Geometric constraints alter cell arrangements within curved epithelial tissues

Abstract

Organ and tissue formation are complex three-dimensional processes involving cell division, growth, migration, and rearrangement, all of which occur within physically constrained regions. However, analyzing such processes in three dimensions in vivo is challenging. Here, we focus on the process of cellularization in the anterior pole of the early Drosophila embryo to explore how cells compete for space under geometric constraints. Using microfluidics combined with fluorescence microscopy, we extract quantitative information on the three-dimensional epithelial cell morphology. We observed a cellular membrane rearrangement in which cells exchange neighbors along the apical-basal axis. Such apical-to-basal neighbor exchanges were observed more frequently in the anterior pole than in the embryo trunk. Furthermore, cells within the anterior pole skewed toward the trunk along their long axis relative to the embryo surface, with maximum skew on the ventral side. We constructed a vertex model for cells in a curved environment. We could reproduce the observed cellular skew in both wild-type embryos and embryos with distorted morphology. Further, such modeling showed that cell rearrangements were more likely in ellipsoidal, compared with cylindrical, geometry. Overall, we demonstrate that geometric constraints can influence three-dimensional cell morphology and packing within epithelial tissues.

FIGURE 1:

Cell arrangements in the Drosophila embryo. (A) Schematic representation of four cells undergoing a T1 transition. Initially, the cells 1 and 1′ are neighbors. The cell interface denoted in red then shortens (intermediate panel) and then forms a new cell interface between cells 2 and 2′. (B) Schematic representation of cellularization in the Drosophila embryo. In early cellularization (left), cell walls invaginate perpendicular to the embryo surface. Nuclei are denoted by black ovals. In late cycle 14 (right), the cell basal surface extends (denoted by red lines) below the nuclei. In the polar regions, the embryo curvature potentially results in cell shape changes away from columnar cells. (C) Possible scenarios for cell shape and packing in the anterior pole: (i) lower cell density in the anterior; (ii) reduced basal surface extension of cells in the anterior, reducing the geometric effects of the curvature; (iii) cells skew toward the trunk, which is under less geometric constraint; (iv) the basal surface of the anterior-most cells reduce in cross-section, with the cells becoming more pyramid-like; (v) cells undergo rearrangements from apical-to-basal to fit into the restricted space as the basal surface extends (in the lower image, the red and yellow cells are neighbors at the basal surface); (vi) a subset of cells fail to extend fully (purple cell), thereby providing more space for neighboring cells.

FIGURE 2:

Quantitative image analysis of cell morphology in the Drosophila embryo anterior. (A) Microfluidic device for mounting embryos vertically. Red bar denotes the cross-section of the well. (B) Transverse view of an embryo expressing H2Av::mCherry (magenta) and Gap43::mVenus (green) positioned in the microfluidic device. (C) Three cross-sectional views from the embryo shown in B (i–iii) with the microfluidic device shown. (D) Projected cells following the stereographic projection with identification of cell centers, see Materials and Methods. (E) Reconstructed cell surfaces after segmentation of projected data. Color coding represents neighbor number of each cell. (F) Left: Light-sheet image of a Drosophila embryo expressing Gap43::mCherry. Right: Segmentation from adaptive watersheds superimposed with color coding representing distance from anterior pole. (G) Nearest-neighbor distance for each segmented cell in confocal (black circles, n = 8 embryos) and light-sheet images (gray lines correspond to two different embryos) at the end of slow phase. Black arrow denotes approximate location of future cephalic furrow. Error bars = SD.

FIGURE 3:

Pseudo-T1 cellular rearrangements along the apical-basal cell axis in the embryo anterior. (A) Example cell, denoted by X, which increases from four to six neighbors between apical and basal surfaces. Pseudo-T1 transitions denoted by magenta and yellow lines. Embryo expressing H2b::mCherry (magenta) and Gap43::mVenus (green). (B) Further example of cells undergoing a pseudo-T1 transition, where z denotes linear distance from anterior pole. (C) Time-lapse images of cells undergoing a pseudo-T1 transition at 4 μm from the apical surface but not at 8 μm from the apical surface. (D) Cell interface length during pseudo-T1 transitions. Magenta denotes interface length before transition, and green corresponds to interface length (with new cells) after the pseudo-T1 transition. Black lines represent the position of the transition. n = 10 embryos at end of slow phase, with 60 individual cell rearrangements. (E) Distribution of the position of the identified pseudo-T1 transitions shown in D along the apical–basal axis (0 μm represents the cell apical surface). (F) The frequency of pseudo-T1 transitions per cell observed in the anterior (dark gray) and trunk (light gray) regions depends on the cell depth. Error bars = SEM. (G) The percentage of observed pseudo-T1 transitions compared with the linear distance from the anterior pole; data collected as in D.

FIGURE 4:

Cell rearrangements do not correlate with actin or myosin localization. (A) Embryos expressing Moe::GFP (gray) and MyoII::mCherry (see also Supplemental Figure S4A). Top row: blue arrow denotes location of pseudo-T1 transition, with the magenta arrow showing the region of high Moe::GFP intensity that does not undergo cell rearrangements. Bottom row: as above, but with cell outlines during pseudo-T1 transition. (B) Merge of Moe::GFP (green) and MyoII::mCherry (magenta) signals. Blue arrows highlight regions with pseudo-T1 transitions. (C) Angle change during pseudo-T1 transitions in the anterior (n = 4 embryos, 8 pseudo-T1 transitions), where 0° represents initial interface alignment. Solid black line denotes the mean angle, with ±1SD denoted by dashed lines. Gray lines represent tracks of the angle in individual pseudo-T1 transitions. Bold dotted lines are guides to the eye. T = 0 min denotes the beginning of the pseudo-T1 transition at a given apical–basal position within each cell. (D) Moe::GFP and (E) MyoII::mCherry intensity on cell interfaces undergoing pseudo-T1 transitions, with nomenclature same as in C.

FIGURE 5:

Cell packing and shape in the anterior pole. (A) Cell neighbor number distribution for cells at different distances from the anterior pole. n = 10 embryos, >1000 cells. No significant change in packing density is observed. (B) The cross-sectional surface area of the cells from apical to basal surfaces in the trunk (triangles) and within 30 μm of the anterior pole (squares). n = 10 embryos, >1000 cells. Error bars = SD. The apical surface area is significantly larger in the anterior pole compared with the trunk (gray region). (C) Embryo expressing Sqh::mCherry in the anterior pole during cellularization. Yellow boxes denote zoomed regions. The white arrows are the same length. (D) Cumulative probability distribution for the change in area from apical to basal surface for cells at different positions relative to the anterior pole. n = 10 embryos, >1000 cells. The area change in the anterior is significantly different from the trunk (p < 10^–3, using a Kolmogorov-Smirnov test). (E) Lateral view of bcd^E1 embryo expressing Gap43::mCherry, imaged on a light-sheet microscope. Black arrows are equal length. (F) The frequency of pseudo-T1 transitions is similar in wild-type and bcd^E1 embryos in the anterior. Error bars = SEM. (G) Anterior–posterior axis view of bcd^E1 embryo expressing Gap43::mCherry, imaged on a light-sheet microscope. Arrows denote cells with significantly reduced basal surface compared with their neighbors. (H) Comparison of fraction of wild-type and bcd^E1 embryos with cells that have significantly reduced basal surface in the anterior region. p-value calculated using two-proportion z-test.

FIGURE 6:

Cells in the anterior skew during cellularization toward the embryo trunk. (A) Time-lapse images of cells expressing Gap43::Venus, imaged on a confocal microscope undergoing skew during cellularization. Solid white arrow denotes normal to apical surface of marked cell and dashed arrow represents its orientation. (B) Quantification of the cellular skew angle as a function of distance from the anterior pole using Gap43::mCherry-expressing embryos imaged on a light-sheet microscope. Measured skew angles were always taken as positive (i.e., independent of orientation), n = 3 embryos, 447 cells. Inset shows example of cellular skew measurement. Error bars = SD. (C) The average skew angle as a function of cell depth using confocal movies of Gap43::Venus. n = 3 embryos, 34 cells tracked in region 10 μm < AP < 40 μm, 11 cells tracked in pole and trunk (squares), error bars = SD. (D) Comparison of skew angle in wild-type (wt) (n = 3) and bcd^E1 (n = 5) embryos expressing Gap43::mCherry. p values calculated using two-tailed test of means, *p < 0.05. Error bars = SEM.

FIGURE 7:

Distorting embryo geometry can alter cell arrangement. (A) Embryo expressing Gap43::mCherry with UAS>fat2-RNAi, trafficjam>Gal4. Embryo oriented anterior to left and dorsal at top. Note that the dorsal side is more curved than in wild-type embryos. (B) fat2-RNAi embryos show reduced neighbor separation and (C) reduced apical surface area (n = 6 for fat2-RNAi embryos and n = 5 for wild-type embryos, with >250 cells in total for each genotype). Error bars are SD. (D) There is not a significant change in the frequency of pseudo-T1 transitions (n = 6 for fat2-RNAi embryos), error bars SEM. (E) Skew in fat2-RNAi embryos is reduced. The dashed line shows the direction parallel to the surface at each point. The same angle is used for all three cells highlighted. (F) Skew against distance from anterior pole for wild-type and fat2-RNAi embryos. Skew is reduced in fat2-RNAi embryos compared with wild type within the proximal tip (p < 0.01). Error bars are SD.

FIGURE 8:

Vertex model incorporating geometric constraints is consistent with both observed cellular skew and cellular rearrangements. (A) Parameters of the vertex model: α_L, γ_b, λ_a control tension along the lateral, basal, and apical edges, respectively; β_V and β_P represent regulations of cell volume and membrane area. Vertices on the apical side are constrained to move along an ellipse (dashed line) that models the interaction with the fixed vitelline membrane (see also Supplemental Figure S8). (B) Output from vertex model simulation. The skew is defined as the angle between the normal to the apical surface (blue arrow) and the cellular edge (red arrow, the size of arrows is proportional to the value of the tilt angle). Cells are colored according to their energy level (in units of the maximal energy level). (C) Cellular skew, as measured in experiments (black circles, error bars = SD) and simulations (blue). Ellipse represents geometry simulated, where the long axis is 2.5 times longer than the short axis. (D) The nucleus sphericity (1 = perfect sphere, 0 = line) as a function of distance from the anterior pole at the end of slow phase (squares, n = 4 embryos, >600 nuclei) and during fast phase (circles, n = 4 embryos, >600 nuclei). Error bars = SD. (E) Comparison of model prediction for skew in fat2-RNAi embryos with experimentally measured skew. Parameters same as for C except the geometry simulated, where the long axis is 1.5 times longer than the short axis. (F) As in B but with reduced embryo length, as in fat2-RNAi embryos. (G) Schematic of vertex model used to explore role of geometry on cell arrangements in three dimensions. (H) Resulting force on tricellular junctions due to cell growth and confinement. The apical (blue) and basal (red) surfaces are connected by lateral cell walls, modeled as springs (black junctions connecting apical and basal vertices). (I) Cell packing on the apical surface. Color coding represents neighbor number of each cell. At initiation (left), all cells are hexagonal. At later times, after 10 μm of effective cell invagination, T1 transitions are only observed on ellipsoidal surfaces (right) and not cylindrical surfaces (center).