Fig 1.
Dictyostelium has two types of memory.
a) Path of a wild-type cell during movement in buffer for 9 minutes; the arrows indicate the pseudopods. b) The pseudopods form a trajectory of the cell. The mean square displacement (<D2>) was calculated and analyzed using Eq (1), yielding a persistence of about 15 pseudopods. c) Splitting pseudopods are frequently extending alternatingly to the right and left, leading to a zig-zag trajectories with persistence. d) Cells frequently extend splitting pseudopods at the front ~30% of the cell, and rarely de novo pseudopods from the side or the rear of the cell. This reveals that the cell has an axis of polarity leading to persistence of direction. e) Schematic of a cell showing that the source of persistence is a combination of memory of the polarity axis enhancing pseudopods to be made in somewhere in the front, and memory of the position of previous pseudopod enhancing the next pseudopod to be made at that position in the front.
Fig 2.
Cells memorize the position of splitting pseudopods.
Analysis of four consecutive pseudopods of which P1 to P3 are three splitting pseudopods and P0 can be a splitting or a de novo pseudopod. a. Schematic for the analysis of pseudopod vectors with polar coordinates (results presented in panels b-e). All four pseudopods are rotated such that P1 directs at 0 degrees, and if needed reflected around the Y-axis such that P1 directs to the right relative to P0; finally P1 to P3 are transposed so that they start in the origin. Panels b-e: direction of P1 (black dot; 0 degrees by definition), P2 (blue dots) and P3 (green dots). The cosine of the angle between P1 and P3 (cos(ϕ1,3), yellow dots) indicates the persistence of splitting pseudopods. b, c. Wild-type, n = 322: P2 is extended at -55 ± 62 degrees and P3 at 2 ± 40 degrees relative to P1; cos(ϕ1,3) = 0.78. d, e. mutant SCAR-SD lacking positional memory, n = 155: P2 is extended at -17 ± 67 degrees and P3 at -1 ± 90 degrees relative to P1; cos(ϕ1,3) = 0.25. The data are means and SD.
Fig 3.
Autocorrelation of the number of extending pseudopods.
a. Number of extending pseudopods of polarized wild-type cells during movement for 15,400 s; a small window of 500 s is shown. b. Autocorrelation of the number of extending pseudopods in polarized wild-type cells during 15,400 s; numbers indicate the time period between the maxima. The autocorrelation time is 28.7± 1.4 s (mean and 95% CI; n = 8). c. Ratio of autocorrelation time/pseudopod interval. The autocorrelation time of mutants and strains were determined as in panel b. The pseudopod interval was derived from [15]. The data shown are means and 95% confidence intervals. ***, the data are significantly different from wild-type. All data, except SCAR-SD, are not significantly different from 2.0 (P>0.1). The data of ratio of SCAR-SD is not significantly different from 1.0 (P>0.1).
Fig 4.
Kinetics of positional memory, defined by cos(ϕ1,3).
The angle between P1 and P3 was measured for different growing times of pseudopod P1 (learning time t1 in panels a, b) and for different intervals between stop of P1 and start of P3 (forgetting time t2 in panels d, e). A small angle between pseudopods P1 and P3 (i.e. cos(ϕ1,3) close to 1.0) implies that pseudopods P1 and P3 are extended in the same direction. Panels b and e are logarithmic transformation of the data in which α = cos(ϕ1,3)t-t0 / cos(ϕ1,3)max. The kinetic constants for learning and forgetting were obtained by linear regression analysis; the data points represented by the black bullets in panels d and e are incorporated in the linear regression. See S1 Fig for a similar analysis using L/R bias instead of cos(ϕ1,3).
Table 1.
Memory of position and polarity axis in Dictyostelium mutants and other species.
Fig 5.
Cells memorize the polarity axis by pseudopod activity and sGC activity in the front.
a. Wild-type cells expressing LimE-GFP (detecting F-actin) and myosin II-RFP. A de novo pseudopod can generate a new polarity axis. b. Pseudopod activity in the front before and after the extension of a de novo pseudopod. Measured were the pseudopod frequency (in 1/s), pseudopod growth rate (in μm/s) and their product. Data are the means and SEM of 98 de novo pseudopods. ***, significantly different from the data value for all pseudopods at P<0.01; *, significant at P<0.05. c. Localization of sGC guanylyl cyclase. The left panel shows enrichment of sGC-GFP in the F-actin cortex of protrusion. This cortical localization is lost upon deletion of the N-terminus of sGC [29], or by addition of the F-actin polymerization inhibitor Latrunculin A (LatA). d. basal in vivo cGMP levels of gc-null cells expressing full length sGC or the N-terminal deletion mutant ΔN-sGC, and basal cGMP and cAMP levels of wild-type AX3 cells in the absence or presence of 10 μM LatA. Data are the means and SD of four determinations in triplicate. e. Localization of Rap1-GFP (using Ral-GDS-GFP and cytosolic-RFP [22]) and myosin II (with myosin II-GFP in cells under agar [33]). f. Fluorescent intensity of Ral-GDS-GFP minus cytosolic-RFP (Ψ) representing Rap1-GTP levels at the boundary of the cell (mean and SEM of 10 cells). Fluorescent intensity of myosin II-GFP in the cortex relative to the intensity in the cytosol (mean and SEM of 5 cells).
Fig 6.
Kinetics of signaling molecules in pseudopods of a new or a retracting polarity axis.
Wild type AX3 cells expressing different markers were analyzed. a. Cells begin to extend a de novo pseudopod at the side of the cell forming a new polarity axis. Time t = 0 is the start of the pseudopod. Indicated are the times at which the sensors for the indicated signaling molecules begin to increase or decrease at the place where the pseudopod later begins. Data are means and SEM of 8 determinations. b. Cells with two extending pseudopods retract one pseudopod. The extension of one pseudopod stops at time t = x and retraction begins at t = 0s. The value of x, is very variable, between 4 and 20 s, but in all cases F-actin declines about 3 s before the pseudopod stops. Data are means and SEM of 10 determinations. c. Images of a cell expressing LimE-GFP (detecting F-actin) and myosin-RFP that retracts the upper pseudopod. The yellow dot is at identical positions in the three images. The upper pseudopod begins retraction at 50s.
Fig 7.
Kinetics of memory of polarity axis.
Wild-type AX3 cells expressing Raf-RBD-GFP are moving in buffer. At t = 0 seconds the cells extend a de novo pseudopod, generating a NEW front. Pseudopod activity (seize and frequency) was measured in the New and Old front, as well as the time of retraction (T) of the pseudopod in the Old or the New front. Panels a show an example in which both the Old and New front exhibit pseudopod activity. Panels b show an example in which only the New front exhibits pseudopod activity. c. All 98 cases of a de novo pseudopod were analyzed for the retraction of either the Old or the New front. d. Detailed analysis of the subset of 28 cases in which only the New front exhibits pseudopod activity and the pseudopod in the Old front is retracted at time T. The experimental data were fitted to Eq (7) yielding a half-time of learning (25.7 ± 4.6 s) and forgetting (88 ± 43) of the polarity axis (optimal fit and 95% CI). The full line is the optimal fit, the dashed lines give the 95% confidence levels.
Fig 8.
Maintenance and adjustment of the polarity axis by pseudopods in the front.
a. angles between three pseudopods; a perfect inverse relationship implies that P1 and P3 are extended in a similar direction, irrespective of the direction of P2. The data were analyzed by linear and polynomial regression analysis, yielding y = -1.0027x, RSS = 4.07*105 and AICc1 = 4841 for linear regression with one parameter and y = 1.64*10−5*x3–1.0027x, RSS = 3.91*105 and AICc2 = 4832 for the polynomial fit with two parameters. The polynomial fit explains the data significantly better than the linear fit (P = 0.01). The quantity exp((AICc1 − AICc2)/2) = 90 indicates that the model with two parameters is 90 times as probable as the model with one parameter. The green area indicate the difference between the linear and polynomial fit, which reveals that P3 is not extended precisely in the direction of P1 if P2 is extended at a very large angle relative to P1; this difference (y = 1.64*10−5*x3) is indicated in panel c. Localization of active Rap1-GTP in a cell that extends a new pseudopod from the front at a large angle of 130 degrees to the left. The fluorescence intensity at the boundary is shown in panel d, showing that the midpoint of Rap1 activation changes by 22 degrees to the left. Panel e shows the change of midpoint of Rap activation as function of the change of pseudopod direction for 12 pseudopods as determined in panels c, d. the data points are mirror imaged; the red line shows the optimal polynomial fit with y = 0.89*10−5*x3. The results reveal that Rap1 is activated in the front half of the cell, and that this localization changes hardly thereby maintaining the direction of the polarity axis.
Fig 9.
Schematic and properties of short-term memory of position and long-term memory of polarity axis.
The extending pseudopod provides signals to two memory systems. Left part: at the position of the extending pseudopod SCAR becomes modified, which enhances the probability to start the next-next pseudopod at that local position. Right part: the extending pseudopod enhances guanylyl cyclase activity generating fast diffusing cGMP in the entire cell, which binds to GbpC and induces myosin filaments in the entire cell. The extending pseudopod also induces Rap1 activation that inhibits myosin filaments in the front of the cell. Since cGMP-binding to and dissociation from GbpC is slow, GbpC integrates information from ~10 successive pseudopods thereby generating a long-term memory of cell polarity. The Table summarizes the properties of memory of position and memory of polarity.