Epithelial folding mediated by apical constriction converts flat epithelial sheets into multilayered, complex tissue structures and is used throughout development in most animals1. Little is known, however, about how forces produced near the apical surface of the tissue are transmitted within individual cells to generate the global changes in cell shape that characterize tissue deformation. Here we apply particle tracking velocimetry in gastrulating Drosophila embryos to measure the movement of cytoplasm and plasma membrane during ventral furrow formation2,3. We find that cytoplasmic redistribution during the lengthening phase of ventral furrow formation can be precisely described by viscous flows that quantitatively match the predictions of hydrodynamics. Cell membranes move with the ambient cytoplasm, with little resistance to, or driving force on, the flow. Strikingly, apical constriction produces similar flow patterns in mutant embryos that fail to form cells before gastrulation (‘acellular’ embryos), such that the global redistribution of cytoplasm mirrors the summed redistribution occurring in individual cells of wild-type embryos. Our results indicate that during the lengthening phase of ventral furrow formation, hydrodynamic behaviour of the cytoplasm provides the predominant mechanism transmitting apically generated forces deep into the tissue and that cell individualization is dispensable.
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We thank S. Thiberge (Imaging core facility) for two-photon microscopy. We thank N. Wingreen, C. Brangwynne, C. Brody, H. Stone, S. Little, S. Di Talia, Y.-C. Wang and Y. Yan for their suggestions on the manuscript. We thank all members of the Wieschaus and Schupbach laboratories for discussions. This work was supported by the National Institutes of Health (National Institute of Child Health and Human Development grant 5R37HD15587) to E.F.W. and by the Howard Hughes Medical Institute. B.H. was supported by the New Jersey Commission on Cancer Research Fellowship. The Imaging core facility was supported by National Institutes of Health Grant P50 GM 071508.
The authors declare no competing financial interests.
Extended data figures and tables
a, Body axis (red lines) of the Drosophila embryo. A transverse cross section of the embryo at 50% egg length is shown in blue. V, ventral; D, dorsal. b, The definition of x, y coordinates used in this study. x axis, ML axis; y axis, AB axis. c, d, Injection of uncoated fluorescent beads (c) or WGA-coated beads (d) into the cytoplasm or the perivitelline space of an embryo, respectively. The embryo is glued to the coverslip on its dorsal side (method 1). e, Injection of uncoated fluorescent beads into the cytoplasm of an embryo with its ventral side glued to a coverslip (method 2). Method 1 is better suited than method 2 for introducing beads into the perivitelline space, whereas method 2 has the advantage of keeping the ventral side free of wound. Note that in method 2 the ventral surface of the embryo is slightly flattened owing to contact with the coverslip. This nevertheless does not affect the hydrodynamic characteristics of the cytoplasmic flow. Method 1 was applied in experiments used for Figs 1 and 2. Method 2 was applied in experiments used for Figs 3 and 4 and Extended Data Fig. 10.
a, Trajectories of beads in a 2-min interval during cellularization. The projection on the AP–ML plane is shown. Colours are used to distinguish individual trajectories. b, Ensemble time-averaged mean squared displacement (MSD) of cytoplasmic beads along the AP, ML and AB axes in cellularizing embryos (n = 5). Error bars, s.d. c, Distribution of beads velocity along the AP, ML and AB axes. Velocity was calculated over a 1-min time interval. d, Log–log plot of the average two-dimensional mean squared displacement of beads (AP–ML plane) embedded in the cytoplasm or the yolk of the wild-type embryos (n = 5) undergoing cellularization, or in the acellular embryos (n = 5) at the corresponding stage. Error bars, s.d. e, Log–log plot of the average two-dimensional mean squared displacement of beads embedded in the cytoplasm of the control embryos (n = 5) or embryos injected with colchicine (n = 2) or cytochalasin D (n = 2). Error bars, s.d. f, Distribution of beads velocity in embryos co-injected with colchicine. Depolymerization of microtubules by colchicine reduces the active, non-equilibrium fluctuations within the cytoplasm and causes a substantial reduction of the beads’ mobility, in particular along the AB axis.
a, Velocity fields (blue) and streamlines (red) of the cytoplasmic flow in the wild-type embryos at t = 4–6 min. Velocity fields were averaged with different sampling radius R. We selected an R value of 18 μm in our study (Supplementary Methods). b, Heat maps showing the relative standard error (RSE) for Vx, Vy and V (RSEx, RSEy and RSE, respectively). c, Heat maps showing the number of trajectories being averaged. d, The average RSE as a function of time.
a, Velocity field (blue arrows) and streamlines (red) of the cytoplasmic flow in the wild-type embryos at different time points during ventral furrow formation. The shortening phase starts approximately at t = 10–12 min. b, Heat map showing the displacement field between t = 0–10 min. c, Relative difference between the measured velocity profiles in the wild-type embryos and the hydrodynamic predictions. Relative standard errors (RSEs) of the velocity profiles are plotted for comparison. Note that the relative difference between measurements and predictions is within 13% between t = 4–12 min. d, Displacement of ferrofluid droplets passed through yolk and cytoplasm of syncytial embryos (denoted by Y in the schematic to the right) plotted against time. Blue curve corresponds to a cellularizing wild-type embryo; other curves are measurements in double-mutant acellular embryos. Magenta dashed line indicates the time point when magnetic field was removed (t = 0). Y values are normalized such that 40, 80, 120 and 160 µm correspond to the surface of the embryo for green, red, black and blue curves, respectively. Grey portion of each curve approximately corresponds to the motion of the droplet through the yolk whereas the remainder of the curve corresponds to movement through the cytoplasm layer. Fluctuations in the tracked bead position around t = 0 are due to unsteady motion of the microscope stage as the magnet position was adjusted manually. If these fluctuations are disregarded, droplet behaviour after removal of the magnet is essentially flat. In two of the four cases (the red and green traces), the directionality of the fluctuation is similar to that expected of recoil, but even if interpreted as such, the magnitude does not exceed 5 µm, which is much smaller than the 30-µm displacement of the droplet through the cytoplasmic layer.
Extended Data Figure 5 The membrane-bound beads and the cytoplasmic beads show distinct patterns of movement during cellularization.
a, Perivitelline injection of WGA-beads at different stages of cellularization leads to their binding to different portions of the plasma membrane. Left: beads injected at very early cellularization are localized to the furrow canals and remain there throughout cellularization. Middle: beads injected during mid-cellularization bind the incipient lateral membrane and move in register with the advancing furrow canals. Right: beads injected during late cellularization remain in the apical region of the cell and do not follow the movement of the furrow canals. Scale bars, 20 μm. b, Velocity field of the membrane-bound beads (left) and the cytoplasmic beads (right) during the last 2 minutes of cellularization. c, The average displacement of beads along the AB axis plotted as a function of time. Only beads located within 15 μm of the ventral midline were included. The value x = 0 is the onset of gastrulation; y = 0 is the apical surface of the embryo. Blue arrows, average apical–basal displacement of beads within Δy = 2-μm and Δt = 30-s intervals. Red, streamlines. d, Velocity of beads along the AB axis during late cellularization (t = −8 to 0 min) as a function of their initial depth at t = −8 min. During the last 8 min of cellularization, the WGA beads show depth-dependent directional movement along the AB axis. Beads bound to the apical portion of the lateral membrane (approximately 0–10 μm) barely move. The velocity of beads below 15 μm rapidly increases with depth and reaches a plateau of maximal velocity at 20 μm, below which the beads move at the same, maximal speed. In contrast, the cytoplasmic beads do not undergo substantial movement during cellularization. Error bars, 95% confidence intervals.
a, Difference (ΔV = Vmembrane − Vcytoplasm) between the velocity fields of the membrane-bound beads and the cytoplasmic beads. Arrows indicate the velocity vectors of ΔV, and the heat map corresponds to its magnitude. b, Generating velocity field that corresponds to residual cellularization. The resulting velocity field was subtracted from the corresponding membrane flow to compensate for the impact of cellularization (Supplementary Methods). c, d, Streamlines of the membrane-bound beads (red) compared with the cytoplasmic beads (blue). The velocity field of the membrane-bound beads was either not compensated (c) or compensated (d) for cellularization. e, Average relative difference between the membrane flow and cytoplasmic flow before (blue) or after (red) compensating for the impact of residual cellularization. f, Average relative left–right difference of the velocity field.
a, Time-lapse images of Sqh–GFP in the control or the acellular embryo imaged at the midsagittal plane. The control and acellular embryos are indistinguishable before cellularization. However, during cellularization, the acellular embryos only make very limited progress in membrane invagination. At the point when cellularization would normally be completed, only discontinuous thread-like strands of membrane are formed extending 10–15 μm into the cytoplasm; meanwhile the nuclei are still located in a common cytoplasm that is not partitioned into individual cells. Scale bar, 100 μm. b, The wild-type and acellular embryos fixed during mid-cellularization and stained for membrane (Neurotactin, green) and myosin (Zipper, red). Scale bar, 50 μm.
a, Immunostaining of mesoderm determinant Snail in the acellular and control embryos fixed at early cellularization, late cellularization or early gastrulation. The pattern of Snail expression in the acellular embryos closely resembles that in the wild-type embryos. At early cycle 14, the Snail proteins are clearly detectable in the prospective mesoderm. The staining appears graded towards the mesoderm/ectoderm boundary at this stage. At mid-cycle 14 and early gastrulation, the staining becomes uniform across the entire prospective mesoderm. Scale bar, 50 μm. b, Quantification of duration between beginning of cycle 14 and the onset of gastrulation. On each box, the central mark (red) is the median, the edges of the box are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points not considered outliers. c, Apical myosin dynamics visualized using Sqh–GFP after the onset of gastrulation (t = 0 min). Scale bar, 30 μm. d, Scanning electron microscope images showing the ventral surface of the wild-type and acellular embryos. Bottom panels show the enlarged view of the boxed regions in the top panels. Membrane blebs are formed in the ventral surface of the acellular embryos, indicating that apical constriction still gathers surface membrane into blebs despite the lack of cells. Scale bar, 50 μm (top); 10 μm (bottom).
a, d, Kymograph of apical Sqh–GFP videos along the ML axis (compensated for the curvature of the embryos) demonstrating the movement of apical myosin towards the ventral midline. The x axis represents the ML axis; scale bar, 50 μm; the y axis represents time, scale bar, 5 min. b, e, Kymographs processed with a band-pass filter. c, f, Trajectories of apical myosin moving towards the ventral midline were tracked from the processed kymographs (showing results tracked from several kymographs). Colours are used to distinguish individual trajectories. g, h, The rate of apical constriction (that is, the rate of convergent movement of the apical cortex) at different times during ventral furrow formation as a function of ML positions. The rate of apical constriction (magenta) was averaged from measurement of individual myosin trajectories over 2-min intervals (blue dots). Red dots are outliers. i, Average rate of apical constriction over time. For each time point, rates were averaged across the mid-ventral region (x = −50 to 50 μm). Insert shows the ratio of rates between the wild-type and acellular embryos over time. Dashed line corresponds to 1.6×. Error bars, s.e.m. j, Average Vx near the ventral cortex (y = 10–14 μm, t = 6–12 min) as a function of ML positions. k, Average Vy near the ventral midline (x = −16 to 16 μm, t = 6–12 min) as a function of AB positions. Error bars, s.d. in j and k.
a, T48 (mild), n = 5 embryos; b, T48 (severe), n = 6 embryos; c, zip-RNAi, n = 10 embryos; d, cta, n = 8 embryos. For each mutant: top, heat maps of Vx and Vy (measurement); middle, heat maps of Vx and Vy (theoretical prediction); bottom left, streamlines of the measured velocity field (red) compared with those deduced from the Stokes equations (blue); bottom right, relative difference between the measured velocity field and the hydrodynamic predictions. At the selected time points, the rate of apical constriction in each mutant is comparable to that in the wild type at t = 6–8 min (Extended Data Fig. 9i).
This file contains Supplementary Methods, Supplementary Notes and additional references. (PDF 287 kb)
The embryo expresses Ecad-GFP as a membrane marker. Top: En face view. Bottom: Transverse cross section view reconstructed from 3D stacks. The green channel (Ecad-GFP) shows a single z-slice, whereas the red channel (beads) shows the maximal projection of multiple slices. t = 0 is the onset of gastrulation. The time format is [mm]:[ss] in all videos unless otherwise indicated. (MP4 10641 kb)
The embryo expresses Ecad-GFP as a membrane marker. Shown is the maximal projection between z = 6 and z = 10 μm (top) or between z = 16 and z = 20 μm (bottom) at the ventral side of the embryo. t = 0 is the onset of gastrulation. (MP4 11593 kb)
Comparing VF formation between embryos injected with WGA-beads (top) and those injected with cytoplasmic beads (bottom).
The embryos express Sqh-GFP as a myosin marker. t = 0 is the onset of gastrulation. (MP4 2976 kb)
Shown is the midsagittal plane of a control (top) and an acellular embryo (bottom) expressing Sqh-GFP. t = 0 is the beginning of cellularization. (MP4 13754 kb)
Shown is the midsagittal plane of a control (top) and an acellular embryo (bottom) expressing Jupiter-GFP (a MT marker) during cellularization. (MP4 18391 kb)
Shown is the maximal projection of Sqh-GFP between z = 0 and z = 10 μm at the ventral side of the embryo. t = 0 is the onset of gastrulation. (MP4 22507 kb)
The control embryo is shown on the left and the acellular embryo on the right. The top shows a transverse cross section view, reconstructed from 3D stacks, and the bottom shows an en face view. t = 0 is the onset of gastrulation. (MP4 21374 kb)
The embryo expresses Sqh-GFP as a morphological marker. Top: En face view. Bottom: Transverse cross section view reconstructed from 3D stacks. t = 0 is the onset of gastrulation. (MP4 12281 kb)
Cell shape changes of virtual-cells derived from the cytoplasmic flow in the wild type (top) or the acellular (bottom) embryos during VF formation.
t = 0 is the onset of gastrulation. (MP4 1721 kb)
Movement of ferrofluid droplets in the wild type (left panel) and acellular (right panel) embryos driven by externally applied magnetic field.
t = 0 indicates time when magnetic field was released. The ferrofluid droplets showed no detectable elastic recoil upon the release of the field. (MP4 16711 kb)
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He, B., Doubrovinski, K., Polyakov, O. et al. Apical constriction drives tissue-scale hydrodynamic flow to mediate cell elongation. Nature 508, 392–396 (2014). https://doi.org/10.1038/nature13070
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