The cell expressing GFP-actin has been recorded by spinning-disk microscopy, focusing on the substrate-attached cell surface. In the course of the recording, a second cell moved in from the bottom and contacted the cell of interest (416–592 s frames). Time after the first frame is indicated in seconds. Bar, 10 μm.

Left panels (A-D) show TIRF images of cells not treated with latrunculin A, which migrate normally on a glass surface; right panels (E–H) show similar images of cells that form waves during the recovery of actin polymerization. (A) Three stages of a cell moving toward the top of the panels with the front and tail regions in contact with the substrate. The numbers indicate seconds. The red and green labels are dispersed throughout the cell, with a gradual enrichment of the red Arp2/3 label during leading edge protrusion. (B) A moving cell with discrete patches of actin. (C) Correlation analysis of intensity pairings in the mRFP and GFP channels of the cell shown in (B). The increase in the density of pixels is color coded from purple to white. Most fluorescence intensities in the mRFP and GFP channels are closely correlated, indicating that the two labels are mixed on the level of microscopic resolution. Only a small fraction of paired pixels is dispersed in a region of high mRFP intensity. (D) The segmentation of the correlogram obtained from the cell in (B). Pairs of fluorescence intensities within the framed regions are projected onto the gray image of the cell (recorded in the GFP channel). Colors conform to those of the frames in (C). Left panel: low fluorescence intensities within the white frame are derived from the extracellular space, showing the shape of the cell on a white background. Middle panel: the majority of fluorescence pairs that are framed in blue are distributed over almost the entire cell surface. Right panel: the scarcely populated area of high mRFP and low GFP intensities within the yellow frame is derived from actin patches, most of them known to be engaged in clathrin-dependent endocytosis (Heinrich et al., 2008). (E) Cell showing a sharp contrast of labeling at a wave. Fluorescence intensities scanned along the line in the left panel are plotted in the right panel. High fluorescence intensities of GFP-cortexillin I (green) and low intensities of mRFP-ARPC1 (red) throughout the external area contrast with high mRFP-ARPC1 and low GFP-cortexillin I intensities along the wave and within the inner area. (F) Wave-forming cell subjected to correlation analysis in parallel to the cell in (B). (G) The split correlation indicates two populations of pixels that are distinguished by the ratios of mRFP to GFP. (H) Segmentation of the correlogram from the wave-forming cell shown in (F). Left panel: low intensities derived from the extracellular space provide a negative image of the cell on a white ground. Middle panel: the blue area shows that high intensities of GFP fluorescence are found exclusively within the external area. Right panel: yellow color indicates that pairs of high mRFP and low GFP intensities are concentrated at the wave and within the inner area. Scale bars, 5 μm.

This cell is labeled with GFP-cortexillin I (green) and mRFP-ARPC1 (red) as the cells shown in Figs. 34. (A) Frames of the time series illustrating reciprocal changes in shape and size of the inner areas dominated by the Arp2/3 complex and the external area enriched in cortexillin I. Time is indicated in seconds after the first frame in (B) to (D).The crossing lines I and II correspond to the scan coordinates of (B) and the numbers added to the scans in the first frame indicate sites where the temporal evolution of phase transitions in the four panels of (D) was probed. The entire sequence is documented in Supplement Material Movies 4 and 5. Bar, 5 μm.(B) Kymographs showing space-time dynamics along the line scans I and II in (A). Dotted lines correspond to positions 1–4 in (A) and (D). (C) Three-dimensional representation of space-time patterns. The cell is viewed from top of the frames in (A), the time axis corresponds to the one in (B). Left panel: merged image showing the mRFP-ARPC1 label as a mesh in red superimposed on the GFP-cortexillin I label surface-rendered in green. Right panel: cell shape obtained by lowering the threshold in the mRFP channel below the cytoplasmic background. (D) Temporal patterns of phase transitions recorded in the GFP-cortexillin I channel, the peaks corresponding to green areas in (A) and (B). The following patterns are illustrated: quasiperiodic dynamics (panel 1 at the crossing point of the line scans); regular periodicity (panel 2); irregular pattern at the border of two alternating zones of phase transitions (panel 3); retraction at the peripheral region of the cell after transition to external area (arrowheads in panel 4). As a result of retraction, substrate surface is exposed, as indicated by the fall of fluorescence intensity to 0.3 units, the level of extracellular background. rf denotes retraction fibers lagged behind on the substrate.

The cell is labeled as in Figs. 6C, 6D with mRFP-LimEΔ (red) and GFP-clathrin light chain (green). (A) Overview of wave initiation and propagation. Arrowheads point to two CCSs at the back of a wave (200 s frame), which increase in fluorescence intensity after the wave has passed (210 s frame). (B) Zoom into the upper part of the cell during the phase of fluctuating and propagating actin structures. These structures are often crescent-shaped and finally condense into inner area surrounded by a stable wave. (C) A primordial wave structure that originates from an actin patch not linked to a CCS; it subsequently expands and vanishes. (D) A straying actin cloud left over from an internalized stationary CCS (arrowhead) and finally fading out. (E) Sequence showing a stationary CCS (arrowhead) entrapped in the wave propagating toward the left. The entire sequence is shown in Supplement Material Movie 8. The numbers indicate seconds after the first frame in (A). Bars, 5 μm in (A) and (B); 2 μm in (C)–(E). (F) CCS displacement from the membrane at the front of waves. In four time series the decline of fluorescence in a CCS (green) was measured simultaneously with the increase in actin label that marks the wave front (yellow/red). The inset shows color coding of the pairs of measurements. Fluorescence intensities were determined in a square of 0.43 μm² around a CCS and normalized by setting the highest value in each curve to 1. The time courses were synchronized using the actin peak as the reference point.

In control cells of D. discoideum (A) and wave-forming cells recovering from actin depolymerization (B–F) filamentous actin was labeled with LimEΔ-GFP and visualized by TIRF microscopy. (A) Two control cells showing the basal actin network and dense accumulations of actin at leading edges. (B) Wave-forming cell showing outside the wave a loose actin network, and circumscribed by the wave an area occupied by dense actin assemblies. (C) Profile of fluorescence intensities in arbitrary units along the scan indicated by a red line in (B). (D–F) Actin structure inside and outside a wave. Full dynamic range of the images acquired using a 14-bit camera cannot be presented in an 8-bit print. Therefore, the same recording is shown in three different representations: with the full dynamic range compressed to 8-bit to discriminate structures in the high intensity range (D); with high intensities being white to visualize the lower intensity range (E); and with the two-dimensional distribution of fluorescence intensities represented by a customized color look-up table of the 0–10,000 gray scale (F). Bars, 5 μm.

(A) Frames of an image series showing two transitions from the wave and inner area colored in red to the green decorated external area. Time is indicated in seconds after the first frame in (B) and (C).The first transition starts in the middle of the cell and extends toward the bottom of the frames (30–56 s). The second transition begins on top and expands at the expense of a retracting wave (198–224 s). The two crossing lines demarcate the scanning coordinates in (B), the numbered positions 1–3 the sites selected for plotting temporal patterns of phase transitions in (C). The whole sequence is shown in Supplement Material Movie 3. Bar, 5 μm. (B) Kymograph presentations illustrating the space-time dynamics along scans I and II in (A). At the rectangles a–f, velocities of wave propagation were estimated. Positions 1–3 are the same as in (A), and the lengths of dotted lines correspond to the spans of time in the panels of (C). (C) Phase transitions at three distinguished positions of the wave pattern (ROIs), as outlined in the text.

(A) and (B) sorting out of myosin-II from the inner area. Waves are recognized by the mRFP-LimEΔ label for actin (red), myosin-II filaments are visualized by GFP-tagged myosin-II heavy chains (green). (C) and (D) internalization of clathrin-coated structures viewed in TIRF images. Double-labeling with mRFP-LimEΔ (red) and GFP-clathrin light chains (green) reveals an enrichment of bright clathrin-coated structures (CCSs) in the external area. In (C), actin-associated internalization of three CCSs in the external area is shown (arrowheads). Most of the CCSs in the inner area contrast with those in the external area by their faint fluorescence. Displacement of CCSs from the membrane at the front of a wave is depicted in (D) (open and closed arrowheads). Bars, 5 μm.

The analysis is based on fluorescence intensities recorded in the mRFP-LimEΔ channel of the image series shown in Fig. 7 and Supplement Material Movie 8. (A) Three-dimensional representation of spatio-temporal patterns. The time axis from top to bottom comprises 1170 s. Left panel: surface rendering of the actin wave. The threshold of fluorescence intensities has been adjusted such that the external area within the cell is abrogated. On top, actin fluctuations preceding the evolution of a closed, circulating wave are depicted. Right panel: representation of the cell envelop, showing protrusions that correlate with the underlying actin wave. For this presentation, the threshold has been kept below the fluorescence intensity in the cytoplasm. (B) Two stages of wave propagation illustrating the measurement of persistence in the wave and inner state versus persistence in the external state. Phase transitions are probed at seven diametrical positions. For example, at position 1 the wave entered in the left panel and quit in the right panel recorded 155 s later. Arrows on top of the wave indicate the direction of its propagation. Bar, 5 μm. (C) Phase transitions at the seven positions indicated in (B), separated by 1.2 μm from the other. Closed bars demarcate persistence in the wave and inner state, open bars persistence in the external state. Time in (B) and (C) is given in seconds after the first frame of Fig. 7A. (D) Histograms summarizing the measured lengths of time at the seven positions. From left to right: period lengths from entry of one wave to entry of the next wave (n=19); time of persistence in the state of wave and inner area (n=26); and time of persistence in the external state (n=19).