Figure 1.
Progressive down-regulation of FGF8 at the caudal precursor zone.
Schematic drawing showing expression of FGF8 (purple) in embryos of 10 (A) and 14 (B) somites respectively. Transcription of FGF8 (red) only occurs at the primitive streak and adjacent epiblast but FGF8 mRNA extends into the presomitic mesoderm and adjacent neural tube due to maintenance of the transcript as the embryo extends. Cells which are left behind the moving caudal neural precursor zone (blue dot) do not regress caudally and stop transcribing FGF8.
Figure 2.
Stationary concentration profiles of A-mRNA and its corresponding protein in one-dimensional model of a migrating DoT.
The solid red line denotes the concentration of A-mRNA along the embryo's axis while the dashed red line denotes the concentration of protein A. A-mRNA is produced in the DoT, i.e. in the red hatched area which has a preset size and moves to the right (the x-coordinate points to the posterior side) with speed c. Production of protein A is proportional to the level of A-mRNA. The schematic gene regulatory network diagram explaining the underlying molecular model is also presented. The detailed description of the model is given in the Materials and Methods Section. Here we presume that the DoT is located in the segment (420, 455) of the medium of total size 600 (space units) and moves with speed c = 0.015 to the right. Other parameters: k1 = 0.0003, k2 = 0.00025, k3 = 0.0005, D2 = 0.5.
Figure 3.
The model with cell differentiation.
The basic model (Figure 2) is extended by imposing the condition that production of A-mRNA stops when the concentration of protein A reaches the threshold value TA (TA = 0.85 in all presented simulations). This defines the location of back (left) side of the moving DoT and therefore provides the mechanism controlling its size. A: The schematic gene regulatory network diagram explaining the used version of the model, for further details see the Materials and Methods Section. B: Concentration profiles of A-mRNA (solid red) and protein A (dashed red) with respect to the moving DoT (red hatched). Parameter values are the same as in Figure 2. C: The DoT size versus the DoT speed in simulations (blue markers) and in analytics (solid red line, given by the equation 9 in the Materials and Methods Section). D: Domains corresponding to the stationary and oscillating dynamics of the DoT size on the parameter plane “k2 versus c” in simulations (blue markers) and in analytics (red line). c is the velocity of the DoT migration and k2 is the kinetics rate (1/k2 is a relaxation time) of protein A (here and everywhere else k3 = 2k2).
Figure 4.
FGF8 transcription is not altered by FGF signaling.
A–B: FGF8 transcription at the caudal precursor zone in control (A) and FGFR antagonist treated (B) chick embryos. No changes in FGF8 transcription are observed following a blockade of FGF signaling. C: Schematic drawing showing the origin of the explants shown in D–E. D–E: FGF8 transcription in caudal precursor zone chick explants following culture in the presence of control (D) and FGF4 containing media (E).
Figure 5.
Possible mechanisms of the involvement of FGF8 in the caudal gene regulatory network.
A–B: the rate of FGF8 transcription is proportional to the level of protein A (see the Materials and Methods Section for details). Note that the FGF8 DoT extends behind the A-mRNA DoT. C–D: the transcription of FGF8 and A-mRNA are launched independently in (roughly) the same group of cells while both down-regulated by the same signal provided by protein A. Note, that the concentration profiles for FGF8 DoT and A-mRNA DoT in this case basically coincide. Values of parameters (in equations 1 and 2) are the same as in Figure 2. For extra parameters (equations 11 and 12): D4 = 0.5, k31 = k41 = 0.0003, k32 = k42 = 2k31.
Figure 6.
The DoT migration in the GGHM.
A: Schematic diagram of the used model (identical to the diagram in Figure 3). B: Three consecutive images from the simulation of primitive streak regression. Initially there is a group of 25 red cells (the DoT) forming a square tissue. The level of A-RNA is high and constant in all red cells. Red cells move (to the right), proliferate and differentiate, i.e. red cell transforms into the green cell when the level of protein A at any point inside the red cell gets above the threshold value TA = 0.8. Green cells do not move nor produce A-mRNA, for simplicity we have also assumed that they do not proliferate. Cell differentiation is regulated by the level of morphogen A (as in Figure 3). Parameters: k1 = 0.001, k2 = 0.003, β = 4.5. C, D: Concentrations of A-mRNA (C) and protein A (D) are shown in shades of red. The border line between red and green zones is along an isoline in the concentration field of protein A corresponding to the threshold value TA = 0.8. E: Increase in the rate of A kinetics, k2, (assuming that k3 = 2k2) reduces the size of the DoT (or number of cells forming the DoT) exponentially.
Figure 7.
The DoT migration in the GGHM with 3 cell types.
A: Schematic diagram of the used model. B: Snapshots from the simulation: red cells – move and produce A-mRNA, blue cells move but don't produce A-mRNA and green cells do not move and do not produce A-mRNA. Red cells transform into blue when the level of protein A rises above TA = 0.75, blue cells – to green when the level of protein A drops below TM = 0.6. Only red cells proliferate. Parameters: k1 = 10−3, k2 = 5·10−4, β = 3.8. C, D: concentration profiles of A-mRNA (C) and protein A (D) after 20500 time steps of simulation.
Figure 8.
The DoT migration due to chemotaxis in 1D model.
The speed of the DoT migration is defined by the formula c = c0(Al−Ar) where Al and Ar are concentrations of protein A on the left and right borders of the DOT. A: The version of the model where the DoT size is fixed (chemotaxis without A-RNA self-repressive production control). The domain in the parameter plane “a versus c0” where the travelling DoT should definitely exist according to the analysis of the model is on the right side of the solid red line (this line represents the border of the domain defined by inequality 16 in the Materials and Methods section. Transition points (between existence and nonexistence) of migrating DoTs in simulations are given by blue markers, dished blue line connecting these markers gives the numerically obtained border. B: The version of the model where the DoT size is controlled by the protein A (chemotaxis with A-mRNA self-repressive production control). The size of the DoT depends on the parameter c0. The difference Al−Ar depends on c0 and saturates when c0→∞ giving a linear asymptotic (red) for the dependence of the DoT size on c0.
Figure 9.
Migration of the DoT due to chemotaxis in GGHM.
A–E: Simulation of the movement of a group of cells transcribing A-mRNA (DoT) that are repelled by a protein A they produce. Three types of behavior can be found in GGHM. Here we assume that cells forming the DoT do not grow, proliferate or differentiate. A: Initial shape of the DoT. The DoT was “forced” to move to the right (see about a preset motion of the DoT in Figure 7) for the first 2000 time steps to provide initial conditions for chemotactic motion. “Self-repelled” DoT can: B: meander (k2 = 0.0005). C: move along straight line (migrate) (k2 = 0.0025). D: move and elongate (deform into “umbrella”-shaped tissue) (k2 = 0.0055). E: domains on a parameter plane (k2 versus β) corresponding to each kind of behavior. Blue dots in B, C and D show location of the DoT's center of mass every 200 time steps. Parameters: k1 = 0.001, β = 120. F: Simulation of the movement of a group of red cells transcribing A-mRNA (DoT) that are chemotactically repelled by a protein A they produce and that, in addition, grow, proliferate and differentiate into green non-actively moving cells (as it was in the case of Figure 6). Initially the DoT is represented by a group of 25 cells. These cells are “forced” to move to the right for the first 2000 time step computations to provide the direction for further chemotactic movement. After T = 2000, red cells are repelled by protein A, and (as directed by the initial conditions) they move to the right leaving the trail of differentiated daughter cells (green).
Figure 10.
Regulative properties of the FGF8 DoT.
FGF8 expression can be maintained in the absence of caudal-most signals and can be progressively down-regulated in the absence of rostral signals. A: Schematic diagram showing the experimental separation of the rostral and caudal parts of the FGF8 DoT (cutting experiment). B: FGF8 expression following the experimental separation of the caudal precursor zone into two. White arrows show how FGF8 is maintained at both the rostral and caudal moieties and black arrow shows the progressive down-regulation of FGF8 in the caudal moiety. C: Simulation of cutting experiment: the chemotactically moving DoT is cut into two pieces (see images at T = 0 and T = 650). We allow the piece corresponding to the caudal moiety to move while the movement in the rostral moiety is arrested by the cut. The concentration of A-mRNA (shown by shades) which is associated with the location of the DoT reproduces the corresponding pattern for FGF8 shown in B. Parameters: k1 = 5·10−4, k2 = 2.5·10−5, β = 1950.