1314 Research Article

IntroductionCell migration plays an essential role during the development ofmost organisms (reviewed in Lauffenburger and Horwitz, 1996;Ridley et al., 2003; Raftopoupou and Hall, 2004). In adults, cellmigration continues to play an important role in processes such aswound healing (Reid et al., 2005; Zhao et al., 2006) and immunesystem function (Parent, 2004). It is well known that cell migrationis a complex process mediated by dynamic changes in the actin-myosin cytoskeleton. It is now generally thought that actinpolymerization at the leading edge provides a crucial driving forcefor extension of growth cones (Dent and Gertler, 2003; Kalil andDent, 2005), keratocytes (Svitkina et al., 1997; Pollard and Borisy,2003; Jurado et al., 2005), fibroblasts (Wang, 1985; Galbraith andSheetz, 1997), neutrophils (Torres and Coates, 1999; Parent, 2004)and Dictyostelium cells (Yumura et al., 1984; Yumura, 1996a;Yumura and Fukui, 1998; Parent, 2004), whereas the detachmentand retraction of the rear of the cell from the substratum is thoughtto be induced by contraction through myosin-II-dependent processesin Dictyostelium cells (Yumura et al., 1984; Yumura and Kitanishi-Yumura, 1990; Yumura, 1993; Small, 1989; Jay and Elson, 1992;Jay et al., 1995; Uchida et al., 2003) and fibroblasts (Chen, 1981;Galbraith and Sheetz, 1997).

If this is the case, then substratum contact sites in the anteriorportions of migrating cells should function as anchorages orscaffolds to allow pushing of the leading edge. This pushing shouldoccur by counter forces generated by actin polymerization andexerted onto the substratum in a direction opposite to that ofextension. At the posterior ends of migrating cells and the tips ofretracting pseudopodia, by contrast, traction forces in the samedirection as the retraction should be exerted onto the substratumby myosin II contraction before detachment from the substratum.However, the relationship between myosin II dynamics and tractionforces has never been demonstrated directly because of the difficulty

in simultaneously recording traction forces and myosin II dynamicsin migrating cells. In this study, we aimed to examine thisrelationship directly.

To determine the mechanical interactions between migrating cellsand the substratum, Dembo and colleagues (Dembo et al., 1996;Dembo and Wang, 1999) proposed procedures to convert themeasurement of elastic substratum deformation under migratingcells into traction stresses using finite element methods; thistechnique was designated ‘force microscopy’ and was used to mapforces in migrating fibroblasts (Beningo et al., 2001; Munevar etal., 2001a; Munevar et al., 2001b; Munevar et al., 2004; Shiu etal., 2004; Curtze et al., 2004). Force microscopy revealed dynamictraction stresses at the leading edges of migrating fibroblasts(Munevar et al., 2001a; Munevar et al., 2001b).

In general, the magnitude and spatial distribution of tractionforces are related to cell shape and the mode of movement (Oliveret al., 1999). Keratocytes are known as fast-moving cells with aconsistent fan shape, whereas fibroblasts are slow-movingirregularly shaped cells. Traction forces were not detected atkeratocyte leading edges but, rather, at the lateral cell edges, wherethey were oriented perpendicular to the direction of cell motion andtowards the center of the cell (Lee et al., 1994; Doyle et al., 2004;Doyle and Lee, 2005; Jurado et al., 2005).

Dictyostelium cells are known as fast-moving irregularly shapedcells (Wessels et al., 1994; Heid et al., 2005). Uchida et al. (Uchidaet al., 2003) and Ladam et al. (Ladam et al., 2005) found thatDictyostelium cells exert rearward traction forces at their front andforward forces at their rear. Tsujioka and colleagues (Tsujioka et al.,2004) also detected rearward traction stresses in migratingDictyostelium cells. Recently, Lombardi et al. (Lombardi et al., 2007)mapped traction stresses in migrating vegetative Dictyostelium cells.They found a lack of traction stress at the front but high stress at therear of the cells, in contrast to Uchida et al. (Uchida et al., 2003),

It has been suggested that myosin II exerts traction forces atthe posterior ends and retracting pseudopodia of migratingcells, but there is no direct evidence. Here, using a combinationof total internal reflection fluorescence (TIRF) microscopy andforce microscopy with a high spatial resolution of ~400 nm,we simultaneously recorded GFP-myosin II dynamics andtraction forces under migrating Dictyostelium cells.Accumulation of filamentous myosin II and a subsequentincrease in traction forces were detected in pseudopodia justbefore retraction. In the case of motorless myosin II, tractionforces did not increase after accumulation, suggesting that thesource of the retraction force is the motor activity of

accumulated myosin II. Simultaneous recording of F-actin andtraction forces revealed that traction forces were exerted underspot-like regions where F-actin accumulated. Cells migratedin a direction counter to the sum of the force vectors exertedat each spot, suggesting that the stress spots act as scaffoldsto transmit the propulsive forces at the leading edge generatedby actin polymerization.

Supplementary material available online athttp://jcs.biologists.org/cgi/content/full/121/8/1314/DC1

Key words: Amoeboid movement, Cell migration, Pseudopod

Summary

Actin-based propulsive forces and myosin-II-basedcontractile forces in migrating Dictyostelium cellsYoshiaki Iwadate* and Shigehiko YumuraDepartment of Functional Molecular Biology, Graduate School of Medicine, Yamaguchi University, Yamaguchi 753-8512, Japan*Author for correspondence (e-mail: iwadate@yamaguchi-u.ac.jp)

Accepted 22 January 2008Journal of Cell Science 121, 1314-1324 Published by The Company of Biologists 2008doi:10.1242/jcs.021576

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1315Force dynamics in migrating Dictyostelium

Tsujioka et al. (Tsujioka et al., 2004), Ladam et al. (Ladam et al.,2005) and del Alamo et al. (del Alamo et al., 2007). Lombardi et al.(Lombardi et al., 2007) suggested that this traction stress asymmetryinduced directed cell movement, and that the degree of this asymmetrydecreased in cells null for the myosin II essential light chain (mlcE–)and was additionally decreased in myosin-II-null cells (mhcA–). Theyclaimed that myosin II motor and actin crosslinking activity wereboth required to develop and maintain asymmetrical patterns oftraction stress, but they found that asymmetrical distributionssometimes even developed in myosin-II-null cells. These findingshave led us to raise two questions: first, are there rearward tractionstresses at the front of cells, as suggested by Uchida et al. (Uchidaet al., 2003), Tsujioka et al. (Tsujioka et al., 2004), Ladam et al.(Ladam et al., 2005) and del Alamo et al. (del Alamo et al., 2007),or not, as suggested by Lombardi et al. (Lombardi et al., 2007)?Second, if not, then what is the source of myosin-II-independenttraction stress at the rear of myosin-II-null cells?

To answer these questions and investigate the relationshipbetween molecular dynamics and traction forces, we simultaneouslyrecorded the distributions of F-actin and traction stresses usingconfocal microscopy with a stress-recording spatial resolution of~400 nm. Rearward traction stresses were detected under spot-likeregions in the front of cells where F-actin accumulated. Cellsmigrated in a direction counter to the sum of the force vectors ateach spot, suggesting that counter forces to F-actin-based propulsionare exerted at the spots. Moreover, we recently developed a newmethod for simultaneously recording molecular dynamics andtraction stresses under migrating cells using TIRF microscopy(Iwadate and Yumura, 2008). Using this new method, we recordedthe accumulation of filamentous myosin II and subsequent increaseof traction stresses under pseudopodia just before their contraction,directly demonstrating that the source of the retraction force is theaccumulated myosin II.

ResultsRearward traction stresses at ʻstress spotsʼ and forwardstresses at the posterior edgeAggregation-competent wild-type cells expressing GFP-ABD120kwere dispersed on a gelatin substratum with fluorescent beadsattached as illustrated in Fig. 1A,B. From the displacement of thebeads by migrating cells, we calculated the stresses in the substratumusing the Pascal-scale and visualized them in pseudocolor. Itshould be noted that the calculated stresses are not representativeof all forces generated by the cell but the forces transmitted to thesubstratum. In a stress map of a typical wild-type cell just beforeposterior edge contraction, several traction stress peaks withrearward directions could be observed as ‘stress spots’ in the anteriorand middle regions (white arrows in Fig. 1D). By contrast, a largestress with a forward direction was observed at the posterior edge(white arrowhead in Fig. 1D). Interestingly, the magnitude of theforward stress under the posterior edge often exceeded that of therearward stress. If the posterior edge stress is exerted passively, asindicated in 3T3 fibroblasts (Munever et al., 2001b), forward stressshould never exceed the rearward stress. Therefore, this observationraised the possibility of ‘active’ exertion of traction stress at theposterior edge.

Stress spots act as scaffolds to transmit the counter force ofactin-mediated propulsion at the leading edgeIn the measurements using elastic substrata, it is plausible that stressspots are generated at cell-substratum attachment sites. In

Dictyostelium cells, an actin-containing structure called the ‘actinfocus’ appears on the ventral membrane (Yumura and Kitanishi-Yumura, 1990) and might act as a focal contact (Uchida and Yumura,2004). To elucidate the relationship between traction forces andactin, we observed the dynamics of F-actin and stresses undermigrating cells using confocal microscopy. F-actin was visualizedby GFP-ABD120k. Figs 2 and 3 show consecutive images of GFP-ABD120K and traction stresses under wild-type (Fig. 2A) andmyosin-II-null cells (Fig. 3A). Large traction stresses were observedunder the stress spots (a�-c� in Fig. 2A) in the anterior and middleregions of the wild-type cells with rearward directions relative to

Fig. 1. Typical stress map under a migrating Dictyostelium cell. (A) Wild-typeDictyostelium cells (strain AX2) or myosin-II-null cells (strain HS1)transformed with GFP-myosin-II, E476K mutant myosin II or ABD120kconstructs were placed on elastic silicone or gelatin substrata embedded withorange- or red-fluorescent marker beads (200-nm or 20-nm diameter). Thefluorescence of GFP and the marker beads was imaged simultaneously underTIRF or confocal microscopy. Migrating cells cause strains in the elasticsubstratum and displacements of the beads in the substratum (arrows). (B) Atypical image of 200 nm marker beads under confocal microscopy. The outlineof a migrating cell is superimposed as a white line. Displacements of ~300marker beads under and surrounding a migrating cell were measured. (C) Thecoordinates of each bead and their displacements were transformed to those ofeach node of a triangle mesh. The length of the sides of each triangle is ~400nm (=8 pixels). The stresses in the surface of the substratum were calculatedusing original software based on the triangle finite element method (seeMaterials and Methods). (D) Stress map for a migrating wild-type cell on agelatin substratum. The distributions of stresses in the substratum werevisualized by pseudocolor. The direction of the strain in the substratum at eachsmall white circle is indicated by a white bar. The length of the white bars isthree times as long as the strain. The yellow allow indicates the direction ofcell migration. Large rearward traction stresses emerged as ‘stress spots’,indicated by the two white arrows. Forward stresses emerged at the posterioredge, as indicated by the white arrowhead. Numerical values in the kPa scaleare indicated near each arrow and arrowhead. Bars, 4 μm (B-D).

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the direction of migration. In many cases, F-actin accumulated atthe same time or just before formation of the stress spots (a-c inFig. 2A). The distance between the center of each F-actinaccumulation spot and corresponding stress spot was very close(0.32±0.22 μm, n=16 from five cells, left column in Fig. 3C). Thevalue of the stresses at each spot reached a maximum 3.9±3.5seconds (n=16 from 5 cells, left column in Fig. 3D) after thefluorescence of GFP-ABD120k at the center of each F-actinaccumulation reached a maximum. Interestingly, the position of eachstress spot never changed until its disappearance, and the stress spotspersisted after the disappearance of accumulated F-actin. Theseobservations indicate that forces generated in migrating cells aretransmitted to the substratum at spots where F-actin accumulates.

Close contact between F-actin accumulation spots and thesubstratum was confirmed by simultaneous fluorescence andinterference reflection microscopy (IRM). The darker area of theIRM image indicates that the cell surface is closer to the substratum.As shown in Fig. 2B, the positions where F-actin accumulated (d-g in Fig. 2B) coincided well with the dark spots surrounded bywhite rings (d�-g� in Fig. 2B) that are a typical feature of actin foci(Uchida and Yumura, 2004).

Next, to clarify whether myosin II generates rearward stress atthe stress spots, stresses were observed under myosin-II-null cells(Fig. 3). Myosin-II-null cells exerted rearward stresses underregions where F-actin accumulated (a-c and a�-c� in Fig. 3A), as inwild-type cells, and close contact of the cell surface to the substratum

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was again confirmed by IRM (d-f and d�-f� in Fig. 3B). The distancesbetween the center of each F-actin accumulation spot andcorresponding stress spot were very close (0.34±0.19 μm, n=15 fromfive cells, right column in Fig. 3C). The value of the stresses ateach spot reached a maximum 4.2±3.3 seconds (n=16 from fivecells, right column in Fig. 3D) after the fluorescence of GFP-ABD120k at the center of each F-actin accumulation reached amaximum. These values are almost the same as those of the wild-type cells. The maximum magnitude and duration for each stressspot with a rearward direction is shown in Fig. 3E,F. There was nosignificant difference in maximum stress between wild-type cells(0.64±0.27 kPa, n=29 in five cells) and myosin-II-null cells(0.71±0.19 kPa, n=24 in three cells, Fig. 3E). There was also nosignificant difference in spot duration time between wild-type cells(23.6±6.1 seconds, n=7 in five cells) and myosin-II-null cells(26.2±9.6 seconds, n=6 in three cells, Fig. 3F). Therefore, myosinII does not contribute to rearward traction stresses, and these stressesmight reflect the counter forces of actin-mediated propulsion.

As the stress spots usually did not emerge at the leading edge,it is difficult to determine directly the relationship between stressspots and actin polymerization at the leading edge. However, therelationship can be estimated indirectly by comparison of theaverage stress vector at all spots and migration direction, usingmyosin-II-null cells to account for the influence of myosin II. Ifthe stress spots act as counter-force-transducing scaffolds, the cellsshould migrate in a direction opposite to the average stress vector.

Fig. 2. Colocalization of rearward tractionstress spots and F-actin accumulationsites, and close contact of the cell surfaceto the substratum in wild-type cells.(A) Simultaneous recording offluorescence of GFP-ABD120k (left) andtraction stresses (right) of a migratingwild-type cell transformed with GFP-ABD120k under confocal microscopy.Stress spots (a�-c�) appeared at locationswhere F-actin accumulated (a-c) in theanterior and middle regions of the cell.The typical sequential stress map shownwas made from three migrating cellsrandomly selected from 11 cells.(B) Simultaneous recording offluorescence of GFP-ABD120k (left) andIRM imaging (right) of a migrating wild-type cell transformed with a GFP-ABD120k construct under confocalmicroscopy. Dark spots surrounded bywhite rings (d�-g�) appeared at locationswhere F-actin accumulated (d-g). Thewhite ring surrounding a dark spot is afeature of focal contacts in Dictyostelium(Uchida and Yumura, 2004). The time-courses are indicated for each picture ofGFP-ABD120k. Yellow arrows at 0seconds in panels A and B indicate thedirection of cell migration. Bars, 4 μm.

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1317Force dynamics in migrating Dictyostelium

The trajectory of a migrating myosin-II-null cell and the averageof strain vectors under the cell are shown in Fig. 4A (see alsosupplementary material Movie 1). The black line shows thetrajectory of the centroid of a migrating myosin-II-null cell over aperiod of 400 seconds. Each blue line emerging from the trajectoryshows the strain vectors in the substratum under the cell. The imagesa-f in Fig. 4A show the stress maps of the cell positioned at pointsa-f in Fig. 4A. Sequential images of the cell outline at the momentwhen the cell was at the positions marked with asterisks in Fig. 4Aare shown in Fig. 4B. The migration speed of this cell was 2.70μm/minute. The average speed of myosin-II-null cells on an elasticsubstratum was 2.58±0.35 μm/minute (n=7). By contrast, theaverage speed of wild-type cells was 6.87±1.63 μm/minute (n=11).These results indicate that the myosin-II null cell migrated in adirection opposite to the average traction stress, suggesting that thestress spots act as scaffolds to transmit counter forces for actin-mediated propulsion at the leading edge.

Myosin II contributes to forward traction stresses at theposterior edgeFig. 5A (see also supplementary material Movie 2) showsconsecutive maps of traction stresses under a migrating wild-typecell. The cell migrated towards the upper left. The cell retracted itsposterior, exerting a large traction stress on the substratum (white

arrow in Fig. 5A). It is noteworthy that there was no equivalentrearward stress, suggesting that the forward stress is not only thecounter force of propulsive rearward forces at the stress spots butalso the sum of the counter force and an active force at the forwardedge. Time-courses of the magnitudes of each traction stress andthe length of the posterior region are summarized in Fig. 5B. Themagnitudes of posterior edge traction stresses (red lines in Fig. 5B)increased strongly at the beginning of retraction, after which theposterior edges retracted quickly. Interestingly, traction stressesbegan to decrease before retraction was completed, suggesting thatthe detachment from the substratum took place during retraction.

Myosin II localizes to the posterior of migrating Dictyosteliumcells (Yumura et al., 1984). To determine whether myosin II is thesource of the actively generated forward traction stress, themagnitudes of forward and rearward stresses at stress spots werecompared between wild-type and myosin-II-null cells. Fig. 5Cshows the values of the traction stresses at each stress spot in theanterior (Fig. 5C, 0.40±0.24 kPa, n=12 in five cells) and at theposterior edges (Fig. 5C, 0.70±0.21 kPa, n=16 in five cells) of wild-type cells. All values were measured when posterior edge stresspeaked. The magnitude of the forward traction stresses significantlyexceeded that of the rearward stresses (P<0.001). However, inmyosin-II-null cells, the magnitude of the forward traction stresses(Fig. 5D, 0.58±0.21 kPa, n=5 in three cells) never exceeded that of

Fig. 3. Rearward traction stresses in myosin-II-null cells are identical to those in wild-type cells. (A) Simultaneous recording of thefluorescence of GFP-ABD120k (left) andtraction stresses (right) of a migratingmyosin-II-null cell transformed with a GFP-ABD120k construct under confocalmicroscopy. Stress spots (a�-c�) appeared atlocations where F-actin accumulated (a-c) inthe anterior and middle regions of the cell.The typical sequential stress map shown wasgenerated from three migrating cellsrandomly selected from 13 cells. The time-courses are indicated for each picture oftraction stresses. The yellow arrows at 0seconds indicate the direction of cellmigration. (B) Simultaneous recording ofthe fluorescence of GFP-ABD120k (left)and IRM imaging (right) of a migratingmyosin-II-null cell transformed with a GFP-ABD120k construct under confocalmicroscopy. Dark spots surrounded by whiterings (d�-f�) appear at the locations where F-actin had accumulated beforehand (d-f).Bars, 4 μm. (C) Average distance betweenthe centers of each F-actin accumulation andcorresponding stress spot in wild-type andmyosin-II-null cells. (D) Average intervalbetween the time at which the fluorescenceof GFP-ABD120k at the center of each F-actin accumulation reached its maximumvalue and the time at which the stress valueat the corresponding stress spot reached itsmaximum. (E) Average maximum values ofrearward traction stresses for each stress spotin wild-type and myosin-II-null cells.(F) Average stress spot duration times forwild-type and myosin-II-null cells. Therewas no significant difference between wild-type cells and myosin-II-null cells in themaximum magnitude or duration of stress ateach stress spot.

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the rearward stresses (Fig. 5D, 0.79±0.29 kPa, n=8 in three cells,P>0.05). These observations strongly suggest that myosin IIcontributes to forward active stresses at the posterior end of wild-type cells.

Myosin II contributes to traction stresses exerted at the tips ofretracting pseudopodiaFreely migrating Dictyostelium cells often elongate pseudopodia inthe lateral direction. These pseudopodia seem to be retracted througha myosin-II-dependent process similar to that operating at theposterior edge. Thus, we observed the traction stresses under theselateral pseudopodia. Intense traction stresses were detected not onlyunder the posterior edge but also under the tips of the retractingpseudopodia in wild-type cells (right images in Fig. 6A,B), whereF-actin also accumulated (left images in Fig. 6A,B). Fig. 6A� and6B� show the time-courses of traction stresses under the tips of eachpseudopod, with the lengths shown in Fig. 6A,B. The magnitude ofthe traction stresses reached a maximum just after the beginning ofretraction in a manner similar to that occurring at the posterior edges(Fig. 5). In myosin-II-null cells (Fig. 6C-F), increased traction stresswas scarcely detected at the tips of pseudopodia (Fig. 6C�-F�),although F-actin still accumulated (left pictures in Fig. 6C-F). Only

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ambiguous increases in traction stresses could be observed at thetips of large pseudopodia (arrow in Fig. 6F�). These weak tractionstresses might be produced by means of the tension of the cell cortex,including the cell membrane and cytoskeleton, in the absence of amyosin-II-mediated process. The time-courses of the length ofpseudopodia in Fig. 6A,B and C-F are the same as those dealt withlater in Fig. 7A and Fig. 8B, respectively.

The timing of pseudopod elongation and retraction was comparedbetween wild-type and myosin-II-null cells (Fig. 6G). Elongationtime was defined as the time at which the length of each pseudopodreached 80% of the maximum length. Retraction time was definedas the time from attaining the maximum length until returning backto the original length. Although there was no significant differencein elongation time between wild-type and myosin-II-null cells, theretraction time in wild-type cells was significantly shorter than inmyosin-II-null cells, suggesting that myosin II mediates thepseudopod retraction.

Myosin II motor activities are required for traction forceexertion in retracting pseudopodiaIn the above experiments, myosin-II-mediated traction forces werestudied indirectly using myosin-II-null cells. During pseudopod

retraction, myosin II has been shown to accumulate(Yumura, 1996b; Moores et al., 1996). We thereforenext investigated the dynamics of myosin IIfilaments and traction stresses by simultaneouscombination of TIRF and force microscopy usingmyosin-II-null cells expressing GFP-labeled myosinII.

Myosin II filaments began to accumulate inpseudopodia during elongation (0–40 seconds inFig. 7A, see supplementary material Movie 3). Theaccumulation of myosin II filaments was followedby increased traction stress in the substratum underthe pseudopod (40–80 seconds in Fig. 7A).Pseudopodia began to retract at the same time asthe start of the increase in traction stress (40 secondsin Fig. 7A). The time-courses of pseudopod area,GFP-labeled myosin II fluorescence intensity andaverage traction stress are summarized in Fig. 7B,C.Increased pseudopod area was followed by theaccumulation of myosin II (Fig. 7B), and tractionstress reached a maximum during pseudopodretraction (Fig. 7C). These observations directlydemonstrate that the accumulation of myosin II inpseudopodia mediates their retraction.

Fig. 4. Myosin-II-null cells migrate in a direction counter to the sum of thestrain vectors at each spot. (A) The trajectory of a migrating myosin-II-nullcell and strain vectors at each point for a period of 400 seconds. The blackline is the trajectory of the centroid of a migrating myosin-II-null cell. Eachblue line emerging from the trajectory indicates the average strain vectorunder the cell. The length of the blue lines is 50 times the real strain in thesubstratum. Blue lines were drawn every 17.5 seconds. The black arrowindicates the direction of migration and represents a length of 1 μm. Thetrajectory was made from one of the three stress map sequences of myosin-II-null cells. (a-f) Stress maps when the cell was positioned at points a-f inA, respectively. Bar, 3 μm (a). (B) The sequential images of the cell outlineat the moment when the cell was at each position marked with asterisks ofthe same color in panel A. The trajectory in panel B is reduced to one-thirdin comparison with panel A. Myosin-II-null cells continued to migrate in adirection opposite to the direction of the traction stresses.

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1319Force dynamics in migrating Dictyostelium

To examine whether the motor activities of myosin II arerequired for the generation of traction forces, the dynamics of theE476K motorless myosin II filament and traction stresses in siliconesubstrata were simultaneously observed using myosin-II-null cellsexpressing GFP-E476K myosin II. E476K myosin II filamentsbegan to accumulate in pseudopodia (0–24 seconds in Fig. 8A,B)in addition to wild-type myosin II. Traction stress slightly increased

only under the tip of the pseudopod (arrows in Fig. 8A) in contrastto wild-type myosin II. These weak traction stresses might beproduced by means of the tension of the cell cortex, including thecell membrane and cytoskeleton, in the absence of a myosin-II-mediated process. These results indicate that myosin II motoractivities are required for the generation of traction stresses duringpseudopod retraction.

DiscussionIn this study, we examined the spatiotemporal patterns of cell-substratum mechanical interactions and their relationships withmolecular dynamics. The maximum value of rearward traction stressmeasured was 0.64±0.27 kPa for wild-type Dictyostelium cells,which agrees well with the data of Tsujioka and colleagues (Tsujiokaet al., 2004). However, the traction stresses under fibroblasts andkeratocytes are slightly different. Munevar and colleagues (Munevaret al., 2001a; Munevar et al., 2001b) observed dynamic tractionstresses at the leading edges of migrating fibroblasts, with maximumvalues of several tens of kPa. Doyle and colleagues (Doyle et al.,2004; Doyle and Lee, 2005) and Jurado and colleagues (Jurado etal., 2005) mapped traction stresses under migrating keratocytes andestimated the maximum value to be several kPa at the lateral edges.The traction stresses exerted by fibroblasts and keratocytes are ~100-fold and tenfold larger, respectively, than those exerted byDictyostelium cells; these differences might arise owing todifferences in cell shape and mode of movement.

Most rearward traction stresses emerged at spots whereaccumulation of F-actin took place (Fig. 2) and did not involvemyosin II (Fig. 3C-F). These findings indicate that traction stressesare generated as a result of actin polymerization at the stress sitesor at the leading edge of the cell. The stress spots persisted afterthe disappearance of accumulated F-actin (Fig. 2A), suggesting thatstress spots do not directly generate the traction force even thoughthere is tight contact between the cell and the substratum. Rather,the stress spots might apply the counter force for actinpolymerization at the leading edge. However, stress spots did notalways emerge near the leading edge, as freely migratingDictyostelium cells randomly extend pseudopodia not only to thesubstratum but also to the upper free space. Therefore, it is difficultto correlate each stress spot to each pseudopod directly. Thus, wecompared the migration direction of cells with the summation ofstrain vectors of stresses during migration. As expected, cellscontinued to migrate in a direction counter to the average forcevector at each spot (Fig. 4). This result suggests that F-actinassemblies in the pseudopod are connected to the actin meshworkin the cortex of the cell body and the stress spots emerge in themeshwork and act as scaffolds to transmit the counter force for theactin-mediated propulsion force at the leading edge.

Uchida and Yumura (Uchida and Yumura, 2004) detected thedeformation of elastic substrata even under very small actin foci(<1 μm), although we could not detect traction stresses in foci ofthe same size. To calculate accurately the stresses in elastic substratausing finite element methods, the strain of the substrata should beat the smallest detectable level. Thus, we adjusted the Young’smodulus of gelatin and silicone substrata to be 2.8 kPa and 1.0 kPa,respectively. The accumulated F-actin colocalized with the closecontact points between cells and the substrata (Fig. 2B and Fig.3B). It is therefore likely that the accumulated actin foci makecontacts between the cell surface and substrata that are strongenough to exert traction forces even after F-actin has dispersed (Fig.2A and Fig. 3A). In this study, the positions of some stress spots

Fig. 5. Myosin II contributes to forward traction stress at the posterior edge.(A) Consecutive maps of traction stresses under a migrating wild-type cell.The time-course is indicated in each picture. The yellow arrows indicate thedirection of cell migration. Posterior cell edges are indicated by a white arrow(b at 27 seconds). The cell retracted its posterior edges quickly at 0-84 secondsafter forward traction stress reached a maximum. Three sequential stress mapswere made from 11 migrating cells, and a typical sequence is shown. Bar, 4μm. (B) Time-courses of the values of traction stresses (red) and the length ofthe posterior region (the length of the perpendicular lines from the posterioredge to the white lines at 0 seconds in panel A). The magnitudes of tractionstresses at the posterior edges (red lines) strongly increased at the beginning ofposterior edge retraction. After the increase in traction stress, the posterioredges retracted quickly. (C) Average values of forward traction stresses at theposterior edges (n=12 in five cells) and rearward traction stresses at the stressspots in the anterior and middle regions (n=16 in five cells) in wild-type cellswhen the forward traction stress reached a maximum. The magnitude of theforward traction stress at the posterior edge significantly exceeds that of therearward stresses at stress spots in the anterior and middle regions (P<0.001).(D) Average values of forward traction stresses at the posterior edges (n=5 inthree cells) and that of rearward traction stresses at the stress spots in theanterior and middle regions (n=8 in three cells) in myosin-II-null cells whenthe forward traction stresses at the posterior edges reached a maximum. Therewas no significant difference between rearward and forward stresses (P>0.05).

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and corresponding F-actin accumulation spots did not completelymatch, as in areas a and a� in Fig. 2A. This might be attributableto the slight difference in the positions between the F-actinaccumulation and the corresponding contact site of the cell surfaceto the substratum. Furthermore, a few stress spots emerged withoutan immediately preceding F-actin accumulation there. The contactsites of the cell surface to the substratum of these stress spots mightbe produced by an F-actin-independent process. These facts raisethe possibility that, in order to exert traction stresses to the

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substratum for cell migration, only the strong contact between thecell surface and the substratum might be required as a scaffold, andit can be produced through an F-actin-independent process, althoughF-actin accumulation is mainly responsible for it.

We detected forward stresses at the posterior edge of the cells;if these stresses were induced passively by the frontal towing force,they should never exceed the rearward stresses at the leading edge.However, in the case of wild-type cells, forward stresses at theposterior edge often exceeded rearward traction stresses at theleading edge (Fig. 1D; Fig. 5A,D). These large forward stresseswere also detected under the tips of retracting pseudopodia,suggesting that some active forces are exerted at the posterior edgesof the cells and the tips of retracting pseudopodia. Jay andcolleagues (Jay et al., 1995) predicted that myosin-II-mediatedforce should induce detachment from the substrata. If this is thecase, then strong forward stresses should be detected just beforethe detachment. In the present study, we directly visualized therelationships among myosin II, traction forces and cell movementby using a combination of TIRF and force microscopy (Iwadateand Yumura, 2008), which revealed that, just before pseudopodcontraction, filamentous myosin II and traction stressesaccumulated at the tips of pseudopodia (Fig. 7). The migrationspeed of myosin-II-null cells on elastic substrata (2.58±0.35μm/minute, n=7) was significantly slower than that of wild-typecells (6.87±1.63 μm/minute, n=11). These observations stronglysuggest that the myosin-II-mediated force at the posterior edgecontributes to the ability to migrate.

Uchida et al. (Uchida et al., 2003), Tsujioka et al. (Tsujioka etal., 2004), del Alamo et al. (del Alamo et al., 2007) and our groupdetected rearward traction stresses under migrating Dictyosteliumcells, although Lombardi et al. (Lombardi et al., 2007) did not.Tsujioka et al. (Tsujioka et al., 2004) noted that the force-field oftraction stresses was not uniform, showing a few regions withrelatively large forces that were mostly stationary with respect tothe substratum. This finding matches the distribution of ‘stress spots’in the present study. The discrepancy in detection of rearwardstresses in the above-mentioned studies might be due to differencesin the types of cells used for measurements. Uchida et al. (Uchidaet al., 2003), Tsujioka et al. (Tsujioka et al., 2004) and our groupused aggregation-competent cells, whereas Lombardi et al.(Lombardi et al., 2007) used vegetative cells. The migrating speedof vegetative cells (1.13 μm/minute) (Lombardi et al., 2007) is much

Fig. 6. Myosin II contributes to traction stresses under the tips of retractingpseudopodia in wild-type cells. (A,B) Fluorescence of GFP-ABD120k (left)and stress maps (right) under two typical pseudopodia from five migratingwild-type cells. Large traction stresses were observed under the tips ofretracting pseudopodia where F-actin accumulated. (A�,B�) Time-courses oftraction stresses (red lines) under the tips of each pseudopod (A,B) andpseudopod lengths (blue lines). (C-F) Fluorescence of GFP-ABD120k (left)and stress maps (right) under four typical pseudopodia from three migratingmyosin-II-null cells. Large traction stresses were not observed under the tips ofretracting pseudopodia where F-actin accumulated. (C�-F�) The time-coursesof pseudopod lengths and traction stresses just under the tip of eachpseudopod. Blue and red lines indicate pseudopod lengths and stresses,respectively. Although a small rise in stress took place under the tip of a largepseudopod (arrow in F�), stresses under the pseudopod tips were unchangedtypically between the elongation and retraction. (G) The average periods ofelongation and retraction of pseudopodia in wild-type (n=5 in three cells) andmyosin-II-null cells (n=7 in three cells). Although there was no significantdifference in elongation time between wild-type and myosin-II-null cells, theretraction time of pseudopodia in wild-type cells was significantly shorter thanin myosin-II-null cells. Bars, 1.5 μm. The look-up table (LUT) of A and B isindicated at the right side of B, and the LUT of C-F is at the right side of D.

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slower than that of aggregation-competent cells(6.87±1.63 μm/minute for wild-type cells on the elasticsubstrata in this study, n=11). The rearward tractionstresses at stress spots might contribute to the fastmigration and the deformation in shape duringmigration. Another possible explanation of thediscrepancy is that resolution of the stress maps dependson the density of marker beads on the substrata. Thedensity of beads in our experiment was very high inorder to detect any slight strain of the elastic substrataunder the cell (Fig. 1B). The space resolution of ourrecording was ~400 nm. To detect ‘stress spots’, a highspatial resolution for strain in the elastic substrata mightbe required. If this is the case, the forward tractionstresses at the rear of migrating vegetative mlcE– andmhcA– cells in the study of Lombardi and colleagues(Lombardi et al., 2007) might be the counter forces torearward traction stresses at stress spots that they didnot detect.

del Alamo and colleagues (del Alamo et al., 2007)showed that traction forces appear at the anterior afterpseudopod expansion in wild-type Dictyostelium cells.By contrast, in this study, some stress spots emergedat the leading edge, as shown in the stress spot c inFig. 2A, just like that described by del Alamo andcolleagues (del Alamo et al., 2007) and others at thebase of an expanding pseudopod, as shown in stressspot b in Fig. 2A, and at the inside of the cell, as shownin the stress spot a in Fig. 2A. These results suggestthat there are two kinds of rearward traction stressesas follows. (1) The stress emerging at the tip ofpseudopodia. The pseudopod, which expanded awayfrom the substratum, captures the substratum at its tip.Then, it exerts rearward traction stresses onto thesubstratum by means of the contracting force of theexpanded cortex. (2) Counter stress generated by actinpolymerization in the expanding pseudopod. This stressshould be exerted at the scaffold for actinpolymerization. The scaffold should be separate fromthe tip of an expanding pseudopod, such as at the baseof it or at the inner region of the cell.

We propose here a model for the migration of fast-moving irregularly shaped cells (Fig. 9). Munevar andcolleagues (Munevar et al., 2001a) proposed a frontaltowing model for the migration of fibroblasts, whichare slow-moving irregularly shaped cells. Our modelincludes a frontal towing and rear contractionmechanism; it is essentially Munevar’s model with anadded myosin II contractile device (‘p’ in Fig. 9A) atthe posterior edge. Actin polymerization (red-filledcircles in Fig. 9A) produces a pushing force (‘F’ inFig. 9A) at the leading edge (‘a’ in Fig. 9A) and a rearward force(‘rf’) at the stress spots as a counter force for elongation ofpseudopodia in the anterior of the cell. A part of the actin-mediatedpropulsion force (F� in Fig. 9A) is transmitted to the posterior edgeof the cell through the elastic transition zone (‘e’ in Fig. 9A), andthis behavior passively induces forward force (‘ff’ in Fig. 9A) atthe posterior end, as shown at the tip of a retracting pseudopod ofthe cell with motorless myosin II (arrows in Fig. 8A). Myosin IImight also exert an active force (‘Fm’ in Fig. 9B) triggered by thepassive force ff, with contraction taking place at the posterior edge

(Fig. 9B). Merkel and colleagues (Merkel et al., 2000) showedthat, in response to the aspiration of a small part of the cell surfaceby a micropipette, myosin II accumulated at the tip of the aspiratedcell lobe. This suggests the possibility that myosin II mightaccumulate in response to mechanical stimulation. Contraction ofthe posterior edge by myosin II might therefore push the anteriorportion forward, as Uchida and colleagues (Uchida et al., 2003)suggested. After this contraction and elongation, a new cycle couldthen begin with elongation of pseudopodia through actinpolymerization (Fig. 9A).

Fig. 7. Traction stresses under retracting pseudopodia mediated by myosin II. (A)Simultaneous recording of GFP-myosin-II fluorescence and traction stresses using acombination of TIRF and force microscopy: the dynamics of myosin II filaments (upperimages) and traction stresses (lower images) under a pseudopod of a migrating myosin-II-null cell are shown. The stress map was made from three migrating cells randomly selectedfrom nine cells. The time elapsed is indicated in each GFP-myosin-II image. Myosin IIfilaments begin to accumulate in the pseudopod during elongation (0-40 seconds), followedby increased traction stress in the silicone substratum just under the pseudopod (40-80seconds). Retraction began at the same time as the beginning of the increase in tractionstress (40 seconds). Bar, 1 μm. (B) Time-courses of pseudopod area (blue) and fluorescenceintensity of GFP-myosin-II (red). (C) Time-courses of fluorescence intensity of GFP-myosin-II (red) and average traction stress in the pseudopod (blue). The increase inpseudopod area was followed by accumulation of myosin II (B). Traction stress in thepseudopod subsequently reached a maximum during retraction (C).

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Materials and MethodsCell cultureDictyostelium discoideum cells were cultured in HL5 medium [1.3% (w/v)bacteriological peptone, 0.75% (w/v) yeast extract, 85.5 mM D glucose, 3.5 mMNa2HPO412H2O, 3.5 mM KH2PO4, pH 6.4] and developed until they becameaggregation competent in BSS (10 mM NaCl, 10 mM KCl, 3 mM CaCl2, actualpH was 6.3). The cell lines used included AX2 cells (referred to as wild-type cellsbut actually an axenic derivative of the wild-type strain NC4) expressingGFP-ABD120k and myosin heavy-chain-null cells (HS1) expressing GFP-ABD120k, GFP-myosin-II, or GFP-E476K-myosin-II. ABD120k is the actin-binding domain of the actin-crosslinking protein ABP120 (Pang et al., 1998) andcan only bind to filamentous actin. Therefore, fluorescence imaging ofGFP-ABD120k reflects the distribution of filamentous actin. The geneencoding GFP-ABD120k was kindly provided by D. A. Knecht (University ofConnecticut, CT). This fusion gene was inserted into the pBIG expressionvector by T. Q. Uyeda (AIST). E476K mutant myosin II cannot hydrolyze ATPin myosin heavy-chain-null cells (Ruppel and Spudich, 1996; Yumura and Uyeda,1997).

Preparation of elastic substrataElastic substrata were made from two kinds of materials: gelatin and silicone.Gelatin substrata were made as described previously (Doyle and Lee, 2002;Doyle and Lee, 2004) but with several modifications. Briefly, stock gelswere made with 4.0% gelatin (90-110 Bloom, G6144-100G, Sigma) dissolvedin BSS containing 3 mM Mes, pH 6.3 with KOH. Stock gels were liquefiedat 30-40°C, and 200 μl were transferred into a round chamber (16 mm indiameter and 2 mm in depth) whose bottom was made of a 22�22 mmcoverslip (No. 1, Matsunami, Japan). After solidification, fluorescent orangemicrospheres (200 nm in diameter, F-8809, Molecular Probes) were attachedto the surface of the substrata. The subsequent procedure was identical tothat described previously (Doyle and Lee, 2002; Doyle and Lee, 2004).

Silicone substrata were made according to Iwadate and Yumura (Iwadateand Yumura, 2008). Briefly, two types of platinum-catalyzed silicone (CY52-276A and B, Dow Corning Toray, Tokyo, Japan) were used. A 300 mg aliquotof CY52-276A and a 250 mg aliquot of B were mixed. The mixture was

spread on a 22�22 mm coverslip (No. 1, Matsunami, Japan). After solidification ofthe mixture, a round chamber (16 mm in diameter and 2 mm in depth) was assembledusing the coated coverslip as the bottom of the chamber. The solidified substratawere kept in a hermetically sealed case with a 50 μl aliquot of the liquid silane (3-aminopropyl triethoxysilan, Sigma Aldrich, Tokyo, Japan) at 70°C for 1 hour in orderto attach the silane to the surface of the silicon substrata by vapor deposition. Red-fluorescent carboxylate-modified microspheres (20 nm in diameter, the peak excitationand emission wavelengths were 580 and 605 nm respectively, F-8786, MolecularProbes) were attached to the surface of the substrata by means of the binding betweenthe amino group in the silane and the carboxyl group in the microspheres.

The Young’s moduli of the elastic substrata were measured using the method ofLo and colleagues (Lo et al., 2000). Briefly, a steel ball (0.5 mm diameter, 7.8 kg/m3)was placed on a substratum embedded with fluorescent beads. The Young’s moduluswas calculated as Y=3(1–p2)2f2/4d3/2r1/2, where f is the force exerted on the sheet, dis the indentation, r is the radius of the steel ball, and p is the Poisson ratio [assumedto be 0.5 for gelatin (Doyle et al., 2004) and silicone (Dembo et al., 1996)]. Typicalvalues of the Young’s modulus for gelatin and silicone substrata were 2.8 kPa and1.0 kPa, respectively.

Fig. 8. The motor activity of myosin II is required for the generation of traction forcesby retracting pseudopodia. (A) Dynamics of E476K myosin II filaments (upperimages) and traction stresses (lower images) under a pseudopod of a migratingmyosin-II-null cell expressing GFP-E476K myosin II. The stress map was made fromthree migrating cells randomly selected from six cells. E476K myosin II filamentsbegan to accumulate in the pseudopod during elongation of the pseudopod (0-24seconds), similar to wild-type myosin II. After elongation, traction stress slightlyincreased only under the tip of the pseudopod (arrows). Bar, 1.5 μm. (B) Time-courses of pseudopod area (blue) and fluorescence intensity of GFP-myosin-II (red).(C) Time-courses of fluorescence intensity of GFP-myosin-II (red) and averagetraction stress in the pseudopod (blue). The increase in pseudopod area was followedby the accumulation of E476K myosin II in the pseudopod, as was the case for normalmyosin II (Fig. 7B). However, the traction stress increased only at the tip of theretracting pseudopod.

Fig. 9. A model for the migration of fast-moving irregularly shapedcells. (A) The migrating cell comprises a frontal towing zone (a) and arear trailing and contractile zone (p). These two zones are connectedby an elastic transition zone (e) that includes the cytoskeleton.Polymerization of actin (red-filled circles) produces a force (F) forpseudopod elongation in the frontal towing zone and a rearward force(rf) at stress points (s) in the anterior or middle of the cell. Part of F� istransmitted to the rear zone through the elastic transition zone, and thispassively generates a forward force (ff) at the stress points in the reartrailing and contractile zones. F� increases as the elastic transitionzone extends. (B) When the passive force F� reaches a threshold level,an active strong force (Fm) is exerted by accumulated myosin II at therear trailing and contractile zones. After contraction of the rear zoneby myosin II, a new cycle of the cell migration process begins (panelA).

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MicroscopyMigrating cells plated on gelatin substrata were observed using a confocal microscope(Zeiss, LSM500, Germany) with a 100� objective lens (PlanFluar 100�). An argonion laser was used at an excitation wavelength of 488 nm. GFP fluorescence wasdetected with a 505-530 nm band-pass filter, and the orange-fluorescent beads weredetected with a 560 nm high-pass filter.

Migrating cells plated on silicone substrata were observed by a TIRF microscopeassembled on an inverted microscope (Olympus, IX71, Japan) with a 60� objectivelens (Plapon 60� OTIRFM). A laser diode (DPBL-9010F, Photop Technologies,China) at a wavelength of 473 nm and a He-Ne laser (Research Electro Optics)at a wavelength of 543 nm were used for excitation of GFP and red beads,respectively. Exiting light from each laser was applied in turn to electric shutters(Copal, No. 0, Japan) in front of the laser heads. The fluorescence of GFP andred beads was detected with a dual band-pass filter (XF3056, Chroma Technology).Fluorescence images were collected using a cooled CCD camera (ORCA ER,Hamamatsu Photonics, Japan). The electromagnetic shuttering and CCD werecontrolled using a custom program developed under LabVIEW 7.1 (NationalInstruments, Japan).

Calculation of traction stresses (I)Traction forces were not calculated as the real values of the ‘forces’ in cells on theNewton-scale but rather as ‘stresses’ in the substratum with the Pascal-scale usingthe triangle finite element method [see below or Iwadate and Yumura (Iwadate andYumura, 2008) for further details]. Briefly, migrating cells cause strains in the elasticsubstratum and displacements of the beads on the substratum (Fig. 1A). Arepresentative sample image of the beads is shown in Fig. 1B. The white lineindicates the outline of the migrating cell on the substratum. An image of beadscomprising 512�512 pixels was divided into approximately 8000 triangle elementsas shown in Fig. 1C. The length of the sides of each triangle is ~400 nm.Displacements of the nodes of each element were calculated from the displacementsof the beads. The strain of each element was calculated from the displacement ofits three nodes. The stresses of each element were calculated from the strains ofthe element under the assumption that the substrata are in a plane stress state (seebelow for further details).

The magnitudes of the stresses at each element under a cell were visualized bypseudocolor. Each node and its displacement vector are superimposed onto thepseudocolor images as white circles and bars, respectively. All of these calculationsand some of the image processing were performed using a custom program developedunder RealBASIC Ver. 3.5 (ASCII Solutions, Japan). Image processing was alsoperformed using ImageJ Ver. 1.33, Image SXM Ver. 1.74 and Photoshop CS (Adobe,Japan).

Calculation of traction stresses (II)In the normal finite element method, the size of the elements should be small andthe density of the elements should be high at the area where the stress is expected

to be large, while the size should be large and the density should be low at the areawhere the stress is expected to be small for accurate and fast calculations. However,the distribution of the stresses exerted by the force of a migrating cell cannot bepredicted. Thus, in this study, to calculate the traction stresses as accurately as possible,a mesh in which very small triangle elements were distributed uniformly was preparedfor the following calculations (Fig. 1C). The length of the sides of each element was~400 nm (=8 pixels).

As shown in Fig. 10A, each triangle element has three nodes, A1, A2 and A3. Theoriginal positions and the displacements of the three nodes are A1 (x1, y1), A2 (x2,y2), A3 (x3, y3) and (u1, v1), (u2, v2), (u3, v3), respectively. The displacement vector,(u, v), of the arbitrary point P, whose original position is (x, y), in the triangle elementis determined as:

In the above calculation, the strains at each point inside the element are assumed tobe distributed linearly. The longitudinal and shearing strains εx, εy and γxy at the minutesquare (Fig. 10B) in each element are determined as:

The strain matrix:

is calculated with equations 1 and 2 as follows:

The normal and shearing stresses σx, σy and τxy at the minute square (Fig. 10C)in each element are calculated from the strain matrix (equation 3) under theassumption that the substratum is in a plane stress state.

In the above equations, E and νmean Young’s modulus and Poisson ratio, respectively.In this study, the magnitude of stress �σm� in each element is defined as:

The magnitude of the stress is constant inside a triangle element in our calculationbecause of the assumption of a linear distribution of strains in the element, asmentioned above. The magnitudes of the stresses for each element under a cell werevisualized with pseudocolor. The elements outside the cell were filled with blackeven if the stress there was not zero.

We thank T. Q. Uyeda (AIST, Japan) for the kind gift of the GFP-ABD120k expression plasmid and D. A. Knecht (University ofConnecticut, CT) for the permission to use it. This work was partlysupported by a Grant-in-Aid for Scientific Research (C) No.16570161to S.Y. from the NIH and a grant to Y.I. from the Yamaguchi UniversityFoundation. We are grateful for their support.

(2).ε x =∂u

∂ x, ε y =

∂v

∂ y, γ xy =

∂u

∂ y+

∂v

∂ x

N =N1 0 N2 0 N 3 0

0 N1 0 N2 0 N 3

⎛⎝⎜

⎞⎠⎟

Um = u1 v1 u2 v2 u3 v3( )T

N1 = (det A)−1{(x2 y3 − x3y2 ) + (y2 − y3 )x + (x3 − x2 )y}

N2 = (det A)−1{(x3y1 − x1y3 ) + (y3 − y1)x + (x1 − x3 )y}

N 3 = (det A)−1{(x1y2 − x2 y1) + (y1 − y2 )x + (x2 − x1)y}

det A = x2 y3 + x1y2 + x3y1 − x1y3 − x2 y1 − x3y2

(1).u

v

⎛⎝⎜

⎞⎠⎟

= N •Um

(5).B = (det A)−1

y2 − y3 0 y3 − y1 0 y1 − y2 0

0 x3 − x2 0 x1 − x3 0 x2 − x1

x3 − x2 y2 − y3 x1 − x3 y3 − y1 x2 − x1 y1 − y2

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

(4)=[εm ] B •Um

(3)[εm ] = ε x ε y γ xy( )T

(9).σ m = {(σ x + τ xy )2 + (σ y + τ xy )2 }1 2

(8).D =E

1 − ν 2

1 ν 0

ν 1 0

0 01 − ν

2

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

(7)[σ m ] = (σ x σ y τ xy )T

(6)[σ m ] = D[εm ]

Fig. 10. The method of calculating the traction stress. (A) Each triangleelement has three nodes, A1, A2 and A3, whose original positions are (x1, y1),(x2, y2), (x3, y3) and displacement vectors are (u1, v1), (u2, v2), (u3, v3),respectively. The strains at each point in one element are assumed to bedistributed linearly. P is an arbitrary point whose original position is (x, y) andthe displacement vector is (u, v). (B) The longitudinal and shearing strains, εx,εy and γxy, at the minute square in the element. (C) The normal and shearingstresses, σx, σy and τxy, at the minute square in the element.

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ReferencesBeningo, K. A., Dembo, M., Kaverina, I., Small, J. V. and Wang, Y. L. (2001). Nascent

focal adhesions are responsible for the generation of strong propulsive forces in migratingfibroblasts. J. Cell Biol. 153, 881-888.

Chen, W. T. (1981). Mechanism of retraction of the trailing edge during fibroblastmovement. J. Cell Biol. 90, 187-200.

Curtze, S., Dembo, M., Miron, M. and Jones, D. B. (2004). Dynamic changes in tractionforces with DC electric field in osteoblast-like cells. J. Cell Sci. 117, 2721-2729.

del Alamo, J. C., Meili, R., Alonso-Latorre, B., Rodriguez-Rodriguez, J., Aliseda, A.,Firtel, R. A. and Lasheras, J. C. (2007). Spatio-temporal analysis of eukaryotic cellmotility by improved force cytometry. Proc. Natl. Acad. Sci. USA 104, 13343-13348.

Dembo, M. and Wang, Y. L. (1999). Stresses at the cell-to-substrate interface duringlocomotion of fibroblasts. Biophys. J. 76, 2307-2316.

Dembo, M., Oliver, T., Ishihara, A. and Jacobson, K. (1996). Imaging the traction stressesexerted by locomoting cells with the elastic substratum method. Biophys. J. 70, 2008-2022.

Dent, E. W. and Gertler, F. B. (2003). Cytoskeletal dynamics and transport in growthcone motility and axon guidance. Neuron 40, 209-227.

Doyle, A. D. and Lee, J. (2002). Simultaneous, real-time imaging of intracellular calciumand cellular traction force production. Biotechniques 33, 358-364.

Doyle, A. D. and Lee, J. (2005). Cyclic changes in keratocyte speed and traction stressarise from Ca2+-dependent regulation of cell adhesiveness. J. Cell Sci. 118, 369-379.

Doyle, A., Marganski, W. and Lee, J. (2004). Calcium transients induce spatiallycoordinated increases in traction force during the movement of fish keratocytes. J. CellSci. 117, 2203-2214.

Galbraith, C. G. and Sheetz, M. P. (1997). A micromachined device provides a new bendon fibroblast traction forces. Proc. Natl. Acad. Sci. USA 94, 9114-9118.

Heid, P. J., Geiger, J., Wessels, D., Voss, E. and Soll, D. R. (2005). Computer-assistedanalysis of filopod formation and the role of myosin II heavy chain phosphorylation inDictyostelium. J. Cell Sci. 118, 2225-2237.

Iwadate, Y. and Yumura, S. (2008). Molecular dynamics and forces of a motile cellsimultaneously visualized by TIRF and force microscopies. Biotechniques In press.

Jay, P. Y. and Elson, E. L. (1992). Surface particle transport mechanism independent ofmyosin II in Dictyostelium. Nature 356, 438-440.

Jay, P. Y., Pham, P. A., Wong, S. A. and Elson, E. L. (1995). A mechanical function ofmyosin II in cell motility. J. Cell Sci. 108, 387-393.

Jurado, C., Haserick, J. R. and Lee, J. (2005). Slipping or Gripping? Fluorescent Specklemicroscopy in fish keratocytes reveals two different mechanisms for generating aretrograde flow of actin. Mol. Biol. Cell 16, 507-518.

Kalil, K. and Dent, E. W. (2005). Touch and go: guidance cues signal to the growth conecytoskeleton. Curr. Opin. Neurobiol. 15, 521-526.

Ladam, G., Vonna, L. and Sackmann, E. (2005). Protrusion force transmission ofamoeboid cells crawling on soft biological tissue. Acta Biomater. 1, 485-497.

Lauffenburger, D. A. and Horwitz, A. F. (1996). Cell migration: a physically integratedmolecular process. Cell 84, 359-369.

Lee, J., Leonard, M., Oliver, T., Ishihara, A. and Jacobson, K. (1994). Traction forcesgenerated by locomoting keratocytes. J. Cell Biol. 127, 1957-1964.

Lo, C. M., Wang, H. B., Dembo, M. and Wang, Y. L. (2000). Cell movement is guidedby the rigidity of the substrate. Biophys. J. 79, 144-152.

Lombardi, M. L., Knecht, D. A., Dembo, M. and Lee, J. (2007). Traction forcemicroscopy in Dictyostelium reveals distinct roles for myosin II motor and actin-crosslinking activity in polarized cell movement. J. Cell Sci. 120, 1624-1634.

Merkel, R., Simson, R., Simson, D. A., Hohenadl, M., Boulbitch, A., Wallraff, E. andSackmann, E. (2000). A micromechanic study of cell polarity and plasma membranecell body coupling in Dictyostelium. Biophys. J. 79, 707-719.

Moores, S. L., Sabry, J. H. and Spudich, J. A. (1996). Myosin dynamics in liveDictyostelium cells. Proc. Natl. Acad. Sci. USA 93, 443-446.

Munevar, S., Wang, Y. and Dembo, M. (2001a). Traction force microscopy of migratingnormal and H-ras transformed 3T3 fibroblasts. Biophys. J. 80, 1744-1757.

Munevar, S., Wang, Y. L. and Dembo, M. (2001b). Distinct roles of frontal and rear cell-substrate adhesions in fibroblast migration. Mol. Biol. Cell 12, 3947-3954.

Munevar, S., Wang, Y. L. and Dembo, M. (2004). Regulation of mechanical interactionsbetween fibroblasts and the substratum by stretch-activated Ca2+ entry. J. Cell Sci. 117,85-92.

Oliver, T., Dembo, M. and Jacobson, M. (1999). Separation of propulsive and adhesivetraction stresses in locomoting keratocytes. J. Cell Biol. 145, 589-604.

Pang, K. M., Lee, E. and Knecht, D. A. (1998). Use of a fusion protein between GFPand an actin-binding domain to visualize transient filamentous-actin structures. Curr.Biol. 8, 405-408.

Parent, C. A. (2004). Making all the right moves: chemotaxis in neutrophils andDictyostelium. Curr. Opin. Cell Biol. 16, 4-13.

Pollard, T. D. and Borisy, G. G. (2003). Cellular motility driven by assembly anddisassembly of actin filaments. Cell 112, 453-465.

Raftopoulou, M. and Hall, A. (2004). Cell migration: Rho GTPases lead the way. Dev.Biol. 265, 23-32.

Reid, B., Song, B., McCaig, C. D. and Zhao, M. (2005). Wound healing in rat cornea:the role of electric currents. FASEB J. 19, 379-386.

Ridley, A. J., Schwartz, M. A., Burridge, K., Firtel, R. A., Ginsberg, M. H., Borisy,G., Parsons, J. T. and Horwitz, A. R. (2003). Cell migration: integrating signals fromfront to back. Science 302, 1704-1709.

Ruppel, K. M. and Spudich, J. A. (1996). Structure-function studies of the myosin motordomain: importance of the 50-kDa cleft. Mol. Biol. Cell 7, 1123-1136.

Shiu, Y. T., Li, S., Marganski, W. A., Usami, S., Schwartz, M. A., Wang, Y. L., Dembo,M. and Chien, S. (2004). Rho mediates the shear-enhancement of endothelial cellmigration and traction force generation. Biophys. J. 86, 2558-2565.

Small, J. V. (1989). Microfilament-based motility in non-muscle cells. Curr. Opin. CellBiol. 1, 75-79.

Svitkina, T. M., Verkhovsky, A. B., McQuade, K. M. and Borisy, G. G. (1997). Analysisof the actin-myosin II system in fish epidermal keratocytes: mechanism of cell bodytranslocation. J. Cell Biol. 139, 397-415.

Torres, M. and Coates, T. D. (1999). Function of the cytoskeleton in human neutrophilsand methods for evaluation. J. Immunol. Methods 232, 89-109.

Tsujioka, M., Machesky, L. M., Cole, S. L., Yahata, K. and Inouye, K. (1999). A uniquetalin homologue with a villin headpiece-like domain is required for multicellularmorphogenesis in Dictyostelium. Curr. Biol. 9, 389-392.

Tsujioka, M., Yoshida, K. and Inouye, K. (2004). Talin B is required for forcetransmission in morphogenesis of Dictyostelium. EMBO J. 23, 2216-2225.

Uchida, K. S. and Yumura, S. (2004). Dynamics of novel feet of Dictyostelium cellsduring migration. J. Cell Sci. 117, 1443-1455.

Uchida, K. S., Kitanishi-Yumura, T. and Yumura, S. (2003). Myosin II contributes tothe posterior contraction and the anterior extension during the retraction phase inmigrating Dictyostelium cells. J. Cell Sci. 116, 51-60.

Wang, Y. L. (1985). Exchange of actin subunits at the leading edge of living fibroblasts:possible role of treadmilling. J. Cell Biol. 101, 597-602.

Wessels, D., Vawter-Hugart, H., Murray, J. and Soll, D. R. (1994). Three-dimensionaldynamics of pseudopod formation and the regulation of turning during the motility cycleof Dictyostelium. Cell Motil. Cytoskeleton 27, 1-12.

Yumura, S. (1993). Reorganization of actin and myosin II in Dictyostelium amoeba duringstimulation by cAMP. Cell Struct. Funct. 18, 379-388.

Yumura, S. (1996a). Spatial distribution of fluorescently labeled actin in livingDictyostelium amoebae. Cell Struct. Funct. 21, 189-197.

Yumura, S. (1996b). Rapid redistribution of myosin II in living Dictyostelium amoebae,as revealed by fluorescent probes introduced by electroporation. Protoplasma 192, 217-227.

Yumura, S. and Kitanishi-Yumura, T. (1990). Immunoelectron microscopic studies ofthe ultrastructure of myosin filaments in Dictyostelium discoideum. Cell Struct. Funct.15, 343-354.

Yumura, S. and Uyeda, T. Q. (1997). Transport of myosin II to the equatorial regionwithout its own motor activity in mitotic Dictyostelium cells. Mol. Biol. Cell 8, 2089-2099.

Yumura, S. and Fukui, Y. (1998). Spatiotemporal dynamics of actin concentration duringcytokinesis and locomotion in Dictyostelium. J. Cell Sci. 111, 2097-2108.

Yumura, S., Mori, H. and Fukui, Y. (1984). Localization of actin and myosin for thestudy of ameboid movement in Dictyostelium using improved immunofluorescence. J.Cell Biol. 99, 894-899.

Zhao, M., Song, B., Pu, J., Wada, T., Reid, B., Tai, G., Wang, F., Guo, A., Walczysko,P., Gu, Y. et al. (2006). Electrical signals control wound healing throughphosphatidylinositol-3-OH kinase-gamma and PTEN. Nature 442, 457-460.

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