Figure 1.
Movies at a rate of 1 frame per second were recorded for Dictyostelium cells moving on a solid support in buffer. The program Quimp3 represents the cell outline using a polygon of ∼150 nodes, and then identifies extending convex protrusions as pseudopodia, described by the x,y,t coordinates of the start and end of their growing phase. The program also calculates the tangent to the surface at the position where the pseudopod started. These data were used to calculate for each pseudopod the size λ, the angle α relative to a specific point in space, the angle β relative to the tangent, and the angle φ relative to the previous pseudopod.
Table 1.
Observed and deduced parameters of wild type and mutant cells.
Figure 2.
A. Pseudopod extension was analyzed for the angle φ1,2 between current and next splitting pseudopod, yielding a bimodal von Mises distribution with mean φ = +/−55 degrees and SD = 28 degrees with 736 pseudopodia. B. The angle φ1,3 between current and next-next pseudopod exhibit a single distribution with mean φ = 2 degrees and SD = 42 degrees with 736 pseudopodia. Panel C shows that the angle between current and next pseudopod does not depend on the angle between current and previous pseudopod. D. Schematic of the alternating extension of Right/Left pseudopod splitting. E. The angle between current pseudopod and the next de novo pseudopod, demonstrating a nearly uniform distribution with 206 pseudopodia. Data in this figure were obtained from 3, 5 and 7h staved cells (see also Table 1).
Figure 3.
The trajectories of wild type and mutant cells (see Fig. S1) were recorded as described in the method section. A. The mean square displacement was determined for ∼20 cells (symbols). The data were fitted according Eq. 4 (lines) yielding the correlation factor of dispersion γobs as indicated in Table 1. B. The correlation factor of dispersion is plotted as a function of the fraction s of splitting pseudopodia, which was determined from the same movies. Symbols are closed circle for wild type (5 h starved in panel A; 1, 3, 5 and 7h starved in panel B); closed triangle for sgc/gca-null cells, diamond for pla2-null cells; square for sgc/pla2-null cells.
Figure 4.
The diagram shows the probabilities, angles and sizes of pairs of pseudopod extensions. Dictyostelium cells frequently extend alternating right/left splitting pseudopodia. Pseudopodia to the left are in red, to the right in blue, and the movement after two pseudopodia is in black. Indicated are the four possible movements with two splitting pseudopodia after the cell has made a right and left pseudopod. The probability for alternating right/left or left/right is (a), while the probability for consecutive right/right or left/left is (1-a), yielding the probabilities of the four pseudopod pairs. The angle between pseudopodia is φ.
Figure 5.
Predicted correlation factor of persistence and step size.
The trajectories of 100,000 cells were obtained by Monte Carlo simulation; the displacement was analyzed with Eq. 4 to obtain the correlation γMC and step size λ (in units of pseudopod size and thus dimensionless). Simulations were performed with the parameter values as indicated on the x-axis, while the other parameters had the following standard values λp = 1; s = 1; a = 1; φ = 55 degrees; σφ = 28 degrees. The data points denote the outcome of the Monte Carlo simulations, the lines are generated using Eq. 9, while the dotted line in panel C is generated using Eq. 8. The asterisks represent the predicted value for 5h starved Dictyostelium cells. A. The effect of angle φ and right/left bias a (a = 1, all pseudopodia alternating right/left; a = 0.5 right/left is random). B. The effect of the fraction of splitting pseudopodia (s). C. The effect of the variance of the angle between pseudopodia (σφ).
Figure 6.
Pseudopod formation and trajectories were recorded for 5h starved Dictyostelium cells; 8 cells were followed during 15 min. The directional displacement is the distance moved after n pseudopodia in the direction of the first pseudopod. Data points are the means of ∼120 measurements, the line is the outcome of Eq. 11 with pseudopod parameters as indicated in Table 1.
Figure 7.
Movement of a mutant with irregular shape.
Pseudopod formation and trajectories were recorded for 5h starved wild type and mutant ddia2-null cells. For the next pseudopod we measured the angle φ and distance d relative to the current pseudopod, the angle αt of the tangent relative to the current pseudopod and the angle β of the pseudopod relative to the tangent. A. The data show the means and SD measured for 312 and 289 pseudopodia from wild type and ddia2-null cells, respectively. The means are not significantly different between wild type and ddia2-null cells, but the SD σφ and σt are significantly larger for ddia2-null compared to wild type (Chi-square, P<0.0001); the SD σd and σβ are not significantly different. B. The shape parameter Ψ was determined at the moment of pseudopod extension. Bars show the frequency distributions for 312 wild type and 289 ddia2-null cells. Data points show σφ, the SD of φ. Linear regression analysis of all data point yields σφ. = 37.6Ψ+22.8; R2 = 0.965. C. Pictures showing three representative cells; numbers indicate the measured values of Ψ. Mutant ddia2-null has an irregular star-like shape, while wild-type cells are smoother and more spherical. Each diagram shows a cell with a pseudopod (dark grey area); the small lines indicate the direction of pseudopodia that emerge by pseudopod splitting perpendicular to the surface. Due to the irregular shape, pseudopodia extending by ddia2-null cells exhibit more angular variation. D. Displacement of wild type and ddia2-null cells during 15 minutes.