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. 2011 Feb 4;144(3):427-38.
doi: 10.1016/j.cell.2010.12.035.

Control of the mitotic cleavage plane by local epithelial topology

Affiliations

Control of the mitotic cleavage plane by local epithelial topology

William T Gibson et al. Cell. .

Abstract

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g., Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage-plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division itself. Here, using mechanical simulations, we show that the polygonal shapes of individual cells can systematically bias the long-axis orientations of their adjacent mitotic neighbors. Strikingly, analyses of both animal epithelia and plant epidermis confirm a robust and nearly identical correlation between local cell topology and cleavage-plane orientation in vivo. Using simple mathematics, we show that this effect derives from fundamental packing constraints. Our results suggest that local epithelial topology is a key determinant of cleavage-plane orientation, and that cleavage-plane bias may be a widespread property of polygonal cell sheets in plants and animals.

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Figures

Figure 1
Figure 1. Local epithelial topology is predicted to influence the geometry of an epithelial cell
(A) A stereotypical simple columnar epithelium. Black spots represent nuclei. (B) The Drosophila wing disc epithelium, with nrg-GFP (green) marking the septate junctions. (B’) A planar network representation of (B). (C) A model for finding the minimum energy configuration of cell packing, based on internal pressure and ideal springs. (D–F) (Initial states, left) Initial conditions for the relaxation algorithm. Each case varies the topology of the marked cell. (Relaxed states, right) At equilibrium, cell shape is specified by a balance between pressure and tension. The central cell’s shape is strongly influenced by the labeled cell’s topology. See also Figure S1
Figure 2
Figure 2. The orientation of a cell’s short axis is predicted to correlate with its quadrilateral and pentagonal neighbors, and to anti-correlate with heptagonal and octagonal neighbors
(A) Neighbor cell topology, N, influences the direction of the cellular long axis (solid line) and short axis (dashed line), based on an ellipse of best-fit (red). Second order and higher neighbors, which are uniformly hexagonal, are not shown. For N< 6, the short axis is oriented towards N-sided cell N; for N>6, it is oriented perpendicular to N. (B) The attraction of the short axis to quadrilateral cells (N=4) is robust to heterogeneity in the local cell neighborhood. (C) We computed the cleavage plane index, or fraction of neighbors in each polygon class (black line) located adjacent to the central cell’s short axis (presumed cleavage plane). Neighbor cells having N<6 are significantly enriched in this position. Conversely, neighbors having N >6 are under-represented. For comparison, for a randomly oriented division plane, all N values occur with similar frequency (green), which is close to the null hypothesis of 2/7 (red). (D) We defined an acute angle, θ, with respect to a cell’s short axis (dashed red line), as well as the neighbor topology in direction θ (green cells). (E) On average, neighbor topology (black) is an increasing function of acute angle θ. Error bars represent the standard deviation in the sample mean topology in direction θ per cell (an average of the 4 positions on the cell cortex corresponding to the θ, over 420 such cells).
Figure 3
Figure 3. In both plants and animals, a dividing cell’s cleavage plane correlates with its quadrilateral and pentagonal neighbors, and anti-correlates with heptagonal and octagonal neighbors
(A) The Drosophila wing imaginal disc, stained with anti-DLG to mark the junctions (green) and anti-PH3 to mark chromatin (blue). (B-D; B’-D’), Cell division proceeds in the plane of the epithelium via a stereotyped division process including interphase (I), mitosis (M), and cytokinesis (C). Actin staining is shown in red. (E) We can infer the topological complement of neighbors, as well as the division orientation of dividing cells, from cytokinetic figures. Junctions are marked by a nrg-GFP protein trap (red). (F–G) We examined > 400 such figures, and sorted the neighbors by polygon class. The neighbors on the division plane (red) are a subset of the full complement of neighbors (green and red). (H) An overlay of the predicted mitotic cleavage plane bias based on our mechanical model (black), with the biases computed from both Drosophila wing disc epithelium (blue) and cucumber epidermis (red). Each is compared with the topological null hypothesis (green). See also Figure S2 for further information.
Figure 4
Figure 4. Drosophila wing disc cells approximately obey a long-axis division rule
(A) Time series analysis illustrates the process in which an interphase cell entering mitosis gradually dilates before reaching full rounding, and then subsequently undergoes cytokinesis, in an orientation approximately predicted by its interphase long axis. (A’) Drawings of the process described in the corresponding panels in A, including the mitotic cell and its immediate neighbors. The long axis of the ellipse of best fit (red) is labeled with a solid line, whereas the dashed line (predicted cleavage plane) represents the short axis. (B) The eventual orientation of the cleavage plane can be predicted based on the interphase long axis orientation. The red line (zero deviation from long-axis division) represents a perfect correlation between the interphase long axis and the long axis of the resulting cytokinetic figure. Blue bars show the number of cells (represented by radial distance from the center) that divided with a particular angular deviation from the interphase long axis. On average, the deviation was approximately 27.1 degrees. The data is represented by the first quadrant (0° to 90°), which is also displayed symmetrically in the other three quadrants (90° to 360°). (C) The bias curve prediction that incorporates the measured deviation of 27 degrees from the long axis (red) is significantly closer to the empirically measured cleavage plane bias (blue) than the naïve long-axis prediction is (black). A Gaussian noise model with 27 degree standard deviation gives a similar result (data not shown). We controlled for the influence of topological relationships by using the same local neighborhoods as were measured from the empirical data (blue). See also the Extended Experimental Procedures and Figure S3, which suggests a long axis mechanism may also operate in Cucumis.
Figure 5
Figure 5. Fundamental packing constraints are sufficient to explain cleavage plane bias
(A) Hexagons pack at 120-degree angles. (B) A 4-sided cell distorts the internal angles of the surrounding hexagons, inducing a long axis. (C) A geometrical argument for division plane bias. The N-sided neighbor cell influences the ratio of the horizontal axis, dm to the vertical axis, hm, in the M-cell. When dm:hm > 1, the N cell is in the predicted cleavage plane position for the M-cell. (D) A plot of the ratio dm:hm, for different values of N and L. Above the gray line, the N-cell is in the M-cell’s predicted division plane; the opposite is true below the gray line. (E–F) Both N and L influence the direction of the long axis in the M cell. (E) The value of N influences the direction of the long axis in the M cell (top cell), for constant L. (F) The long axis of the M-cell is influenced by the side length, L, for a constant N-value. See also Figure S4.
Figure 6
Figure 6. Cleavage plane bias participates in cell shape emergence, and is required for wild-type cell packing
(A) The topological simulator does not model cellular mechanics, but does explicitly keep track of topological neighbor relationships. Based on topological weights, division likelihood, division symmetry, and cleavage plane bias are matched to empirically measured statistics in a Monte-Carlo framework (see Figures S2A–C). (B) Hexagonal frequency declines by approximately 4% in the absence of bias. Arrows highlight this difference. (C) The distribution of mitotic cells shows pronounced alterations in the absence of bias. Arrows highlight the differences. (D) The finite element simulator models cellular mechanics, division, and rearrangement. The simulator captures mechanics in terms of a net, interfacial tension, which is modeled using rod-like finite elements. Division likelihoods are informed by the empirically measured values (Figure S2A). Cleavage plane bias approximates the empirical values, and is achieved using long-axis divisions. For finite element simulations incorporating cellular rearrangements (T1 transitions), see Figure S6. (E) In the absence of bias, hexagonal frequency declines by about 4% (compare with panel B). (F) The distribution of mitotic cells again shows pronounced alterations (compare with panel C). See also Figures S5–S6.

Comment in

References

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