An adhesion-dependent switch between mechanisms that determine motile cell shape

Abstract

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.

Figure 1. Adhesion strength of the underlying surface affects keratocyte migration speed and shape.

(A) Phase contrast images of representative cells crawling at low (left), intermediate (center), and high (right) adhesion strengths (0.8, 4, and 500 µg/ml PLL-PEG-RGD, respectively). (B) Principal modes of shape variation, as determined by principal component analysis of aligned cell outlines, are shown for populations of cells at low (left), intermediate (center), and high (right) adhesion strengths (n>200 cells for each population). For each population of cells, the mean cell shape and shapes one and two standard deviations from the mean are shown for each shape mode. The variation accounted for by each mode is indicated. (C–F) Average cell speed (C), area (D), aspect ratio (E), and left-right asymmetry (F) are shown for live cells plated on surfaces coated with the indicated PLL-PEG-RGD concentrations. Error bars indicate standard error of the mean.

Figure 2. Oscillations in cell shape emerge as adhesion strength increases.

(A–B) Phase contrast images (A) and cell contours (B) from representative cells crawling at low (top), intermediate (middle), and high (bottom) adhesion strength. (C) Edge velocity maps for each cell shown in (A). The velocity of the cell boundary at each point, s, around the cell perimeter is plotted over time. Hot colors represent protrusion of the cell boundary, and cold colors represent retraction. (D) Velocity of the cell boundary at the center of the leading edge (s = 0) is plotted over time. The upper inset is the autocorrelation function for the edge velocity, and the lower inset is the power spectrum of the autocorrelation function. Velocity of the leading edge of the cell plated on the high adhesion strength surface oscillated with a period of 256 seconds. (E) The variance of the edge velocity at s = 0 is plotted versus the maximum power in the edge velocity power spectrum for cells plated on low (n = 8), intermediate (n = 8), and high (n = 11) adhesion strength surfaces. Squares represent the average values for each population; error bars indicate standard error of the mean.

Figure 3. Individual cells transition between adhesion-dependent migration regimes.

Cells crawling on micropatterned surfaces were imaged as they crossed boundaries between low and intermediate adhesion strength regions (A–F) and medium and high adhesion strength regions (G–L). (A,G) Phase images. The green overlay represents the region of medium (A) or high (G) adhesion strength. Edge velocity maps (B,H), cell velocity (C,I), area (D,J), and aspect ratio (E,K) are plotted over time for the cells shown in A and G. The dotted and dashed lines indicate when the leading and trailing edges crossed the boundaries, respectively. (F,L) Average cell speed, area, and aspect ratio are plotted for three cells before (left) and after (right) crawling from low to medium adhesion strength regions (F) or medium to high adhesion strength regions (L). Error bars indicate standard deviation for the individual cells.

Figure 4. General model for keratocyte shape.

(A) The expansion/retraction rate of the cell boundary is given by , where is the expansion/retraction rate, is the rate of actin polymerization, is the normal component of the centripetal bulk flow of the viscous F-actin network, and is the position along the cell boundary. In a migrating cell, the actin network, myosin, and adhesions must be organized such that is greater than at the front of the cell (s = 0), and is greater than in the cell rear (s = 100). The corners of the cell are defined by the point where (s = ±50). (B-D) Cell-substrate adhesions (green springs) oppose myosin-driven retrograde flow (blue arrows) of the actin network (red). When adhesion is strong, or contractile forces are low, the actin network is stationary with the respect to the underlying surface () and actin polymerization drives protrusion of the cell boundary (B). When adhesion is weak or contractile forces are high (C, D), the actin network moves with respect to the underlying surface (). If the rate of polymerization is equal to the rate of retrograde flow () then the cell boundary is stationary (C), but if actin polymerization is less than the rate of retrograde flow () the cell boundary retracts (D).

Figure 5. Simulated myosin and retrograde flow patterns.

Coupled myosin and flow distributions were computed on the fixed cell shapes for the indicated values for the adhesion drag coefficient, ζ, and cell speed, V_cell. Cell shape and V_cell were taken from the experimental data. (A) Myosin distributions. (B) Actin network retrograde flow. The direction and magnitude of local actin network movement with respect to the underlying substrate is indicated by color-coded arrows; hot colors correspond to faster flow. (C) Distributions of the computed normal component of the centripetal flow around the boundary (blue), polymerization rate (red) and net protrusion/retraction rate (black). The centripetal flow rates at the boundary were taken from the flow maps shown in (B). The actin polymerization rates are the rates required to maintain the input cell shape, given the simulated retrograde flow patterns. See Text S1 for a detailed description of the model parameters.

Figure 6. Adhesion strength affects myosin distribution patterns.

Images of cells plated on low (left), intermediate (center), and high (right) adhesion strength surfaces and labeled for actin with fluorescent phalloidin (A) and immunolabeled for myosin (B). (C) Overlays of the actin and myosin images; actin is pseudo-colored red, and myosin is pseudo-colored green. (D,E) Experimental (D) and simulated (E) myosin distributions, measured from the cell rear (point 0) to the cell front (point 100) on either side of the cell body, for cells plated on low (n = 31 cells), intermediate (n = 22 cells), or high (n = 20 cells) adhesion strength surfaces. Error bars indicate standard error of the mean.

Figure 7. Actin polymerization and retrograde flow rates decrease as adhesion strength increases.

(A) Images of keratocytes labeled with a low concentration of AlexaFluor546-phalloidin, plated on low (left), intermediate (center), and high (right) adhesion strength surfaces. (B,C) Actin network flow maps in the cell frame of reference (B), corresponding to actin polymerization, and in the lab frame of reference (C), corresponding to retrograde flow of the actin network, are shown for the cells shown in (A). (D) Average actin polymerization rates (red lines), actin retrograde flow rates (blue lines) measured in populations of cells plated on low (n = 36 cells), intermediate (n = 46 cells), and high (n = 25 cells) adhesion strength surfaces are plotted for each point around the cell perimeter. The gray lines are the effective cell boundary expansion/retraction rates calculated by adding the measured actin polymerization and retrograde flow rates. Error bars indicate standard error of the mean.

Figure 8. The balance between adhesion strength and myosin activity determines actin polymerization and retrograde flow rates and cell speed and shape.

(A,B) Representative flow maps in the cell frame of reference, corresponding to actin polymerization (A), and lab frame of reference, corresponding to retrograde flow (B), are shown for cells crawling at low (left), intermediate (center), and high (right) adhesion strength and treated with either 10 nM calyculin A (top), 10 µM blebbistatin (bottom), or no drug (middle). Average cell speed (C), area (D), and aspect ratio (E) for populations of cells treated with blebbistatin (blue lines) or calyculin A (orange lines) are shown for cells plated on surfaces coated with the indicated PLL-PEG-RGD concentrations. The data for control cells, shown in Figure 1, is re-plotted here for comparison (black lines). Error bars indicate standard error of the mean.

Figure 9. Simulated adhesion and actin filament distribution patterns.

Coupled adhesions and actin distributions were computed from the actin network flow patterns shown in Figure 5 for low (left), medium (center) and high (right) adhesion strengths. (A) Simulated adhesion distributions. (B) Simulated F-actin distributions. (C) Distributions of the computed adhesion (green) and F-actin (red) densities around the cell perimeter. Units are non-dimensionalized (n.d.). See Text S1 for simulation parameters.

Figure 10. Large, elongated adhesions spatially correlate with a reduction in branched actin network density.

(A,B) Images of cells immunolabeled for vinculin (A) and labeled for actin with fluorescent phalloidin (B). (C) Average actin intensity (red line) and adhesion area (green line) are plotted for points along the cell perimeter for cells plated on low (n = 176 cells), medium (n = 136 cells), and high (n = 179 cells) adhesion strength surfaces. Actin intensities are normalized such that the mean intensity for each cell is equal to 1. Error bars indicate standard error of the mean.

Figure 11. Dynamical simulations of cell shape for different adhesion drag coefficents recapitulate experimentally observed differences in cell shape.

Cell shape and actin network flow were simulated using an iteration procedure (see Text S1). Cell shape and actin flow at the cell boundary are shown for the input shape (A), the stable shape that evolved at low adhesion strength (B; ζ = 0.04 nNs/µm⁴), and the stable shape that evolved at intermediate adhesion strength (C; ζ  = 0.2 nNs/µm⁴).