Actin-based propulsive forces and myosin-II-based contractile forces in migrating Dictyostelium cells.

It has been suggested that myosin II exerts traction forces at the posterior ends and retracting pseudopodia of migrating cells, but there is no direct evidence. Here, using a combination of total internal reflection fluorescence (TIRF) microscopy and force microscopy with a high spatial resolution of approximately 400 nm, we simultaneously recorded GFP-myosin II dynamics and traction forces under migrating Dictyostelium cells. Accumulation of filamentous myosin II and a subsequent increase in traction forces were detected in pseudopodia just before retraction. In the case of motorless myosin II, traction forces did not increase after accumulation, suggesting that the source of the retraction force is the motor activity of accumulated myosin II. Simultaneous recording of F-actin and traction forces revealed that traction forces were exerted under spot-like regions where F-actin accumulated. Cells migrated in a direction counter to the sum of the force vectors exerted at each spot, suggesting that the stress spots act as scaffolds to transmit the propulsive forces at the leading edge generated by actin polymerization.

If this is the case, then substratum contact sites in the anterior portions of migrating cells should function as anchorages or scaffolds to allow pushing of the leading edge. This pushing should occur by counter forces generated by actin polymerization and exerted onto the substratum in a direction opposite to that of extension. At the posterior ends of migrating cells and the tips of retracting pseudopodia, by contrast, traction forces in the same direction as the retraction should be exerted onto the substratum by myosin II contraction before detachment from the substratum. However, the relationship between myosin II dynamics and traction forces has never been demonstrated directly because of the difficulty in simultaneously recording traction forces and myosin II dynamics in migrating cells. In this study, we aimed to examine this relationship directly.
To determine the mechanical interactions between migrating cells and the substratum, Dembo and colleagues (Dembo et al., 1996;Dembo and Wang, 1999) proposed procedures to convert the measurement of elastic substratum deformation under migrating cells into traction stresses using finite element methods; this technique was designated 'force microscopy' and was used to map forces in migrating fibroblasts (Beningo et al., 2001;Munevar et al., 2001a;Munevar et al., 2001b;Munevar et al., 2004;Shiu et al., 2004;Curtze et al., 2004). Force microscopy revealed dynamic traction stresses at the leading edges of migrating fibroblasts (Munevar et al., 2001a;Munevar et al., 2001b).
In general, the magnitude and spatial distribution of traction forces are related to cell shape and the mode of movement (Oliver et al., 1999). Keratocytes are known as fast-moving cells with a consistent fan shape, whereas fibroblasts are slow-moving irregularly shaped cells. Traction forces were not detected at keratocyte leading edges but, rather, at the lateral cell edges, where they were oriented perpendicular to the direction of cell motion and towards 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 shaped cells (Wessels et al., 1994;Heid et al., 2005). Uchida et al. (Uchida et al., 2003) and Ladam et al. (Ladam et al., 2005) found that Dictyostelium cells exert rearward traction forces at their front and forward forces at their rear. Tsujioka and colleagues (Tsujioka et al., 2004) also detected rearward traction stresses in migrating Dictyostelium 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 the rear of the cells, in contrast to Uchida et al. (Uchida et al., 2003), It has been suggested that myosin II exerts traction forces at the posterior ends and retracting pseudopodia of migrating cells, but there is no direct evidence. Here, using a combination of total internal reflection fluorescence (TIRF) microscopy and force microscopy with a high spatial resolution of ~400 nm, we simultaneously recorded GFP-myosin II dynamics and traction forces under migrating Dictyostelium cells. Accumulation of filamentous myosin II and a subsequent increase in traction forces were detected in pseudopodia just before retraction. In the case of motorless myosin II, traction forces did not increase after accumulation, suggesting that the source of the retraction force is the motor activity of accumulated myosin II. Simultaneous recording of F-actin and traction forces revealed that traction forces were exerted under spot-like regions where F-actin accumulated. Cells migrated in a direction counter to the sum of the force vectors exerted at each spot, suggesting that the stress spots act as scaffolds to transmit the propulsive forces at the leading edge generated by actin polymerization. Force 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 asymmetry induced directed cell movement, and that the degree of this asymmetry decreased in cells null for the myosin II essential light chain (mlcE -) and was additionally decreased in myosin-II-null cells (mhcA -). They claimed that myosin II motor and actin crosslinking activity were both required to develop and maintain asymmetrical patterns of traction stress, but they found that asymmetrical distributions sometimes even developed in myosin-II-null cells. These findings have led us to raise two questions: first, are there rearward traction stresses at the front of cells, as suggested by Uchida et al. (Uchida et 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-independent traction stress at the rear of myosin-II-null cells?
To answer these questions and investigate the relationship between molecular dynamics and traction forces, we simultaneously recorded the distributions of F-actin and traction stresses using confocal microscopy with a stress-recording spatial resolution of 400 nm. Rearward traction stresses were detected under spot-like regions in the front of cells where F-actin accumulated. Cells migrated in a direction counter to the sum of the force vectors at each spot, suggesting that counter forces to F-actin-based propulsion are exerted at the spots. Moreover, we recently developed a new method for simultaneously recording molecular dynamics and traction stresses under migrating cells using TIRF microscopy (Iwadate and Yumura, 2008). Using this new method, we recorded the accumulation of filamentous myosin II and subsequent increase of traction stresses under pseudopodia just before their contraction, directly demonstrating that the source of the retraction force is the accumulated myosin II.

Results
Rearward traction stresses at ʻstress spotsʼ and forward stresses at the posterior edge Aggregation-competent wild-type cells expressing GFP-ABD120k were dispersed on a gelatin substratum with fluorescent beads attached as illustrated in Fig. 1A,B. From the displacement of the beads by migrating cells, we calculated the stresses in the substratum using the Pascal-scale and visualized them in pseudocolor. It should be noted that the calculated stresses are not representative of all forces generated by the cell but the forces transmitted to the substratum. In a stress map of a typical wild-type cell just before posterior edge contraction, several traction stress peaks with rearward directions could be observed as 'stress spots' in the anterior and middle regions (white arrows in Fig. 1D). By contrast, a large stress with a forward direction was observed at the posterior edge (white arrowhead in Fig. 1D). Interestingly, the magnitude of the forward stress under the posterior edge often exceeded that of the rearward stress. If the posterior edge stress is exerted passively, as indicated in 3T3 fibroblasts (Munever et al., 2001b), forward stress should never exceed the rearward stress. Therefore, this observation raised the possibility of 'active' exertion of traction stress at the posterior edge.
Stress spots act as scaffolds to transmit the counter force of actin-mediated propulsion at the leading edge In the measurements using elastic substrata, it is plausible that stress spots are generated at cell-substratum attachment sites. In Dictyostelium cells, an actin-containing structure called the 'actin focus' 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 and actin, we observed the dynamics of F-actin and stresses under migrating cells using confocal microscopy. F-actin was visualized by GFP-ABD120k. Figs 2 and 3 show consecutive images of GFP-ABD120K and traction stresses under wild-type ( Fig. 2A) and myosin-II-null cells (Fig. 3A). Large traction stresses were observed under the stress spots (aЈ-cЈ in Fig. 2A) in the anterior and middle regions of the wild-type cells with rearward directions relative to the direction of migration. In many cases, F-actin accumulated at the same time or just before formation of the stress spots (a-c in Fig. 2A). The distance between the center of each F-actin accumulation spot and corresponding stress spot was very close (0.32±0.22 μm, n=16 from five cells, left column in Fig. 3C). The value of the stresses at each spot reached a maximum 3.9±3.5 seconds (n=16 from 5 cells, left column in Fig. 3D) after the fluorescence of GFP-ABD120k at the center of each F-actin accumulation reached a maximum. Interestingly, the position of each stress spot never changed until its disappearance, and the stress spots persisted after the disappearance of accumulated F-actin. These observations indicate that forces generated in migrating cells are transmitted to the substratum at spots where F-actin accumulates.
Close contact between F-actin accumulation spots and the substratum was confirmed by simultaneous fluorescence and interference reflection microscopy (IRM). The darker area of the IRM image indicates that the cell surface is closer to the substratum. As shown in Fig. 2B, the positions where F-actin accumulated (dg in Fig. 2B) coincided well with the dark spots surrounded by white rings (dЈ-gЈ in Fig. 2B) that are a typical feature of actin foci (Uchida and Yumura, 2004).
Next, to clarify whether myosin II generates rearward stress at the stress spots, stresses were observed under myosin-II-null cells (Fig. 3). Myosin-II-null cells exerted rearward stresses under regions where F-actin accumulated (a-c and aЈ-cЈ in Fig. 3A), as in wild-type cells, and close contact of the cell surface to the substratum Journal of Cell Science 121 (8) was again confirmed by IRM (d-f and dЈ-fЈ in Fig. 3B). The distances between the center of each F-actin accumulation spot and corresponding stress spot were very close (0.34±0.19 μm, n=15 from five cells, right column in Fig. 3C). The value of the stresses at each spot reached a maximum 4.2±3.3 seconds (n=16 from five cells, right column in Fig. 3D) after the fluorescence of GFP-ABD120k at the center of each F-actin accumulation reached a maximum. These values are almost the same as those of the wildtype cells. The maximum magnitude and duration for each stress spot with a rearward direction is shown in Fig. 3E,F. There was no significant 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 no significant 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, myosin II does not contribute to rearward traction stresses, and these stresses might 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 stress spots and actin polymerization at the leading edge. However, the relationship can be estimated indirectly by comparison of the average stress vector at all spots and migration direction, using myosin-II-null cells to account for the influence of myosin II. If the stress spots act as counter-force-transducing scaffolds, the cells should migrate in a direction opposite to the average stress vector. Stress spots (aЈ-cЈ) appeared at locations where F-actin accumulated (a-c) in the anterior and middle regions of the cell. The typical sequential stress map shown was made from three migrating cells randomly selected from 11 cells. (B) Simultaneous recording of fluorescence of GFP-ABD120k (left) and IRM imaging (right) of a migrating wildtype cell transformed with a GFP-ABD120k construct under confocal microscopy. Dark spots surrounded by white rings (dЈ-gЈ) appeared at locations where F-actin accumulated (d-g). The white ring surrounding a dark spot is a feature of focal contacts in Dictyostelium (Uchida and Yumura, 2004). The timecourses are indicated for each picture of GFP-ABD120k. Yellow arrows at 0 seconds in panels A and B indicate the direction of cell migration. Bars, 4 μm. Force dynamics in migrating Dictyostelium The trajectory of a migrating myosin-II-null cell and the average of strain vectors under the cell are shown in Fig. 4A (see also supplementary material Movie 1). The black line shows the trajectory of the centroid of a migrating myosin-II-null cell over a period of 400 seconds. Each blue line emerging from the trajectory shows the strain vectors in the substratum under the cell. The images a-f in Fig. 4A show the stress maps of the cell positioned at points a-f in Fig. 4A. Sequential images of the cell outline at the moment when the cell was at the positions marked with asterisks in Fig. 4A are shown in Fig. 4B. The migration speed of this cell was 2.70 μm/minute. The average speed of myosin-II-null cells on an elastic substratum was 2.58±0.35 μm/minute (n=7). By contrast, the average 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 a direction opposite to the average traction stress, suggesting that the stress spots act as scaffolds to transmit counter forces for actinmediated propulsion at the leading edge.
Myosin II contributes to forward traction stresses at the posterior edge  Fig. 5A). It is noteworthy that there was no equivalent rearward stress, suggesting that the forward stress is not only the counter force of propulsive rearward forces at the stress spots but also the sum of the counter force and an active force at the forward edge. Time-courses of the magnitudes of each traction stress and the length of the posterior region are summarized in Fig. 5B. The magnitudes of posterior edge traction stresses (red lines in Fig. 5B) increased strongly at the beginning of retraction, after which the posterior edges retracted quickly. Interestingly, traction stresses began to decrease before retraction was completed, suggesting that the detachment from the substratum took place during retraction.
Myosin II localizes to the posterior of migrating Dictyostelium cells (Yumura et al., 1984). To determine whether myosin II is the source of the actively generated forward traction stress, the magnitudes of forward and rearward stresses at stress spots were compared between wild-type and myosin-II-null cells. Fig. 5C shows the values of the traction stresses at each stress spot in the anterior (Fig. 5C, 0.40±0.24 kPa, n=12 in five cells) and at the posterior edges (Fig. 5C, 0.70±0.21 kPa, n=16 in five cells) of wildtype cells. All values were measured when posterior edge stress peaked. The magnitude of the forward traction stresses significantly exceeded that of the rearward stresses (P<0.001). However, in myosin-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 (F) Average stress spot duration times for wild-type and myosin-II-null cells. There was no significant difference between wildtype cells and myosin-II-null cells in the maximum magnitude or duration of stress at each stress spot. the rearward stresses (Fig. 5D, 0.79±0.29 kPa, n=8 in three cells, P>0.05). These observations strongly suggest that myosin II contributes to forward active stresses at the posterior end of wildtype cells.

Myosin II contributes to traction stresses exerted at the tips of retracting pseudopodia
Freely migrating Dictyostelium cells often elongate pseudopodia in the lateral direction. These pseudopodia seem to be retracted through a myosin-II-dependent process similar to that operating at the posterior edge. Thus, we observed the traction stresses under these lateral pseudopodia. Intense traction stresses were detected not only under the posterior edge but also under the tips of the retracting pseudopodia in wild-type cells (right images in Fig. 6A,B), where F-actin also accumulated (left images in Fig. 6A,B). Fig. 6AЈ and 6BЈ show the time-courses of traction stresses under the tips of each pseudopod, with the lengths shown in Fig. 6A,B. The magnitude of the traction stresses reached a maximum just after the beginning of retraction in a manner similar to that occurring at the posterior edges ( Journal of Cell Science 121 (8) ambiguous increases in traction stresses could be observed at the tips of large pseudopodia (arrow in Fig. 6FЈ). These weak traction stresses might be produced by means of the tension of the cell cortex, including the cell membrane and cytoskeleton, in the absence of a myosin-II-mediated process. The time-courses of the length of pseudopodia in Fig. 6A,B and C-F are the same as those dealt with later in Fig. 7A and Fig. 8B, respectively.
The timing of pseudopod elongation and retraction was compared between wild-type and myosin-II-null cells (Fig. 6G). Elongation time was defined as the time at which the length of each pseudopod reached 80% of the maximum length. Retraction time was defined as the time from attaining the maximum length until returning back to the original length. Although there was no significant difference in elongation time between wild-type and myosin-II-null cells, the retraction time in wild-type cells was significantly shorter than in myosin-II-null cells, suggesting that myosin II mediates the pseudopod retraction.

Myosin II motor activities are required for traction force exertion in retracting pseudopodia
In the above experiments, myosin-II-mediated traction forces were studied indirectly using myosin-II-null cells. During pseudopod retraction, myosin II has been shown to accumulate (Yumura, 1996b;Moores et al., 1996). We therefore next investigated the dynamics of myosin II filaments and traction stresses by simultaneous combination of TIRF and force microscopy using myosin-II-null cells expressing GFP-labeled myosin II.
Myosin II filaments began to accumulate in pseudopodia during elongation (0-40 seconds in Fig. 7A, see supplementary material Movie 3). The accumulation of myosin II filaments was followed by increased traction stress in the substratum under the pseudopod (40-80 seconds in Fig. 7A). Pseudopodia began to retract at the same time as the start of the increase in traction stress (40 seconds in Fig. 7A). The time-courses of pseudopod area, GFP-labeled myosin II fluorescence intensity and average traction stress are summarized in Fig. 7B,C. Increased pseudopod area was followed by the accumulation of myosin II (Fig. 7B), and traction stress reached a maximum during pseudopod retraction (Fig. 7C). These observations directly demonstrate that the accumulation of myosin II in pseudopodia mediates their retraction. To examine whether the motor activities of myosin II are required for the generation of traction forces, the dynamics of the E476K motorless myosin II filament and traction stresses in silicone substrata were simultaneously observed using myosin-II-null cells expressing GFP-E476K myosin II. E476K myosin II filaments began 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 contrast to wild-type myosin II. These weak traction stresses might be produced by means of the tension of the cell cortex, including the cell membrane and cytoskeleton, in the absence of a myosin-IImediated process. These results indicate that myosin II motor activities are required for the generation of traction stresses during pseudopod retraction.

Discussion
In this study, we examined the spatiotemporal patterns of cellsubstratum mechanical interactions and their relationships with molecular dynamics. The maximum value of rearward traction stress measured was 0.64±0.27 kPa for wild-type Dictyostelium cells, which agrees well with the data of Tsujioka and colleagues (Tsujioka et al., 2004). However, the traction stresses under fibroblasts and keratocytes are slightly different. Munevar and colleagues (Munevar et al., 2001a;Munevar et al., 2001b) observed dynamic traction stresses at the leading edges of migrating fibroblasts, with maximum values of several tens of kPa. Doyle and colleagues (Doyle et al., 2004;Doyle and Lee, 2005) and Jurado and colleagues (Jurado et al., 2005) mapped traction stresses under migrating keratocytes and estimated the maximum value to be several kPa at the lateral edges. The traction stresses exerted by fibroblasts and keratocytes are ~100fold and tenfold larger, respectively, than those exerted by Dictyostelium cells; these differences might arise owing to differences in cell shape and mode of movement.
Most rearward traction stresses emerged at spots where accumulation of F-actin took place (Fig. 2) and did not involve myosin II (Fig. 3C-F). These findings indicate that traction stresses are generated as a result of actin polymerization at the stress sites or at the leading edge of the cell. The stress spots persisted after the disappearance of accumulated F-actin ( Fig. 2A), suggesting that stress spots do not directly generate the traction force even though there is tight contact between the cell and the substratum. Rather, the stress spots might apply the counter force for actin polymerization at the leading edge. However, stress spots did not always emerge near the leading edge, as freely migrating Dictyostelium cells randomly extend pseudopodia not only to the substratum but also to the upper free space. Therefore, it is difficult to correlate each stress spot to each pseudopod directly. Thus, we compared the migration direction of cells with the summation of strain vectors of stresses during migration. As expected, cells continued to migrate in a direction counter to the average force vector at each spot (Fig. 4). This result suggests that F-actin assemblies in the pseudopod are connected to the actin meshwork in the cortex of the cell body and the stress spots emerge in the meshwork and act as scaffolds to transmit the counter force for the actin-mediated propulsion force at the leading edge.
Uchida and Yumura (Uchida and Yumura, 2004) detected the deformation of elastic substrata even under very small actin foci (<1 μm), although we could not detect traction stresses in foci of the same size. To calculate accurately the stresses in elastic substrata using finite element methods, the strain of the substrata should be at the smallest detectable level. Thus, we adjusted the Young's modulus of gelatin and silicone substrata to be 2.8 kPa and 1.0 kPa, respectively. The accumulated F-actin colocalized with the close contact points between cells and the substrata (Fig. 2B and Fig.  3B). It is therefore likely that the accumulated actin foci make contacts between the cell surface and substrata that are strong enough to exert traction forces even after F-actin has dispersed ( Fig.  2A and Fig. 3A). In this study, the positions of some stress spots and corresponding F-actin accumulation spots did not completely match, as in areas a and aЈ in Fig. 2A. This might be attributable to the slight difference in the positions between the F-actin accumulation and the corresponding contact site of the cell surface to the substratum. Furthermore, a few stress spots emerged without an immediately preceding F-actin accumulation there. The contact sites of the cell surface to the substratum of these stress spots might be produced by an F-actin-independent process. These facts raise the possibility that, in order to exert traction stresses to the Journal of Cell Science 121 (8) substratum for cell migration, only the strong contact between the cell surface and the substratum might be required as a scaffold, and it can be produced through an F-actin-independent process, although F-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 the posterior edge often exceeded rearward traction stresses at the leading edge ( Fig. 1D; Fig. 5A,D). These large forward stresses were also detected under the tips of retracting pseudopodia, suggesting that some active forces are exerted at the posterior edges of the cells and the tips of retracting pseudopodia. Jay and colleagues (Jay et al., 1995) predicted that myosin-II-mediated force should induce detachment from the substrata. If this is the case, then strong forward stresses should be detected just before the detachment. In the present study, we directly visualized the relationships among myosin II, traction forces and cell movement by using a combination of TIRF and force microscopy (Iwadate and Yumura, 2008), which revealed that, just before pseudopod contraction, filamentous myosin II and traction stresses accumulated at the tips of pseudopodia (Fig. 7). The migration speed of myosin-II-null cells on elastic substrata (2.58±0.35 μm/minute, n=7) was significantly slower than that of wild-type cells (6.87±1.63 μm/minute, n=11). These observations strongly suggest that the myosin-II-mediated force at the posterior edge contributes to the ability to migrate. Uchida et al. (Uchida et al., 2003), Tsujioka et al. (Tsujioka et al., 2004), del Alamo et al. (del Alamo et al., 2007 and our group detected rearward traction stresses under migrating Dictyostelium cells, although Lombardi et al. (Lombardi et al., 2007) did not. Tsujioka et al. (Tsujioka et al., 2004) noted that the force-field of traction stresses was not uniform, showing a few regions with relatively large forces that were mostly stationary with respect to the substratum. This finding matches the distribution of 'stress spots' in the present study. The discrepancy in detection of rearward stresses in the above-mentioned studies might be due to differences in the types of cells used for measurements. Uchida et al. (Uchida et al., 2003), Tsujioka et al. (Tsujioka et al., 2004) and our group used aggregation-competent cells, whereas Lombardi et al. (Lombardi et al., 2007) used vegetative cells. The migrating speed of vegetative cells (1.13 μm/minute) (Lombardi et al., 2007) is much Although there was no significant difference in elongation time between wild-type and myosin-II-null cells, the retraction time of pseudopodia in wild-type cells was significantly shorter than in myosin-II-null cells. Bars, 1.5 μm. The look-up table (LUT) of A and B is indicated at the right side of B, and the LUT of C-F is at the right side of D. Force dynamics in migrating Dictyostelium slower than that of aggregation-competent cells (6.87±1.63 μm/minute for wild-type cells on the elastic substrata in this study, n=11). The rearward traction stresses at stress spots might contribute to the fast migration and the deformation in shape during migration. Another possible explanation of the discrepancy is that resolution of the stress maps depends on the density of marker beads on the substrata. The density of beads in our experiment was very high in order to detect any slight strain of the elastic substrata under the cell (Fig. 1B). The space resolution of our recording was ~400 nm. To detect 'stress spots', a high spatial resolution for strain in the elastic substrata might be required. If this is the case, the forward traction stresses at the rear of migrating vegetative mlcEand mhcAcells in the study of Lombardi and colleagues (Lombardi et al., 2007) might be the counter forces to rearward traction stresses at stress spots that they did not detect.
del Alamo and colleagues (del Alamo et al., 2007) showed that traction forces appear at the anterior after pseudopod expansion in wild-type Dictyostelium cells. By contrast, in this study, some stress spots emerged at the leading edge, as shown in the stress spot c in Fig. 2A, just like that described by del Alamo and colleagues (del Alamo et al., 2007) and others at the base of an expanding pseudopod, as shown in stress spot b in Fig. 2A, and at the inside of the cell, as shown in the stress spot a in Fig. 2A. These results suggest that there are two kinds of rearward traction stresses as follows. (1) The stress emerging at the tip of pseudopodia. The pseudopod, which expanded away from the substratum, captures the substratum at its tip. Then, it exerts rearward traction stresses onto the substratum by means of the contracting force of the expanded cortex. (2) Counter stress generated by actin polymerization in the expanding pseudopod. This stress should be exerted at the scaffold for actin polymerization. The scaffold should be separate from the tip of an expanding pseudopod, such as at the base of it or at the inner region of the cell.
We propose here a model for the migration of fastmoving irregularly shaped cells (Fig. 9). Munevar and colleagues (Munevar et al., 2001a) proposed a frontal towing model for the migration of fibroblasts, which are slow-moving irregularly shaped cells. Our model includes a frontal towing and rear contraction mechanism; it is essentially Munevar's model with an added myosin II contractile device ('p' in Fig. 9A) at the posterior edge. Actin polymerization (red-filled circles in Fig. 9A) produces a pushing force ('F' in Fig. 9A) at the leading edge ('a' in Fig. 9A) and a rearward force ('rf') at the stress spots as a counter force for elongation of pseudopodia in the anterior of the cell. A part of the actin-mediated propulsion force (FЈ in Fig. 9A) is transmitted to the posterior edge of the cell through the elastic transition zone ('e' in Fig. 9A), and this behavior passively induces forward force ('ff' in Fig. 9A) at the posterior end, as shown at the tip of a retracting pseudopod of the cell with motorless myosin II (arrows in Fig. 8A). Myosin II might also exert an active force ('Fm' in Fig. 9B) triggered by the passive force ff, with contraction taking place at the posterior edge ( Fig. 9B). Merkel and colleagues (Merkel et al., 2000) showed that, in response to the aspiration of a small part of the cell surface by a micropipette, myosin II accumulated at the tip of the aspirated cell lobe. This suggests the possibility that myosin II might accumulate in response to mechanical stimulation. Contraction of the posterior edge by myosin II might therefore push the anterior portion forward, as Uchida and colleagues (Uchida et al., 2003) suggested. After this contraction and elongation, a new cycle could then begin with elongation of pseudopodia through actin polymerization (Fig. 9A). Simultaneous recording of GFP-myosin-II fluorescence and traction stresses using a combination of TIRF and force microscopy: the dynamics of myosin II filaments (upper images) and traction stresses (lower images) under a pseudopod of a migrating myosin-IInull cell are shown. The stress map was made from three migrating cells randomly selected from nine cells. The time elapsed is indicated in each GFP-myosin-II image. Myosin II filaments begin to accumulate in the pseudopod during elongation (0-40 seconds), followed by increased traction stress in the silicone substratum just under the pseudopod (40-80 seconds). Retraction began at the same time as the beginning of the increase in traction stress (40 seconds). Bar, 1 μm. (B) Time-courses of pseudopod area (blue) and fluorescence intensity of GFP-myosin-II (red). (C) Time-courses of fluorescence intensity of GFPmyosin-II (red) and average traction stress in the pseudopod (blue). The increase in pseudopod area was followed by accumulation of myosin II (B). Traction stress in the pseudopod subsequently reached a maximum during retraction (C).

Preparation of elastic substrata
Elastic 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 gels were made with 4.0% gelatin (90-110 Bloom, G6144-100G, Sigma) dissolved in BSS containing 3 mM Mes, pH 6.3 with KOH. Stock gels were liquefied at 30-40°C, and 200 μl were transferred into a round chamber (16 mm in diameter and 2 mm in depth) whose bottom was made of a 22ϫ22 mm coverslip (No. 1, Matsunami, Japan). After solidification, fluorescent orange microspheres (200 nm in diameter, F-8809, Molecular Probes) were attached to the surface of the substrata. The subsequent procedure was identical to that described previously (Doyle and Lee, 2002;Doyle and Lee, 2004).
Silicone substrata were made according to Iwadate and Yumura (Iwadate and Yumura, 2008). Briefly, two types of platinum-catalyzed silicone (CY52-276A and B, Dow Corning Toray, Tokyo, Japan) were used. A 300 mg aliquot of CY52-276A and a 250 mg aliquot of B were mixed. The mixture was spread on a 22ϫ22 mm coverslip (No. 1,Matsunami,Japan). After solidification of the mixture, a round chamber (16 mm in diameter and 2 mm in depth) was assembled using the coated coverslip as the bottom of the chamber. The solidified substrata were kept in a hermetically sealed case with a 50 μl aliquot of the liquid silane (3aminopropyl triethoxysilan, Sigma Aldrich, Tokyo, Japan) at 70°C for 1 hour in order to attach the silane to the surface of the silicon substrata by vapor deposition. Redfluorescent carboxylate-modified microspheres (20 nm in diameter, the peak excitation and emission wavelengths were 580 and 605 nm respectively, F-8786, Molecular Probes) were attached to the surface of the substrata by means of the binding between the 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 of Lo and colleagues (Lo et al., 2000). Briefly, a steel ball (0.5 mm diameter, 7.8 kg/m 3 ) was placed on a substratum embedded with fluorescent beads. The Young's modulus was calculated as Y=3(1-p 2 ) 2 f 2 /4d 3/2 r 1/2 , where f is the force exerted on the sheet, d is the indentation, r is the radius of the steel ball, and p is the Poisson ratio [assumed to be 0.5 for gelatin (Doyle et al., 2004) and silicone (Dembo et al., 1996)]. Typical values of the Young's modulus for gelatin and silicone substrata were 2.8 kPa and 1.0 kPa, respectively. Fig. 8. The motor activity of myosin II is required for the generation of traction forces by retracting pseudopodia. (A) Dynamics of E476K myosin II filaments (upper images) and traction stresses (lower images) under a pseudopod of a migrating myosin-II-null cell expressing GFP-E476K myosin II. The stress map was made from three migrating cells randomly selected from six cells. E476K myosin II filaments began to accumulate in the pseudopod during elongation of the pseudopod (0-24 seconds), similar to wild-type myosin II. After elongation, traction stress slightly increased only under the tip of the pseudopod (arrows). Bar, 1.5 μm. (B) Timecourses of pseudopod area (blue) and fluorescence intensity 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 in pseudopod area was followed by the accumulation of E476K myosin II in the pseudopod, as was the case for normal myosin II (Fig. 7B). However, the traction stress increased only at the tip of the retracting pseudopod. The migrating cell comprises a frontal towing zone (a) and a rear trailing and contractile zone (p). These two zones are connected by an elastic transition zone (e) that includes the cytoskeleton. Polymerization of actin (red-filled circles) produces a force (F) for pseudopod 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 FЈ is transmitted to the rear zone through the elastic transition zone, and this passively generates a forward force (ff) at the stress points in the rear trailing and contractile zones. FЈ increases as the elastic transition zone extends. (B) When the passive force FЈ reaches a threshold level, an active strong force (Fm) is exerted by accumulated myosin II at the rear trailing and contractile zones. After contraction of the rear zone by myosin II, a new cycle of the cell migration process begins (panel A). Force dynamics in migrating Dictyostelium

Microscopy
Migrating cells plated on gelatin substrata were observed using a confocal microscope (Zeiss, LSM500, Germany) with a 100ϫ objective lens (PlanFluar 100ϫ). An argon ion laser was used at an excitation wavelength of 488 nm. GFP fluorescence was detected with a 505-530 nm band-pass filter, and the orange-fluorescent beads were detected with a 560 nm high-pass filter.
Migrating cells plated on silicone substrata were observed by a TIRF microscope assembled on an inverted microscope (Olympus, IX71, Japan) with a 60ϫ objective lens (Plapon 60ϫ 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 and red 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 were controlled using a custom program developed under LabVIEW 7.1 (National Instruments, Japan).

Calculation of traction stresses (I)
Traction forces were not calculated as the real values of the 'forces' in cells on the Newton-scale but rather as 'stresses' in the substratum with the Pascal-scale using the triangle finite element method [see below or Iwadate and Yumura (Iwadate and Yumura, 2008) for further details]. Briefly, migrating cells cause strains in the elastic substratum and displacements of the beads on the substratum (Fig. 1A). A representative sample image of the beads is shown in Fig. 1B. The white line indicates the outline of the migrating cell on the substratum. An image of beads comprising 512ϫ512 pixels was divided into approximately 8000 triangle elements as 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 displacements of the beads. The strain of each element was calculated from the displacement of its three nodes. The stresses of each element were calculated from the strains of the element under the assumption that the substrata are in a plane stress state (see below for further details).
The magnitudes of the stresses at each element under a cell were visualized by pseudocolor. Each node and its displacement vector are superimposed onto the pseudocolor images as white circles and bars, respectively. All of these calculations and some of the image processing were performed using a custom program developed under RealBASIC Ver. 3.5 (ASCII Solutions, Japan). Image processing was also performed 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 and the 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 area where 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 be predicted. 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 prepared for 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, A 1 , A 2 and A 3 . The original positions and the displacements of the three nodes are A 1 (x 1 , y 1 ), A 2 (x 2 , y 2 ), A 3 (x 3 , y 3 ) and (u 1 , v 1 ), (u 2 , v 2 ), (u 3 , v 3 ), respectively. The displacement vector, (u, v), of the arbitrary point P, whose original position is (x, y), in the triangle element is determined as: In the above calculation, the strains at each point inside the element are assumed to be distributed linearly. The longitudinal and shearing strains ε x , ε y and γ xy at the minute square ( 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 σ x , σ y and τ xy at the minute square (Fig. 10C) in each element are calculated from the strain matrix (equation 3) under the assumption that the substratum is in a plane stress state.
In the above equations, E and ν mean Young's modulus and Poisson ratio, respectively. In this study, the magnitude of stress ͉σ m ͉ in each element is defined as: The magnitude of the stress is constant inside a triangle element in our calculation because of the assumption of a linear distribution of strains in the element, as mentioned above. The magnitudes of the stresses for each element under a cell were visualized with pseudocolor. The elements outside the cell were filled with black even 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 of Connecticut, CT) for the permission to use it. This work was partly supported by a Grant-in-Aid for Scientific Research (C) No.16570161 to S.Y. from the NIH and a grant to Y.I. from the Yamaguchi University Foundation. We are grateful for their support. (2) . Each triangle element has three nodes, A 1 , A 2 and A 3 , whose original positions are (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ) and displacement vectors are (u 1 , v 1 ), (u 2 , v 2 ), (u 3 , v 3 ), respectively. The strains at each point in one element are assumed to be distributed linearly. P is an arbitrary point whose original position is (x, y) and the displacement vector is (u, v). (B) The longitudinal and shearing strains, ε x , ε y and γ xy , at the minute square in the element. (C) The normal and shearing stresses, σ x , σ y and τ xy , at the minute square in the element.