Computer simulation of cellular patterning within the Drosophila pupal eye

Abstract

We present a computer simulation and associated experimental validation of assembly of glial-like support cells into the interweaving hexagonal lattice that spans the Drosophila pupal eye. This process of cell movements organizes the ommatidial array into a functional pattern. Unlike earlier simulations that focused on the arrangements of cells within individual ommatidia, here we examine the local movements that lead to large-scale organization of the emerging eye field. Simulations based on our experimental observations of cell adhesion, cell death, and cell movement successfully patterned a tracing of an emerging wild-type pupal eye. Surprisingly, altering cell adhesion had only a mild effect on patterning, contradicting our previous hypothesis that the patterning was primarily the result of preferential adhesion between IRM-class surface proteins. Instead, our simulations highlighted the importance of programmed cell death (PCD) as well as a previously unappreciated variable: the expansion of cells' apical surface areas, which promoted rearrangement of neighboring cells. We tested this prediction experimentally by preventing expansion in the apical area of individual cells: patterning was disrupted in a manner predicted by our simulations. Our work demonstrates the value of combining computer simulation with in vivo experiments to uncover novel mechanisms that are perpetuated throughout the eye field. It also demonstrates the utility of the Glazier-Graner-Hogeweg model (GGH) for modeling the links between local cellular interactions and emergent properties of developing epithelia as well as predicting unanticipated results in vivo.

Figure 1. Patterning the fly eye.

(A) Cross-section of an adult eye reveals the precise hexagonal arrangement of ommatidia. The reddish pigment granules are contained within the interweaving 2°/3° hexagonal lattice. Membranes highlighted with methylene blue. (B–F) Images illustrating progressive stages of pupal eye development; times are as indicated. (B) The completed pattern. Cell types are false colored for clarity. An ommatidial core (OC) of cone cells (c) and primary pigment cells (1°) is highlighted in green. Orange highlights the hexagonal lattice of secondary (2°) and tertiary (3°) pigment cells; bristle groups alternate with 3°s at the vertices. (C) At the beginning of pupal patterning, cone cell clusters are arrayed within a large collection of undifferentiated cells. (D) 1°s envelop the cones and isolate them from the rest of the developing eye. Multiple layers of IPCs remain between developing ommatidia (orange highlights a sample region). (E) Cell rearrangement generates a single layer of cells between ommatidia (orange). At this stage, the cell number is noticeably reduced and 3°s begin to appear (arrows). (F) Further death and rearrangement generate a single cell (2°) on each side of the hexagon and a single cell (3°) at each vertex. At this stage a few extra cells remain (•). Our simulations model patterning that occurs between the stages shown in (E) and (F) and further refined to (B). Bars represent 5 µm.

Figure 2. Apical OC expansion and initial simulation inputs.

(A) TEM of an ommatidium in an 18 hour APF eye. The central photoreceptors (R), cone (c) and 1° cells are pseudo-colored green. Note that the left 1° nucleus (asterisks) is rising, that on the right (only partially seen) is already higher resulting in a larger apical profile; the neighboring 2° nuclei are basal, these cells have larger basal footprints. Select 2° cells are pseudo-colored orange. (B) The OC increases in apical surface area (µm²) over time as measured from live images. The error bars indicate one standard deviation. (C, D) Example of a 22 hour APF pupal eye stained with an E-cadherin-specific antibody to visualize surface cell boundaries. This image was traced to provide a starting point for the simulations, which were then run multiple times as noted. The region used in the tracing is false colored as in Figure 1. Bars represent 10 µm.

Figure 3. Simulation of wild-type development.

(A) Image captured at 10,000 MCS exhibited numerous ectopic cells and few 3°s (arrows). Cell death has not yet been initiated. (B) Image from 11,000 MCS. Cell death has been initiated and there are fewer cells and more 3°s (arrows). (C) Image from 25,000 MCS. There are fewer cells and most central ommatidia have cells in the 3° locus (arrows). (D) Image from 50,000 MCS. There are a few extra 2°-like cells (•) and all central ommatidia show a complete complement of 3°s. Asterisk labels the ommatidium shown in inset with 3°s colored red.

Figure 4. Secondary and tertiary formation depends on cell death.

(A) Image captured at 50,000 MCS from a simulation of reduced cell death (L = 12) showed numerous ectopic, end-to-end 2°-like cells (•) and vertices with three cells in the 3° locus (arrows). Asterisk labels an ommatidium enlarged in inset. (B) Graph showing the decrease in cell number over time for different levels of cell death. L controlled the ‘strength’ of cell death as described in Results. Cell death was initiated at 10,000 MCS and each line represents the result of a single representative simulation from at least two repetitions. (C) Graph showing formation of 2°s over time for different levels of cell death. Each line represents the result of a single representative simulation from at least two repetitions. (D) Graph showing formation of 3°s over time for different levels of cell death. Each line represents the result of a single representative simulation from at least two repetitions. (E) Graph showing number of both 2° and 3°s at 15,000 MCS as cell death parameters are changed to increase the total cell number. Each point represents a different cell death parameter in the simulations from (B), (C) and (D).

Figure 5. Inhibiting cell death impeded 2° and 3° formation in vivo.

(A–D) Examples of ommatidia from GMR-Gal4/UAS-Diap1 retinae. For cell counts all IPCs lying within the hexagonal outline as drawn were counted; cells partly within the hexagon were counted as a half-cell. 3°s were defined as contacting three 1°s (colored orange); a correctly specified 2° locus was defined as one occupied by only one cell; examples of end-to-end 2°-like cells are labeled with •. Total cell count for each ommatidium is indicated at its center. Our analysis included only ommatidia surrounded by three correctly positioned bristle groups. Bars represent 10 µm. (E) Graph showing the decrease in 2° (plotted in green) and 3° (black) cell number as IPC number increased. The total number of ommatidia analyzed (N) per data point plotted is indicated below the y-axis.

Figure 6. Adhesion did not affect formation of 2°s or 3°s in the presence of cell death.

All images are final images from 50,000 MCS trials. (A) In a simulation in which IPCs were more adherent to OCs than to each other, 3°s and most 2°s emerged correctly at all central ommatidia. Several ectopic end-to-end 2°-like cells are indicated (•) (B) In a simulation in which OC:IPC and IPC:IPC adhesion was set as identical, 3°s still correctly emerged within all central ommatidia. An increase in cell death resulted in some missing 2°s (arrowheads). (C) 3°s also emerged within a simulation in which IPCs were more adherent to each other than to OCs; occasional loss of 3°s was observed (arrow). Increased cell death (PCD) resulted in missing 2°s (arrowheads). Asterisks label enlarged ommatidia (insets). (D and E) Graphs quantifying how in the presence of reduced cell death (L = 10), preferential adhesion most efficiently enhanced the ability of 2°s (D) and 3°s (E) to form. Each line represents the result of a single representative simulation from at least two repetitions. When OC:IPC adhesion was the same (‘flat adhesion’) or less (‘anti-preferential adhesion’) than IPC:IPC adhesion 2°s and 3°s still formed though less efficiently.

Figure 7. Progressive differences between IPCs and OC surface proportions promoted 2° and 3° formation.

(A and B) Graphs showing formation of 2°s (A) and 3°s (B) over time for different size ratios between IPC and OC apical surface areas. Cell death was initiated at 10,000 MCS. The ‘wild-type’ curve indicates 2° and 3° formation when OC apical surfaces expanded but IPCs did not expand during progressive MCS. ‘Wild-type, growing IPCs’ indicates OCs expansion and IPC surface doubling. ‘No Death’ curve indicates expanding OCs with no cell death. ‘No OC Expansion’, No Death' curve indicates constant OC surface area (no expansion) and no cell death. (C) A graph indicating the decrease in cell number for the different simulations. Each line represents the result of a single representative simulation from at least two repetitions. (D) Image capture at 50,000 MCS from a simulation with no OC expansion nor cell death; the pattern fails to resolve; asterisk labels enlarged ommatidium (inset) (E) Three dimensional schematic emphasizing how the vertical movement of nuclei (red arrows) expands the 1°s' surface profiles (blue arrows), in turn laterally ‘crowding’ the neighboring IPCs into a hexagonal pattern. (F, G and H) Reducing OC expansion by expressing smurf introduced patterning errors in vivo. Bars represent 10 µm. (F) Ectopic expression of smurf in paired 1°s led to mild patterning defects, primarily in cell number. (G and H; corresponding tracings in G′ and H′) Reducing growth of single 1°s (marked by GFP) reduced the apical surface profile (E-Cadherin shown in magenta); the neighboring IPC arrangement and 3° cell loci failed to properly resolve. (I and J) Central region of images captured at 0 MCS and 50,000 MCS in simulations in which (I) the entire central OC indicated in red or (J) only half of the OC was prevented from expanding. Arrowheads indicate defects also commonly observed in vivo – missing or ectopic cells. (K) Reduced rst activity (rst^CT) led to consistently uneven IPC distribution in 20 hr APR eyes; within this tracing, an example of a rare fused ommatidium is indicated (arrow). Inset: our computer model consistently failed to pattern this rst tracing even after 50,000 MCS The failure to pattern using the same parameters as our wild type tracing indicates that the 20 hr APF rst eye field must already show differences with wild type tissue.