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, 5 (5), e10571

Modeling Gastrulation in the Chick Embryo: Formation of the Primitive Streak

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Modeling Gastrulation in the Chick Embryo: Formation of the Primitive Streak

Bakhtier Vasiev et al. PLoS One.

Abstract

The body plan of all higher organisms develops during gastrulation. Gastrulation results from the integration of cell proliferation, differentiation and migration of thousands of cells. In the chick embryo gastrulation starts with the formation of the primitive streak, the site of invagination of mesoderm and endoderm cells, from cells overlaying Koller's Sickle. Streak formation is associated with large-scale cell flows that carry the mesoderm cells overlying Koller's sickle into the central midline region of the embryo. We use multi-cell computer simulations to investigate possible mechanisms underlying the formation of the primitive streak in the chick embryo. Our simulations suggest that the formation of the primitive streak employs chemotactic movement of a subpopulation of streak cells, as well as differential adhesion between the mesoderm cells and the other cells in the epiblast. Both chemo-attraction and chemo-repulsion between various combinations of cell types can create a streak. However, only one combination successfully reproduces experimental observations of the manner in which two streaks in the same embryo interact. This finding supports a mechanism in which streak tip cells produce a diffusible morphogen which repels cells in the surrounding epiblast. On the other hand, chemotactic interaction alone does not reproduce the experimental observation that the large-scale vortical cell flows develop simultaneously with streak initiation. In our model the formation of large scale cell flows requires an additional mechanism that coordinates and aligns the motion of neighboring cells.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Critical stages of the development of the primitive streak in the chick embryo.
Wnt 8c expression during formation of Koller's sickle and the primitive streak. (A, B) At stage HH1 Wnt8c (A) and Chordin (B) RNAs are expressed in the Area Opaca. At this time the embryo is growing and the epiblast increases in size as shown by the outward-pointing velocity arrows (C). At stage HH2, Wnt8c (D) and Chordin (E) RNA are both expressed along the primitive streak, but the cell flow patterns have changed to two counter-rotating cells flows (F). At stage HH4, Wnt8c (G) is expressed in the base of the streak, while Chordin RNA is expressing in the tip of the streak and the surrounding forming neural plate (H). During this phase the large-scale rotational movements start to transform into flows along the anterior-posterior axis of elongation of the embryo (I). AO Area Opaca, AP Area Pellucida, black arrow tip of the streak, red arrow base of the streak. In the velocity flow fields the thick horizontal white bar indicates cell flow speeds of 1 µm/min. Images C, F and I were taken at t = 0 minutes, t = 300 minutes and t = 800 minutes from the start of the experiment at HH1. See Supplementary Materials, movie S1.
Figure 2
Figure 2. Simulation of differentiation in the early epiblast.
The embryo in these simulations contains (initially) 625 cells, i.e. 1 simulated cell corresponds to 16 cells in the real embryo. (A) Simulation showing that the embryo attains a stable circular shape, provided that the adhesion between cells is strong enough (J1,2>2J2,2). (B) To create the AP and AO we assign the AP cell type (red) to all cells whose centre-of-mass lies inside a circle of radius 77 voxels from the center of the embryo and the AO cell type (green) to the remaining cells. The AO (green cells) correspond to the AO in Fig. 1A (area where Wnt8c RNA is expressed). (C) Concentration field of the differentiation morphogen in the epiblast (according to Eq. 9). Gray-scale indicates concentration from 0 (black) to 1.5 (white). (D) Simulation of mesoderm (blue) differentiation. AP cells differentiate into mesoderm if the concentration of the differentiation morphogen in (C) is greater than 0.7. Blue cells form a Koller's Sickle, i.e. corresponding to the Wnt8c RNA expressing area in Fig. 1B. See Supplementary Materials Movie S2 for a movie of this process. See Simulation Details and Supplementary Materials Table S1 for the model architecture and parameter values. Simulations generated using the code in Supplementary Materials Code S1.
Figure 3
Figure 3. Migration of S cells (blue) and ST cells (yellow) in response to an attractant generated by AP cells (red) (M1).
(A) Concentration of the chemotactic agent. Gray-scale indicates concentration from 0 (black) to 1.5 (white). (B) Typical pattern at 5000 time steps beginning from Fig. 2D, when all AP mesoderm cells respond chemotactically and have the same adhesivity J1,3 = 3 (for remaining values of Ji,j see Eq. 2). The migrating mesoderm cells disperse in the AP. See Supplementary Materials Movie S3 for a movie of this process. (C) Typical pattern at 5000 time steps beginning from Fig. 2D, when all AP mesoderm cells respond chemotactically and adhere more strongly to each other than to cells in the AP and AO, J1,3 = 7, J2,3 = 9. The migrating sickle cells form streams. (D, E) Computational results when only a small, are chemotactically sensitive to the chemo-attractant. (D) Initial location of the subgroup of mesoderm cells (yellow) that will ultimately form the streak tip (ST). (E) Typical pattern at 7000 time steps beginning from the conditions in D, when only ST mesoderm cells respond chemotactically and the adhesion matrix J is that in Eq. 2. See Supplementary Materials Movie S4 for a movie of this process. (F) Typical pattern at 7000 time steps beginning from D, when only ST mesoderm cells respond chemotactically and the adhesion matrix J is that in Eq. 2 except that J3,3 = J4,4 = 2 and J3,4 = 4. Chemotaxis follows Eq. 4, with βk = 80 if a cell responds chemotactically and βk = 0 otherwise. See Simulation Details for other parameter values. Simulations generated using the code in Supplementary Materials, Code S1.
Figure 4
Figure 4. The effects of the strength of the chemotactic response (β in Eq. 4) and adhesion between ST (yellow) and S (blue) cells (J 3,4) on the dynamics of the formation of the primitive streak.
Results are shown after 7000 simulation time steps starting from the initial condition given in Fig. 3D using mechanism M1. The image in the middle of the panel corresponds to the parameters used in the simulation presented in Fig. 3F.
Figure 5
Figure 5. Formation of the primitive streak for different chemotactic mechanisms.
(A) Typical concentration of a chemotactic agent produced by ST cells (mechanisms M2, M2b and M4). Gray-scale indicates concentration from 0 (black) to 1.5 (white). (B) Typical pattern at 7000 time steps beginning from Fig. 3D, when ST cells produce a repellent for AP cells (βk = −60 for AP cells) (mechanism M2). See Supplementary Materials Movie S5 for a movie of this process. (C) Typical pattern at 7000 time steps beginning from Fig. 3D, when ST cells produce a repellent for AP and AO cells (βk = −60 for AP cells and βk = −15 for AO cells) (mechanism M2b). (D) Typical concentration of a chemotactic agent produced by S cells (mechanisms M1, M3). Gray-scale indicates concentration from 0 (black) to 1.5 (white). (E) Typical pattern at 7000 time steps beginning from Fig. 3D, when S cells produce a repellent for ST cells (βk = −40 for ST cells) (mechanism M3). See Supplementary Materials Movie S7 for a movie of this process. (F) Typical pattern at 7000 time steps beginning from Fig. 3D, when ST cells produce an attractant for S cells (βk = 40 for S cells)(mechanism M4). Chemotaxis follows Eq. 4. with βk = 0 if a cell does not respond chemotactically. In (A)–(F) J3,3 = J4,4 = 2, J3,4 = 4, other values as in Eq. 2. In (E) and (F) J2,4 = 9, other values as in Eq. 2. See Simulation Details for other parameter values. Simulations generated using the code in Supplementary Materials, Code S1.
Figure 6
Figure 6. Interaction between two primitive streaks for different model hypotheses.
(A) Initial cell configuration, with separate groups of S and ST cells at the bottom and the left side of the embryo. Each group can extend to form a primitive streak. (B) Typical pattern at 7000 time steps beginning from Fig. 6A, when AP cells produce an attractant for ST cells (mechanism M1). The two extending primitive streaks do not interact until they contact each other (See Supplementary Materials Movie S8, Middle panel). (C) Typical pattern at 7000 time steps beginning from Fig. 6A, when ST cells produce a repellent for AP cells (mechanism M2). The primitive streaks attract each other, resulting in collision and fusion of their tips (See Supplementary Materials Movie S8, Right Panel). (D) Typical pattern at 7000 time steps beginning from Fig. 6A, when S cells produce a repellent for ST cells (mechanism M3). The extending streaks repel each other, so the tips bend apart (See Supplementary Materials Movie S8, Left panel). (E) Typical pattern at 7000 time steps beginning from Fig. 6A, when ST cells produce an attractant for S cells (mechanism M4). The extending streaks fuse after collision. See Supplementary Materials Movie S8 for movie of these processes. (F) Experiment showing an embryonic twin with two spontaneous streaks. The extending streaks repel each other so the tips bend apart. Streaks visualized through in situ hybridization for expression of Brachyury RNA . See Fig. 5 and Simulation Details for parameter values. Simulations generated using the code in Supplementary Materials, Code S1.
Figure 7
Figure 7. Cell flow patterns during streak formation for different mechanisms.
Our four models (M1)–(M4) for cell attraction and repulsion and four models of growth and induced polarization produce sixteen possible sets of combined mechanisms. (Left) Typical cell patterns at 7000 time steps beginning from Fig. 3D and (Right) Corresponding cell-flow velocity fields for each case. In the absence of proliferation, limited, local vortical motion occurs without induced polarization. However, large-scale vertical motion requires induced polarization. Chemorepulsion mechanisms (mechanism M2, ST repels AP) and (mechanism M3, S repels ST) produce the most robust streak/streak tip structures. Simulations generated using CompuCell3D. For parameters, see Supplementary Materials Table S1.
Figure 8
Figure 8. Simulated vorticity of cell flows measured along a horizontal line, perpendicular to the primitive streak and crossing the center of the embryo.
(A) From a simulation where S cells repel ST cells (mechanism M2), polarization off, growth off (see Fig. 7). (B) From a simulation where S cells repel ST cells (mechanism M2), polarization on, growth on (see Fig. 7). Both plots are rescaled to units of mm (to measure the distance along the measurement line) and min−1 (to measure vorticity) according to the space and time unit definitions given in the Simulation Methodology Section. The midline of the embryo crosses the plots in the middle (1 mm in A and 1.25 mm in B). The vorticity is measured according to the formula formula image where formula image are horizontal and vertical components of cell flow velocities. These velocities calculated as the ratio of total cell shifts over all simulation time. The vorticity is negative for clockwise and positive for counter-clockwise rotation. It is zero at the midline of embryo and increases to the left and decreases to the right with maximum/minimum at about quarter of embryo's radius from the midline. It returns smoothly to zero at the embryo boundaries.

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