Fig 1.
Basal pseudopod properties of polarized Dictyostelium cells.
(A) Images of wild-type AX3 cells with frame number (1 s per frame, 245 nm pixel size) and two extending pseudopods. P1 starts at frame 25, P2 starts at frame 36, P1 stops at frame 40 and P2 stops at frame 45. The arrow connects the tip of a pseudopod at start and stop, respectively. The bar is 5 μm. (B) The rate of the tip of 10 pseudopods in the direction of the arrow at different times before, during and after extension was recorded at higher temporal and spatial resolution (0.64 s per frame, 99 nm pixel size). The rate is presented as % of the average rate during extension, which varied between 0.37 and 0.66 μm/s for the 10 pseudopods. Data during START were aligned in time for the last time moment that the speed is below 50% (open circles), and data during STOP were aligned for the first time moment that the speed is below 50% (closed circles). Date in color are five individual pseudopods; data in black are means and SEM, with n = 10 pseudopods. (C) Histograms of the rates, growth times and sizes of 996 pseudopods. The size has the smallest variation and skew. (D) Histogram of time that cells extend simultaneously 0, 1, 2, 3 or 4 pseudopods; the total time is 15,356 seconds.
Table 1.
Pseudopod dynamics.
Fig 2.
The START of pseudopods is inhibited by other pseudopods.
In 622 cases out of 996 pseudopods from polarized cells, no other pseudopod was present at the moment these pseudopods stop. Investigated was how these “naive” cells start new pseudopods. (A) Cumulative number of started first pseudopods; the inset shows the probability to start a new pseudopod (PSTART). (B) Kinetic plot, analyzing the start of the first pseudopod (closed circles); time is seconds after stop of the previous pseudopod, cum is the cumulative number of cells that have started a new pseudopod at time t and total = 622. Data were fitted by linear regression with n = 14 time points, yielding and intercept with the time-axis of -0.17 ± 0.27 s and a rate of 0.140 ± 0.005 s-1 (optimal value and 95% confidence interval of the linear fit). The squared symbols show the kinetics at which these 622 cells with a first extending pseudopod will extend a second pseudopod (217 cases); time is seconds after start of the first pseudopod, cum is the cumulative number of cells that have started a second pseudopod and total is the number of the 622 cells that are still extending the first pseudopod at the time indicated. Linear regression yields an intercept with the time-axis of -0.28 ± 0.17 s and a rate of 0.040 ± 0.007 s-1. The triangle symbols show the kinetics at which these 217 cells with two extending pseudopod will extend a third pseudopod (31 cases); time is seconds after start of the second pseudopod, cum is the cumulative number of cells that have started a third pseudopod and total is the number of the 217 cells that are still extending the first and the second pseudopod at the time indicated. Linear regression yields an intercept with the time-axis of -0.66 ± 0.69 s and a still lower rate of 0.011 ± 0.001 s-1. The intercepts with the time-axes are statistically not significantly different from zero (t-test, P>0.1). (C) The probability to start a new pseudopod (PSTART) was calculated for the group of cells before they extend a pseudopod, during the period that they extend one pseudopod, and after they have extended a pseudopod. The results reveal that the probability is always ~0.14/s for cells having no other pseudopod (open circles), and always ~0.05/s for cells with one extending pseudopod, indicating that the low probability of START of a second pseudopod appears and disappears virtually immediately. See also S2 Fig in S1 File for additional experiments supporting this conclusion.
Fig 3.
Pseudopods STOP by local inhibition at the tip of that pseudopod.
(A) Growth time and size of pseudopods in polarized wild-type cells that at start have different number of other pseudopods; the data show the means and SEM; n = number of pseudopods as indicated. (B) Growth time and size of pseudopods in all 16 strains at different number of other pseudopods relative to cells without other extending pseudopods; the data show the means and SEM; n = number of strains as indicated. (C) Schematic of a cell with an extending pseudopod, and in colors the regions of interest for the start of the next pseudopod. (D) Kinetics of the next pseudopods that start at different distances from the tip of the previous pseudopod. For each time interval before and after the STOP of the current pseudopod the number of the next starting pseudopods was recorded, and their distance from the tip of the current pseudopod was measured. The data are presented for each time interval as the fraction of pseudopods starting at the indicated distance, with total number of starting pseudopods at that time interval as indicated by the number above the figure. Pseudopods that start between -11s and -5s are binned and shown at -8s, start between -5s and -2s are shown at -3.5s, start at -2s and -1s are shown at -1.5s; other data points are the pseudopods that start at the time shown.
Fig 4.
The STOP of pseudopods is regulated by time, size and rate.
(A) Cumulative number of pseudopods that have stopped at different times after start. (B) The probability that a pseudopod stops (PSTOP) is defined as the fraction of pseudopods that stop in a 1s time-interval divided by the pseudopods that have not yet stopped at the beginning of that time-interval. PSTOP is not constant as PSTART, but increases with the time of extension. (C) Kinetic plots of the same data as a function of time2; cum is the cumulative number of pseudopods that have stopped and total = 996. Linear regression with n = 21 time points yield intercept with the time2-axis of -3.33 ± 3.70 and slope of 0.00629 ± 0.00019 s-2 (optimal value and 95% confidence interval of the linear fit). (D) The growth time of a pseudopod is inversely related to the rate of extension; black dots are individual pseudopods, red symbols are means and SD of multiple pseudopods binned for rate intervals of 0.075 μm/s. (E) The size of pseudopods as function of the rate of extension. The data are the means and SEM of multiple pseudopods binned for a specific rate interval. The filled line for wild-type on agar (red symbols) represent the optimal fit of the model according to Eq 1. The blue symbols represent pseudopods of wild-type cells moving under agar; pseudopods stop prematurely, especially at higher rates (see Table 1 for parameter values).
Fig 5.
Number of extending pseudopods.
(A) Schematic of pseudopod extension as deduced from the analysis of START and STOP. Cn is a cell with n extending pseudopods. The formation of a pseudopod is given by the rate constant α, that is reduced A-fold by each extending pseudopod (see Fig 2). The termination of pseudopod extension is given by the macroscopic rate constant that is independent of the number of extending pseudopods (Fig 3A and 3B); a cell with e.g. three pseudopods has three possibilities to stop one of its pseudopods, giving
. (B) Prediction of the number of extending pseudopods using
= 2.0, and different values of A. (C) Experimental observations for polarized wild-type and two mutants. Equations S17 and S18 in S1 Text in S1 File were used to predict (panel B) or to fit experimental data (panel C); the optimal value and 95% confidence interval for the fitted values of
and A are given in S2 Table.
Fig 6.
Summary and unified model of pseudopod extension.
(A) Schematic of pseudopod extension for all stains and conditions. An excitable system triggers the START of pseudopod extension with rate constant α. Each extending pseudopod inhibits the start of a new pseudopod A-fold. The pseudopod extends at a rate v, thereby -with time t- reaching a larger size s. The STOP of the pseudopod is mediated by processes that depends on a combination of rate, time and size; together they represent a macroscopic rate constant of stopping . The relative contribution of rate, time and size to STOP is given for polarized Dictyostelium cells. Panels B and C present a physical model. (B) The strong polymerization of branched F-actin (bF-actin) induces a forward force; at the start of pseudopod extension, the force F0 is mediated by about 4000 bF-actin filament at the emerging tip (see S6 Fig in S1 File). (C) The experiments reveal that multiple counterforces contribute to pseudopod STOP; see text for details. Panels D-G presents the outcome of mutant analysis in Dictyostelium. (E) The extending pseudopod. In Dictyostelium a Ras-bF-actin-excitable system triggers pseudopod extension by activating Rac1 and the Scar complex, which induces Arp2/3-mediated actin nucleation and branching; scar-null cells stop prematurely. (F) Inhibition of new pseudopods. The cortex is a ~100 nm thick sheet under the plasma membrane consisting of parallel F-actin filaments (pF-actin), myosin filament and additional F-actin-binding proteins; formins stimulate and stabilize the pF-actin/myosin structure. Branched-F-actin is not easily formed in a strong cortex. Observations reveal that an extending pseudopod very fast generates an unknown global signal X that inhibits new pseudopods. This inhibition requires RacE and the pF-actin/formin/myosin cortex (cluster a in S7 Fig in S1 File). (G) The uropod. In Dictyostelium, a cGMP-based signaling pathway activates the interaction between myosin filaments and pF-actin filaments, leading to contraction of the uropod. Pseudopods that extend at a very high rate stop prematurely in cells with a very strong uropod (cluster b in S7 Fig in S1 File). In mammalian cells the three major components of the cell -pseudopod, cortex and uropod- play similar roles as in Dictyostelium, but the excitable system in panel E may have other small GTP-proteins such as CDC42, and the uropod in panel G is not regulated by cGMP but by the Rho-kinase Rock.