Microtubules (MTs) are dynamic polymers in the sense thatthey are continuously being built and degraded in living cells.This MT turnover most likely plays a key role in cellularprocesses requiring a change in cell shape or remodeling of cellcytoplasm such as during cell motility or cell morphogenesisor in the construction of cytoplasmic structures such as themitotic spindle. To quantify MT dynamics, two experimentalapproaches with complementary strengths and weaknesseshave generally been used (see Desai and Mitchison, 1997;Joshi, 1998, for reviews). One approach is basically apopulation method which attempts to determine the rapidity ofMT turnover by measuring the kinetics of fluorescenceredistribution after photobleaching or photoactivation (FRAP).The other approach attempts to determine the course of MTturnover by visualizing and directly assessing the dynamicbehavior of individual MTs.
FRAP analyses give values for turnover times which areaverages 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 processrepresenting turnover. For most interphase cells, FRAPanalyses resulted in half times for MT turnover ranging from5 to 20 minutes with epithelial cells tending to be slower thanfibroblasts (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 isthat MT turnover in interphase cells is rather rapid althoughcharacteristic half-times for turnover are cell type specific.
In contrast to the FRAP analyses, direct imaging approacheshave 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 ofthe dynamic instability model (Mitchison and Kirschner, 1984)which stipulates that MT plus ends can exist in either of two
Turnover is important for the maintenance and remodelingof the cytoskeleton during the processes of cellmorphogenesis, mitosis and motility. Microtubule (MT)turnover is thought to occur by dynamic instability, growthand shortening at distal (plus) ends. Recent observation ofMT release from the centrosome and depolymerizationfrom proximal (minus) ends indicates the existence of aminus end pathway. To evaluate the relative contributionsof plus and minus end pathways to turnover, we analyzedMT dynamics in a model system, the fish melanophore, alarge non-motile cell with a regular radial array of longMTs. MT ends were tracked in digital fluorescence time-lapse sequences and life histories of individual MTs wereanalyzed using random walk theory generalized to the caseof diffusion with drift. Analysis of plus end dynamics gavean apparent diffusion coefficient of D=7.5 µm2/minute. Therandom walk model predicts that the half-time for turnoverdriven solely by plus end dynamics will depend stronglyon position in the cell. Based on the experimentallydetermined value of D, turnover of MTs near the center ofa typical melanophore of radius 70 µm was calculated torequire over 5 hours, a paradoxically long time.
To examine MT behavior deep in the cytoplasm, wedeveloped a novel, sequential subtraction mode of imageanalysis. This analysis revealed a subpopulation of MTswhich shortened from their minus ends, presumably afterconstitutive release from the centrosome. Given the relativeslowness of plus end dynamics to turn over the root of along MT, the turnover of MTs near the cell center isdetermined primarily by the minus-end pathway. MTsreleased from the centrosome become replaced by newlynucleated ones. The relative contributions of plus andminus end pathways was estimated from the diffusioncoefficient, D, for the plus end, the length distribution ofMTs, t he frequency of free minus ends, and the rate ofminus-end shortening. We conclude that, in large animalcells with a centrosomally focussed array of MTs, turnoveroccurs by a combination of plus and minus end pathways,the plus end dominating at the cell periphery and the minusend dominating near the cell center.
Contribution of plus and minus end pathways to microtubule turnover
I. A. Vorobjev1, V. I. Rodionov2, I. V. Maly1 and G. G. Borisy2,*1Laboratory of Cell Motility, A. N. Belozersky Institute, Moscow State University, Moscow, Russia2Laboratory of Molecular Biology, University of Wisconsin, 1525 Linden Drive, Madison, WI 53706, USA*Author for correspondence (e-mail: [email protected])
Accepted 6 May; published on WWW 24 June 1999
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states, growing or shortening, and that stochastic transitions,termed catastrophes and rescues, occur between these twostates. 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 thedynamics of MT plus ends.
A few reports have recognized limitations of the dynamicinstability model (Odde et al., 1995; Odde, 1997). In contrastto the two-state model which stipulates fixed rates of growthand shortening, MTs have been reported to display intrinsicallyvariable 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 amodel-independent approach. One approach to quantitativeanalysis of MT turnover in vivo has employed the conceptualframework of a random walk to the behavior of MT ends(Vorobjev et al., 1997). With this approach, the stochasticgrowth and shortening behavior of the MT plus end ischaracterized as a 1-dimensional random walk analogous to thediffusion of a molecule and the overall level of dynamicactivity is captured by a single number, an apparent diffusioncoefficient. For the plus ends of MTs in PtK1 cells, thediffusion coefficient was determined to be D=2.4 µm2/minute(Vorobjev et al., 1997).
Independent of the molecular details underlying MTdynamics, it should be possible to link the behavior ofindividual MTs with the turnover kinetics of the MTpopulation. However, theoretical calculations based on MonteCarlo simulations of plus end dynamics using dynamicinstability parameters obtained for newt lung cells (Gliksmanet al., 1993) yielded a turnover half-time (3.5 hours) far slowerthan typical FRAP measurement values. Random walk analysisproduced a similar disparity. A characteristic turnover time canbe calculated from the apparent diffusion constant as the timerequired for the MT plus end to ‘diffuse’ to its minus end,generally assumed to be at the centrosome. Assuming a typicallength for MTs in PtK1 cells of 20 µm, a diffusion coefficientof 2.4 µm2/minute predicts a value for the turnover time of overone hour, long compared to experimental measurements. Thusanalysis of individual MT dynamics seems to be in apparentcontradiction with the rapidity of their turnover.
The disparity between experimental values of MT turnovertime and values calculated from the behavior of individual MTsprompts a number of questions. Is our understanding of MTturnover incomplete or are the FRAP measurements wrong insome way, or both? Are determinations of the kineticparameters of MTs or the experimental determination of D inerror or are our estimates of MT length incorrect? Thesequestions suggest that a more comprehensive revisiting of MTdynamics and an effort to obtain a coherent quantitative picturewould be worthwhile.
The possibility that our understanding of MT turnover isincomplete has been raised by recent observations concerningthe activity of the minus end. Minus ends had generally beenthought to be associated with and anchored in the centrosome.However, recent observations of MT release from thecentrosome and depolymerization from proximal (minus) ends(Keating et al., 1997; Waterman-Storer and Salmon, 1997;Vorobjev et al., 1997) and MT treadmilling (Rodionov andBorisy, 1997; Rodionov et al., 1999) indicate the existence ofa minus end pathway. In most instances, minus-end shortening,
when it occurred, was rapid with velocities in the range of 4-12 µm/minute depending on the cell type. Assuming ashortening rate of 5 µm/minute, a 20 µm MT would requireonly 4 minutes to completely depolymerize from its minus end.Thus, the minus end pathway has the capacity, in principle, torapidly eliminate long MTs. Turnover would be accomplishedwhen the eliminated MTs were replaced by MTs newlynucleated at the centrosome.
In this study, we have sought to quantitatively determine thecontributions of plus-end dynamics and the putative minus-endpathway to MT turnover in a model system where all therequired parameters could be estimated. We have chosen thefish melanophore as an experimental system because it displaysa number of favorable properties. It is non-motile, radiallysymmetric and large. The lack of motility eliminates the needto consider changes in the spatial arrangement of MTs whichnecessarily accompany crawling motions. The radial symmetrypermits analysis of MT dynamics to be simplified to a 1-dimensional problem, namely, dynamic behavior along aradius. Because the melanophore is large, it contains many longMTs, accentuating the possibility of discriminating betweenplus and minus end behavior. Indeed, fish melanophores havea diameter sometimes exceeding 200 µm. Although the preciselength distribution of MTs in melanophores has not beendetermined, many MTs are thought to run from the centrosometo the cell margin, being up to 100 µm long (Murphy andTilney, 1974; Schliwa and Euteneuer, 1983; Rodionov et al.,1994). Melanophores normally contain pigment granulesdispersed throughout the cytoplasm which interferes withvisualization of MTs. However, melanophores may be inducedto aggregate their pigment granules by stimulation withadrenalin permitting the MT array to be visualized in anessentially transparent cytoplasm.
On the basis of plus end dynamics alone, one might expectthat turnover of the long MTs of the fish melanophore wouldrequire a long time. However, experimentally determinedturnover half-times for the major part of MTs in melanophoresas measured by fluorescence recovery after photobleaching orfluorescence redistribution after photoactivation was of theorder of 5 minutes (Rodionov et al., 1994). Thus, themelanophore seems to highlight the apparent disparity betweenFRAP measurements and theoretical considerations. In thisstudy, we provide estimates of the contribution to turnover ofboth the plus and minus-end pathways. We show that MT plusends in fish melanophores are highly dynamic and that this isresponsible for turnover at the periphery of the cell. However,the turnover half-time of a MT depends upon its length andturnover of MT ‘roots’ near the centrosome requires thecontribution of the minus-end pathway.
In addition, we show that the shortening of MTs from theirminus ends has consequences for the distribution of MT plusends, favoring their accumulation at the margin.
MATERIALS AND METHODS
Cell culture Black tetra (Gymnocorymbus ternetzi) melanophores were obtainedfrom fish scales as described elsewhere (Rodionov et al., 1994) andcultured in DMEM (Hepes modification) (Sigma Chemical Co., StLouis, MO), pH 7.2, supplemented with 20% fetal bovine serum
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(HyClone Labs, Logan, UT) and antibiotics (100 i.u./ml penicillin, 0.1mg/ml streptomycin, 0.1 mg/ml gentamycin). Cells were used formicroinjection on the day after plating. Aggregation of pigmentgranules was induced by addition of adrenalin to 10 µM.
Preparation of Cy3-tubulin Cy3-labelled porcine brain tubulin was prepared as describedelsewhere (Keating et al., 1997) and stored in 10 µl aliquots in liquidnitrogen. Prior to microinjection, a 10 µl aliquot of Cy3-tubulin wasdiluted 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 particulatematerial and minimize micropipette clogging, and stored on ice untilthe time of injection.
Imaging and data analysis Cells injected with Cy3-tubulin were treated with the oxygen-depleting enzyme Oxyrase (Oxyrase, Inc., Ashland, OH) to reducephotodamage 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 finalconcentration of 20 mM and the dishes were covered with a layer ofmineral oil (Squibb and Sons, Princeton, NJ). Injected cells wereobserved on a Nikon Diaphot 300 inverted microscope equipped witha Plan ×100, 1.25 NA objective using a rhodamine filter set. Imagesof 16-bit depth were collected with a CH250 slow scan, cooled CCDcamera (Photometrics Ltd, Tucson, AZ) driven by Metamorphimaging software (Universal Imaging Corp., Westchester, PA). Theimage was projected onto the CCD chip at a magnification of ×250which corresponded to a resolution of 1 pixel=0.105 µm (9.6pixels/µm). Exposure times were 0.2 or 0.3 seconds, and images werecollected at 5.0-10.0 second intervals. Cells were kept at roomtemperature (~24°C) during observation. A typical series comprised100-150 frames covering a period of 8-20 minutes. 16-bit imageswere processed and rescaled with Metamorph software or NIH-Image software (National Institute of Health) and 8-bit imagesprepared 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 to40%.
Analysis of microtubule dynamicsPosition of MT ends were traced by mouse-driven cursor under NIH-Image software, and from consecutive images a matrix was generatedfor the MTs in each cell (Table 1). The mean velocity of displacementwas determined as:
vd = Σ(µi ti)/Σ(ti2) ,
and the mean rate of growth of the variance with time was determinedas:
s = Σ(σi2 ti)/Σ(ti2) .
A suitable conceptual framework for the conditions occurring in themelanophore is to treat MT dynamics at the plus end as a 1-D randomwalk (Berg, 1993). Under the random walk approach the behavior ofa MT end is considered an analogue of that for a diffusing particle.In the steady-state, the mean square displacement of a MT end fromits 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, thekinetics of MT turnover can in principle be calculated directly fromthe diffusion coefficient. The diffusion plus drift formalism can alsobe used to characterize the dynamics of a system even when it is notin steady-state. In the non-steady-state the drift coefficient (vd) is ameasure of the imbalance of growth and shortening whereas thediffusion coefficient is a measure of the absolute magnitude(squared) of the growth and shortening excursions at MT ends (seeResults and Discussion for details). All values given in the text aremean ± s.d.
Sequential subtraction analysis The position and behavior of MTs ends in the deep cytoplasm ofmelanophores were analyzed by subtraction of sequential images (In−In+1) in time-lapse series using Metamorph imaging software. Theresultant difference images displayed intensity variations reflectingthe dynamics of MTs, primarily the growth and shortening ofindividual MTs but also lateral displacements. The magnitude of theintensity difference (typically 20-40 analog-to-digital units, ADUs)reflected the fluorescence of a single MT. The length of a domain ofintensity difference was proportional to the instantaneous velocity ofgrowth or shortening. Histogram stretching was carried out to setshortening events to white and growth events to black which wereclearly identifiable as individual white or black domains. In contrast,lateral shifts were identified as parallel domains of white and blacksegments. During the time interval between two images (typically 5-7 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 cellradius, the number of MT excursions was calculated in subtractionimages in three different regions in the cell. The regions weresegments 8 µm height and separated by a distance of 10 µm from eachother within the selected sector (7°-15°). The distal segment wasplaced to sample peripheral cytoplasm with its outer margin as closeas possible to the cell boundary. Its center was located at ~0.9 cellradius (R). The relative position of the other segments along the cellradius depended on the cell size.
End displacements were measured in sequential subtraction imagesand the mean rate of shortening or growth determined as displacementdivided by the time of observation.
RESULTS
MT dynamics during the approach to steady-stateEvaluation of the relative contribution of plus and minus endpathways to MT turnover in the steady-state requires firstestablishing that the experimental system is indeed at steady-state. By definition, steady-state for MT dynamics means time-invariant kinetic parameters, polymer level and spatialdistribution. Since aggregation of pigment granules requiredstimulation by adrenalin, a first experimental question waswhen steady-state was achieved after stimulation. In the courseof establishing conditions for the steady-state, we observedremarkable behavior of the MT minus end which influencedthe design of subsequent experiments.
Aggregation of pigment granules is rapid with a half-timeof approximately 2.5 minutes (Rodionov et al., 1991).Consequently, our first analyses began at 10 minutes (4 half-times) after addition of adrenalin. Melanophores at this timeafter stimulation displayed a characteristic radial system of
Table 1. Analysis of microtubule dynamicsFor MT1 For MT2 For MT3 ...... For MTn
∆l(ti) is the displacement of a given MT end (plus or minus) with respect toits position in the first frame. Further data handling was performed usingMathcad Professional (MathSoft Inc.) and Sigma Plot (Jandel ScientificCorp., San Rafael, CA). A matrix mean displacement µi and its variance σiwere calculated for each time interval.
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long MTs, some straight, some wavy, running from the centralpart of the cell toward the periphery. The area accessible forvisualization of individual MTs extended to approximately 10-15 µm from the cell margin. Deeper in the cytoplasm, thedensity of MTs generally precluded the direct observation ofMT ends. Surprisingly, besides long MTs running towards thecell center, MTs with free proximal ends were also observed.
Time-lapse analysis for the interval 10-30 minutes afteraddition of adrenalin revealed free MTs rapidly shorteningfrom the minus (proximal) end (Fig. 1). This result by itselfindicated the existence of an active minus-end pathway whichmight contribute significantly to MT turnover. MT plus endsaway from the cell margin showed variations in growth rateand infrequent transitions to shortening phase which wererapidly rescued (Fig. 2A). Overall, these MTs showed netgrowth. As MTs grew close to the cell margin, their plus endsspent most of their time in pause, rarely depolymerized for ashort distance and regrew back to the margin (Fig. 2B). Freeminus ends shortened or were stable (paused), but never grew(Fig. 2C). The behavior of the plus end was independent ofwhether or not the minus end of the MT was free. Short freeMTs showed the same plus end excursions as long ones.
Stochastic excursions of the plus ends of MTs inmelanophores made it possible for us to apply random walkanalysis (Vorobjev et al., 1997). Random walk analysis interms of diffusion plus drift (Berg, 1993) was applied to
I. A. Vorobjev and others
Fig. 1. MT dynamics during approach to thesteady-state. Fluorescently labelledmicrotubules were imaged at the peripheryof living melanophores shortly afterpigment aggregation. Melanophores withdispersed pigment were injected with Cy-3tubulin and 2 hours later pigmentaggregation was induced with adrenalin.Time-lapse series of images of microtubuleswere acquired beginning 20 minutes afteradrenalin treatment. Distal (plus) ends ofMTs displayed dynamic instability.Numerous free MTs (colorized in red)depolymerized from their proximal (minus)ends. Time in seconds shown in lower leftcorner. Bar, 5 µm.
Fig. 2. Life history plots of MTs during approach to the steady-state.(A) Dynamics of distal (plus) end deep in the cytoplasm. Phases ofgrowth are significantly longer than phases of shortening resulting inoverall growth (drift) to the margin. (B) Dynamics of distal (plus)end at the margin. Prolonged pauses are interrupted with briefepizodes of growth and shortening. (C) Dynamics of a MT with freeproximal (minus) end. Continuous polymerization at distal (plus) endand 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.
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quantify the behavior of the MT population (see Materials andMethods). The coefficient of drift, vd, is defined as the factorof proportionality between mean displacement of the ends ofa population of MTs and elapsed time. In molecular terms, thedrift coefficient is proportional to the difference between therates of the one-way reactions of tubulin polymerization anddepolymerization at the MT end; it equals zero at steady-state(when both reactions are on average balanced) and in generalcan serve as a measure of deviation from steady-state. Thecoefficient of diffusion, D, is defined as the factor ofproportionality between the variance of the end displacementsabout the drift component. When the drift component is zero,this simplifies to the mean square displacement of MT endsachieved in a given time, x2=2Dt. Mean square displacementof MT ends (correcting for any drift) are a measure of thedynamic activity or ‘diffusion’ of the end.
Linear regression analysis was performed to determine driftand diffusion coefficients from end displacement data (Fig. 3)which in turn were derived from life history plots (100-150frames, 5 second intervals). Individual MT life history plotswere often short because their dynamic activity carried the MToutside the region of observation. Consequently, for purposesof the regression analysis, life history plots were broken into 1
minute windows. Positive values of drift coefficients aredefined to signify displacement toward the cell margin. Thiscorresponds to growth for the plus end and to shortening forthe minus end. For MT behavior during the interval 10-30minutes after stimulation with adrenalin, drift and diffusioncoefficients for plus ends depended on proximity to the cellmargin. Away from the cell margin, plus ends had a driftcoefficient of 3.3±0.4 µm/minute and a diffusion coefficient of6.3±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 impressionfrom viewing the time-lapse series that MT plus ends reducetheir dynamic activity and stop their net growth as theyapproach the cell margin. The minus ends of free MTs showeda drift coefficient of 4.6±0.3 µm/minute and a diffusioncoefficient of 3.7±0.7 µm2/minute. Further, minus endscontinued to shorten even near the cell margin. For eachcategory of MT end, the sample analyzed consisted of 33 MTsdrawn from 7 cells.
Fig. 3. Random walk analysis of MT dynamics during the approachto steady-state. The behavior of plus ends of MTs away from the cellmargin 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 driftregression line (variance of displacement) of the same plus endsversus time. Regression line provides diffusion coefficient of 6.3±0.9µm2/minute. Broken lines, 70% confidence intervals. Data obtainedfrom 33 MTs in 7 cells.
Fig. 4. MT dynamics at steady-state. Fluorescently labelledmicrotubules were imaged at the periphery of living melanophoresafter pigment aggregation. Imaging was begun 2 hours after injectionof Cy-3 labeled tubulin and 1 hour after stimulation of aggregationby adrenalin. Arrowheads directed to the right indicate growing endsof MTs and arrowheads directed to the left indicate shortening ends.Time in seconds shown in lower left corner. Bar, 5 µm.
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The difference in behavior of plus and minus ends resultedin the inevitable disassembly of free MTs as their plus endsneared the cell margin. As a consequence, free MTs were lostfrom the population whereas those MTs with their minus endsanchored at the centrosome accumulated in the population. Atthe end of the observation window (10-30 minutes afteradrenalin stimulation), free MTs became very rare. Thedecreasing number of free minus ends during the observationwindow and the different dynamics of the plus ends adjacentto the cell margin versus those deeper in the cytoplasmindicated that despite the complete aggregation of pigmentgranules, a steady-state for MTs was not achieved earlier than30 minutes after adrenalin stimulation. The results alsodemonstrate that a significant minus-end pathway for MTdynamics exists in the melanophore.
MT dynamics in the steady-stateWith continued incubation of melanophores after adrenalinstimulation (1-3 hours), the radial array seemed to becomebetter 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 stochasticduration and variable rate of both kinds of excursions.
MT plus end dynamics were quantified by obtaining lifehistory displacement plots (Fig. 5A). To evaluate the diffusionmodel, displacement frequency distributions were computedfor increasing time intervals, two of which (5 seconds and 50seconds) are shown in Fig. 5B,C. Consistent with diffusion, thedisplacement frequency distribution gradually broadened andflattened out but showed a mean value of approximately zero.The fact that the histogram of instantaneous rates wasmonotonically declining for both growth and shortening ratesindependent of the size of the time bins suggested a fractalcharacter for the plus-end dynamics (Vorobjev et al., 1997).The displacement data at 5 seconds may also be considered aninstantaneous growth and shortening velocity distribution.Shortening or growth were considered to have occurred whenthe displacement of a MT end between subsequent frames wasat least two pixels (0.21 µm). The most frequent bin was zerodetectable change and to either side of this category, thefrequency distribution was monotonically declining. That is,neither growth nor shortening was characterized by a single
I. A. Vorobjev and others
Fig. 5. Analysis of MT dynamics atsteady-state. (A) Life history plot of anindividual MT at the cell margin. MT endgrows and shortens but the netdisplacement is close to zero.(B) Frequency histograms of plus enddisplacements after 5 second and 50second time intervals. The displacementfrequency distribution graduallybroadened but showed a mean value ofapproximately zero. Data presented fromtime-lapse series, 100 images, 5 secondintervals; 4410 measurements on 46 MTsin a single cell. (C) Drift component ofthe random walk. Regression lineindicates that drift coefficient is close tozero (−0.04±0.41 µm/minute).(D) Diffusion component of the randomwalk. Regression line gives value fordiffusion coefficient of 7.5±1.2µm2/minute. Broken lines, 70%confidence intervals. Data shown,averaged for 5 cells (See text for details).
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velocity. The mean instantaneous growth rate was 6.8±7.0µm/minute while the mean shortening rate was almost twiceas great, 11.9±6.3 µm/minute.
The drift coefficient was calculated by linear regressionanalysis of mean displacement over time and found to be −0.038±0.41 µm/minute (Fig. 5C). This value isindistinguishable from zero at the significance level 0.95(Student criterion used). Consequently, plus ends in theaggregated cells apparently are at steady-state. However, itshould be noted that the large standard deviation obtained inthe 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 invariance of displacement over time (Fig. 5D). The coefficientvaried significantly for individual cells. For four cells where asufficiently large number of MTs could be analyzed, valuesobtained 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 cellvariation is not understood, we pooled data for a number ofcells to generate a population average. For a sample consistingof 75 MTs (15 MTs from each of 5 cells), we calculated anaverage diffusion coefficient D=7.5±1.2 µm2/minute. Thus,quantitation of MT plus end dynamics in the steady-statemelanophore apparently conformed to a pure random 1-D walkof MTs along the cell radius.
A random walk mechanism is implicitly based on theassumption that growth and shortening of MT plus ends occursin the same way throughout the cytoplasm. That is, kineticparameters and the frequency of growth and shortening are thesame both at the cell periphery and deeper in the cytoplasm.The random walk model views the ends of MTs as analogousto molecules in a container. Thus, a pure random walk modelpredicts that MT plus ends will be distributed randomly alongthe cell radius. That is, the length distribution of MTs will beuniform, short and long MTs will exist in equal numbers andthe average MT length will be half the cell radius. Further, apure random walk model is based solely on dynamic behaviorof plus ends. In contrast to the observed behavior of the pre-steady-state melanophore, no minus end MT activity isrequired. These features are examined in the followingsections.
Dynamics and distribution of MT plus ends alongthe cell radius At steady-state, the plus ends of MTs in melanophores could beseen clearly only near the cell margin and it was unclear howmany of them were hidden in the deeper parts of the cytoplasm.Diagrams generally depict cytoplasmic MTs as extendingcontinuously from the centrosome to near the cell margin. Thisview implies that few or no MT ends will be found in theinternal parts of cytoplasm and is in apparent contradiction withthe random walk behavior of plus ends which predicts that theyare uniformly distributed throughout the cytoplasm. Also, if MTends do exist throughout the cytoplasm, the question ariseswhether their dynamic behavior is the same as at the periphery.Consequently, we tried to visualize MT ends and evaluate theirbehavior deep in the cytoplasm.
Direct fluorescence visualization of individual MTs islimited by the dynamic range of the imaging detector anddisplay technology. Deep in the cytoplasm, a single MT is
difficult to visualize directly because of the superposition ofmany other MTs (Fig. 6A). However, given the large and lineardynamic range of a scientific grade CCD, single MTs can bevisualized by performing differential image analysis. In thisanalysis, sequential images are subtracted from each other. Theresulting images showed an almost uniform background onwhich MT shortening appeared (after intensity histogramstretching) as a white segment and MT growth as a blacksegment (Fig. 6B). A limitation of difference image analysiscomes from lateral displacements of MTs. However, thesewere distinguished from growth or shortening because lateralshifts led to parallel black and white lines whereas growth orshortening led to individual black or white segments. Duringthe time interval between two images (5-7 seconds), lateralshifts of MTs in melanophores were infrequent and slight.Subtraction of images taken at longer time intervals from eachother resulted in increase of heterogeneity of the central partof the image, probably because of lateral displacements ofnumerous MTs that exceeded a single MT signal (data notshown). Consequently, differential image analysis wasrestricted to single frame differencing. As a threshold fordetectability, we considered an active MT end to be visualizedif the difference image showed a white or black segment of atleast 5 pixels (0.5 µm) length. Within this limitation, dynamicMT ends were clearly visible throughout the cytoplasm.
Differential imaging time-lapse series were quantified toevaluate whether MT dynamics were uniform throughout thecytoplasm and to determine the distribution of MT ends. MTexcursions were visualized clearly up to 60 µm from the cellmargin, a distance which approached the centrosome. Whenshortening occurred at the plus end, the retrograde movementof the white segment could occasionally be followed for twoframes (15 seconds), and rarely for three (22 seconds). In themajority of cases, a white segment was observed only in asingle subtraction frame. This indicated that shortening of MTplus ends was generally brief. A shortening event was oftenfollowed by a growth event; that is, a white segment movingretrogradely was succeeded by a black segment at the samelocation moving anterogradely (data not shown). Nocytoplasmic nucleation of MTs was detected. For quantitationpurposes, cell sectors were divided into zones along the cellradius (R), shortening and growth events enumerated and theirratio computed. For the three zones of the cell in Fig. 6C, theratio 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 (0.45-0.30 R), 0.53±0.08, respectively, indicating that growth andshortening events occurred in similar proportions along the cellradius. Differential images gave not only the number of eventsbut an estimate of their velocity as well since the length of asegment was proportional to the instantaneous rate of the event.On average, shortening excursions were about twice the lengthof growing ones, similar to the ratio of velocities of 1.75obtained by direct visualization (see previous section).Considering the relative number of growth and shorteningsegments with their relative length, we conclude thatthroughout the melanophore cytoplasm, growing MT plus endsare about twice as numerous as shortening plus ends and thatshortening is about twice as fast as growth. These parametersequate to the steady-state because they indicate an overallbalance between polymerization and depolymerization and,therefore, no net change in MT polymer.
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Although the difference imaging clearly indicated thepresence of active MT plus ends throughout the cytoplasm, itwas also evident that the distribution of plus ends along theradius was not random; many more ends were found near thecell margin than deeper in the cytoplasm. Because of thethreshold for detection of 0.5 µm, the number of growth andshortening events recorded is undoubtedly an underestimate ofthe actual number of active MT ends. Nevertheless, therecorded number may be taken as proportional to the realnumber. On this assumption, the relative number of growingand shortening ends along the cell radius may be computed(Fig. 6D). In 6 cells examined by differential time-lapse, 1107growth and 596 shortening events were recorded in zone 1, 474growth and 286 shortening events in zone 2, and 354 growthand 187 shortening events in zone 3. Thus, the number of activeMT ends at the periphery (zone 1) was 2.2 times the numberin the middle (zone 2) and 3.10±0.93 times the number deepin the cytoplasm (zone 3). This quantitative analysis of MTdynamics in the steady-state makes two main points. One is inkeeping with the random walk model; namely, that the kineticparameters and the frequency of growth and shortening aresimilar both at the cell periphery and deeper in the cytoplasm.However, we wish to note that the limitations of subtractionanalysis in the deep cytoplasm, namely the inability to followindividual MTs for an extended period, prevented a detailed
evaluation of MT dynamics in terms of the diffusion plus driftmodel as we performed by direct imaging of MTs at theperiphery. Therefore, the absence of a small drift componentin the interior is not precluded by the data. The other point,that the distribution of MT plus ends is non-random, isinconsistent with a pure random walk model and prompts thequestion as to what other process is occurring.
Free minus ends at steady-stateObservations of MT dynamics made shortly after adrenalinstimulation of pigment aggregation revealed numerous freeMTs near the cell margin and rapid shortening from the minusend. Although not as numerous, free MTs were also detectablein the steady-state. In an analysis of 6 cells (100-150 frames,10-12 minutes observation each) in which 170 MT plus endswere tracked, 2 minus ends were seen by direct visualization,giving an approximate minus end frequency of ~1%. Wewondered whether this level of free MTs near the peripheryindicated a low but constitutive release of MTs from thecentrosome followed by minus-end shortening. Such minus-end depolymerization would release tubulin subunits thatwould, in the steady-state, necessarily polymerize onto thepopulation of MT plus ends. This polymerization wouldimbalance growth and shortening at the plus ends and generatea drift toward the cell margin. Such drift could account for the
I. A. Vorobjev and others
Fig. 6. Sequential subtraction analysisof MT dynamics at steady-state.Fluorescently labeled MTs wereimaged in living melanophoresbeginning 2 hours after injection oflabelled tubulin and 1 hour afterstimulation of aggregation by additionof adrenalin. (A) Image of MTs from atime-lapse sequence used for analysis.(B) Differential image obtained bysubtracting from the image in A thenext image in the time-lapse series.Black segments and white segmentsrepresent MT growth and shortening,respectively, during the time interval.(C) Diagram extracted from thedifference image by bit slicing,illustrating growth (green) andshortening (red) excursions. Whiteboxes (1,2,3) indicate the regions fromwhich data were compiled. Yellowspot shows estimated position of thecell center. The angular density ofgreen segments and red segmentsdecreases towards the cell center. Theratio between frequency of growth andshortening events in all boxes wasnearly the same. (D) Distribution ofactive MT ends along the cell radius asdetermined by the number of growthor shortening events. Number of MTsindicated relative to number ofshortening MTs at the cell margin(zone 1) set to 100. Data shown,averages for 6 cells (see text fordetails).
2285Pathways of microtubule turnover
departure of the MT end distribution from the uniformdistribution predicted by the random walk model. ConstitutiveMT release would also contribute to MT turnover.
Time-lapse sequences of differential images wereexamined to determine whether minus end shortening events
could be discerned. White segments moving in a cell margin-to-centrosome (retrograde) direction were the basis forpreviously assigning these events as plus end shortening. Bythe same reasoning, white segments moving in a centrosome-to-cell margin (anterograde) direction were assigned as minusend shortening. Review of the differential time-lapse seriesindeed uncovered free minus ends deep in the cytoplasmshortening toward the periphery (Fig. 7). For shorteningminus ends, the white segment moved anterogradepersistently, although with variable velocity, and sometimescould be traced for over a minute. This is consistent withobservations of minus end behavior described for thecondition of approach to the steady-state. A differencebetween plus and minus end shortening was that in the lattercase the white segment never converted into a black one; thatis, shortening of the minus end was never seen to besucceeded by growth.
Minus end shortening was deemed to have taken place if twocriteria were met. The white segment had to moveanterogradely and it had to be visible in at least threesuccessive frames. Using these criteria, we recorded minus endshortenings appearing in a time lapse series and determined itsrate to be 10.4±4.0 µm/minute (n=23). In contrast to ourprevious observations of MTs in the steady-state where thetotal number of minus ends visualized was small because ofthe limitations of direct fluorescence imaging, differenceimaging permitted the scoring of many minus end eventsthroughout the cytoplasm. In contrast to MT plus ends whichwere enriched at the cell periphery, MT minus ends weredistributed more evenly through the cytoplasm. For 6 cells onwhich detailed analysis was performed as described in theprevious section, 139 minus end shortening events wererecorded. Each minus end was followed on average for 46seconds (from 3 to 12 sequential subtracted images). From thetotal number of MTs and estimates of our MT detectionprobabilities, we calculated the proportion of free minus endsto total MT ends to be 0.98±0.8%. Given the experimentallimitations on detection of minus end shortening, this value isprobably an underestimate and the average velocity of minusend shortening is probably an overestimate. The relativefrequency of appearance of minus ends varied with individualcells, but for 11 cells examined, on average, there was nodifference between cells exposed to adrenalin for 1 or for 3hours (data not shown). This indicates that minus endappearance and shortening are true steady-state phenomenaand that after 1 hour incubation in adrenalin, free MTs withshortening minus ends are continuously replaced, probably byrelease from the centrosome. The consequences of constitutiverelease and minus end depolymerization for the MT lengthdistribution and MT turnover will be considered in theDiscussion.
Fig. 7. Minus-end shortening revealed by sequential subtractionanalysis. Subtraction of sequential fluorescence images revealedwhite (shortening) segments moving in a centrosome-to-cell margindirection. These segments, interpreted as minus end shortening, arecolorized with red overlay (two MTs highlighted). Length of redsegment reflects instantaneous velocity (1.2 µm segment/frame=10µm/minute shortening velocity). Elapsed time in seconds shown atlower left. Bar, 5 µm.
2286
DISCUSSION
Approach to steady-stateThe melanophore has been studied as an exemplar system forthe transport of organelles along MTs (Beckerle and Porter,1982; Rodionov et al., 1991). It both aggregates and dispersespigment granules rapidly, the aggregation reaction occurringwith a half-time of approximately 2.5 minutes (Rodionov et al.,1991). We induced aggregation of pigment granules in orderto clear the cytoplasm for visualization of MT behavior.Consequently, after inducing aggregation, we expected to beable to analyze MT dynamics almost immediately at theperiphery of the cell and within 10 minutes (4 half-times)throughout the interior of the cell. Unexpectedly, we observednon-steady-state behavior of MTs during the time regime of 10minutes to 30 minutes. MT plus ends were dynamicundergoing stochastic excursions, catastrophes and rescues, buttended to drift toward the cell margin at a velocity of 2.4µm/minute. At the cell margin, MT plus ends appeared lessdynamic and were frequently ‘paused’. However, thisappearance of reduced dynamics can be interpreted in terms ofthe membrane being a barrier to MT advance and thepersistence of growth tending to keep the MT plus end near thebarrier. When the drift component of MT plus ends is large, anend that moves away from the margin in an episode ofshortening is quickly returned to the margin. Thus, the plusends 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 endswere numerous and shortened toward the cell margin evenfaster, with a drift velocity of 4.6 µm/minute. Thus, minus endstended to catch up to plus ends with the progressive eliminationof free MTs.
The origin of the free MTs is not clear. The action ofadrenalin on fish melanophores has been interpreted to initiatea signal cascade leading to the activation of dynein, the minus-end directed motor responsible for transport of pigmentgranules toward MT minus ends (Haimo and Thaler, 1994;Nillson and Wallin, 1998). However, adrenalin action may alsoexert effects on the MT system itself, leading to the transientappearance of free MTs. Conceivably, the downstream signalcascade may induce release of MTs from the centrosome.Alternatively, the possibility that many free MTs pre-existed inthe melanophore in the dispersed state cannot be excluded. Theminus ends of such free MTs could have gone undetectedbecause of the high density of MTs and their minus-ends,stable in the dispersed state, could have been destabilized bythe action of adrenalin.
Whatever the explanation, the phenomenon of plus end driftand numerous free minus ends shortly after adrenalinstimulation was informative. The fact of rapid minus-endshortening provided clear evidence for the instability of minusends in intact melanophores and for the existence of a robustminus-end pathway. Previously, minus-end shortening inmelanophores had only been observed in cytoplasmicfragments (Rodionov and Borisy, 1997). Interestingly, the driftvelocity for minus ends in intact melanophores (4.6µm/minute) was essentially identical to the average shorteningvelocity of minus-ends in cytoplasmic fragments (4.4µm/minute), suggesting that under the conditions where MTminus ends were numerous, depolymerization reflected
cytoplasmic conditions independent of the presence of thenucleus, centrosome or other cell body components.
Sequential substraction anaysisDirect fluorescence imaging of individual MTs has generallyonly been accomplished near the cell margin where thethinness of the lamella has minimized the backgroundcontributed by soluble tubulin and obviated the out-of-focusfluorescence of MTs in nearby planes. To overcome thislimitation we introduced sequential subtraction analysis whichallowed us to visualize single MT displacements deep inthe cytoplasm. Subtraction analysis is a simple idea forrepresenting displacement of a MT end as a domain of intensitydifference in successive fluorescence images. The methodrequires a linear fluorescence detector with a large dynamicrange. Image sensors with such properties became availablewith the introduction of scientific grade, cooled charge-coupleddevices. In combination with image processing software togenerate intensity histograms and to stretch contrast withoutloss of significant information, growth and shorteningdisplacements of MTs could be objectively represented asblack or white segments, respectively.
The ability to characterize MT dynamics deep in thecytoplasm permitted several important conclusions to be drawnwhich otherwise would be inaccessible. From a singlesubtraction image, the numbers of black and white segmentsgive the relative proportions of growth and shortening events.The length of the segments indicate their relative velocities andtheir distribution within the cell indicates their approximationto or deviation from randomness. Comparison of numbers andlengths of segments in the interior and at the peripherypermitted us to conclude that the dynamic parameters of MTsdid not significantly vary with location along the cell radius inmelanophores. From sequential subtraction images, transitionsbetween growth and shortening could be assessed. Moreimportantly, time-lapse sequences permitted minus-endbehavior to be identified and distinguished from plus-endbehavior. Thus, the relative contributions of the minus andplus-end pathways could be directly assessed. Sequentialsubstraction analysis has been applied to CHO and PtK cells(I. A. Vorobjev and G. G. Borisy, unpublished results) and islikely to be applicable to the study of MT dynamics in manyother cell types.
Random walk dynamics explains MT turnover at thecell periphery In the steady-state, the dynamics of the plus end was fit wellby a random walk model. Plus ends underwent excursions ofgrowth and shortening (catastrophes and rescues) of variablemagnitude and variable rate. The net drift of the plus ends wasclose to zero and their overall behavior conformed closelyto a 1-dimensional random walk with apparent diffusioncoefficient, D=7.5 µm2/minute. It should be noted that implicitin the random walk model is the assumption of reflection at thecell periphery. Consistent with this assumption, the majority ofMTs were straight and directed along the cell radius. However,some plus ends which reached the plasma membrane curvedalong the leading edge and became oriented circumferentially.Nevertheless, to a first approximation, the random walk modelprovides a useful framework for characterizing MT behavior.
From the basic diffusion equation relating mean square
I. A. Vorobjev and others
2287Pathways of microtubule turnover
distance and time, x2=2Dt, the experimental value of Dsignifies that, on average, a MT plus end in a melanophorewanders 3.9 µm from its initial position in 1 minute, that towander 10 µm would require 6.7 minutes and to wander 70 µm(the approximate distance back to the centrosome) wouldrequire 327 minutes. These simple calculations serve todemonstrate that a random walk of the plus end is sufficient toaccount for rapid turnover of MTs (t1/2<7 minutes) near theperiphery of the cell (x<10 µm), as has been reported inmelanophores (Rodionov et al., 1994). However, random walkanalysis also indicates that the characteristic half-time forturnover by this mechanism is predicted to be stronglydependent on distance from the plus end, increasingapproximately as the square of the distance. A precisecalculation of the dependence of turnover half-time on distancefrom the cell margin would also have to take into considerationthe length distribution of MTs.
Most reports on MT turnover in the literature give only asingle estimate of turnover half-time as if position dependencewere not significant. Two studies, one in fibroblasts (Sammaket al., 1987) and one in neurons (Lim et al., 1990) have giventurnover values as a function of distance. Both studies showedincreasing turnover times with distance from the leading edge.However, neither study gave half-times of hours as predictedby pure plus end dynamics. Consequently, even though thesestudies as well as the current study show a significantdependence of turnover on position, they also suggest that anadditional mechanism is required to account for turnover nearthe cell center.
An apparent diffusion coefficient has also been determinedfor MTs in PtK1 cells (Vorobjev et al., 1997), the value for thissystem (2.4 µm2/minute) being approximately 3 times less thanfor the fish melanophore. The larger value of D for themelanophore means that the dynamics of individual MTs inmelanophores is faster than in PtK1 cells. However, since themelanophore is also more than 3 times larger in radius than aPtK1 cell, turnover of MTs in the melanophore is not faster. Infact, it is slower on a cellular basis because turnover half-timeincreases approximately as the square of the cell radius. It willbe interesting to see if comparison of MT dynamics in differenttypes of cells yields a generalization about the relationshipbetween cell size and the apparent diffusion coefficient of MTs.
Minus end pathway for MT turnoverThe origin of free MTs in the melanophore can be most readilyexplained by release from the centrosome as has beendocumented for PtK1 cells (Keating et al., 1997). Becauseshortening from the minus end is rapid, even MTs as long asthe cell radius will become completely depolymerized in arelatively short time. Our results gave two estimates ofshortening velocity, 4.6 µm/minute in the pre-steady-state asdetermined by direct observation and 10.4 µm/minute in thesteady-state as determined by sequential subtraction analysis.Because subtraction analysis used a threshhold for identifyingshortening events (the minimal detectable instantaneous rate ofminus end shortening was 4.4 µm/minute), slow shorteningwas underrepresented. Consequently, the 10.4 µm/minutevalue is probably an upper bound for the average speed ofshortening and a value closer to ~5 µm/minute is more likelyto 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 cellradius (70 µm). The released MTs will be replaced by newnucleation at the centrosome which means that the kinetics ofturnover contributed by the minus-end pathway are determinedprimarily by the frequency of the release process. A half-timefor release may be calculated based on an exponentialreplacement process as ln2/k where k is the release rate. Therelease rate can be calculated in principle from the incidenceof observing free minus ends and the time for their completedepolymerization. Although neither quantity could bedetermined precisely, the available data permit an estimate ofthe 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 (Vorobjevet al., 1997; Keating et al., 1997) and 0.1% in newt lung cells(Waterman-Storer and Salmon, 1997). Taking an average valuefor the release rate of k=0.0069 minute−1 (approximately 0.7%per minute), gives a half-time for release of 100 minutes. Thisis larger but of the same order of magnitude as the retentiontime of 43 minutes estimated for MTs to remain attached tothe pigment mass in a cytoplasmic fragment of melanophores(Rodionov and Borisy, 1997). Assuming an average time fordepolymerization of a released MT from its minus end to be10 minutes, an overall half-time for turnover via the minusend pathway in the melanophore may be estimated asapproximately 110 minutes.
In the steady-state, all tubulin released from the minus endshas to be accepted by the plus ends. This polymerization willcause the plus ends to drift towards the cell margin, the driftbeing superimposed on the random walk. Conservation of masspermits the value of drift for the plus ends to be calculated fromthe frequency of minus end occurrence (0.98±0.8%) and theminus end shortening rate (10.4±4.0 µm/minute) which equals0.102±0.092 µm/minute. Such a low value is within theexperimental error attached to our determination of the driftcoefficient (−0.038±0.41 µm/minute) and thus would not bedirectly visible in plus end behavior nor be an obviousdeparture from random walk behavior. Nevertheless, this minordrift of the plus ends does have an important consequence forthe MT length distribution.
A pure random walk model without drift predicts a randomdistribution of MT lengths. In contrast, our observationsrevealed a non-random distribution of the plus ends. Such non-random distribution could be explained by some attractant forMT growth secreted by the cell margin. A gradient of suchattractant would conceivably make it more probable for a MTto reach the cell margin as compared to the pure random walk.However, a simpler and alternative explanation is that the non-random distribution of MT plus ends arises as a result of thedrift component caused, in turn, by minus end shortening. Theextent to which minus end shortening (and therefore drift)perturbs the random MT length distribution can be estimatedusing the theory of diffusion with drift (Berg, 1993). Againanalogizing the plus ends of MTs with individual diffusingmolecules, the steady-state is determined when a gradient ofMT plus end position (and therefore length) balances the smalloutward drift component. The distribution of MT plus endsover 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, vdis drift of the plus ends, and D is diffusion coefficient. The
2288
position in the cell where the number of MT ends is twice thatat the centrosome is given as
x(doubling) = ln2 D/vd .
Taking D=7.5 µm2/minute, and vd=0.1 µm/minute, thedoubling distance is calculated as 52 µm. The distribution ofMT ends as determined by substraction analysis showed anincrease in the number of ends with increasing cell radiusroughly consistent with this prediction. Alternatively, a driftcoefficient may be calculated from the end distribution data.Carrying out this calculation, we obtain a value for the driftcoefficient of vd=0.29 µm/minute. This value is higher thanthat calculated from the minus end shortening but still smalland, in any event, too low to be measured with precision fromplus end dynamics. The calculations show that a driftcomponent in the range 0.1-0.3 µm/minute results in a non-random distribution of the plus ends with their 1-D densityascending exponentially towards the cell margin. The salientpoint is that, in a large cell, the increase in number of MTends towards the cell margin will be substantial even withonly a small fraction of shortening minus ends. This will givean impression that the majority of MTs run from the cellcenter to the margin, consistent with immunofluorescentand electron microscopic observations (Byers and Porter,1977; Schliwa, 1979; Schliwa and Euteneuer, 1978). Ourcalculations on the relative frequency of MTs ends along cellradius derived from subtraction images confirm this pictureand, more importantly, provide an explanation for how sucha distribution could arise in terms of a random walk modelwith drift.
Contribution of plus and minus end pathways to theoverall MT turnoverAnalysis of the plus end and minus end pathways permits usto make a quantitative assessment of their relative contributionto MT turnover. Turnover by the plus-end pathway isaccomplished by episodes of shortening followed by regrowth(catastrophes and rescues), amounting to a 1-D walk whichbecomes less probable the greater the distance to be ‘walked’.Consequently, for the plus end pathway, the calculated half-time of turnover strongly depends on distance from the cellmargin, being small close to the cell margin, and increasingrapidly with distance away from the margin. In contrast,turnover by the minus-end pathway is the result of replacementof released MTs by ones newly nucleated at the centrosome.Subunits generated by minus-end shortening are madeavailable for stochastic addition onto all available plus ends.For the minus end pathway, the turnover half-time does notdepend on the distance from the margin but rather isdetermined principally by the rate of release of MTs from thecentrosome. Consequently, the relative impact of the twopathways depends upon position with the cell (Fig. 8). Nearthe cell margin, the minus end pathway has almost no impact.Turnover of the peripheral domains of MTs is determinedprimarily by the plus end pathway. In contrast, deep in thecytoplasm, far from the cell margin, the plus end pathway hasonly a weak influence. Turnover of the root domains of MTsnear the centrosome is determined primarily by the minus endpathway.
Quantitative assessment of the two pathways may be madeon the basis of the random walk model with drift. The random
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 increaseapproximately with the square of the distance from the cellmargin. For D=7.5 µm2/minute and a cell radius of 70 µm, thehalf-time would be over 5 hours at the centrosome. Theturnover half-time contributed by the minus end pathway maybe estimated from the observed drift coefficient and the averageMT 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 consistentwith a centrosomal release rate of 0.7% per minute and a minusend depolymerization velocity in the range 5-10 µm/minute.However, the uncertainty in the determination of individualquantities involved in the calculation generates an uncertaintyin the computed half-time and permits us to conclude only thatit lies in the range, 50-200 minutes. Nevertheless, independentof the absolute value of the minus-end turnover time, certainqualitative features emerge. Of particular importance is that theminus end turnover half-time is independent of position in thecell and therefore constant over the cell radius. From Fig. 8, itcan be seen that the contributions of these two turnovercomponents will become equal at some distance from the celledge. Fig. 8. illustrates that the turnover of a MT is notcharacterizable by a singular quantity but, rather, must be
I. A. Vorobjev and others
Fig. 8. Relative contribution of plus and minus end pathways to MTturnover. The diagram shows dependence of the half time for MTturnover on the distance from the cell center for each of the plus andminus end pathways, considered separately. For the plus endpathway, the turnover half time rapidly increases with increasingdistance from the margin. In contrast, for the minus end pathway thehalf time does not depend on the distance from the margin but isdetermined by the frequency of release of MTs from the centrosome.The relative impact of the two pathways depends on the positionwithin the cell. For a model melanophore of radius, 70 µm, averagelength of MTs, 50 µm, diffusion coefficient, D=7.5 µm2/minute, driftcoefficient, vd=0.25 µm/minute (corresponds to release frequency of0.7% minute−1 and minus end shortening speed of 10 µm/minute),the point of equivalent impact of the two pathways is approximately43 µm from the cell margin. The diagram indicates that turnover ofthe peripheral domains of MTs is determined primarily by the plusend pathway whereas turnover of the root domains of MTs near thecentrosome is determined primarily by the minus end pathway.
2289Pathways of microtubule turnover
discussed in terms of position along its length. Long MTs arelikely to turn over their proximal segments by release from thecentrosome followed by minus end shortening. In contrast, thedistal segments of all MTs, long ones as well as short ones, areturned over primarily from the plus end. We conclude that thetwo pathways serve complementary roles. The plus endpathway enables rapid turnover of the peripheral domains ofMTs without the necessity to also turn over the roots. Incontrast, the minus end pathway provides an efficientmechanism for turning over the roots of MTs independent ofthe activity at the plus ends.
Contribution of the minus-end pathway to turnover dependson the frequency of release from the centrosome andprobability of stabilization of free minus ends by cappingfactors (discussed by Keating et al., 1997). These parametersmay vary between different cell types. For example, our recentwork with cytoplasmic fragments (Rodionov et al., 1997) andcytoplasts (Rodionov et al., 1999) demonstrated that minus-endcapping activity is low in melanophores and fibroblasts, butsubstantial in epithelial-type cells. Frequency of release mayalso be cell-type specific and is likely to be a subject ofregulation. With the methodology developed in the presentstudy it will be possible to precisely determine the role of theminus-end pathway in microtubule turnover in a wide varietyof cell types.
We thank Alexander Verkhovsky for stimulating discussions and acritical reading of the manuscript and John Peloquin for preparationof 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 IRCaward 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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