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Journal of Cell Science 112, 2277-2289 (1999) Printed in Great Britain © The Company of Biologists Limited 1999 JCS0417

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Contribution of plus and minus end pathways to microtubule turnover
I. A. Vorobjev1, V. I. Rodionov2, I. V. Maly1 and G. G. Borisy2,*
1Laborator 2Laborator

y of Cell Motility, A. N. Belozersky Institute, Moscow State University, Moscow, Russia y of Molecular Biology, University of Wisconsin, 1525 Linden Drive, Madison, WI 53706, USA

*Author for correspondence (e-mail: ggborisy@facstaff.wisc.edu)

Accepted 6 May; published on WWW 24 June 1999

SUMMARY Turnover is important for the maintenance and remodeling of the cytoskeleton during the processes of cell morphogenesis, mitosis and motility. Microtubule (MT) turnover is thought to occur by dynamic instability, growth and shortening at distal (plus) ends. Recent observation of MT release from the centrosome and depolymerization from proximal (minus) ends indicates the existence of a minus end pathway. To evaluate the relative contributions of plus and minus end pathways to turnover, we analyzed MT dynamics in a model system, the fish melanophore, a large non-motile cell with a regular radial array of long MTs. MT ends were tracked in digital fluorescence timelapse sequences and life histories of individual MTs were analyzed using random walk theory generalized to the case of diffusion with drift. Analysis of plus end dynamics gave an apparent diffusion coefficient of D=7.5 µm2/minute. The random walk model predicts that the half-time for turnover driven solely by plus end dynamics will depend strongly on position in the cell. Based on the experimentally determined value of D, turnover of MTs near the center of a typical melanophore of radius 70 µm was calculated to require over 5 hours, a paradoxically long time. To examine MT behavior deep in the cytoplasm, we developed a novel, sequential subtraction mode of image analysis. This analysis revealed a subpopulation of MTs which shortened from their minus ends, presumably after constitutive release from the centrosome. Given the relative slowness of plus end dynamics to turn over the root of a long MT, the turnover of MTs near the cell center is determined primarily by the minus-end pathway. MTs released from the centrosome become replaced by newly nucleated ones. The relative contributions of plus and minus end pathways was estimated from the diffusion coefficient, D, for the plus end, the length distribution of MTs, t he frequency of free minus ends, and the rate of minus-end shortening. We conclude that, in large animal cells with a centrosomally focussed array of MTs, turnover occurs by a combination of plus and minus end pathways, the plus end dominating at the cell periphery and the minus end dominating near the cell center.

Key words: Microtubule dynamics, Centrosome, Diffusion, Fluorescence microscopy, Melanophore

INTRODUCTION Microtubules (MTs) are dynamic polymers in the sense that they are continuously being built and degraded in living cells. This MT turnover most likely plays a key role in cellular processes requiring a change in cell shape or remodeling of cell cytoplasm such as during cell motility or cell morphogenesis or in the construction of cytoplasmic structures such as the mitotic spindle. To quantify MT dynamics, two experimental approaches with complementary strengths and weaknesses have generally been used (see Desai and Mitchison, 1997; Joshi, 1998, for reviews). One approach is basically a population method which attempts to determine the rapidity of MT turnover by measuring the kinetics of fluorescence redistribution after photobleaching or photoactivation (FRAP). The other approach attempts to determine the course of MT turnover by visualizing and directly assessing the dynamic behavior of individual MTs. FRAP analyses give values for turnover times which are averages over a population of MTs at a specific position in the

cell. The recovery of bleaching (or loss of photoactivated mark) have been approximated by a single exponential process representing turnover. For most interphase cells, FRAP analyses resulted in half times for MT turnover ranging from 5 to 20 minutes with epithelial cells tending to be slower than fibroblasts (Sammak et al., 1987; Saxton et al., 1984; Pepperkok et al., 1990; Rodionov et al., 1994). In neurons, FRAP measurements gave half-times of 15 minutes to 1 hour (Lim et al., 1990; Okabe and Hirokawa, 1992; Reinsch et al., 1991). Thus, the general consensus of the FRAP approach is that MT turnover in interphase cells is rather rapid although characteristic half-times for turnover are cell type specific. In contrast to the FRAP analyses, direct imaging approaches have provided data on the dynamics of individual MTs (Sammak and Borisy, 1988; Schulze and Kirschner, 1988; Cassimeris et al., 1988; Shelden and Wadsworth, 1993; Waterman-Storer and Salmon, 1997; Vorobjev et al., 1997). Direct imaging data have generally been analyzed in terms of the dynamic instability model (Mitchison and Kirschner, 1984) which stipulates that MT plus ends can exist in either of two


2278 I. A. Vorobjev and others states, growing or shortening, and that stochastic transitions, termed catastrophes and rescues, occur between these two states. Thus, a body of data exists in the literature on the `dynamicity' of MTs (Dhamodharan and Wadsworth, 1995; Yvon and Wadsworth, 1997) which, in general means the dynamics of MT plus ends. A few reports have recognized limitations of the dynamic instability model (Odde et al., 1995; Odde, 1997). In contrast to the two-state model which stipulates fixed rates of growth and shortening, MTs have been reported to display intrinsically variable rates of growth and shortening both in vitro (Gildersleeve et al., 1992) and in vivo (Vorobjev et al., 1997). This has led to attempts to characterize MT dynamics by a model-independent approach. One approach to quantitative analysis of MT turnover in vivo has employed the conceptual framework of a random walk to the behavior of MT ends (Vorobjev et al., 1997). With this approach, the stochastic growth and shortening behavior of the MT plus end is characterized as a 1-dimensional random walk analogous to the diffusion of a molecule and the overall level of dynamic activity is captured by a single number, an apparent diffusion coefficient. For the plus ends of MTs in PtK1 cells, the diffusion coefficient was determined to be D=2.4 µm2/minute (Vorobjev et al., 1997). Independent of the molecular details underlying MT dynamics, it should be possible to link the behavior of individual MTs with the turnover kinetics of the MT population. However, theoretical calculations based on Monte Carlo simulations of plus end dynamics using dynamic instability parameters obtained for newt lung cells (Gliksman et al., 1993) yielded a turnover half-time (3.5 hours) far slower than typical FRAP measurement values. Random walk analysis produced a similar disparity. A characteristic turnover time can be calculated from the apparent diffusion constant as the time required for the MT plus end to `diffuse' to its minus end, generally assumed to be at the centrosome. Assuming a typical length for MTs in PtK1 cells of 20 µm, a diffusion coefficient of 2.4 µm2/minute predicts a value for the turnover time of over one hour, long compared to experimental measurements. Thus analysis of individual MT dynamics seems to be in apparent contradiction with the rapidity of their turnover. The disparity between experimental values of MT turnover time and values calculated from the behavior of individual MTs prompts a number of questions. Is our understanding of MT turnover incomplete or are the FRAP measurements wrong in some way, or both? Are determinations of the kinetic parameters of MTs or the experimental determination of D in error or are our estimates of MT length incorrect? These questions suggest that a more comprehensive revisiting of MT dynamics and an effort to obtain a coherent quantitative picture would be worthwhile. The possibility that our understanding of MT turnover is incomplete has been raised by recent observations concerning the activity of the minus end. Minus ends had generally been thought to be associated with and anchored in the centrosome. However, recent observations of MT release from the centrosome and depolymerization from proximal (minus) ends (Keating et al., 1997; Waterman-Storer and Salmon, 1997; Vorobjev et al., 1997) and MT treadmilling (Rodionov and Borisy, 1997; Rodionov et al., 1999) indicate the existence of a minus end pathway. In most instances, minus-end shortening, when it occurred, was rapid with velocities in the range of 412 µm/minute depending on the cell type. Assuming a shortening rate of 5 µm/minute, a 20 µm MT would require only 4 minutes to completely depolymerize from its minus end. Thus, the minus end pathway has the capacity, in principle, to rapidly eliminate long MTs. Turnover would be accomplished when the eliminated MTs were replaced by MTs newly nucleated at the centrosome. In this study, we have sought to quantitatively determine the contributions of plus-end dynamics and the putative minus-end pathway to MT turnover in a model system where all the required parameters could be estimated. We have chosen the fish melanophore as an experimental system because it displays a number of favorable properties. It is non-motile, radially symmetric and large. The lack of motility eliminates the need to consider changes in the spatial arrangement of MTs which necessarily accompany crawling motions. The radial symmetry permits analysis of MT dynamics to be simplified to a 1dimensional problem, namely, dynamic behavior along a radius. Because the melanophore is large, it contains many long MTs, accentuating the possibility of discriminating between plus and minus end behavior. Indeed, fish melanophores have a diameter sometimes exceeding 200 µm. Although the precise length distribution of MTs in melanophores has not been determined, many MTs are thought to run from the centrosome to the cell margin, being up to 100 µm long (Murphy and Tilney, 1974; Schliwa and Euteneuer, 1983; Rodionov et al., 1994). Melanophores normally contain pigment granules dispersed throughout the cytoplasm which interferes with visualization of MTs. However, melanophores may be induced to aggregate their pigment granules by stimulation with adrenalin permitting the MT array to be visualized in an essentially transparent cytoplasm. On the basis of plus end dynamics alone, one might expect that turnover of the long MTs of the fish melanophore would require a long time. However, experimentally determined turnover half-times for the major part of MTs in melanophores as measured by fluorescence recovery after photobleaching or fluorescence redistribution after photoactivation was of the order of 5 minutes (Rodionov et al., 1994). Thus, the melanophore seems to highlight the apparent disparity between FRAP measurements and theoretical considerations. In this study, we provide estimates of the contribution to turnover of both the plus and minus-end pathways. We show that MT plus ends in fish melanophores are highly dynamic and that this is responsible for turnover at the periphery of the cell. However, the turnover half-time of a MT depends upon its length and turnover of MT `roots' near the centrosome requires the contribution of the minus-end pathway. In addition, we show that the shortening of MTs from their minus ends has consequences for the distribution of MT plus ends, favoring their accumulation at the margin.

MATERIALS AND METHODS
Cell culture Black tetra (Gymnocorymbus ternetzi) melanophores were obtained from fish scales as described elsewhere (Rodionov et al., 1994) and cultured in DMEM (Hepes modification) (Sigma Chemical Co., St Louis, MO), pH 7.2, supplemented with 20% fetal bovine serum


Pathways of microtubule turnover 2279
(HyClone Labs, Logan, UT) and antibiotics (100 i.u./ml penicillin, 0.1 mg/ml streptomycin, 0.1 mg/ml gentamycin). Cells were used for microinjection on the day after plating. Aggregation of pigment granules was induced by addition of adrenalin to 10 µM. Preparation of Cy3-tubulin Cy3-labelled porcine brain tubulin was prepared as described elsewhere (Keating et al., 1997) and stored in 10 µl aliquots in liquid nitrogen. Prior to microinjection, a 10 µl aliquot of Cy3-tubulin was diluted with 5 µl PM buffer (0.1 M Pipes, 1 mM MgCl2, pH 6.9), centrifuged at 200,000 g for 15 minutes at 4oC to remove particulate material and minimize micropipette clogging, and stored on ice until the time of injection. Imaging and data analysis Cells injected with Cy3-tubulin were treated with the oxygendepleting enzyme Oxyrase (Oxyrase, Inc., Ashland, OH) to reduce photodamage and photobleaching (Mikhailov and Gundersen, 1995). Oxyrase was added to observation dishes at a final dilution of 2-3% (v/v) of the original stock, along with lactic acid at a final concentration of 20 mM and the dishes were covered with a layer of mineral oil (Squibb and Sons, Princeton, NJ). Injected cells were observed on a Nikon Diaphot 300 inverted microscope equipped with a Plan â100, 1.25 NA objective using a rhodamine filter set. Images of 16-bit depth were collected with a CH250 slow scan, cooled CCD camera (Photometrics Ltd, Tucson, AZ) driven by Metamorph imaging software (Universal Imaging Corp., Westchester, PA). The image was projected onto the CCD chip at a magnification of â250 which corresponded to a resolution of 1 pixel=0.105 µm (9.6 pixels/µm). Exposure times were 0.2 or 0.3 seconds, and images were collected at 5.0-10.0 second intervals. Cells were kept at room temperature (~24°C) during observation. A typical series comprised 100-150 frames covering a period of 8-20 minutes. 16-bit images were processed and rescaled with Metamorph software or NIHImage software (National Institute of Health) and 8-bit images prepared for presentation with Adobe Photoshop (Adobe Systems, Mountain View, CA). To highlight MTs of interest in some figures, red overlays were painted in Adobe Photoshop with opacity set to 40%. Analysis of microtubule dynamics Position of MT ends were traced by mouse-driven cursor under NIHImage software, and from consecutive images a matrix was generated for the MTs in each cell (Table 1). The mean velocity of displacement was determined as: vd = (µi ti)/(ti2), and the mean rate of growth of the variance with time was determined as: s= (i2 ti)/(ti2). A suitable conceptual framework for the conditions occurring in the melanophore is to treat MT dynamics at the plus end as a 1-D random walk (Berg, 1993). Under the random walk approach the behavior of a MT end is considered an analogue of that for a diffusing particle. In the steady-state, the mean square displacement of a MT end from its initial position will be proportional to the elapsed time x2=s t. For a 1-D random walk, the diffusion coefficient D=s/2 (Berg, 1993). When average displacement of the MT end is zero, the kinetics of MT turnover can in principle be calculated directly from the diffusion coefficient. The diffusion plus drift formalism can also be used to characterize the dynamics of a system even when it is not in steady-state. In the non-steady-state the drift coefficient (vd) is a measure of the imbalance of growth and shortening whereas the diffusion coefficient is a measure of the absolute magnitude (squared) of the growth and shortening excursions at MT ends (see Results and Discussion for details). All values given in the text are mean ± s.d.

Table 1. Analysis of microtubule dynamics
For MT1 l(t1) l(t2) l(t3) ...... l(ti) For MT2 l(t1) l(t2) l(t3) ...... l(ti) For MT3 l(t1) l(t2) l(t3) ...... l(ti) ...... For MTn l(t1) l(t2) l(t3) ...... l(ti)

l(ti) is the displacement of a given MT end (plus or minus) with respect to its position in the first frame. Further data handling was performed using Mathcad Professional (MathSoft Inc.) and Sigma Plot (Jandel Scientific Corp., San Rafael, CA). A matrix mean displacement µi and its variance i were calculated for each time interval.

Sequential subtraction analysis The position and behavior of MTs ends in the deep cytoplasm of melanophores were analyzed by subtraction of sequential images (In- In+1) in time-lapse series using Metamorph imaging software. The resultant difference images displayed intensity variations reflecting the dynamics of MTs, primarily the growth and shortening of individual MTs but also lateral displacements. The magnitude of the intensity difference (typically 20-40 analog-to-digital units, ADUs) reflected the fluorescence of a single MT. The length of a domain of intensity difference was proportional to the instantaneous velocity of growth or shortening. Histogram stretching was carried out to set shortening events to white and growth events to black which were clearly identifiable as individual white or black domains. In contrast, lateral shifts were identified as parallel domains of white and black segments. During the time interval between two images (typically 57 seconds), lateral shifts of MTs were infrequent and rather small. These were readily distinguished from growth and shortening events. To evaluate quantitatively the distribution of MT ends along the cell radius, the number of MT excursions was calculated in subtraction images in three different regions in the cell. The regions were segments 8 µm height and separated by a distance of 10 µm from each other within the selected sector (7°-15°). The distal segment was placed to sample peripheral cytoplasm with its outer margin as close as possible to the cell boundary. Its center was located at ~0.9 cell radius (R). The relative position of the other segments along the cell radius depended on the cell size. End displacements were measured in sequential subtraction images and the mean rate of shortening or growth determined as displacement divided by the time of observation.

RESULTS MT dynamics during the approach to steady-state Evaluation of the relative contribution of plus and minus end pathways to MT turnover in the steady-state requires first establishing that the experimental system is indeed at steadystate. By definition, steady-state for MT dynamics means timeinvariant kinetic parameters, polymer level and spatial distribution. Since aggregation of pigment granules required stimulation by adrenalin, a first experimental question was when steady-state was achieved after stimulation. In the course of establishing conditions for the steady-state, we observed remarkable behavior of the MT minus end which influenced the design of subsequent experiments. Aggregation of pigment granules is rapid with a half-time of approximately 2.5 minutes (Rodionov et al., 1991). Consequently, our first analyses began at 10 minutes (4 halftimes) after addition of adrenalin. Melanophores at this time after stimulation displayed a characteristic radial system of


2280 I. A. Vorobjev and others

Fig. 1. MT dynamics during approach to the steady-state. Fluorescently labelled microtubules were imaged at the periphery of living melanophores shortly after pigment aggregation. Melanophores with dispersed pigment were injected with Cy-3 tubulin and 2 hours later pigment aggregation was induced with adrenalin. Time-lapse series of images of microtubules were acquired beginning 20 minutes after adrenalin treatment. Distal (plus) ends of MTs displayed dynamic instability. Numerous free MTs (colorized in red) depolymerized from their proximal (minus) ends. Time in seconds shown in lower left corner. Bar, 5 µm.

long MTs, some straight, some wavy, running from the central part of the cell toward the periphery. The area accessible for visualization of individual MTs extended to approximately 1015 µm from the cell margin. Deeper in the cytoplasm, the density of MTs generally precluded the direct observation of MT ends. Surprisingly, besides long MTs running towards the cell center, MTs with free proximal ends were also observed. Time-lapse analysis for the interval 10-30 minutes after addition of adrenalin revealed free MTs rapidly shortening from the minus (proximal) end (Fig. 1). This result by itself indicated the existence of an active minus-end pathway which might contribute significantly to MT turnover. MT plus ends away from the cell margin showed variations in growth rate and infrequent transitions to shortening phase which were rapidly rescued (Fig. 2A). Overall, these MTs showed net growth. As MTs grew close to the cell margin, their plus ends spent most of their time in pause, rarely depolymerized for a short distance and regrew back to the margin (Fig. 2B). Free minus ends shortened or were stable (paused), but never grew (Fig. 2C). The behavior of the plus end was independent of whether or not the minus end of the MT was free. Short free MTs showed the same plus end excursions as long ones. Stochastic excursions of the plus ends of MTs in melanophores made it possible for us to apply random walk analysis (Vorobjev et al., 1997). Random walk analysis in terms of diffusion plus drift (Berg, 1993) was applied to
Fig. 2. Life history plots of MTs during approach to the steady-state. (A) Dynamics of distal (plus) end deep in the cytoplasm. Phases of growth are significantly longer than phases of shortening resulting in overall growth (drift) to the margin. (B) Dynamics of distal (plus) end at the margin. Prolonged pauses are interrupted with brief epizodes of growth and shortening. (C) Dynamics of a MT with free proximal (minus) end. Continuous polymerization at distal (plus) end and deplymerization at proximal (minus) end results in treadmilling, but since shortening exceeds growth, the MT depolymerized. Reference point for each plot is the position of the end at zero time.


Pathways of microtubule turnover 2281

Fig. 3. Random walk analysis of MT dynamics during the approach to steady-state. The behavior of plus ends of MTs away from the cell margin was analyzed in terms of a diffusion plus drift model. (A) Drift component. Mean displacement of plus ends versus time. Regression line provides drift coefficient of 3.3±0.4 µm/minute. (B) Diffusion component. Mean square displacement about drift regression line (variance of displacement) of the same plus ends versus time. Regression line provides diffusion coefficient of 6.3±0.9 µm2/minute. Broken lines, 70% confidence intervals. Data obtained from 33 MTs in 7 cells.

quantify the behavior of the MT population (see Materials and Methods). The coefficient of drift, vd, is defined as the factor of proportionality between mean displacement of the ends of a population of MTs and elapsed time. In molecular terms, the drift coefficient is proportional to the difference between the rates of the one-way reactions of tubulin polymerization and depolymerization at the MT end; it equals zero at steady-state (when both reactions are on average balanced) and in general can serve as a measure of deviation from steady-state. The coefficient of diffusion, D, is defined as the factor of proportionality between the variance of the end displacements about the drift component. When the drift component is zero, this simplifies to the mean square displacement of MT ends achieved in a given time, x2=2Dt. Mean square displacement of MT ends (correcting for any drift) are a measure of the dynamic activity or `diffusion' of the end. Linear regression analysis was performed to determine drift and diffusion coefficients from end displacement data (Fig. 3) which in turn were derived from life history plots (100-150 frames, 5 second intervals). Individual MT life history plots were often short because their dynamic activity carried the MT outside the region of observation. Consequently, for purposes of the regression analysis, life history plots were broken into 1

Fig. 4. MT dynamics at steady-state. Fluorescently labelled microtubules were imaged at the periphery of living melanophores after pigment aggregation. Imaging was begun 2 hours after injection of Cy-3 labeled tubulin and 1 hour after stimulation of aggregation by adrenalin. Arrowheads directed to the right indicate growing ends of MTs and arrowheads directed to the left indicate shortening ends. Time in seconds shown in lower left corner. Bar, 5 µm.

minute windows. Positive values of drift coefficients are defined to signify displacement toward the cell margin. This corresponds to growth for the plus end and to shortening for the minus end. For MT behavior during the interval 10-30 minutes after stimulation with adrenalin, drift and diffusion coefficients for plus ends depended on proximity to the cell margin. Away from the cell margin, plus ends had a drift coefficient of 3.3±0.4 µm/minute and a diffusion coefficient of 6.3±0.9 µm2/minute. Near the cell margin the vd was -0.16±0.14 µm/minute and the D was 1.2±0.1 µm2/minute. These determinations quantitate the qualitative impression from viewing the time-lapse series that MT plus ends reduce their dynamic activity and stop their net growth as they approach the cell margin. The minus ends of free MTs showed a drift coefficient of 4.6±0.3 µm/minute and a diffusion coefficient of 3.7±0.7 µm2/minute. Further, minus ends continued to shorten even near the cell margin. For each category of MT end, the sample analyzed consisted of 33 MTs drawn from 7 cells.


2282 I. A. Vorobjev and others

Fig. 5. Analysis of MT dynamics at steady-state. (A) Life history plot of an individual MT at the cell margin. MT end grows and shortens but the net displacement is close to zero. (B) Frequency histograms of plus end displacements after 5 second and 50 second time intervals. The displacement frequency distribution gradually broadened but showed a mean value of approximately zero. Data presented from time-lapse series, 100 images, 5 second intervals; 4410 measurements on 46 MTs in a single cell. (C) Drift component of the random walk. Regression line indicates that drift coefficient is close to zero (-0.04±0.41 µm/minute). (D) Diffusion component of the random walk. Regression line gives value for diffusion coefficient of 7.5±1.2 µm2/minute. Broken lines, 70% confidence intervals. Data shown, averaged for 5 cells (See text for details).

The difference in behavior of plus and minus ends resulted in the inevitable disassembly of free MTs as their plus ends neared the cell margin. As a consequence, free MTs were lost from the population whereas those MTs with their minus ends anchored at the centrosome accumulated in the population. At the end of the observation window (10-30 minutes after adrenalin stimulation), free MTs became very rare. The decreasing number of free minus ends during the observation window and the different dynamics of the plus ends adjacent to the cell margin versus those deeper in the cytoplasm indicated that despite the complete aggregation of pigment granules, a steady-state for MTs was not achieved earlier than 30 minutes after adrenalin stimulation. The results also demonstrate that a significant minus-end pathway for MT dynamics exists in the melanophore. MT dynamics in the steady-state With continued incubation of melanophores after adrenalin stimulation (1-3 hours), the radial array seemed to become better organized with straighter long MTs and few free MTs (Fig. 4). Plus ends of MTs underwent random transitions from

growth to shortening and showed apparently stochastic duration and variable rate of both kinds of excursions. MT plus end dynamics were quantified by obtaining life history displacement plots (Fig. 5A). To evaluate the diffusion model, displacement frequency distributions were computed for increasing time intervals, two of which (5 seconds and 50 seconds) are shown in Fig. 5B,C. Consistent with diffusion, the displacement frequency distribution gradually broadened and flattened out but showed a mean value of approximately zero. The fact that the histogram of instantaneous rates was monotonically declining for both growth and shortening rates independent of the size of the time bins suggested a fractal character for the plus-end dynamics (Vorobjev et al., 1997). The displacement data at 5 seconds may also be considered an instantaneous growth and shortening velocity distribution. Shortening or growth were considered to have occurred when the displacement of a MT end between subsequent frames was at least two pixels (0.21 µm). The most frequent bin was zero detectable change and to either side of this category, the frequency distribution was monotonically declining. That is, neither growth nor shortening was characterized by a single


Pathways of microtubule turnover 2283 velocity. The mean instantaneous growth rate was 6.8±7.0 µm/minute while the mean shortening rate was almost twice as great, 11.9±6.3 µm/minute. The drift coefficient was calculated by linear regression analysis of mean displacement over time and found to be -0.038±0.41 µm/minute (Fig. 5C). This value is indistinguishable from zero at the significance level 0.95 (Student criterion used). Consequently, plus ends in the aggregated cells apparently are at steady-state. However, it should be noted that the large standard deviation obtained in the calculation does not preclude a minor drift of the plus ends. This possibility will be considered further below. The diffusion coefficient was calculated from the increase in variance of displacement over time (Fig. 5D). The coefficient varied significantly for individual cells. For four cells where a sufficiently large number of MTs could be analyzed, values obtained were: 15.9±2.4 (21 MTs), 11.4±1.5 (83 MTs), 7.1±0.8 (34 MTs), and 2.5±0.2 (46 MTs) µm2/minute. Although the source and significance of individual cell variation is not understood, we pooled data for a number of cells to generate a population average. For a sample consisting of 75 MTs (15 MTs from each of 5 cells), we calculated an average diffusion coefficient D=7.5±1.2 µm2/minute. Thus, quantitation of MT plus end dynamics in the steady-state melanophore apparently conformed to a pure random 1-D walk of MTs along the cell radius. A random walk mechanism is implicitly based on the assumption that growth and shortening of MT plus ends occurs in the same way throughout the cytoplasm. That is, kinetic parameters and the frequency of growth and shortening are the same both at the cell periphery and deeper in the cytoplasm. The random walk model views the ends of MTs as analogous to molecules in a container. Thus, a pure random walk model predicts that MT plus ends will be distributed randomly along the cell radius. That is, the length distribution of MTs will be uniform, short and long MTs will exist in equal numbers and the average MT length will be half the cell radius. Further, a pure random walk model is based solely on dynamic behavior of plus ends. In contrast to the observed behavior of the presteady-state melanophore, no minus end MT activity is required. These features are examined in the following sections. Dynamics and distribution of MT plus ends along the cell radius At steady-state, the plus ends of MTs in melanophores could be seen clearly only near the cell margin and it was unclear how many of them were hidden in the deeper parts of the cytoplasm. Diagrams generally depict cytoplasmic MTs as extending continuously from the centrosome to near the cell margin. This view implies that few or no MT ends will be found in the internal parts of cytoplasm and is in apparent contradiction with the random walk behavior of plus ends which predicts that they are uniformly distributed throughout the cytoplasm. Also, if MT ends do exist throughout the cytoplasm, the question arises whether their dynamic behavior is the same as at the periphery. Consequently, we tried to visualize MT ends and evaluate their behavior deep in the cytoplasm. Direct fluorescence visualization of individual MTs is limited by the dynamic range of the imaging detector and display technology. Deep in the cytoplasm, a single MT is difficult to visualize directly because of the superposition of many other MTs (Fig. 6A). However, given the large and linear dynamic range of a scientific grade CCD, single MTs can be visualized by performing differential image analysis. In this analysis, sequential images are subtracted from each other. The resulting images showed an almost uniform background on which MT shortening appeared (after intensity histogram stretching) as a white segment and MT growth as a black segment (Fig. 6B). A limitation of difference image analysis comes from lateral displacements of MTs. However, these were distinguished from growth or shortening because lateral shifts led to parallel black and white lines whereas growth or shortening led to individual black or white segments. During the time interval between two images (5-7 seconds), lateral shifts of MTs in melanophores were infrequent and slight. Subtraction of images taken at longer time intervals from each other resulted in increase of heterogeneity of the central part of the image, probably because of lateral displacements of numerous MTs that exceeded a single MT signal (data not shown). Consequently, differential image analysis was restricted to single frame differencing. As a threshold for detectability, we considered an active MT end to be visualized if the difference image showed a white or black segment of at least 5 pixels (0.5 µm) length. Within this limitation, dynamic MT ends were clearly visible throughout the cytoplasm. Differential imaging time-lapse series were quantified to evaluate whether MT dynamics were uniform throughout the cytoplasm and to determine the distribution of MT ends. MT excursions were visualized clearly up to 60 µm from the cell margin, a distance which approached the centrosome. When shortening occurred at the plus end, the retrograde movement of the white segment could occasionally be followed for two frames (15 seconds), and rarely for three (22 seconds). In the majority of cases, a white segment was observed only in a single subtraction frame. This indicated that shortening of MT plus ends was generally brief. A shortening event was often followed by a growth event; that is, a white segment moving retrogradely was succeeded by a black segment at the same location moving anterogradely (data not shown). No cytoplasmic nucleation of MTs was detected. For quantitation purposes, cell sectors were divided into zones along the cell radius (R), shortening and growth events enumerated and their ratio computed. For the three zones of the cell in Fig. 6C, the ratio of shortening to growth events was: zone 1 (0.85-0.95 R), 0.54±0.06; zone 2 (0.75-0.60 R), 0.60±0.12; and zone 3 (0.450.30 R), 0.53±0.08, respectively, indicating that growth and shortening events occurred in similar proportions along the cell radius. Differential images gave not only the number of events but an estimate of their velocity as well since the length of a segment was proportional to the instantaneous rate of the event. On average, shortening excursions were about twice the length of growing ones, similar to the ratio of velocities of 1.75 obtained by direct visualization (see previous section). Considering the relative number of growth and shortening segments with their relative length, we conclude that throughout the melanophore cytoplasm, growing MT plus ends are about twice as numerous as shortening plus ends and that shortening is about twice as fast as growth. These parameters equate to the steady-state because they indicate an overall balance between polymerization and depolymerization and, therefore, no net change in MT polymer.


2284 I. A. Vorobjev and others
Fig. 6. Sequential subtraction analysis of MT dynamics at steady-state. Fluorescently labeled MTs were imaged in living melanophores beginning 2 hours after injection of labelled tubulin and 1 hour after stimulation of aggregation by addition of adrenalin. (A) Image of MTs from a time-lapse sequence used for analysis. (B) Differential image obtained by subtracting from the image in A the next image in the time-lapse series. Black segments and white segments represent MT growth and shortening, respectively, during the time interval. (C) Diagram extracted from the difference image by bit slicing, illustrating growth (green) and shortening (red) excursions. White boxes (1,2,3) indicate the regions from which data were compiled. Yellow spot shows estimated position of the cell center. The angular density of green segments and red segments decreases towards the cell center. The ratio between frequency of growth and shortening events in all boxes was nearly the same. (D) Distribution of active MT ends along the cell radius as determined by the number of growth or shortening events. Number of MTs indicated relative to number of shortening MTs at the cell margin (zone 1) set to 100. Data shown, averages for 6 cells (see text for details).

Although the difference imaging clearly indicated the presence of active MT plus ends throughout the cytoplasm, it was also evident that the distribution of plus ends along the radius was not random; many more ends were found near the cell margin than deeper in the cytoplasm. Because of the threshold for detection of 0.5 µm, the number of growth and shortening events recorded is undoubtedly an underestimate of the actual number of active MT ends. Nevertheless, the recorded number may be taken as proportional to the real number. On this assumption, the relative number of growing and shortening ends along the cell radius may be computed (Fig. 6D). In 6 cells examined by differential time-lapse, 1107 growth and 596 shortening events were recorded in zone 1, 474 growth and 286 shortening events in zone 2, and 354 growth and 187 shortening events in zone 3. Thus, the number of active MT ends at the periphery (zone 1) was 2.2 times the number in the middle (zone 2) and 3.10±0.93 times the number deep in the cytoplasm (zone 3). This quantitative analysis of MT dynamics in the steady-state makes two main points. One is in keeping with the random walk model; namely, that the kinetic parameters and the frequency of growth and shortening are similar both at the cell periphery and deeper in the cytoplasm. However, we wish to note that the limitations of subtraction analysis in the deep cytoplasm, namely the inability to follow individual MTs for an extended period, prevented a detailed

evaluation of MT dynamics in terms of the diffusion plus drift model as we performed by direct imaging of MTs at the periphery. Therefore, the absence of a small drift component in the interior is not precluded by the data. The other point, that the distribution of MT plus ends is non-random, is inconsistent with a pure random walk model and prompts the question as to what other process is occurring. Free minus ends at steady-state Observations of MT dynamics made shortly after adrenalin stimulation of pigment aggregation revealed numerous free MTs near the cell margin and rapid shortening from the minus end. Although not as numerous, free MTs were also detectable in the steady-state. In an analysis of 6 cells (100-150 frames, 10-12 minutes observation each) in which 170 MT plus ends were tracked, 2 minus ends were seen by direct visualization, giving an approximate minus end frequency of ~1%. We wondered whether this level of free MTs near the periphery indicated a low but constitutive release of MTs from the centrosome followed by minus-end shortening. Such minusend depolymerization would release tubulin subunits that would, in the steady-state, necessarily polymerize onto the population of MT plus ends. This polymerization would imbalance growth and shortening at the plus ends and generate a drift toward the cell margin. Such drift could account for the


Pathways of microtubule turnover 2285
Fig. 7. Minus-end shortening revealed by sequential subtraction analysis. Subtraction of sequential fluorescence images revealed white (shortening) segments moving in a centrosome-to-cell margin direction. These segments, interpreted as minus end shortening, are colorized with red overlay (two MTs highlighted). Length of red segment reflects instantaneous velocity (1.2 µm segment/frame=10 µm/minute shortening velocity). Elapsed time in seconds shown at lower left. Bar, 5 µm.

departure of the MT end distribution from the uniform distribution predicted by the random walk model. Constitutive MT release would also contribute to MT turnover. Time-lapse sequences of differential images were examined to determine whether minus end shortening events

could be discerned. White segments moving in a cell marginto-centrosome (retrograde) direction were the basis for previously assigning these events as plus end shortening. By the same reasoning, white segments moving in a centrosometo-cell margin (anterograde) direction were assigned as minus end shortening. Review of the differential time-lapse series indeed uncovered free minus ends deep in the cytoplasm shortening toward the periphery (Fig. 7). For shortening minus ends, the white segment moved anterograde persistently, although with variable velocity, and sometimes could be traced for over a minute. This is consistent with observations of minus end behavior described for the condition of approach to the steady-state. A difference between plus and minus end shortening was that in the latter case the white segment never converted into a black one; that is, shortening of the minus end was never seen to be succeeded by growth. Minus end shortening was deemed to have taken place if two criteria were met. The white segment had to move anterogradely and it had to be visible in at least three successive frames. Using these criteria, we recorded minus end shortenings appearing in a time lapse series and determined its rate to be 10.4±4.0 µm/minute (n=23). In contrast to our previous observations of MTs in the steady-state where the total number of minus ends visualized was small because of the limitations of direct fluorescence imaging, difference imaging permitted the scoring of many minus end events throughout the cytoplasm. In contrast to MT plus ends which were enriched at the cell periphery, MT minus ends were distributed more evenly through the cytoplasm. For 6 cells on which detailed analysis was performed as described in the previous section, 139 minus end shortening events were recorded. Each minus end was followed on average for 46 seconds (from 3 to 12 sequential subtracted images). From the total number of MTs and estimates of our MT detection probabilities, we calculated the proportion of free minus ends to total MT ends to be 0.98±0.8%. Given the experimental limitations on detection of minus end shortening, this value is probably an underestimate and the average velocity of minus end shortening is probably an overestimate. The relative frequency of appearance of minus ends varied with individual cells, but for 11 cells examined, on average, there was no difference between cells exposed to adrenalin for 1 or for 3 hours (data not shown). This indicates that minus end appearance and shortening are true steady-state phenomena and that after 1 hour incubation in adrenalin, free MTs with shortening minus ends are continuously replaced, probably by release from the centrosome. The consequences of constitutive release and minus end depolymerization for the MT length distribution and MT turnover will be considered in the Discussion.


2286 I. A. Vorobjev and others DISCUSSION Approach to steady-state The melanophore has been studied as an exemplar system for the transport of organelles along MTs (Beckerle and Porter, 1982; Rodionov et al., 1991). It both aggregates and disperses pigment granules rapidly, the aggregation reaction occurring with a half-time of approximately 2.5 minutes (Rodionov et al., 1991). We induced aggregation of pigment granules in order to clear the cytoplasm for visualization of MT behavior. Consequently, after inducing aggregation, we expected to be able to analyze MT dynamics almost immediately at the periphery of the cell and within 10 minutes (4 half-times) throughout the interior of the cell. Unexpectedly, we observed non-steady-state behavior of MTs during the time regime of 10 minutes to 30 minutes. MT plus ends were dynamic undergoing stochastic excursions, catastrophes and rescues, but tended to drift toward the cell margin at a velocity of 2.4 µm/minute. At the cell margin, MT plus ends appeared less dynamic and were frequently `paused'. However, this appearance of reduced dynamics can be interpreted in terms of the membrane being a barrier to MT advance and the persistence of growth tending to keep the MT plus end near the barrier. When the drift component of MT plus ends is large, an end that moves away from the margin in an episode of shortening is quickly returned to the margin. Thus, the plus ends appear relatively quiescent. As steady-state is attained (see below), the drift component decreases and the `quiescence' of MTs at the margin also decreases. Minus ends were numerous and shortened toward the cell margin even faster, with a drift velocity of 4.6 µm/minute. Thus, minus ends tended to catch up to plus ends with the progressive elimination of free MTs. The origin of the free MTs is not clear. The action of adrenalin on fish melanophores has been interpreted to initiate a signal cascade leading to the activation of dynein, the minusend directed motor responsible for transport of pigment granules toward MT minus ends (Haimo and Thaler, 1994; Nillson and Wallin, 1998). However, adrenalin action may also exert effects on the MT system itself, leading to the transient appearance of free MTs. Conceivably, the downstream signal cascade may induce release of MTs from the centrosome. Alternatively, the possibility that many free MTs pre-existed in the melanophore in the dispersed state cannot be excluded. The minus ends of such free MTs could have gone undetected because of the high density of MTs and their minus-ends, stable in the dispersed state, could have been destabilized by the action of adrenalin. Whatever the explanation, the phenomenon of plus end drift and numerous free minus ends shortly after adrenalin stimulation was informative. The fact of rapid minus-end shortening provided clear evidence for the instability of minus ends in intact melanophores and for the existence of a robust minus-end pathway. Previously, minus-end shortening in melanophores had only been observed in cytoplasmic fragments (Rodionov and Borisy, 1997). Interestingly, the drift velocity for minus ends in intact melanophores (4.6 µm/minute) was essentially identical to the average shortening velocity of minus-ends in cytoplasmic fragments (4.4 µm/minute), suggesting that under the conditions where MT minus ends were numerous, depolymerization reflected cytoplasmic conditions independent of the presence of the nucleus, centrosome or other cell body components. Sequential substraction anaysis Direct fluorescence imaging of individual MTs has generally only been accomplished near the cell margin where the thinness of the lamella has minimized the background contributed by soluble tubulin and obviated the out-of-focus fluorescence of MTs in nearby planes. To overcome this limitation we introduced sequential subtraction analysis which allowed us to visualize single MT displacements deep in the cytoplasm. Subtraction analysis is a simple idea for representing displacement of a MT end as a domain of intensity difference in successive fluorescence images. The method requires a linear fluorescence detector with a large dynamic range. Image sensors with such properties became available with the introduction of scientific grade, cooled charge-coupled devices. In combination with image processing software to generate intensity histograms and to stretch contrast without loss of significant information, growth and shortening displacements of MTs could be objectively represented as black or white segments, respectively. The ability to characterize MT dynamics deep in the cytoplasm permitted several important conclusions to be drawn which otherwise would be inaccessible. From a single subtraction image, the numbers of black and white segments give the relative proportions of growth and shortening events. The length of the segments indicate their relative velocities and their distribution within the cell indicates their approximation to or deviation from randomness. Comparison of numbers and lengths of segments in the interior and at the periphery permitted us to conclude that the dynamic parameters of MTs did not significantly vary with location along the cell radius in melanophores. From sequential subtraction images, transitions between growth and shortening could be assessed. More importantly, time-lapse sequences permitted minus-end behavior to be identified and distinguished from plus-end behavior. Thus, the relative contributions of the minus and plus-end pathways could be directly assessed. Sequential substraction analysis has been applied to CHO and PtK cells (I. A. Vorobjev and G. G. Borisy, unpublished results) and is likely to be applicable to the study of MT dynamics in many other cell types. Random walk dynamics explains MT turnover at the cell periphery In the steady-state, the dynamics of the plus end was fit well by a random walk model. Plus ends underwent excursions of growth and shortening (catastrophes and rescues) of variable magnitude and variable rate. The net drift of the plus ends was close to zero and their overall behavior conformed closely to a 1-dimensional random walk with apparent diffusion coefficient, D=7.5 µm2/minute. It should be noted that implicit in the random walk model is the assumption of reflection at the cell periphery. Consistent with this assumption, the majority of MTs were straight and directed along the cell radius. However, some plus ends which reached the plasma membrane curved along the leading edge and became oriented circumferentially. Nevertheless, to a first approximation, the random walk model provides a useful framework for characterizing MT behavior. From the basic diffusion equation relating mean square


Pathways of microtubule turnover 2287 distance and time, x2=2Dt, the experimental value of D signifies that, on average, a MT plus end in a melanophore wanders 3.9 µm from its initial position in 1 minute, that to wander 10 µm would require 6.7 minutes and to wander 70 µm (the approximate distance back to the centrosome) would require 327 minutes. These simple calculations serve to demonstrate that a random walk of the plus end is sufficient to account for rapid turnover of MTs (t1/2<7 minutes) near the periphery of the cell (x<10 µm), as has been reported in melanophores (Rodionov et al., 1994). However, random walk analysis also indicates that the characteristic half-time for turnover by this mechanism is predicted to be strongly dependent on distance from the plus end, increasing approximately as the square of the distance. A precise calculation of the dependence of turnover half-time on distance from the cell margin would also have to take into consideration the length distribution of MTs. Most reports on MT turnover in the literature give only a single estimate of turnover half-time as if position dependence were not significant. Two studies, one in fibroblasts (Sammak et al., 1987) and one in neurons (Lim et al., 1990) have given turnover values as a function of distance. Both studies showed increasing turnover times with distance from the leading edge. However, neither study gave half-times of hours as predicted by pure plus end dynamics. Consequently, even though these studies as well as the current study show a significant dependence of turnover on position, they also suggest that an additional mechanism is required to account for turnover near the cell center. An apparent diffusion coefficient has also been determined for MTs in PtK1 cells (Vorobjev et al., 1997), the value for this system (2.4 µm2/minute) being approximately 3 times less than for the fish melanophore. The larger value of D for the melanophore means that the dynamics of individual MTs in melanophores is faster than in PtK1 cells. However, since the melanophore is also more than 3 times larger in radius than a PtK1 cell, turnover of MTs in the melanophore is not faster. In fact, it is slower on a cellular basis because turnover half-time increases approximately as the square of the cell radius. It will be interesting to see if comparison of MT dynamics in different types of cells yields a generalization about the relationship between cell size and the apparent diffusion coefficient of MTs. Minus end pathway for MT turnover The origin of free MTs in the melanophore can be most readily explained by release from the centrosome as has been documented for PtK1 cells (Keating et al., 1997). Because shortening from the minus end is rapid, even MTs as long as the cell radius will become completely depolymerized in a relatively short time. Our results gave two estimates of shortening velocity, 4.6 µm/minute in the pre-steady-state as determined by direct observation and 10.4 µm/minute in the steady-state as determined by sequential subtraction analysis. Because subtraction analysis used a threshhold for identifying shortening events (the minimal detectable instantaneous rate of minus end shortening was 4.4 µm/minute), slow shortening was underrepresented. Consequently, the 10.4 µm/minute value is probably an upper bound for the average speed of shortening and a value closer to ~5 µm/minute is more likely to be the true average. Nevertheless, with either estimate, complete depolymerization of a released MT will be rapid, requiring 7-14 minutes for a MT of length equal to the cell radius (70 µm). The released MTs will be replaced by new nucleation at the centrosome which means that the kinetics of turnover contributed by the minus-end pathway are determined primarily by the frequency of the release process. A half-time for release may be calculated based on an exponential replacement process as ln2/k where k is the release rate. The release rate can be calculated in principle from the incidence of observing free minus ends and the time for their complete depolymerization. Although neither quantity could be determined precisely, the available data permit an estimate of the release rate to be in the range, 0.2% to 1.3% per minute. These rates compare to values of 1-6% in PtK1 cells (Vorobjev et al., 1997; Keating et al., 1997) and 0.1% in newt lung cells (Waterman-Storer and Salmon, 1997). Taking an average value for the release rate of k=0.0069 minute-1 (approximately 0.7% per minute), gives a half-time for release of 100 minutes. This is larger but of the same order of magnitude as the retention time of 43 minutes estimated for MTs to remain attached to the pigment mass in a cytoplasmic fragment of melanophores (Rodionov and Borisy, 1997). Assuming an average time for depolymerization of a released MT from its minus end to be 10 minutes, an overall half-time for turnover via the minus end pathway in the melanophore may be estimated as approximately 110 minutes. In the steady-state, all tubulin released from the minus ends has to be accepted by the plus ends. This polymerization will cause the plus ends to drift towards the cell margin, the drift being superimposed on the random walk. Conservation of mass permits the value of drift for the plus ends to be calculated from the frequency of minus end occurrence (0.98±0.8%) and the minus end shortening rate (10.4±4.0 µm/minute) which equals 0.102±0.092 µm/minute. Such a low value is within the experimental error attached to our determination of the drift coefficient (-0.038±0.41 µm/minute) and thus would not be directly visible in plus end behavior nor be an obvious departure from random walk behavior. Nevertheless, this minor drift of the plus ends does have an important consequence for the MT length distribution. A pure random walk model without drift predicts a random distribution of MT lengths. In contrast, our observations revealed a non-random distribution of the plus ends. Such nonrandom distribution could be explained by some attractant for MT growth secreted by the cell margin. A gradient of such attractant would conceivably make it more probable for a MT to reach the cell margin as compared to the pure random walk. However, a simpler and alternative explanation is that the nonrandom distribution of MT plus ends arises as a result of the drift component caused, in turn, by minus end shortening. The extent to which minus end shortening (and therefore drift) perturbs the random MT length distribution can be estimated using the theory of diffusion with drift (Berg, 1993). Again analogizing the plus ends of MTs with individual diffusing molecules, the steady-state is determined when a gradient of MT plus end position (and therefore length) balances the small outward drift component. The distribution of MT plus ends over the cell radius, N(x), will be stationary when N(x) = N0 exp(x vd/D) , where N0 is the number of MTs attached to the centrosome, vd is drift of the plus ends, and D is diffusion coefficient. The


2288 I. A. Vorobjev and others position in the cell where the number of MT ends is twice that at the centrosome is given as x(doubling) = ln2 D/vd . Taking D=7.5 µm2/minute, and vd=0.1 µm/minute, the doubling distance is calculated as 52 µm. The distribution of MT ends as determined by substraction analysis showed an increase in the number of ends with increasing cell radius roughly consistent with this prediction. Alternatively, a drift coefficient may be calculated from the end distribution data. Carrying out this calculation, we obtain a value for the drift coefficient of vd=0.29 µm/minute. This value is higher than that calculated from the minus end shortening but still small and, in any event, too low to be measured with precision from plus end dynamics. The calculations show that a drift component in the range 0.1-0.3 µm/minute results in a nonrandom distribution of the plus ends with their 1-D density ascending exponentially towards the cell margin. The salient point is that, in a large cell, the increase in number of MT ends towards the cell margin will be substantial even with only a small fraction of shortening minus ends. This will give an impression that the majority of MTs run from the cell center to the margin, consistent with immunofluorescent and electron microscopic observations (Byers and Porter, 1977; Schliwa, 1979; Schliwa and Euteneuer, 1978). Our calculations on the relative frequency of MTs ends along cell radius derived from subtraction images confirm this picture and, more importantly, provide an explanation for how such a distribution could arise in terms of a random walk model with drift. Contribution of plus and minus end pathways to the overall MT turnover Analysis of the plus end and minus end pathways permits us to make a quantitative assessment of their relative contribution to MT turnover. Turnover by the plus-end pathway is accomplished by episodes of shortening followed by regrowth (catastrophes and rescues), amounting to a 1-D walk which becomes less probable the greater the distance to be `walked'. Consequently, for the plus end pathway, the calculated halftime of turnover strongly depends on distance from the cell margin, being small close to the cell margin, and increasing rapidly with distance away from the margin. In contrast, turnover by the minus-end pathway is the result of replacement of released MTs by ones newly nucleated at the centrosome. Subunits generated by minus-end shortening are made available for stochastic addition onto all available plus ends. For the minus end pathway, the turnover half-time does not depend on the distance from the margin but rather is determined principally by the rate of release of MTs from the centrosome. Consequently, the relative impact of the two pathways depends upon position with the cell (Fig. 8). Near the cell margin, the minus end pathway has almost no impact. Turnover of the peripheral domains of MTs is determined primarily by the plus end pathway. In contrast, deep in the cytoplasm, far from the cell margin, the plus end pathway has only a weak influence. Turnover of the root domains of MTs near the centrosome is determined primarily by the minus end pathway. Quantitative assessment of the two pathways may be made on the basis of the random walk model with drift. The random

Fig. 8. Relative contribution of plus and minus end pathways to MT turnover. The diagram shows dependence of the half time for MT turnover on the distance from the cell center for each of the plus and minus end pathways, considered separately. For the plus end pathway, the turnover half time rapidly increases with increasing distance from the margin. In contrast, for the minus end pathway the half time does not depend on the distance from the margin but is determined by the frequency of release of MTs from the centrosome. The relative impact of the two pathways depends on the position within the cell. For a model melanophore of radius, 70 µm, average length of MTs, 50 µm, diffusion coefficient, D=7.5 µm2/minute, drift coefficient, vd=0.25 µm/minute (corresponds to release frequency of 0.7% minute-1 and minus end shortening speed of 10 µm/minute), the point of equivalent impact of the two pathways is approximately 43 µm from the cell margin. The diagram indicates that turnover of the peripheral domains of MTs is determined primarily by the plus end pathway whereas turnover of the root domains of MTs near the centrosome is determined primarily by the minus end pathway.

walk component is reflected in the diffusion coefficient, D, which provides a quantitative measure of the plus end pathway. The turnover half-time for the plus end pathway will increase approximately with the square of the distance from the cell margin. For D=7.5 µm2/minute and a cell radius of 70 µm, the half-time would be over 5 hours at the centrosome. The turnover half-time contributed by the minus end pathway may be estimated from the observed drift coefficient and the average MT length. For vd=0.25 µm/minute, cell radius, R=70 µm, average MT length=R/2, the half-time is ln2 R/2/vd=97 minute. This estimate of minus end turnover half-time is consistent with a centrosomal release rate of 0.7% per minute and a minus end depolymerization velocity in the range 5-10 µm/minute. However, the uncertainty in the determination of individual quantities involved in the calculation generates an uncertainty in the computed half-time and permits us to conclude only that it lies in the range, 50-200 minutes. Nevertheless, independent of the absolute value of the minus-end turnover time, certain qualitative features emerge. Of particular importance is that the minus end turnover half-time is independent of position in the cell and therefore constant over the cell radius. From Fig. 8, it can be seen that the contributions of these two turnover components will become equal at some distance from the cell edge. Fig. 8. illustrates that the turnover of a MT is not characterizable by a singular quantity but, rather, must be


Pathways of microtubule turnover 2289 discussed in terms of position along its length. Long MTs are likely to turn over their proximal segments by release from the centrosome followed by minus end shortening. In contrast, the distal segments of all MTs, long ones as well as short ones, are turned over primarily from the plus end. We conclude that the two pathways serve complementary roles. The plus end pathway enables rapid turnover of the peripheral domains of MTs without the necessity to also turn over the roots. In contrast, the minus end pathway provides an efficient mechanism for turning over the roots of MTs independent of the activity at the plus ends. Contribution of the minus-end pathway to turnover depends on the frequency of release from the centrosome and probability of stabilization of free minus ends by capping factors (discussed by Keating et al., 1997). These parameters may vary between different cell types. For example, our recent work with cytoplasmic fragments (Rodionov et al., 1997) and cytoplasts (Rodionov et al., 1999) demonstrated that minus-end capping activity is low in melanophores and fibroblasts, but substantial in epithelial-type cells. Frequency of release may also be cell-type specific and is likely to be a subject of regulation. With the methodology developed in the present study it will be possible to precisely determine the role of the minus-end pathway in microtubule turnover in a wide variety of cell types.
We thank Alexander Verkhovsky for stimulating discussions and a critical reading of the manuscript and John Peloquin for preparation of Cy-3 tubulin. This work was supported by NIH grant GM25062 (G.G.B.), CRDF award RB1-168 (G.G.B. and I.A.V.), Fogarty IRC award TW00748 (G.G.B. and I.A.V.), NSF grant MCB-9728252 (V.I.R.), and RBSF grant to I.A.V.
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