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CIL and JAT conceived and designed the experiments. CIL and MMVD performed the experiments. CIL, ZP, CAW, and AM analyzed the data. ZP, CAW, DAF, FBG, AM, and JAT contributed reagents/materials/analysis tools. CIL, ZP, AM, and JAT wrote the paper. ZP wrote a methods section. FBG made an intellectual contribution. AM wrote mathematical methods, results, and interpretation.

The authors have declared that no competing interests exist.

Variations in cell migration and morphology are consequences of changes in underlying cytoskeletal organization and dynamics. We investigated how these large-scale cellular events emerge as direct consequences of small-scale cytoskeletal molecular activities. Because the properties of the actin cytoskeleton can be modulated by actin-remodeling proteins, we quantitatively examined how one such family of proteins, enabled/vasodilator-stimulated phosphoprotein (Ena/VASP), affects the migration and morphology of epithelial fish keratocytes. Keratocytes generally migrate persistently while exhibiting a characteristic smooth-edged “canoe” shape, but may also exhibit less regular morphologies and less persistent movement. When we observed that the smooth-edged canoe keratocyte morphology correlated with enrichment of Ena/VASP at the leading edge, we mislocalized and overexpressed Ena/VASP proteins and found that this led to changes in the morphology and movement persistence of cells within a population. Thus, local changes in actin filament dynamics due to Ena/VASP activity directly caused changes in cell morphology, which is coupled to the motile behavior of keratocytes. We also characterized the range of natural cell-to-cell variation within a population by using measurable morphological and behavioral features—cell shape, leading-edge shape, filamentous actin (F-actin) distribution, cell speed, and directional persistence—that we have found to correlate with each other to describe a spectrum of coordinated phenotypes based on Ena/VASP enrichment at the leading edge. This spectrum stretched from smooth-edged, canoe-shaped keratocytes—which had VASP highly enriched at their leading edges and migrated fast with straight trajectories—to more irregular, rounder cells migrating slower with less directional persistence and low levels of VASP at their leading edges. We developed a mathematical model that accounts for these coordinated cell-shape and behavior phenotypes as large-scale consequences of kinetic contributions of VASP to actin filament growth and protection from capping at the leading edge. This work shows that the local effects of actin-remodeling proteins on cytoskeletal dynamics and organization can manifest as global modifications of the shape and behavior of migrating cells and that mathematical modeling can elucidate these large-scale cell behaviors from knowledge of detailed multiscale protein interactions.

The spatiotemporal coordination of the assembly, disassembly, and organization of the actin cytoskeleton is essential for efficient cell migration. The underlying mechanisms by which the actin cytoskeleton is organized and remodeled into specific architectures, which are then conveyed over large scales into observable cell morphologies, remain unclear. However, careful observation of large-scale morphology and behavior can shed light on these mechanisms. The heterogeneity of wild-type populations [

The actin cytoskeleton can be remodeled by many different families of proteins, including the enabled/vasodilator-stimulated phosphoprotein (Ena/VASP) family, which affects dynamic processes such as growth, capping, and bundling of actin filaments [

Ena/VASP proteins have been of special interest in the field of cell migration, because they have been found to be both positive and negative regulators of cell speed in diverse motile cell types ranging from the actin-based movement of the intracellular pathogen

Cell morphology represents the global manifestation of the cell's structural organization of the cytoskeleton and thus reflects the specific migratory behavior of different cell types. For example, epithelial fish keratocytes, which are among the fastest locomoting cells, exhibit flat lamellipodia as they glide along two-dimensional surfaces, whereas neutrophils have thicker, more amorphous pseudopodia that allow them to crawl through three-dimensional tissues with speeds comparable to that of keratocytes [

To confirm our initial observation, we measured cell shape, leading-edge shape, filamentous actin (F-actin) distribution, cell speed, directional persistence, and VASP enrichment at the leading edge in a population of keratocytes. Systematic quantitative analysis revealed that these parameters correlated with VASP enrichment at the leading edge, spanning a clear continuum of coordinated phenotypes. Moreover, we have developed a mathematical model that explains the properties of this continuum—in particular, the quantitative correlations observed between the observable, large-scale parameters—in terms of small-scale molecular interactions between VASP and the growing actin architecture. Specifically, our model suggests that the role of Ena/VASP in protecting growing filaments allows for larger-scale cohesion in the actin meshwork, promoting smooth canoe shapes and faster migration. By experimentally manipulating Ena/VASP availability at the leading edge and thus local actin filament growth kinetics due to Ena/VASP activity, we were able to alter the prevailing morphology and trajectory of keratocytes within a population in a way that was accurately predicted by our model. Together, our results suggest that Ena/VASP proteins play a major role in cell morphology and motility by modulating the organization and thus promoting the large-scale coherence of the actin network. Our general approach of using detailed mathematical modeling to connect quantitative measurements of large-scale cell morphological and behavioral features to specific protein biochemical activities should be broadly applicable to many cytoskeleton-associated proteins involved in cell migration.

Populations of primary migrating epithelial fish keratocytes are heterogeneous in cellular morphologies, sizes, and motile behaviors. Most descriptions of keratocytes focus on a subpopulation of cells with stereotyped canoe-like shapes [

A population of primary keratocytes is heterogeneous in morphology. (A) Keratocytes can have a smooth leading edge, showing strong VASP immunofluorescence that appears as a thin line at leading edge (arrowheads). (B) Keratocytes may also have rough leading edges with weak or absent VASP at the leading edge. VASP also appears localized at focal adhesions (arrows), which are more apparent in cells with rough leading edges. Immunofluorescence was performed using polyclonal anti-murine VASP antibodies. Scale bar = 10 μm.

Differences in morphology became more evident when we observed by immunofluorescence that VASP was localized as a uniform thin line at the leading edge of keratocytes with smooth leading edges and did not appear at the edge of cells with rough margins (

To test whether Ena/VASP proteins directly modulated leading-edge shape, we manipulated their availability at the leading edge of keratocytes. To decrease Ena/VASP availability, we used a construct (FP4-mito) derived from the

(A) EGFP-AP4-mito (negative control) binds to mitochondria in the cell body, but does not mislocalize VASP, which, by immunofluorescence, appears as a thin line at the leading edge of cells with a smooth morphology (arrowheads).

(B) EGFP-FP4-mito mislocalizes VASP at the surface of mitochondria thus preventing its function at the leading edge. Weak VASP localization was only observed at the leading edge in two cells out of more than 50 cells examined. Scale bar = 10 μm.

(C) Keratocytes were classified as either having a smooth or rough leading edge within populations of migrating keratocytes expressing the aforementioned EGFP-tagged constructs. Cells with a rough leading-edge morphology are more prevalent than those classified as having a smooth morphology when EGFP-FP4-mito is expressed (70%) compared with controls, EGFP (55%) and EGFP-AP4-mito (59%). The incidence of rough keratocytes is significantly lower (43%) when EGFP-VASP is overexpressed (when compared to EGFP-FP4-mito,

(D) Keratocytes exhibiting smooth leading edges are significantly faster than those with rough leading-edge morphology (EGFP,

(E) To perform qualitative comparisons of keratocyte turning during migration, trajectories of smooth or rough keratocytes were reoriented to start at

We also used these time-lapse sequences to examine differences in motile behavior between cells with smooth and rough morphologies. When we measured migration speed, we found that smooth cells were significantly faster than rough cells (

Since Ena/VASP availability influenced the fraction of smooth, straight-moving keratocytes within a population, we next examined whether manipulating VASP availability at the leading edge would alter cell trajectories. When Ena/VASP proteins were mislocalized (EGFP-FP4-mito), smooth cells moved in more curved trajectories that were similar to those of rough cells and significantly different from smooth cells expressing control constructs (

Thus far, we had observed that VASP localization was related to broad classes of keratocyte leading-edge morphologies and that we could manipulate morphology by mislocalizing or overexpressing VASP. We wondered whether morphological variation among wild-type keratocytes might be related to VASP levels at the leading edge, and therefore we performed a detailed, quantitative characterization of a keratocyte population. Instead of using a binary and subjective classification of smooth versus rough, we characterized the natural morphological heterogeneity of keratocytes along several measurable and objective phenotypic continua.

To measure cell morphology rigorously, we determined mathematically the major modes of shape variation by applying the principal components analysis (PCA) to a population of keratocyte shapes represented as aligned, polygonal contours [

(A, B) Using immunofluorescence, VASP intensity levels were measured along lines (∼5 μm wide) positioned across lamellipodia in the middle of cells roughly perpendicular to the leading edge of keratocytes (arrows). The relative levels of VASP at the leading edge of a population of keratocytes were compared using VASP peak-to-base ratios, which were calculated by dividing the highest mean fluorescence intensity at the leading edge (peak) by the lowest mean intensity found interior to the leading edge (base). For cells with low VASP at the leading edge, peak and base positions were assigned based on mean positions from cells (

(C) The keratocyte population examined (

(D) The shapes of keratocytes were compared using PCA, which identified the major modes of shape variation of polygonal cell contours extracted from intensity-thresholded fluorescent images. A shape mode value of zero corresponds to the mean shape and the negative or positive values correspond to standard deviations describing canoe (+SD) or round D shape (−SD) on the ^{2}

(E) To compare leading-edge shapes, we measured and normalized their degree of local curvature. Local leading-edge curvature negatively correlates (^{2}

(F) A significant negative correlation is also observed between cell shape and local leading-edge curvature (^{2}

To evaluate the shapes of leading edges quantitatively instead of qualitatively classifying them as smooth or rough, we measured the degree of roughness of the leading edges by calculating the sum of the local curvature at each of 90 points along front of the cell contours (see

To examine the behavior of live keratocytes with smooth or rough leading edges, we followed their contours, which were generated from each frame of time-lapse sequences of keratocytes overexpressing EGFP-VASP. The shape of the leading edge in rough cells varied widely, whereas smooth cells maintained a constant shape with minor fluctuations (

Outlines of migrating keratocytes overexpressing EGFP-VASP were generated from each frame of time-lapse image sequences separated by 10 s to examine the shape of cells as they migrate. Outlines are colored from blue to red to represent time (0–240 s), superimposed, and plotted on the same scale for visual comparison. Speed can be estimated from the distances traveled by each keratocyte because outlines correspond to the same total time. Fluorescent images correspond to the first (A) and fifth (B) frames of each time-lapse sequence and are scaled to match to the outlines. (A) The leading edge and overall shape of a smooth, coherent keratocyte does not vary extensively as the cell migrates. (B) In the case of a rough and rounder keratocyte, outlines show that the leading edge changes shape rapidly and widely. This keratocyte is unable to maintain persistent coordinated protrusion of its lamellipodium. Specific segments of the leading edge extend forward while adjacent regions lag behind (notice blue and orange outlines). This keratocyte migrates at approximately half the speed of the coherent keratocyte in (A)

Our results indicated that the five parameters considered thus far—VASP peak-to-base ratio, cell shape, local leading edge curvature, speed, and directional persistence—all correlated with each other, creating a continuum of keratocyte phenotypic morphologies. One extreme of this continuum contained fast, straight-moving cells with VASP enriched at the leading edge, canoe-like shapes, and smooth leading edges (

Because previous studies have indicated that keratocyte leading-edge shape may be related to actin filament (F-actin) density [

(A) The distributions of VASP (gray line in the graph) and F-actin (black line in the graph) were measured along the length of the leading edge of cells (position indicated by the arrow). The cell shown has VASP enriched at its smooth leading edge (VASP peak-to-base ratio = 1.84). The distribution of F-actin along the leading edge of this smooth cell is peaked in the middle and strongly correlates with that of VASP (^{2}

(B) A keratocyte with rough leading edge and very weak VASP at the leading edge (VASP peak-to-base ratio = 0.76) has a very flat distribution of VASP (gray line in the graph) and F-actin (solid black line in the graph) measured along the leading edge (arrow). The distributions of VASP and F-actin along the leading edge of this cell strongly correlate with each other (^{2}

(C) The F-actin density along the leading edge of a representative coherent cell with high VASP peak-to-base ratio—2.79 (gray line)—is increased compared to that of a decoherent cell with low VASP peak-to-base ratio—1.13 (black line). Mean intensity values are not normalized and were obtained from keratocytes imaged from the same coverslip. F-actin distributions between different cells were compared by calculating a ratio (F-actin peak ratio) of the mean F-actin intensity values from the middle half of the leading edge (0.25 to 0.75 position along the edge, indicated by the thick regions of each line in the graph), which generally correspond to the highest intensity values in peaked F-actin distributions, to the mean of the F-actin values from the rest of the leading edge (positions 0 to 0.25 and 0.75 to 1.00 along the edge, indicated by the thin regions of each line). Cells with peaked F-actin distributions had larger F-actin peak ratios than did cells with flat distributions. The F-actin peak ratio of the coherent cell (gray line) is 1.45, whereas that of the decoherent cell (black line) is 0.94. Also compare the cells in (A) and

(D) VASP peak-to-base ratios significantly correlate with F-actin peak ratios (^{2}

(E, F) For comparisons of F-actin and Arp3, mean intensity values were measured along lines (∼0.5 μm wide) positioned along the leading edge of keratocytes, immediately interior to cell edge. Anti-Arp3 mean fluorescence intensities measured along the leading edge of keratocytes are consistent with those of F-actin. A representative smooth cell (E) exhibits peaked Arp3 and F-actin distributions along the leading edge while a rough cell (F) has flat distributions. Scale bar = 10 μm.

When we examined the relationship of the Arp2/3 complex to F-actin and cell morphology, we found that Arp3 distribution, as measured by immunofluorescence, corresponded to that of F-actin in both coherent and decoherent cells, which had peaked and flat distributions, respectively (

To unify our observations into a functional context, we developed a mathematical model that accounted for self-organization of keratocyte leading edge and VASP-mediated F-actin growth dynamics. This model allowed us to make predictions about keratocyte shape and was based on the following assumptions about actin dynamics and protrusion at the leading edge:

(1) The F-actin network is organized in a dendritic array such that actin filaments are oriented at ±35° relative to the locally normal direction of protrusion [

(2) Growing barbed ends at the leading edge elongate with a rate limited by membrane resistance and local concentration of actin monomers (G-actin) [

(3) Arp2/3-mediated filament branching takes place with equal rate per each existent leading-edge filament [

(4) VASP associates with/dissociates from barbed ends with constant rates and remains associated with elongating barbed ends until it dissociates [

(5) VASP protects barbed ends from capping; unprotected barbed ends are capped at a constant rate [

(6) The barbed ends of elongating actin filaments undergo lateral flow along the leading edge with a rate proportional to local protrusion [

(7) The shape of the leading edge is determined by the graded radial extension model [

(8) The length of the leading edge is a constant parameter. At the sides of the leading edge, boundary densities of the uncapped (VASP-free and VASP-associated) barbed ends are constant parameters in the model. These parameters are crucial for the model predictions (discussed below).

These assumptions, which are expressed mathematically in

(A) In coherent cells, long actin filaments are protected from capping and undergo significant lateral flow (arrows), smoothing heterogeneities at the leading edge. According to the Graded Radial Extension model, _{n}(_{n} represents the local protrusion rate, and θ is the orientation of the normal to the leading edge at position

(B) In decoherent cells, short filaments that are not protected from capping undergo less-extensive lateral flow (arrows) and may focus into heterogeneities at the leading edge causing the unstable protrusion of microregions.

(C) Barbed end density and nascent filament branching were chosen so that when VASP activity is low, the F-actin density along the leading edge appears flat (bottom curve). When high VASP activity was entered into our model, the F-actin density along the leading edge emerged as an inverted parabola (top curve), with F-actin density peaked in the middle, as observed experimentally in coherent cells. Position is normalized by the half-length of the leading edge. The prediction that peaked F-actin density is proportional to the level of VASP is qualitatively consistent with the experiment (see

(D) Based on protrusion rate as a function of barbed end distribution along the leading edge, the computed leading edge profile is wide (canoe-shaped) in coherent cells with high VASP at the leading edge (top curve) and short (D shaped) in decoherent cells with low VASP at the leading edge (bottom curve). Position (

When we investigated the stability of the leading edge of coherent keratocytes mathematically, we found that high VASP activity maintains greater density of barbed ends abutting the membrane at the front, leading to low membrane resistance per filament. This low resistance allows the protrusion rate to become insensitive to F-actin density, and instead limited by G-actin concentration. The even distribution of G-actin along the leading edge, together with the lateral flow of actin filaments, leads to the smooth leading edge of coherent cells (

When we modeled the F-actin profiles along the leading edge of cells, we found that they depended crucially on the boundary conditions at the sides of the leading edge and on the total branching rate. We assumed that at the sides of the leading edge the cell, where the large adhesions are located, there are specific local conditions generating and maintaining a constant density of uncapped barbed ends. If this fixed boundary density is equal to the average density being maintained along the leading edge by the dynamic balance between branching and capping, then the F-actin density along the leading edge is constant (

The characteristic canoe shape of coherent cells is achieved through a graded distribution of extension along the leading edge. Experimentally, we observed that coherent cells with high VASP at the leading edge have increased F-actin density at the leading edge (

Since our model predicted that VASP was responsible for the morphological phenotypes observed, we tested our model by acutely delocalizing Ena/VASP proteins from the leading edge of keratocytes. VASP was delocalized by competition with the pharmacological barbed end capper, cytochalasin D [

(A) Time-lapse images show that overexpressed EGFP-VASP, which is enriched at the leading edge before addition of 1.0 μM cytochalasin D (time: 1:00, left panel), becomes weaker at the leading edge ∼2 min after cytochalasin treatment (time: 2:50, middle panel). Cytochalasin D was added at 70 s (∼1.2 min). Approximately 3 min after cytochalasin treatment (time: 4:20, right panel), EGFP-VASP can barely be seen at the leading edge of this keratocyte that begins to exhibit a D shape rather than the original canoe shape. Time = min:s. Scale bar = 10 μm. Fluorescence intensities measured across the leading edge (arrows) quantitatively confirm the enrichment of EGFP-VASP at the leading edge before cytochalasin treatment and its delocalization a few minutes after addition of the drug (bottom graphs).

(B) The levels of EGFP-VASP at the leading edge and the width of the keratocyte in (A) were compared as a function of time. Cell width (axis perpendicular to migration) was measured from one side of the cell to the other (dotted line in (A)). EGFP-VASP intensity levels were measured inside a circle (4 μm diameter) placed in the middle of the cell at the leading edge (dotted circles in (A)) in each frame of the time-lapse sequence. These two parameters temporally correlate with each other (^{2} =

(C) The frequencies of VASP peak-to-base ratios obtained from immunofluorescence images of keratocytes treated with cytochalasin D confirm that VASP becomes displaced from the leading edge. The keratocyte population with high VASP peak-to-base ratios observed in wild-type cells (see

(D) Shape mode analysis reveals that cytochalasin treatment (open diamonds) eliminates the population of keratocytes with canoe shapes (>1 in ^{2}

(E) Cytochalasin treatment (open diamonds) eliminates the correlation between local leading-edge curvature and VASP enrichment at the leading edge (^{2}

(F) The negative correlation between cell shape and local leading edge curvature observed in control cells (closed diamonds) is abolished in cells treated with cytochalasin (open diamonds, ^{2}

(G) After cytochalasin treatment, a typical cell has VASP absent from the leading edge (VASP peak-to-base ratio = 0.83) and an F-actin peak ratio of 0.96 corresponding to a flat F-actin distribution along the leading edge. Cytochalasin treatment eliminated cells with peaked F-actin distributions corresponding to high F-actin peak values from our population. In addition, no significant correlation was found between F-actin peak ratios and enrichment of VASP at the leading edge (VASP peak-to-base ratio) in our population of cytochalasin treated cells (^{2}

Our quantitative comparison of shape showed that cytochalasin treatment eliminated keratocytes with extreme canoe shapes (

During extensive observation of different keratocyte morphologies, we hypothesized that coherent keratocytes with high VASP at the leading edge represented a mature state of cellular organization and migration. We evaluated the contribution of VASP in the generation of smooth lamellipodia in coherent cells by obstructing lamellipodial protrusion and examining its subsequent emergence and recovery. When we placed a barrier in the path of movement of a coherent keratocyte with EGFP-VASP enriched at the leading edge, the front edge of the lamellipodium that reached the barrier became temporarily stalled and the levels of VASP at the leading edge dramatically decreased (

We developed a method to generate nascent lamellipodia during recovery of protrusion after temporarily stalling a section of the lamellipodium. A glass micropipette, acting as a barrier, was lowered into the path of movement of a migrating keratocyte overexpressing EGFP-VASP and forced down until a section flexed parallel to the surface. The pipette was left in place until the cell was in firm contact with the pipette and subsequently removed by translating the pipette in the direction of cell migration. A coherent keratocyte shows EGFP-VASP as a uniform thin line at the leading (time: 0:00, min:s). Fluorescent images are shown in both regular and inverted contrast for clarity. Insets show inversed and zoomed in images of the corresponding boxed areas of the leading edge. When this keratocyte reaches the edge of the barrier, the lamellipodium temporarily stops protruding forward and acquires a very flat shape corresponding to the shape of the barrier (time: 0:48, 0:57). The cell continues migrating in the original direction of motion while EGFP-VASP becomes displaced from the edge of the region in contact with the barrier (see inset). When the micropipette barrier is removed (between 0:57 and 1:00), the leading edge of the lamellipodium immediately resumes protrusion and appears rough with several protruding microregions enriched in EGFP-VASP (time: 1:00). The levels of EGFP-VASP quickly recover along the impacted region and become uniform (time: 1:06). Only 18 s after removal of the barrier, the keratocyte's original shape and EGFP-VASP localization at the leading edge are restored (time: 1:18). Scale bar = 20 μm.

Ena/VASP proteins have not only been implicated in the global determination of migration speeds in different cell types [

Our initial observations of epithelial fish keratocytes revolved around cell shape and leading-edge morphology. Keratocytes have broad, flat lamellipodia that lack filopodia and have been generally described as having a characteristic fan or canoe shape [

EGFP-VASP delocalization from the leading edge of keratocytes after cytochalasin D treatment showed that Ena/VASP proteins might be binding at or near the barbed end of actin filaments, in agreement with a previous study in fibroblasts, which proposed that this mechanism protects actin filament barbed ends from capping [

A mathematical model helped us understand how the underlying actin network organization and dynamics were influenced by these VASP activities and how that could lead to distinct cellular morphologies

When keratocyte migration was examined as a function of cell morphology, we found that coherent, smooth cells migrated significantly faster than decoherent, rough cells, which demonstrates that cell morphology is tightly coupled to the speed of migrating keratocytes. These results are consistent with previous descriptions of keratocytes with fast protrusion rates as fan-shaped, whereas cells with slower protrusion rates were described as irregular or fibroblast-like in shape [

When we examined the directional component of velocity in keratocytes, we observed that rough, decoherent, wild-type keratocytes had increased curvature of trajectory compared to smooth, coherent, wild-type keratocytes. Unlike the smooth and regular leading edge of coherent keratocytes, the leading edge of decoherent cells can fluctuate widely during protrusion. In other words, different regions of the leading edge may protrude at different rates in an uncoordinated fashion. This phenomenon may be associated with greater frequency of cell turning, because either the whole left or right half of the lamellipodium would advance faster than the other half, effectively changing the average orientation of the leading edge and consequently changing the direction of migration. Thus, morphological variations manifest themselves during cell migration creating different behavioral patterns. We also found that Ena/VASP protein mislocalization led to increased trajectory curvature. This result is consistent with previous studies showing that intracellular

Epithelial fish keratocytes can rapidly migrate in a graceful gliding motion, all the while maintaining a relatively uniform and persistent shape. This migratory behavior requires the exquisite coordination of the intricate cellular migration machinery composed of three processes—protrusion, adhesion, and retraction—which are typically dissected separately. This work, in which we focused on the lamellipodial protrusive actin-based machinery resulting in the elongation and capping of actin filaments, is no exception. Future work, armed with broader and more detailed mathematical models, should strive to integrate our increasing understanding of these individual parts of the machinery and to understand how they interact to generate spatiotemporally coordinated cell migration in different cell types. We believe that this work, though limited in scope and susceptible to hidden variables and as-yet unknown molecular players, provides an example of how information from multiple spatial and organizational scales can be successfully brought together to explain part of a complex phenomenon.

Within the reductionist context of this work, quantitative analysis and mathematical modeling were crucial to the understanding of cell shape and motile behavior in terms of the molecular activity of Ena/VASP proteins. In view of the strong correlation between VASP enrichment at the leading edge and the quantitative morphological parameters analyzed in fixed cells, a more quantitative characterization of the morphology (shape, leading-edge curvature) of live migrating cells may be warranted in the future to provide more detailed insights about the dynamics and activity of Ena/VASP. It is important to note that even though our mathematical model was able to recapitulate and provide a self-consistent explanation of our quantitative observations of cell morphology, F-actin organization, and motile behavior, it was only able to do so in a qualitative manner. Ideally, future modeling will be able quantitatively bridge experimental data and theory. Some steps in this direction are discussed in

Overall, cell morphology represents a large-scale manifestation of underlying cytoskeletal organization and dynamics. Regulation and modulation of the actin cytoskeleton are likely to be major biological mechanisms affecting cell migration. Actin-remodeling proteins localize to propulsive structures in morphologically diverse cell types—neutrophils, fibroblasts, neurons, and intracellular bacterial pathogens—where they play crucial roles in the morphogenesis and maintenance of pseudopods, lamellipodia, filopodia, or bacterial comet tails, all of which inherently have different actin network organizations. Ena/VASP proteins, which are capable of enhancing the elongation of actin filaments by competing with capping protein for barbed-end binding, have emerged as important actin-remodeling proteins and strong candidates for the modulation of the underlying actin cytoskeleton that dictates cell morphology and migration.

Keratocytes were cultured from the scales of the Central American cichlid

Keratocytes were transfected using a small-volume electroporator for adherent cells as previously described [

Indirect immunofluorescence was performed using rabbit polyclonal anti-murine VASP (2010) and anti-murine EVL (1404) antibodies [

Indirect Arp2/3 immunofluorescence was performed using rabbit polyclonal anti-human Arp3 antibodies as described previously [

Images were acquired using an Axioplan microscope (Carl Zeiss Microimaging;

FP4-mito, AP4-mito, and mouse VASP in pMSCV [

Because individual keratocytes are heterogeneous in their responses to pharmacological agents, they were treated with 0.5 μM for 5 min; 0.8 μM for 2, 3, and 5 min; or 1.0 μM cytochalasin D (Sigma;

Time-lapse images were collected at 10-s intervals using a Nikon Diaphot-300 inverted microscope with a CCD camera (MicroMAX 512BFT; Princeton Instruments;

To compare immunolocalized Arp3 and F-actin along the leading edge and the enrichment of immunolocalized VASP (VASP peak-to-base ratios) across the leading edge of keratocytes, measurements were obtained using the “linescan” option in MetaMorph and background subtracted. F-actin and VASP distributions along the leading edge were calculated using the cell outline polygons as guides (see “cell shape analysis” section below). For each vertex point along the leading edge of a given cell, intensities were sampled at 20 points (∼2 μm) for F-actin and ten points for VASP (∼1 μm ranging from ∼0.3 μm outside to ∼0.7 μm inside the outlines) spaced one pixel apart along the inward normal and averaged.

Micropipettes were pulled using a P-92 Flaming-Brown micropipette puller (Sutter Instruments;

Cell morphology was measured by representing cell shapes as polygonal outlines and comparing those outlines with the PCA, as described [

This analysis determined that three principal “shape modes,” which are illustrated in

To calculate the roughness of each cell's leading edge, we used a measure that we refer to as “local leading-edge curvature.” Mathematically, the curvature of a function at a particular point is defined as the reciprocal of the radius of the circle that has the same tangent as the function at that point. A sharply bending curve will share a tangent with a small circle, and thus have a large curvature; in the limit, a straight line is tangent to an infinitely large circle and has zero curvature. The curvature of a parametric plane curve [^{2}+^{2})^{3/2}, where prime signifies the first derivative at point p and double prime the second derivative. We calculated the curvature at each of 90 points along the leading edge of the keratocyte outlines, using central-difference approximations to the derivatives. To determine the values of “local leading-edge curvature,” we summed the absolute values of the curvatures along the leading edge, and multiplied this by the length of the leading edge to account for the fact that smaller keratocytes will have higher total curvature due to their size alone. (Under this measure, a perfectly smooth semicircle sampled at 90 points would have a value of 90π [≈283]). Overall, rough leading edges have high local leading-edge curvature values and smooth leading edges have low values.

To examine the contours of migrating keratocytes (

The mean speeds per cell for each pair of transfected keratocyte populations (e.g., EGFP versus AP4-mito, EGFP versus FP4-mito, etc.) and for rough and smooth cells (e.g., EGFP rough versus EGFP smooth) were statistically compared using the Mann-Whitney test. Trajectories were evaluated by comparing mean angles between 2 and 45 μm (distance traveled) using the same test. The proportions of smooth and rough cells present in all combinations of populations of transfected keratocytes were compared using the two-sample test for binomial proportions [

Briefly, we modeled the densities of right- (left-) oriented growing barbed ends along the leading edge with functions b^{+}(^{−}(^{+}(^{−}(

According to the model assumptions, the following equations govern these densities:

We considered these equations on the leading edge: −

The meaning of these conditions, choice of the model parameters, and methods of solution of equations are thoroughly explained in

We described the leading-edge profile with the function

To investigate the local stability of the leading edge, we solved the system:
_{l} is the local density of barbed ends.

A keratocyte overexpressing EGFP-VASP transitions from the rough to the smooth leading-edge morphology as it migrates is shown. EGFP-VASP appears more prominent in focal adhesions (arrowheads) throughout the lamellipodium when the cell exhibits a rough leading edge (time: 0:00, 0:50). Sparse amounts of EGFP-VASP can be observed at dynamic protrusive leading-edge microregions (time: 0:00, 0:50) that eventually coalesce and persist in time and space to achieve the smooth morphology (time: 8:13). Time = min:s. Scale bar = 10 μm.

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Cell morphology was measured by representing cell shapes as polygonal outlines and comparing those outlines with the principal components analysis. Three primary modes of shape variability accounted for over 95% of all morphological variation of the 43 untreated and 27 cytochalasin-treated cells: one mode corresponding to approximately to cell size (left), one corresponding to aspect ratio (i.e., whether cells were shaped more like a wide canoe or a rounded D, middle), and one corresponding to the position of the cell body along the front to back direction of the cell (right). Of these modes, only the second mode—describing shapes ranging from canoe to D— correlated with VASP distribution. To quantify the shape of an individual cell, we measured its position along each mode in terms of standard deviations (σ) from the mean shape (μ).

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One extreme of the continuum contains cells with VASP enriched at the leading edge, canoe-shape, and smooth leading edges. High VASP peak-to-base ratios correspond to VASP enriched at the leading edge, high local leading-edge curvature values correspond to rough leading edges, and larger positive cell-shape values correspond to canoe shapes. The small dots on each plane are projections of the larger dots in the middle.

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Smooth, coherent keratocytes (top), which have EGFP-VASP enriched as a thin line at the leading edge, maintain their shape and migrate faster than rough, decoherent cells (bottom). The coherent keratocyte shown migrates at approximately twice the speed of the decoherent one

(8.6 MB MOV)

A glass micropipette, acting as a barrier, was lowered into the path of movement of a migrating, coherent keratocyte overexpressing EGFP-VASP. When the keratocyte reaches the barrier, the lamellipodium temporarily stops protruding forward, while EGFP-VASP becomes displaced from the edge of the region in contact with the barrier. When the micropipette barrier is removed (between 0:57 and 1:00), the leading edge of the lamellipodium immediately resumes protrusion and appears rough with several protruding microregions enriched in EGFP-VASP. Only 18 s after removal of the barrier, the keratocyte's original shape and uniform EGFP-VASP localization at the leading edge are restored. Time = min:s. Scale bar = 25 μm.

(9.5 MB MOV)

We thank Melanie Barzik for providing reagents used in this study. We also thank Kinneret Keren and Susanne M. Rafelski for critical reading of this manuscript and for helpful discussions.

actin-related protein

enhanced green fluorescent protein

enabled

Ena/VASP-like protein

filamentous actin

principal component analysis

vasodilator-stimulated phosphoprotein