Fig 1.
Stages of tooth development considered for this study.
A, Bud stage of the mouse first molar (E13), shown as a frontal section (HE staining). B, Cap stage of the mouse first molar (E15.5), shown as a frontal section (HE staining). C, Diagram depicting the growth angle of the cervical loops (black lines) in a cap stage tooth germ (frontal section). Color legend indicates different tissue types.
Fig 2.
Tooth model initial conditions.
A, B, Depiction of the model initial conditions as frontal (A), and sagittal (B) sections. The cells lining the border of the epithelium (cells in green) and the uppermost layer of suprabasal cells are fixed in space, representing the physical barrier imposed by the oral epithelium surrounding the base of the tooth germ. The space under the mesenchymal layer however, is empty, allowing the tooth germ to grow in depth, bucco-lingually and antero-posteriorly. C-E, The three hypotheses raised as different distributions of cell proliferation in the different tissues, frontal sections shown. Non proliferative cells have been darkened. Blue: enamel epithelium. Yellow: Suprabasal layer. Purple: mesenchyme. Red: enamel knot.
Fig 3.
Parameter screening of the tissue specific proliferation rates (sepi, ssup and smes).
Variation in tooth germ morphology with different combinations of either sepi, ssup or smes, keeping the other two constant, under the different hypotheses (frontal sections depicted). A, B, E, variation in sepi for hypothesis I, II and III respectively (initial conditions depicted on the left). A, ssup = 0.022, smes = 0.10. B, ssup = 0.041, smes = 0.20, E, ssup = 0.029, smes = 0.20. In all cases, cervical loops form when sepi is relatively high and ssup is relatively low, but only in hypotheses II and III these are oriented downwards as in tooth development. C, F, Variation in ssup for hypotheses II and III respectively. C, sepi = 0.36, smes = 0.20. F, sepi = 0.045, smes = 0.20. Increasing values of ssup prevent the formation of cervical loops. D, G, Variation in tooth morphology for different values of smes under hypotheses II and III respectively. D, sepi = 0.50, ssup = 0.041. G, sepi = 0.082, ssup = 0.029. A relatively high mesenchymal proliferation is necessary for the proper formation of the cervical loops. Colours as in Fig 2. sepi, ssup and smes values are expressed in h-1.
Fig 4.
Comparison of growth rates with experimental data.
A, B, Initial conditions for the 2D tooth development model for hypothesis II and III respectively. Distribution of proliferating cells for each hypothesis is indicated with the same colours as in Fig 2. Examples of best fitting tooth germ morphologies for hypothesis II (sepi = 0.36, ssup = 0.11, smes = 0.20) and III (sepi = 0.05, ssup = 0.03, smes = 0.25) respectively. E, F, Epithelium perimeter (blue) and surface area (red) measured over developmental time for the teeth shown in C and D respectively, compared to the empirical growth curves (blue crosses and red triangles) from tooth sections (6). X axis shows time in percentual units, Y axis represents size (see S1 Appendix for details).
Fig 5.
Comparison of cell movements with experimental data.
A, Experimental cell trajectories as shown in (6) (with permission). B, C, in silico trajectories (black lines) of suprabasal cells for hypothesis II and III respectively (same simulations as in Fig 4). D, empirical cell trajectories from Morita et al., highlighting a group of epithelial cells at the tip of each cervical loop. E, F, in silico trajectories of epithelial cells only for the morphologies shown in B and C respectively. Epithelial cells are shown before (green cylinders) and after (blue cylinder) the tracking interval and cell trajectories are shown as black lines. In hypothesis II (E), cells that were previously at the tip of the cervical loops move away from it and are replaced by cells coming from the centre by the end of the tracking period. In contrast, in hypothesis III (F) epithelial cells that start at the tip of the loops stay there after the tracking period, which is more consistent with the experimental data (D).
Fig 6.
Parameter screening of differential adhesion parameters.
A, Tooth germ morphologies are shown with different combinations of mesenchymal homotypic adhesion and suprabasal homotypic adhesion values, while the other parameters are set to 1.0. High values of mesenchymal homotypic adhesion result in low growth angles whereas high values of suprabasal homotypic adhesion results in high growth angles. B, Morphologies are shown with different combinations of mesenchymal homotypic adhesion and epithelial-mesenchymal adhesion values (other adhesion parameters set to 1.0). High values of epithelial-mesenchymal adhesion result in low growth angles. Frontal sections shown. Colours as in Fig 3. All the simulations in this screening used the following growth parameters: sepi = 0.063, ssup = 0.021, smes = 0.182.
Fig 7.
Mechanical forces acting on the different tooth tissues in the model.
Spatial distribution of forces are shown for three different tooth morphologies at cap stage simulated with different adhesion parameters: bss = 5.0, bmm = 1.0 (A), bss = 0.0, bmm = 5.0 (B), bss = 5.0, bmm = 0 (C), while the other adhesion parameters are equal to 1.0. Intensity and directionality of forces in the mesenchyme and suprabasal layer are depicted with rods connecting each pair of neighbouring cells. Rod colour indicates sign (i.e. negative = compression; positive = tension) and intensity of force. Rods are not displayed in epithelial cells, instead cylinder colour corresponds to the average of all the forces acting on it. For each simulation, frontal sections are shown from an oblique view (left column) and also the suprabasal tissue alone seen from below (right column, note that we only show the suprabasal cells in contact with the epithelium for a clearer picture of single rods). The growth parameters used in all three simulations are the same as for the simulations in Fig 6.
Fig 8.
Anteror-posterior (AP) cervical loops tend to be shorter than bucco-lingual (BL) ones when the tooth germ at the initial conditions is longer in the AP axis than in the BL axis.
A-D, an example simulation with initial conditions that are longer in the AP axis respect to the BL axis, seen from different angles: oblique (A), frontal section (B), sagittal section (C) and from below (D). Differences in the length of the cervical loops between the AP sides and BL sides can be observed. Growth and adhesion parameters used: sepi = 0.063, ssup = 0.021, smes = 0.182, bee = 1.0, bes = 1.0, bem = 5.0, bss = 1.0, bmm = 5.0. E-H, an example simulation with initial conditions equally long in the AP and BL axes, seen from different angles: oblique (E), frontal section (F), sagittal section (G) and from below (H). It can be seen that in this case cervical loops have the same length on all sides. Growth parameters used: sepi = 0.37, ssup = 0.12, smes = 0.20, all adhesion parameters equal to 1. Only epithelium and suprabasal layer are shown. The colour code indicates the heigth (i.e. position in the Z axis).
Fig 9.
Epithelium-mesenchyme separation experiments.
A, Pictures of the same E14.5 tooth germ before immersion in dispase with the four 2D configuration of landmarks used in Geometric Morphometrics analyses (left), 14 mins after (middle) and 40 minutes after (right). Landmark configurations were collected for each of the 120 time frames which compose the total duration of the separation experiment. B, Depiction of mechanical stresses in the in silico separation assay before separation (left) and C, after the tissues have reached mechanical equilibrium (right). Colour rods indicate direction and intensity (yellow for tension, blue for compression) at a certain cell-cell contact (as in Fig 7). Growth and adhesion parameters used: sepi = 0.055, ssup = 0.033, smes = 0.245, bee = 5.0, bes = 5.0, bem = 5.0, bss = 5.0, bmm = 5.0. D, PCA of tooth germ variation during separation from experimental data from three different tooth germs (red, yellow and blue dots, n = 120 each), and from the simulation data shown in B (black dots, n = 120). The arrows point the flow of time for each dataset. The outline drawings of tooth germs show the patterns of shape changes associated with each PC from the overall average shape (solid grey outline with grey background and open circles) for different PC scores (solid black outline and solid black circles). Note that the outline drawings are depicted for an easier visualisation.