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First published online 22 August 2006
doi: 10.1242/jcs.03152

Journal of Cell Science 119, 3833-3844 (2006)
Published by The Company of Biologists 2006
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Dissection of amoeboid movement into two mechanically distinct modes

Kunito Yoshida1,* and Thierry Soldati1,2,{ddagger}

1 Department of Biological Sciences, Sir Alexander Fleming Building, Imperial College, South Kensington, London, SW7 2AZ, UK
2 Départment de Biochimie, Faculté des Sciences, Université de Genève, Sciences II, 30 quai Ernest Ansermet, CH-1211-Genève-4, Switzerland


Figure 1
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  		Fig. 1. Microscopy of live vegetative cells expressing GFP-ABD. Fluorescent images of GFP-ABD-expressing, vegetative wild-type (A-D) and myosin-II-null (E) cells in SB were captured sequentially with a CCD camera. (A and B are two excerpts from the same sequence. See supplementary material Movie 1.) Intercalated phase-contrast images are shown at t=20 seconds in A, 0 seconds in B, and 2 seconds in E. In A, every frame is shown from left to right. The arrowhead indicates a spherical bleb that formed suddenly; it was initially devoid of F-actin cortex but gradually acquired it. In B, every second frame is shown sequentially from left to right. (C) Higher magnification of the blebbing domain followed in B. The arrow indicates examples of blebs forming beside pre-existing or growing filopodia. The asterisk shows a detached cortical layer moving centripetally. (D) Kymograph obtained by scanning in the direction of the dotted arrow shown in C for the corresponding period. The vertical ticks on the time axis (t) are separated by 1 second. The arrow, arrowhead, and asterisk correspond to F-actin layers shown in B and C. (E) Every second frame is shown from left to right. Bars, 10 µm (A-C,E); 3 µm (D).

 

Figure 2
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  		Fig. 2. Visualization of the three-dimensional structure of the actin cortex. Confocal images of fixed wild type (A,B) and myosin-II-null cells (C,D) in SB stained with Alexa Fluor 568-phalloidin to visualize F-actin. (B,D) Z-sections along the dotted lines in A and C, respectively. Arrowheads in A and B indicate actin arcs that compartmentalize the protrusion. Bars, 5 µm.

 

Figure 3
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  		Fig. 3. Spatiotemporal mapping of pseudopod formation. (A) Sequence of fluorescent images of GFP-ABD-expressing, vegetative wild-type cells recorded at intervals of 250 ms and shown every 15 seconds. Bar, 10 µm. (B-E) Cell boundary activity of the cell in A was mapped in polar coordinates (left-right corresponding to 0-360 degrees) along the time axis (from top to bottom over 135 seconds). (B) Membrane velocity, (C) F-actin intensity and (D) radial distance from the centroid. (E) The same images as B-D, coloured in red, green, and blue, respectively were merged. Areas of the protruding sites are shown at higher magnification in supplementary material Fig. S2. To improve appearance of the structures, the original sequence was low-pass filtered at 1 Hz using a windowed-sinc filter (see http://rsb.info.nih.gov/ij/plugins/windowed-sinc-filter.html). Bleb formation was detected as bright areas in B and dark areas in C at the timing of emergence (resulting in red parts in E) as shown with the arrowheads in B, C and supplementary material Fig. S2. The arrows in A indicate persisting filopodia that also appear in D.

 

Figure 4
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  		Fig. 4. Microscopy of live chemotaxing cells expressing GFP-ABD. (A-F) Chemotaxing GFP-ABD-expressing cells developed for 8 hours in submerged conditions. (A,B) Fluorescence (top panel) and the corresponding phase-contrast (bottom panel) images at the indicated times. (C,D) Kymographs corresponding to A and B, respectively. Vertical streaks correspond to intercalated phase-contrast images taken every fifth second. The kymographs were aligned and overlaid with plots of the temporal change of centroid velocity calculated from the fluorescent images. Note that the peaks of centroid velocity coincide with bleb formation (arrowheads). A and C were imaged in SB, and B and D in high osmolarity buffer (HI). (C) Spans from -10 to 40 seconds in the sequence shown in A. (D) Spans from 15 to 65 seconds in the sequence shown in B. The arrowheads in A and C indicate a bleb in formation. The arrowheads in B and D indicate a filopodium in formation. (E,F) Higher magnifications of the leading edge of the cells presented in A and B at indicated times. Bars, 10 µm (A,B); 1 µm (C,D); 0.125 µm/second for the centroid velocity plots (C,D); 5 µm in (E,F).

 

Figure 5
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  		Fig. 5. The oscillatory nature of cell motility. Representative traces of growth rate against time for the cell area gained (red) and lost (blue) (A,B), and the centroid velocity against time (C,D) of vegetative wild-type (A,C) and myosin-II-null (B,D) cells expressing GFP. All cells were imaged in SB. (E) Cross-correlogram between the rates of gain-of-area and loss-of-area are shown for vegetative cells. Cross-correlation (Chatfield, 2003Go) was calculated with home-developed Perl scripts as the average for each cell population. For a cell sample i, it was defined as:

Formula
where {sigma} (V) indicates the standard deviation of V and Ti is the recording period of the sample i. Area around lag 0 in E is shown at higher magnification in F. Wild-type (WT; red and green) and myosin-II-null (myosin II-; blue and orange) cells in buffer without (SB; red and blue) and with (HI; green and orange) 100 mM sorbitol. The averages of correlation functions from 59 (red), 59 (green), 50 (blue) and 49 (orange) cells are shown. The lines of apparently varying width actually consist of vertical lines representing mean ± s.e.m.

 

Figure 6
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  		Fig. 6. Effects of buffer osmolarity on velocity of cell movement. The mean values of the rates of gain (A) and loss (B) of cell area, and the centroid velocities (C) are plotted as a function of the sorbitol concentration. Filled symbols, wild type; open symbols, myosin-II-null cells. Data from a slow strain of myosin-II-null cells are shown. Data of various lengths, from 43-149 cells for filled circles and 18-60 for open circles are shown. The error bars indicate the s.e.m. (D) Mean values of the rates of gain-of-area measured in buffers without (SB) or with (HI) 100 mM sorbitol, measured 30-60 minutes after application of 100 µM of blebbistatin (BLEB) or 0.2% DMSO (DMSO). WT and MII-indicate wild type and a fast strain of myosin-II-null cells, respectively. Data were normalized to the mean areas of the corresponding cell and then pooled for statistics (n=22-38 cells).

 

Figure 7
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  		Fig. 7. Effects of osmolarity and myosin II deficiency on directionality of cells during chemotaxis. Representative contour traces of chemotaxing cells at 5-second intervals are shown. (A) AX2 without sorbitol during 535 seconds. Bar, 10 µm. (B) AX2 with 100 mM sorbitol during 525 seconds. (C) A myosin-II-null cell without sorbitol during 465 seconds. (D) A myosin-II-null cell with 100 mM sorbitol during 995 seconds. The red dots at the upper right show the source of the chemoattractant, cAMP. (E) Effects of sorbitol on the velocities of chemotaxing cells. Centroid velocities of cells starved for 8-9 hours were assayed in the absence (random) or presence (chemotaxis) of a capillary filled with 200 µM cAMP. Values are means ± s.e.m. Effects of sorbitol were significant for wild-type cells without or with a cAMP source, but less significant for myosin-II-null cells with a cAMP source. At high osmolarity, the difference between wild-type and myosin-II-null cells in the presence of cAMP was insignificant. (F) For a cell i with the centroid located at a point C(t) at time t moving to a point C'(t+{tau}) after time period of {tau} in the gradient of chemoattractant emitted from the source placed at point N, the chemotaxis index was defined as the mean of cos{phi} weighted by |Figure 7|, with {phi} designating the angle between Figure 7 and Figure 7, i.e.

CI_|<|i|>|(|<|\tau|>|)=\frac|<||<|\sum_|<|t=0|>|^|<|T_|<|i|>|-|<|\tau|>||>||>||Figure 7|cos|<|\phi|>||>||<||<|\sum_|<|t=0|>|^|<|T_|<|i|>|-|<|\tau|>||>||>||Figure 7||>|.
The average function CI({tau}) was calculated with home-developed Perl scripts for a cell population, weighted by the data length Ti-{tau}. (G) Chemotaxis index shown as a function of time. Wild-type (WT; red and green) and myosin-II-null (MII-; blue and orange) cells in buffer without (SB; red and blue) or with (HI; green and orange) 100 mM sorbitol. The averages of the chemotaxis indices from 56 (red), 42 (green), 44 (blue), and 54 (orange) cells are shown. The line-width represents the means ± s.e.m.

 

Figure 8
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  		Fig. 8. Model of bleb mode and filopodia-lamellipodia mode motility. (A) At equilibrium, the membrane-cortex system is fully intact and no detachment has occurred. The cytoplasmic pressure is balanced by the pressure resulting from cortical tension. We can write the balance of forces across the cell membrane as:

Formula 4(1)

Formula 4(2)

Formula 6(3)
where P is the cytoplasmic pressure; Tc, cortical tension, Tm, membrane tension; {gamma}, membrane-cortex adhesion term; and R, radius of the spherical cell. The cytoplasmic pressure consists of two terms, {Delta}{Pi} the osmotic pressure across the membrane and the remainder Po a hydrostatic pressure purely due to contraction at {Delta}{Pi}=0. If {gamma} exceeds a threshold value {gamma}th, the membrane will detach from its supporting cortex and a bleb will form (B). This may be achieved either mechanically, through increase of P, or through decrease of {gamma}th due to some biochemical reaction that partially weakens or dissociates the bond. Detachment results in complete dissipation of {gamma} in the corresponding area, which generates a pressure gradient of cytoplasmic fluid across the cell and pushes the detached membrane (C). The initial extension rate would be expected to be proportional to P-2Tm/R={Delta}{Pi} + Po-2Tm/R, the differential osmotic pressure, and equal to 2{gamma}/R the lost adhesion term. In this model, we assume that the cell forms protrusions using energy stored in the equilibrium between inner pressure and cortical tension. Increase of milieu osmolarity would decrease the osmotic gradient, {Delta}{Pi}, and thereby decrease the cortical tension according to equations 1 and 3 above. The decrease in cytoplasmic pressure allows the opposite end of the cell to retract, resulting in net centroid translocation. (D) Finally, a new layer of actin cortex is regenerated and the equilibrium state is restored (E). (F) Myosin-II-null cells move by using a pushing force generated by actin polymerization, without membrane detachment.

 

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© The Company of Biologists Ltd 2006