shortens minus-end and increases plus-end run length, whereas aggregation signal induces the opposite changes (Rodionov et al., 2003
). In contrast, in Xenopus melanophores only the length of minus-end runs appears to be regulated, leaving the length of plus-end runs constant throughout pigment aggregation and dispersion (Gross et al., 2002
). These observations suggest important differences in the mechanisms of regulation of net pigment transport direction between the two pigment cell types. Here we use MTA to reinvestigate regulation of pigment transport in melanophores and directly compare the movement of pigment granules in the two pigment cell types. We find that despite the differences in the values of the pigment granule movement parameters, the general patterns of regulation of MT motors are similar in fish and Xenopus melanophores.
| MATERIALS AND METHODS |
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Permanent cell lines of Xenopus melanophores were obtained as described in (Daniolos et al., 1990
) and cultured in Xenopus tissue culture medium (70% L15 medium supplemented with antibiotics, 20% fetal bovine serum, and 5 µg/ml insulin).
Pigment aggregation was induced with 5 x 107 M adrenalin (fish melanophores) or 108 M melatonin (frog melanophores). Pigment dispersion in fish melanophores was induced by washing out adrenalin via 56 changes of fish tissue culture medium. In some experiments, caffeine (5 mM) was introduced into the last washing solution to facilitate dispersion. To induce pigment dispersion in frog melanophores, cells were washed 35 times with Xenopus tissue culture medium to remove melatonin and treated with melanocyte stimulating hormone (108 M).
Real-time analysis of MT-based transport of pigment granules
The movement of pigment granules was recorded with a Nikon TE300 inverted microscope (Nikon, Tokyo, Japan) equipped with a 100x 1.25 NA Plan Achromat objective lens. Time series (15 s long) of phase contrast images were acquired at a video rate of 30 frames/s with a Watec-902B CCD video camera (Watec, Tokyo, Japan) via stream acquisition option of Metamorph image acquisition and analysis software (Universal Imaging, Downington, PA). To increase the spatial resolution of images, an additional projection lens (2x) was placed in front of the camera chip.
Pigment granules were tracked with the particle tracking module of Metamorph software. Tracking was performed at the edge of expanding or retracting pigment mass where individual granules could be observed. To avoid artifacts introduced by interaction of pigment granules with each other, only trajectories of granules that never collided with their neighbors were used for the analysis.
| RESULTS |
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Multiscale trend analysis
MTA is a general statistical method (Zaliapin et al., 2004
) that involves construction of a sequence of embedded piecewise linear approximations of time series; it is shown to possess a series of well-defined statistical properties nicely connected to the self-affine structure of the time series. In this work, we apply MTA to intracellular transport of pigment granules of melanophores and develop a new method of pigment granule analysis. The method is based on constructing a hierarchy of piecewise linear approximations of the granule trajectories with progressively increasing accuracy; this hierarchy is then used for detection of pauses and runs.
Specifically, the zero level of the hierarchy is formed by the best least-square linear approximation L0(t) of P(t) over the entire observational interval; L0(t) consists of a single linear segment. We define the approximation error for L0(t) as
![]() | (1) |
Formally, to construct the approximation L1(t) we first introduce the quality measure for an arbitrary piecewise linear approximation L(t; N,E) consisting of N linear segments and having total fitting error E:
![]() | (2) |
![]() | (3) |
1, Ei
E0. The slope of the linear segment [p0,pi] shows the increase of the fitting quality per one additional segment of approximation. By the criteria in Eqs. 2 and 3, we choose the approximation with the maximal quality increase. Finally, N1 linear segments of the approximation L1(t) comprise the first level of our hierarchy. To construct the next approximation, L2(t), we apply the above procedure to one of N1 segments of the first-level approximation L1(t). The choice of this segment corresponds to the maximization of the corresponding error decrease (E1 E2). The N2 segments of this approximation comprise the second level of the hierarchy. Similarly, at each consecutive step, we apply the above procedure to one of the segments of the current approximation Lk(t) to form the next approximation Lk+1(t). Each segment of the approximation Lk+1(t) is embedded into or coincides with a segment from Lk(t); this is why we call the system of our approximations embedded and this is why they form a well-defined hierarchy.
As a result, a series of piecewise linear approximations Lk(t)k = 0, 1, ... of the original series P(t) is obtained. The approximations are of increasing detail and the larger the index k the larger the number Nk of linear segments within Lk(t), and the smaller their characteristic duration.
For the correct decomposition of granule trajectories it is critical to choose the appropriate level k0 of the approximation hierarchy. If the k0 is too small, there is a risk that individual runs will be combined, whereas too large k0 values will lead to the depiction of irrelevant low-amplitude oscillations in the granule positions. The problem of choosing right k0 can be solved using the MTA spectrum: a graph showing the fitting error Ek of approximation Lk(t) as a function of the number Nk of its linear segments. By definition, this function is monotonously decreasing. For purely self-affine time series characterized by a single Hurst exponent H, the error Ek and scale Nk are connected via (Zaliapin et al., 2004
):
![]() | (4) |
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The above procedure was applied to the 988 trajectories of frog granules and 666 trajectories of fish granules, producing, respectively, 12,381 and 9272 individual runs.
An example of pigment granule spectrum is given in the Fig. 2 A inset. It is clear that the spectrum breaks into two almost linear segments at the level k0 = 6. Fig. 2 shows the granule trajectory on the background of the MTA decomposition at this level. The piecewise linear approximation at corner level k0 = 6 accurately reflects prominent segments of distinct velocities within the analyzed trajectory. We therefore used this decomposition level for the analysis of pigment granule movement along MTs. Other trajectories have different corner levels; nevertheless, the corner level is present in every analyzed trajectory and can be easily and reliably detected. In fact, the very existence of runs, i.e., movements of a granule at a preferred speed for significant time, does ensure the existence of a spectrum corner point, since such runs facilitate the efficiency of piecewise linear approximation at scales >k0.
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12,000 segments for 988 individual trajectories (356 for aggregation, 632 for dispersion). It is clear that the velocity distribution is strikingly bimodal, with peaks at 50 nm/s and 390 nm/s. The same bimodal distribution was observed when the data for aggregation and dispersion was examined separately. We conclude that the low- and the high-velocity peaks on the histogram correspond, respectively, to pauses and runs and therefore the value V0 = 100 should be used as a velocity threshold. It is helpful to consider run velocities in logarithmic scale because it makes the two peaks of the velocity distribution approximately normal (so-called log-normal distribution).
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![]() | (5) |
Amazingly, the results of both "individual" and "group" threshold selections led to similar numerical values, illustrating the objective existence of different movement regimes as well as stability of threshold-selection procedure.
Fig. 4 A shows two-dimensional scatter plots of run durations versus displacements based on the data obtained for 220 individual runs of aggregating pigment granules in Xenopus melanophores using the above procedure. Diagonal lines on the plot indicate constant velocities of runs. It is clear that a threshold velocity of
100 nm/s separates the two nonoverlapping velocity clusters, a fast component (upper cluster on the plot) that likely corresponds to the active motor-based transport and a slow component (lower cluster) that does not result in significant granule displacement and in this analysis was designated as pauses. The separation of runs and pauses based on the analysis of individual trajectories (Fig. 4) is in a good agreement with statistical data shown in Fig. 3, which confirms that the velocity threshold V0 = 100.
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Net pigment transport rates are significantly different in fish and Xenopus melanophores as evidenced from time sequences of phase contrast images of cells. Pigment aggregation and dispersion occur
2-fold faster in fish than in Xenopus pigment cells (
5 and 10 min for aggregation and dispersion in fish melanophores compared to 1015 and 2030 min for frog cells; Fig. 1). Given the smaller size of Xenopus melanophores (Fig. 1), this means that it takes more time for pigment granules to cover shorter distances during aggregation and dispersion.
These differences in the net pigment transport rates can be caused by the lower velocities of the movement of pigment granules during uninterrupted runs or by more frequent pauses in Xenopus melanophores. Regulation of only one component of MT transport, as suggested for minus-end runs in frog melanophores (Gross et al., 2002
), instead of simultaneous reciprocal regulation of both plus- and minus-end runs, as seen in fish cells (Rodionov et al., 2003
), can also explain lower net transport rates. To find out which parameters of the granule movement are responsible for the observed differences, we tracked individual pigment granules in fish or frog melanophores at increasing time intervals after stimulation of pigment aggregation or dispersion and used MTA to decompose granule trajectories into periods of uninterrupted runs and pauses.
We found that the rates of uninterrupted runs averaged throughout dispersion or aggregation were slightly lower in frog than in fish melanopohores (Fig. 5 A). Average rates for frog were: plus-end runs, 458.4 ± 5.7 nm/s (n = 5479); minus-end runs, 552.8 ± 19.8 nm/s (n = 1006). Average rates for fish were: plus-end runs, 662.2 ± 8.4 nm/s (n = 4089); minus-end runs, 636.9 ± 23.5 nm/s (n = 2335). The difference in plus-end rates is consistent with the suggestion that plus-end pigment granule transport in fish and Xenopus melanophores is driven by different members of the kinesin family, kinesin 1 in fish (suggested in Rodionov et al., 1991
) and kinesin 2 in frog (shown in Tuma et al., 1998
). The difference in minus-end rates could be explained by the possible differences in the properties of the dynein motor molecules in the two experimental systems. However, such a difference in rates (20% overall) cannot fully explain the observed differences in net pigment displacement rates in the two experimental systems.
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The differences in pause durations became particularly clear when we compared the kinetics of changes of the fraction of time that pigment granules spent in uninterrupted runs and pauses during pigment aggregation and dispersion. In fish melanophores, the fraction of time that granules spent in pauses was only 20% during aggregation and
40% during dispersion (Fig. 6 A). In contrast, in frog melanophores pigment granules were stationary most (6080%) of the time (Fig. 6 B). Therefore, long pauses appear to be the major reason for the slow transport rate in Xenopus melanophores.
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In fish melanophores, the length of plus-end MT runs displays distinct kinetics during pigment dispersion, which plays an important role in the switching between the MT and actin transport systems (Rodionov et al., 2003
). A rapid increase of plus-end MT run length at early stages is followed by its slow decrease as the granules approach the cell margin. To find out whether similar fine tuning of plus-end run length occurs in Xenopus melanophores, we calculated the length of plus end runs at increasing time intervals after the stimulation of pigment dispersion. We found that the overall kinetics of changes in the length of plus-end runs was strikingly similar in fish and frog cells (Fig. 7, A and B). A rapid twofold increase in the plus-end run length in frog pigment cells was followed by a slow decrease to a low basal level (Fig. 7 B). We therefore conclude that the mechanisms of regulation of pigment transport are conserved among the pigment cell types.
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| DISCUSSION |
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Remarkably, MTA decomposition detects the characteristic timescale created by pigment granule runs, which is uniquely determined by the corner level k0. Simplistically, the timescale can be defined as an average duration of the runs detected at the corner level. It should be stressed, however, that the durations of runs vary significantly within a given decomposition level and it is sometimes more efficient to describe them by a probabilistic distribution rather than a mere average, or to trace their time variability considering the original decomposition. The qualitative meaning of the term "timescale" should depend on a particular problem at hand. It is important that our analysis is capable of detecting important global scaling characteristics of the process under study. Analysis and comparison of such characteristics might be illuminating for deeper understanding of the intracellular processes.
The ability for self-adaptation to characteristic durations and velocities of runs sets MTA apart from other algorithms such as a threshold-based algorithm for the analysis of the movement trajectories. The advantages of MTA are clearly seen when we compare the results of decomposition of pigment granule trajectories obtained with the two algorithms (Fig. 4). Semilogarithmic plots of the lengths of uninterrupted runs as a function of run durations show that although the majority of the runs are identified by both methods (Fig. 4, B and C), the previously published analysis (Gross et al., 2002
; Welte et al., 1998
) (Fig. 4 C) has two drawbacks. First, it fails to recognize runs that have short (<1/10 s) duration; second, for slow-moving granules this analysis tends to confuse slow (<100 nm/s) runs and pauses. This leads to an overlap of values for the velocities of runs and pauses. In contrast, MTA uses a velocity-based approach that allows much better separation of runs and pauses (Fig. 4 B). Another advantage of MTA is that this method does not rely on information about the experimental system, whereas the previously published algorithm uses definition of runs and pauses that requires experimentally obtained numerical parameters measured in preliminary experiments and thus varies from system to system. We therefore believe that MTA is an advanced algorithm that can be widely used for the analysis of bidirectional transport of various organelles along MTs.
Comparison of MT transport in fish and Xenopus melanophores
The movement statistics extracted with MTA explain slower rates of net pigment transport in frog melanophores compared to fish pigment cells. The major cause of low net transport rates appears to be the very long time that pigment granules spend in pauses. Further, even when pigment granules in Xenopus melanophores move, the rate of their movements is on average 20% lower, and that of their runs
50% shorter, than in fish pigment cells. Therefore, differences in the durations of pauses and the rates and lengths of uninterrupted runs make transport far less efficient in Xenopus melanophores than in fish pigment cells.
Despite these significant differences in the values of the movement parameters and net pigment transport rates we find that general patterns of regulation of MT-based transport are similar in the two pigment cell types. The movement of pigment granules to the cell center during aggregation is driven by a rapid and dramatic increase in the length of minus-end runs, which is maintained at a high level throughout the pigment aggregation. Pigment dispersion is induced by a decrease in the length of minus-end runs and concurrent increase in the length of plus-end runs. However, this increase is temporal and the length of plus-end runs returns to a low basal level with time during dispersion. Our previous work has shown that in fish melanophores the kinetics of changes of plus-end runs determines the sequence in which the two major transport systems act during dispersion (Rodionov et al., 2003
). Long runs at early stages determine predomination of MT transport, but as the run length drops the granules switch onto actin filaments. Our finding that kinetics of changes in plus-end run length is similar in Xenopus melanophores and fish pigment cells suggests conservation of the mechanisms responsible for the switching of pigment granules between the two major transport systems among pigment cells from different organisms.
The conclusion about the similarity of the mechanisms of MT transport regulation apparently contradicts the results of published studies that imply significant differences in regulation of MT transport direction in fish and Xenopus melanophores. First, the granule tracking analysis performed in Gross et al. (2002)
indicated that in Xenopus melanophores only the length of minus-end runs is regulated by signaling events. Second, the balance of plus- and minus-end MT transport components seem to be different in fish and Xenopus melanophores, as evidenced from the experiments that involve complete depolymerization of actin cytoskeleton with latrunculin (Rodionov et al., 1998
; Rogers and Gelfand, 1998
). In fish melanophores latrunculin treatment induces redistribution of pigment granules to the cell rim as would be predicted from the prevalence of the plus-end-directed component of MT transport (Rodionov et al., 1998
). Surprisingly, in frog melanophores actin depolymerization leads to accumulation of pigment granules in the cell center (Rogers and Gelfand, 1998
).
To explain our results and the data obtained by others, we propose a hypothesis for the regulation of pigment transport in melanophores (Fig. 8). We suggest that regulation of plus-end runs was overlooked in the study of Gross et al. (2002)
, who compared the MT transport statistics at late stages of aggregation and dispersion, when plus-end runs returned to a low basal level, and that in both fish and frog cells regulation involves a transient increase in plus-end run length. We hypothesize, however, that implications of the suppression of the plus-end-directed component of MT transport at later stages of dispersion are different in the two pigment cell types. In fish melanophores, MT transport remains directed to the periphery even when dispersion is complete, whereas in frog melanophores, a drop in the plus-end run length leads to the reversal of net MT transport direction. Thus, actomyosin transport in fish melanophores prevents pigment granules from redistribution to the cell margin, whereas in frog melanophores it prevents granules from accumulation at the cell center. Future experiments will test this hypothesis and elucidate molecular mechanisms that are responsible for the regulation of MT motors in melanophores.
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| ACKNOWLEDGEMENTS |
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This work was supported by National Institutes of Health grants GM-62290 and NCRR RR13186 to V.I.R.
Submitted on November 29, 2004; accepted for publication February 22, 2005.
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