July 1, 2004;
Multicellular computer simulation of morphogenesis: blastocoel roof thinning and matrix assembly in Xenopus laevis.
In the blastocoel roof
) of the Xenopus laevis embryo
, epibolic movements are driven by the radial intercalation of deep
cell layers and the coordinate spreading of the overlying superficial
cell layer. Thinning of the lateral
margins of the BCR
by radial intercalation requires fibronectin
(FN), which is produced and assembled into fibrils by the inner deep
cell layer of the BCR
. A cellular automata (CA) computer model was developed to analyze the spatial and temporal movements of BCR
cells during epiboly. Simulation parameters were defined based on published data and independent results detailing initial tissue
geometry, cell numbers, cell intercalation rates, and migration rates. Hypotheses regarding differential cell adhesion and FN assembly were also considered in setting system parameters. A 2-dimensional model simulation was developed that predicts BCR
thinning time of 4.8 h, which closely approximates the time required for the completion of gastrulation in vivo. Additionally, the model predicts a temporal increase in FN matrix assembly that parallels fibrillogenesis in the embryo
. The model is capable of independent predictions of cell rearrangements during epiboly, and here was used to predict successfully the lateral
dispersion of a patch of cells implanted in the BCR
, and increased assembly of FN matrix following inhibition of radial intercalation by N-cadherin
[+] show captions
Fig. 1. The BCR thins during gastrulation. Confocal micrographs of bisected early (Stage 9, A and B) and late (Stage 11.5, C and D) Xenopus laevis gastrula
stage embryos. At the beginning of gastrulation (A and B), the roof consists of an outer layer of epithelial cells and 2– 3 layers of deep cells. Near the end of
gastrulation (C and D), the deep layers have radially intercalated so that the roof is composed of only two layers of cells: the superficial epithelial cells and one
layer of deep cells. During gastrulation, FN is assembled under the BCR cells. Boxes indicate the center of the BCR. Underlying mesoderm has migrated along
the inner surface of the roof in C and D but is easily distinguished by the line of FN staining that separates the BCR from the mesoderm (C). (B and D) Higher
magnification images of similar regions of the BCR to those boxed in A and C, cell outlines visualized using antisera to C-cadherin (scale bars = 300 Am in A
and C; scale bars = 75 Am in B and D). The area between the white bars in A and C represents the area modeled in the CA simulation. The area outlined by the
box is shown at higher magnification in B and D, and represents the center portion (which is 3-cell layers thick) of what was actually modeled.
Fig. 2. Cellular behavior is governed by the set of rules incorporated in the simulation. (A) This diagram represents a sequence of cell movements and actions
that are possible given the defined set of rules: (1) an inner deep layer cell is selected at random to move. The black arrow and the three yellow arrows
emanating from the selected cell represent the possible directions the cell can move in. The black arrow represents the randomly selected direction. The red cell
intercalates between the two green cells on either side of the black arrow, (2) all of the green cells to the left of the intercalated red cell are displaced one cell
diameter to the left, (3) the superficial cell layer extends (spreads) to cover the protruding green cell layer, (4) an orange deep cell drops down to fill the gap
created by the intercalated red cell. The superficial cell layer conforms to fill the gap created by the orange cell, (5) the FN intensity associated with each bottom
(yellow) deep layer cell is incremented if the residency time and cell-to-cell contact criteria are met. (B) The tissue geometry after the events described in (A)
Fig. 3. Time sequence of the simulated process of BCR thinning in the Xenopus laevis embryo. The model begins with multiple cell layers and terminates when
the inner deep cells (green, red, and orange blocks) have radially intercalated into the bottom layer of deep cells (yellow blocks). The radial intercalation of
deep cell layers between one another leads to lateral extension, or elongation of the BCR. The superficial layer of cells (blue blocks) extends to cover the deep
Fig. 4. The model predicts the lateral dispersion of implanted cells. To simulate the microsurgical implantation of a graft of labeled cells in the CA model, the
initial morphology of the simulated BCR was modified by adding 10 extra deep cells (shown in red) (A). The length of the implanted patch, measured as the
distance between the end cells, late in stage 8/early in stage 9 is represented by a. The simulation predicts the spatial fate of the implanted cells 5 h later (B).
The maximum distance between cells at this time point is represented by b. The dispersion length ratio is calculated by dividing b by a. The simulation predicts
a dispersion length ratio of 1.9 +/- 0.3 (n = 25 simulation runs). The schematic of the analogous experimental manipulation shows how a homotypic,
homochronic graft of deep cells from an alexa-488 dextran-labeled donor embryo was implanted into an unlabeled host embryo late in stage 8/early stage 9 (C).
Fluorescence image overlaid onto a visible light image of cells grafted into a pigmented embryo late in stage 8– early in stage 9 (D), and 5 h later (E) (scale
bar = 30 Am). The length of the implant (maximum distance between implanted cells) was measured along the long axis of the oval-shaped implant (F), late in
stage 8 –early in stage 9 (denoted as a) and 5 h later (denoted as b) and similarly along the short axis of the oval-shaped implant (perpendicular to a and to b).
Fluorescence images of cells grafted into an albino embryo collected in the FITC channel immediately after implantation late in stage 8/early in stage 9 (G) and
5 h later (H) (scale bar = 30 um). The ratio of b to a represents the dispersion length, and the average experimental dispersion length ratios measured along the
long axis and short axis of the oval-shaped implants were 1.6 +/- 0.5 and 1.7 +/- 0.3, respectively (n = 6 embryos).
Fig. 5. The Model Predicts FN Matrix Assembly. (A) CA simulation prediction of FN intensity at stages 9, 10, 11, and 12 (scale bar = 100 Am). The bottom layer in the model is a grayscale representation of FN intensity. Black corresponds to negligible FN and white corresponds to the highest relative value of FN. (B) Photomicrographs of the BCR roof at stages 9, 10, 11, and 12 (scale bar = 100 Am). Bright white areas indicate high levels of FN. At each time point, the FN content is homogeneous and uniform across the entire area of the BCR; therefore, the sections in (B) are representative of the entire BCR area, in terms of FN content.
Fig. 6. Relationship between predicted FN content and experimentally
observed FN content. (A) The predicted values of FN content were obtained
from the output of the simulation (black bars). The observed values (white
bars) were obtained by using Scion Image to analyze images of the BCR
roof stained for FN. The FN values from the simulation were scaled so the
mean predicted value would equal the mean observed value at stage 11 (* =
statistically different from experimentally observed at that time point, P <
0.05). (B) There is a strong positive correlation between the model’s
predicted FN values and the experimentally observed FN values
(correlation coefficient = 0.9211).
Fig. 7. Matrix accumulation increases with cell residency time. A patch of cells unable to undergo radial intercalation (non-intercalating cells, pink boxes) was simulated at t = 0 h (A) and t = 4 h (B). FN
accumulation was simulated in both the patch and in neighboring cells that were free to undergo radial intercalation. Grayscale circles represent total FN accumulation at each time scale with white representing
highest levels and black representing lowest levels (A–C). Enlargement in (C) corresponds to a portion of the simulation that is comparable in size to a region of the BCR in an intact embryo (D). Confocal section
of BCR in (D) processed for immunolocalization of FN (green) and myc-tagged N-cadherin (red) in a patch of cells at stage 10+. FN accumulation is greatest under the N-cadherin expressing patch of cells, which
also fail to rearrange and thin this region of the BCR. Neighboring cells in the BCR that lack N-cadherin thin normally and display significantly less FN at this stage.