Distribution of traction forces associated with shape changes during amoeboid cell migration

Abstract

Amoeboid motility results from the cyclic repetition of shape changes leading to periodic oscillations of the cell length (motility cycle). We analyze the dominant modes of shape change and their association to the traction forces exerted on the substrate using Principal Component Analysis (PCA) of time-lapse measurements of cell shape and traction forces in migrating Dictyostelium cells. Using wild-type cells (wt) as reference, we investigated Myosin II activity by studying Myosin II heavy chain null cells (mhcA-) and Myosin II essential light chain null cells (mlcE-). We found that wt, mlcE-and mhcA- cells utilize similar modes of shape changes during their motility cycle, although these shape changes are implemented at a slower pace in Myosin II null mutants. The number of dominant modes of shape changes is surprisingly few with only four modes accounting for 75% of the variance in all cases. The three principal shape modes are dilation/elongation, bending, and bulging of the front/back. The second mode, resulting from sideways protrusion/retraction, is associated to lateral asymmetries in the cell traction forces, and is significantly less important in mhcA- cells. These results indicate that the mechanical cycle of traction stresses and cell shape changes remains remarkably similar for all cell lines but is slowed down when myosin function is lost, probably due to a reduced control on the spatial organization of the traction stresses.

Fig. 1.

Illustration of the different stages of the motility cycle of an amoeboid cell , adapted from [1]

Figure 2.

(a) Example of the temporal evolution of the major cell semiaxis, a (blue) and the strain energy, U_s (red) for a wt cell. The strain enegy, U_s, represents the work the cell needs to exert to deform the substrate. (b) Auto-correlation of the strain energy, R_UsUs (red); and cross-correlation between cell length and strain energy, R_LUs (black); as a function of the time separation. (c) Histogram of the correlation coefficient between the strain energy U_s and the length of the cell L for wt (blue, N=31 cells), mhcA- (red, N=27 cells) and mlcE- (green, N=14 ells) cells.

Figure 3.

Scatter plot ofthe average velocity of N = 86 chemotaxing Dictyostelium cells versus the period of their motility cycle. The ata points come from five different cell lines: N = 25 wt cells (blue squares), N = 21 mhcA-cells (red triangles), N = 38 mlcE- cells (green circles), and N = 2 talA- cells (cyan triangles). The dashed magenta hyperbola (V = L/T) is a least square fit to the data, yielding L=15.7 µm.The V – T plane has been divided into tiles that have been colored according to the number of cells whose speed and motility period lie within each tile. Darker tiles contain more cells, as indicated in the color. The correlation coefficient between V and 1/T is 0.71 (p=10⁻¹⁴).

Figure 4.

Representation of the steps of the algorithm used to calculate the phase averages. (a) After the major semiaxis of the cell, a(t), is recorded for every frame, the peaks and valleys of each time history are identified. Panel (a) shows the time evolution of the semiaxis of a wt cell (blue line) and the determined location of the peaks and valleys of that time evolution. Panel (b) shows the output of the algorithm for the automatic dissection of the motility cycle into stages: protrusion (blue), contraction (red), retraction (black) and relaxation (green).

Figure 5.

PCA of the shape and traction forces of a migrating wt Dictyostelium cell. (a): average shape and traction forces. The white contour indicates the contour of the cell. The color contours indicate the magnitude of the stresses and the arrows indicate their direction. (b)-(e): four most dominant shape modes patterns for positive (top) and negative (bottom) values of the weight factor. The bar plots in the lower panels show the distribution of instantaneous weight factors for this cell during the whole time history of the cell (yellow bars) and during each stage of the motility cycle (color curves). For all panels “F” is the front of the cell and “B” is the back of the cell.

Figure 6.

PCA of the shape and traction forces of a migration mhcA-Dictyostelium cell

Figure 7.

PCA of the shape and traction forces of a migrating mlcE-Dictyostelium cell.

Figure 8:

Box plots of the percentage of cell shape variance associated to each of the four principal modes for wt (blue, N=23 cells), mhcA-(red, N =22 cells) and mlcE- (green, N=15). (a) during the overall motion of the cells; (b) during protrusion; (c) during contraction; (d) during retraction; (e), during relaxation. The cell shape variance contained in each mode is determined from the histograms of the weight factors (examples of those are presented for wt , mhcA- and mlcE-cells in Figures 5–7).