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Myosin II controls cellular branching morphogenesis and migration in three dimensions by minimizing cell-surface curvature

Abstract

In many cases, cell function is intimately linked to cell shape control. We used endothelial cell branching morphogenesis as a model to understand the role of myosin II in shape control of invasive cells migrating in 3D collagen gels. We applied principles of differential geometry and mathematical morphology to 3D image sets to parameterize cell branch structure and local cell-surface curvature. We find that Rho/ROCK-stimulated myosin II contractility minimizes cell-scale branching by recognizing and minimizing local cell-surface curvature. Using microfabrication to constrain cell shape identifies a positive feedback mechanism in which low curvature stabilizes myosin II cortical association, where it acts to maintain minimal curvature. The feedback between regulation of myosin II by curvature and control of curvature by myosin II drives cycles of localized cortical myosin II assembly and disassembly. These cycles in turn mediate alternating phases of directionally biased branch initiation and retraction to guide 3D cell migration.

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Figure 1: Quantification of cell morphological skeleton shows that myosin II limits branch complexity in three dimensions.
Figure 2: Myosin II regulates cell-surface curvature locally.
Figure 3: Cortical myosin II associates with minimal surface curvature.
Figure 4: Externally imposed local curvature modulates myosin IIA localization to the cortex.
Figure 5: Curvature-dependent myosin II association with the cell cortex is independent of myosin II motor activity.
Figure 6: Myosin II dynamically associates with the cortex to control cycles of AEC branching and movement by local minimization of surface curvature to guide cell migration.
Figure 7: Myosin II biases branch orientation in the direction of migration and shows differential association with inner high-curvature and outer low-curvature saddles at a branch base.

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Acknowledgements

This work was initiated as a collaborative effort between R.S.F. and G.D. (NIH R21 CA124990). H.E. and G.D. are supported by NIH R01 GM090317. R.S.F., R.S.A., K.A.M. and C.M.W. are supported by the NHLBI Division of Intramural Research.

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Authors and Affiliations

Authors

Contributions

H.E., R.S.F., C.M.W. and G.D. designed experiments and wrote the manuscript. R.S.F. performed all imaging and FRAP experiments. H.E. designed, implemented and applied analysis software. R.S.A. provided transgenic mice. R.S.F., K.A.M., R.A.D., L.G. and C.S.C. performed microfabricated coffin experiments.

Corresponding authors

Correspondence to Robert S. Fischer, Clare M. Waterman or Gaudenz Danuser.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Surface enhanced segmentation of membrane-labeled cells.

(A) Raw membrane label fluorescence image and (B) Surface filtered image showing a cross-section of one filter kernel as inset. Bar equals 10 μm. (C) Thresholded surface filter response. The surface filter enhances the weak contrast of small dim features (arrow). Inset: variations in the surface labeling leads to holes in the segmented filter response (D,E) Two–stage intensity thresholding first determines foreground voxels (D), and then a high-intensity population within the foreground (E). (F) The union of the thresholded surface filter response and thresholded intensity image gives the initial segmentation of the cell volume. Inset: intensity thresholding provides complementary information to the surface filtering. (G) Morphological post-processing of the initial segmentation to remove features in the background and improve robustness of the cell-surface representation. (H) A plot of fold-intensity over background as a function of distance from the segmented cell surface. Green line is for myosin IIB-GFP, blue line is for membrane stain (see methods). Negative numbers indicate region outside of the segmented volume of the cell. (I) Visual inspection of the raw image fluorescence (gray) with the segmentation (red) superimposed allow validation of the segmentation. XY, XZ, and YZ panels are shown to illustrate all views.

Supplementary Figure 2 Determination of local curvature at the cell surface.

(AF) The segmented voxels representing the cell surface (A) are first smoothed (B) and then an isosurface is determined (C), along with the normal vectors to the surface (D). The surface curvature at each isosurface mesh face is calculated (E) followed by local averaging (F). (G) Surface segmentation and mean curvature validation of imaged microspheres. Fluorescent microspheres of 6 μm (top) and 10 μm (bottom) diameter beads were imaged and segmented as described for cells, and local mean surface curvature was deteremined. (H) Distributions of intensity percentiles as a function of curvature on bead samples. Solid line equals mean value, dashed line indicates 95% confidence limits about the mean from n = 3 beads. (I) Probability distributions of measured local curvature for 10 μm (red) and 6 μm (blue) beads. Note that the dertermined peaks correspond tightly to the known radii of curvature of imaged beads. Solid lines indicate mean from n = 3 beads each, with shaded area around lines indicating ±1.96 SEM. (J) Simulated z-stretched PSFs (inset) were convolved with a simluated test image to test for potential artifacts in segmentation on imaging geometry. (K) shows correlation of depth-normalized intensity versus maximal absolute principle curvature. In the central 90 percentile of intensity ranges, the correlation is flat, indicating that no bias is derived from an extended z-stretch on segemted. (L) Even with a simulated test image of known geometry and simulated z-stretched PSF, only a slight bias is introduced (red lines), with a slight positive slope when compared with the simulated intensity (blue lines). When this is corrected by depth-normalization, the bias is reduced (green lines). In H,K and M dashed lines indicate boot-strapped 95% confidence intervals and in K and M solid lines indicate means from n = 10 simulations each.

Supplementary Figure 3

(A,B) Surface points in control (A) and blebbistatin (B) treated cells can be classified into different categories (coloured highlights) by thresholding the Mean and Gaussian curvature. (C,D). This permits comparison of the fraction of surface mesh triangles in each category between experimental conditions (Fig. 1). (EH) Local surface curvature versus F-actin at the cortex. (E) 2D histogram of maximum absolute curvature versus F-actin intensity via phalloidin stain for an example cell (shown in F). The colours represent log10 of the surface points counted, as in Fig. 3. Green box indicates region of voxels selected with a given range of curvature and F-actin intensity. These are then mapped back to the cell surface (F, green). Similarly, a higher range of F-actin intensities at a higher range of curvature values (G) can be mapped onto the surface (H, green), highlighting predominantly tip structures.

Supplementary Figure 4 Artifacts in surface intensity sampling due to cell geometry and depth-dependent fluorescence variation.

(A) A simulated cell image in which intensity varies only with the distance from the cell surface but is uniform along the surface shows correlation between curvature and intensity (B, blue). Inset, red: Illustration of sampling sphere. (C) The correlation is due to variation in effective sample depth with curvature. Inset: cartoon to illustrate that the effective mean sample depth varies with curvature. Cell is shown in red, sampling sphere in blue. Different cell curvatures give different sample geometries (green, compare top and bottom) n = 10 simulations. (D) Similar depth variation is seen in experimental data. (E) Depth normalization (see Supplementary Information ‘Curvature and Image Intensity Correlation’) removes systematic intensity variation with depth in experimental images, but when applied to simulated image some artifact remains (B, red) due to variation in sample size with curvature. n = 10 simulations. (F). (G) An image with only noise shows the same correlation between intensity and curvature (H), and a correlation between intensity and sample size (I). A random signal with spatial autocorrelation of σAC = 1 (J) shows diminished artifactual correlation (K), which decreases further with σAC = 2 (L). Green vertical lines in (H,K,L) indicate the percentile levels of image intensities below/above which the surface curvature and intensity display a significant correlation, for example, the curvature values for a small range of particular intensity values deviate significantly from the mean surface curvature value over the entire cell. (M) Applying depth normalization to the experimental data only alters the observed correlations at very low intensities, that is, below the 10th percentile. In B,H,I,K,L and M dashed lines indicate boot-strapped 95% confidence intervals and solid lines indicate means from n = 10 simulations each.

Supplementary Figure 5 Membrane localized Td-Tomato-CAAX does not show curvature-dependence in cells confined in agarose chambers.

Endothelial cells confined in agarose coffins were imaged and registered to obtain average positional intensity, as described in main text and Methods. (A) Normalized mean intensity of GFP-myosin IIA (green), Td-Tomato-CAAX (purple) and calculated mean curvature as a function of distance along the confined borders of cells as shown in Fig. 4. CAAX signal shows some fluctuations, but are not correlated with curvature. (B) Probability distribution of mean curvature versus mean Td-Tomato-CAAX for all points along confined cell boundaries. n = 6 cells, 95126 points. Spearman’s ρ = −0.093, p = 8.8 × 10−164. Solid white line indicates mean and dashed lines indicate bootstrapped 95% confidence intervals.

Supplementary Figure 6 Inhibition of rho-ROCK or myosin II activity increases cell branch complexity but has no effect on myosin II localization to the cortex.

(A) Cells were treated with blebbistatin, Y-27632, or C-3 and branch path complexity determined as described in Fig. 1. Note control and blebbistatin data is re-plotted from Fig. 1 here for comparison. (B) Comparison of drug treatments or mutations (R702C) on cortical localization of myosin IIA (left) compared to myosin IIB (right). Plot shows mean curvature as a function of myosin IIA or IIB intensity percentile. Solid lines indicate mean and dashed lines indicate bootstrapped 95% confidence intervals. (C) An AEC expressing myosin IIA-GFP (green) in a 3D collagen gel was fixed and phospho-serine-19 myosin II regulatory light chain was immunolocalized (purple). Maximal intensity projection of a 3D reconstruction, inset: Co-localization plot of fluorescence intensities. Bar equals 10 μm. (DF) Computation of a cell center reference that is robust against cell morphological variations. (D) The Euclidean distance transform (blue) measures distance from the cell surface (grey). (E) The maximum of the distance transform (yellow) defines the centermost point in the cell volume (F), which deviates significantly from the actual centroid (blue). (G) Autocorrelation of cell center speed over time (blue line). Dashed line shows 99% confidence bounds. N = 8 cells for 240 time points.

Supplementary Figure 7 Model of myosin II mini-filament assembly onto cortical actin patches of different curvature.

Myosin II mini-filaments form stiff 300 nm rods, with bouquets of heads that extend an additional 40–50 nm on either side of the rod, giving a total length of nearly 400 nm (ref. 13). Given an isotropic meshwork of actin filaments (green) at the cortex, the maximal engagement of heads at each end may occur in regions of minimal curvature (A). For simplicity, consider alteration of curvature along a single axis. As the cortex and membrane curve concavely (B), the optimal orientation of the myosin minifilament for full head engagement is along the axis of least curvature. Intriguingly, in a pseudopodial extension this axis corresponds to the longitudinal axis and aligns myosin minifilaments with the direction pseudopod retraction. If the curvature of the cortex is convex (C), optimal head engagement will fail only as the curvature becomes higher than will allow both head bouquets to access the cortex equally. Here again, myosin minifilament orientation along the axis of lowest curvature allows maximal head engagement (D). Consistent with this, recent simulation data support the notion that myosin-II minifilaments can rotate in the cortex to maximally engage and generate stress30. Such limitations on a >300 nm filament would effectively prevent maximal engagement of heads in a tip structure of similar size (E). In the cell, these examples may be multiplied over larger curvature scales as groups of myosin II minifilaments assemble on to the cortex in larger macromolecular assemblies31.

Supplementary information

Supplementary Information

Supplementary Information (PDF 3701 kb)

Morphology of AEC migrating in a 3D collagen gel.

3D z-stacks of AECs expressing TdTm-CAAX were acquired at 10 minute intervals using a spinning disk confocal microscope. Shown is maximum intensity projection reconstruction. Grid scale: Major tick marks, 10 μm. Total elapsed time shown at lower right in min. (MOV 953 kb)

Thinning-based skeletonization of AEC surface to determine morphological skeleton.

First frame: rendering of the segmented surface. Subsequent frames show successive rounds of computational thinning to achieve the morphological skeleton. Frame size is 130 μm lateral × 65 μm axial. (MOV 197 kb)

Curvature category mapping on the surface of a control cell.

Segmented surface of a control cell colorized with curvature categories as described in Fig. 1 and Supplementary Fig. 2. Rotation is around the z-axis of imaging. Total frame size is 100 μm × 63 μm. (MOV 2016 kb)

Curvature category mapping on the surface of a cell treated with 20 μM blebbistatin, with curvature categories as described in Fig. 1 and Supplementary Fig. 2.

Rotation is about an axis 70 degrees off of the z-axis, to show sides of thin branches. Total frame size is 95 μm × 60 μm. (MOV 2557 kb)

3D Branch tracking of an AEC migrating in 3D collagen gel.

Maximum intensity reconstruction of fluorescence (red) of an AEC expressing TdTm-CAAX migrating in a 3D collagen gel. Time-lapse 3D image sequence was collected by spinning disk confocal microscopy at 10 min intervals (elapsed time shown in lower right as hours:min:sec). In each frame, the position of the cell morphological skeleton is shown in green (branches) and blue (body segments), and branch tips and vertices are highlighted with large and small red spheres, respectively. Morphological skeleton evolution over time is shown in colour scale from purple (T = 0) to white (T = 300 min) show in white. Scale grid = 5 μm, minor tick marks = 1 μm. Total elapsed time shown at lower right in minutes. (MOV 4965 kb)

Centroid tracking of an AEC migrating in 3D collagen gel.

Maximum intensity reconstruction of fluorescence (red) of an AEC expressing TdTm-CAAX migrating in a 3D collagen gel collected by 3D spinning disk confocal microscopy imaging at 10 min intervals. The blue sphere shows the centermost point, the coloured trace shows path over time, with red indicating the starting frame and white indicating final position. Grid scale = major tick marks, 5 μm, minor tick marks = 1 μm. Total elapsed time shown at lower right in minutes. (MOV 1750 kb)

Maximal curvature mapped to surface of a control cell during migration and shape change.

Red values indicate highest maximal local curvature, blue values indicate lowest values. Scale grid is in microns. Time interval between frames is 300 s. (MOV 1988 kb)

Example of a segmented region of interest fused for analysis of local curvature and cortical GFP-myosin IIA intensity over time.

Maximum intensity reconstruction of fluorescence (red) of time-lapse 3D imaging of an AEC expressing GFP-myosin-IIA collected by spinning disk confocal microscopy at 10 minute intervals during migration in a 3D collagen gel. Grey area indicates region segmented and cropped for surface curvature measurement and cortical GFP-myosin-IIA intensity. Time stamp shown in lower left in min, total time 60 min. Grid spacing = 10 μm. (MOV 439 kb)

Myosin IIA accumulation at normal and non-normal branch bases.

Maximum intensity reconstruction of fluorescence (red) of time-lapse 3D imaging of an AEC expressing GFP-myosin-IIA collected by spinning disk confocal microscopy at 3 minute intervals during migration in a 3D collagen gel. Frame playback is paused during movie presentation to illustrate regions of cortical GFP-myosin IIA accumulation at the base of branches oriented normal or non-normal to the major axis of the cell body. Grid spacing = 10 μm. Total elapsed time shown at lower left in min. (MOV 2125 kb)

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Elliott, H., Fischer, R., Myers, K. et al. Myosin II controls cellular branching morphogenesis and migration in three dimensions by minimizing cell-surface curvature. Nat Cell Biol 17, 137–147 (2015). https://doi.org/10.1038/ncb3092

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