A biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo

Abstract

The article provides a biomechanical analysis of ventral furrow formation in the Drosophila melanogaster embryo. Ventral furrow formation is the first large-scale morphogenetic movement in the fly embryo. It involves deformation of a uniform cellular monolayer formed following cellularisation, and has therefore long been used as a simple system in which to explore the role of mechanics in force generation. Here we use a quantitative framework to carry out a systematic perturbation analysis to determine the role of each of the active forces observed. The analysis confirms that ventral furrow invagination arises from a combination of apical constriction and apical-basal shortening forces in the mesoderm, together with a combination of ectodermal forces. We show that the mesodermal forces are crucial for invagination: the loss of apical constriction leads to a loss of the furrow, while the mesodermal radial shortening forces are the primary cause of the internalisation of the future mesoderm as the furrow rises. Ectodermal forces play a minor but significant role in furrow formation: without ectodermal forces the furrow is slower to form, does not close properly and has an aberrant morphology. Nevertheless, despite changes in the active mesodermal and ectodermal forces lead to changes in the timing and extent of furrow, invagination is eventually achieved in most cases, implying that the system is robust to perturbation and therefore over-determined.

Figure 1. Digitisation procedure and epithelial fate.

(a) The angular coordinate system is defined in the reference configuration at t = −10.43 min, which is considered as initial configuration. The presumptive mesoderm is defined as the tissue that ultimately forms the ventral furrow in the wt embryo. By tracking backward in time, this tissue was found to be nominally 18 cells wide in the wt embryo and to span a ±44° angle about the dorsal (D)-ventral (V) midline at the reference instant t = −10.43 min. Only a mesodermal sub-region is thought to be active by undergoing apical constriction. Myosin II that is initially localized on the basal side of the epithelium (red-dotted line) vanishes in this sub-region to reappear apically (on the opposite end of cells). In the wild type and bnt-mutant embryos, this sub-region was respectively found to span approximately ±30° (green lines) and ±40° (blue lines) astride the dorsal-ventral midline. (b) Digitisation procedure of an intermediate-stage frame from the in-vivo imaged sequence of a wt embryo: a polygonal mesh (blue lines) has been overlaid on the tissue to track displacements at nodal points, referred to as registration nodes (magenta dots). Polygonal partitions can correspond to single cells, multiple cells or sub-cellular regions, depending on the measurements refinement required in that particular portion of tissue. Arrows point the radial thickness of the epithelium, which was measured on the mesh as the distance between basal and apical node along the same side of a given cell. The height of the furrow (h) has been measured as that of the most ventral nodal point with respect to its position in the reference frame at t = −10.43 min.

Figure 2. Schematic of the multi-scale model of the 2Dsection of the Drosophila embryo.

(a) Biological architecture of the Drosophila single epithelial cell. (b) Each architectural constituent of the epithelial cell plays a structural role during cell shape changes. Such roles can be either active or passive, depending on whether that constituent is able to generate force or it is deformed by forces actively generated by neighbouring elements. Actin-myosin forces are known to be active systems for force generation whereas microtubules are known to maintain stiffness. Apical junction complexes, instead, keep cell junctions connected and, therefore, transmit forces from one cell to other cells in the epithelium. The inner cytoplasm is a viscous incompressible fluid that resists and responds to cell compression by exerting an inner pressure. (c) In order to build a finite element model of the single epithelial cell, the phenotypical effects of the complex force fields originating from the molecular level can be thought as an equivalent field of net forces acting along the cell edges. The incompressibility of the inner cytoplasm can be simulated by enforcing the surface of the region enclosed by the cell membrane to remain constant in time. (d) Individual cells (green) are broken into quadrilateral finite elements (blue), which are used to calculate the forces generated by their passive (viscous) components during each time step t_i of the simulation. Elements are joined to each other at nodes, and the set of forces (blue arrows) that would be needed to drive a particular set of nodal motions u _i (magenta arrows) is denoted by f _i. These passive forces f _i and their corresponding displacements u _i are related by Eqn. (1). The forces generated by active cellular components are resolved into edge forces which act on both of the nodes that mark their ends. Some of these edge forces are shown (red arrows), as is their vector sum at a representative node (blue arrows). Similar vector sums for each node give rise to the collection of nodal driving forces f _i* which are set to be equal to the passive forces f _i generated by the cytoplasm. Setting these forces equal to each other means that the vectorial driving forces acting at each node are just balanced by viscous resistance from the cytoplasm at that node. (e) A finite element model of the 2D section of the Drosophila embryo is built by matching to in vivo images at the cellular level. 2D geometry has been sized on the in vivo dimensions of the wild type embryo at the reference initial instant t = −10.43 min (fig. 1b–2a). Mesodermal region covers approximately 60 degrees across the ventral point V and is highlighted in dark green, whereas ectodermal region is highlighted in bright green. The presence of the vitelline membrane has been simulated by constraining the motion of apical nodes unilaterally, in such a way that apical nodes could not displace at distances from the centre of the circular epithelium greater than the radius of the circular vitelline membrane (red circle). The effect of the presence of the inner viscous yolk in the real embryo has been modelled, instead, by imposing a user defined pressure to the basal nodes. The value of the pressure is than chosen in such a way that surface variations of the inner yolk region (orange area) are approximately of the same magnitude of in vivo yolk area variations (Fig. S1).

Figure 3. Modelling ventral furrow invagination: wild type genotype.

(a) Selected multi-photon images (columns) of in vivo transverse cross-sections of a wild type embryo during ventral furrow formation. The embryo is labelled with Sqh-GFP and is oriented with its dorsal surface upward (Fig. 1a). The time interval between successive frames is 45 sec. Time zero was set by using apical-basal cell height profiles on the dorsal side (Fig. S2a). (b) Selected frames (columns) of in silico transverse cross-sections of a wild type genotype. The embryo's 2D geometry is oriented with its dorsal side upward. Undeformed initial configuration (panel b′) corresponds to in vivo deformations at t = −10.43 min (see panel d). (c) In silico force distributions utilised to simulate invagination in b). Total invagination interval [−1.43, 6 min] has been subdivided in the three subintervals [−10.43 min, 1.2 min], [1.2 min,2 min] and [2 min, 6 min] respectively referred to as the first, second and third invagination intervals. Force trends are a discretisation of the in vivo force distribution available in Brodland et al. . Smooth variations in time and position of in vivo force distributions over epithelial regions have been discretised to in silico force distributions that vary with time but not with position over epithelial regions. It is worth noticing that the components constituting the in vivo mechanism of invagination (mesodermal apical constriction, ectodermal basal constriction, ectodermal and mesodermal radial shortening) have been preserved. (d) Time-trends of average radial mesodermal and ectodermal thicknesses of the epithelium. Measurements in vivo have been repeated on a set of three different animals of the same genotype, and average trend and error bars (standard error of the mean) are obtained through statistical analysis of this data set (see Methods). It is worth noticing that mesodermal cells character begins differentiating from the ectodermal one approximately at t = −10.43 min (red vertical line), before which all cells share a communal epithelial fate. In silico, mesodermal radial thickness M (see schematic in panel e) has been measured at different angles of an angular section of the epithelium, which spans approximately 50 degrees astride ventral point V (25 degrees in each direction from V). In silico measurements for ectodermal radial thickness E, instead, stretched approximately up to 120 degrees astride the dorsal point D (60 degrees in each direction from D). (e) Time-trends of furrow's height h at the ventral side (see schematic in panel d).

Figure 4. Modelling ventral furrow invagination: bnt-mutant genotype.

Selected multi-photon images of in vivo transverse cross-sections of a bicoid,nano,torso-like mutant embryo during ventral furrow formation. bnt-mutant has germ-band extension and posterior mid-gut invagination suppressed. The embryo is labelled with Sqh-GFP and oriented with its dorsal surface upward (Fig. 1a). Time interval between successive frames is 45 sec and instant zero was set by using apical-basal cell height profiles on the dorsal side (Fig. S2b). (a) Selected multi-photon images (columns) of in vivo transverse cross-sections of a bnt-mutant embryo during ventral furrow formation. The embryo is labelled with Sqh-GFP and is oriented with its dorsal surface upward (Fig. 1a). The time interval between successive frames is 45 sec. Time zero was set by using apical-basal cell height profiles on the dorsal side (see panel d). (b) Selected frames (columns) of in silico transverse cross-section of a bnt-mutant genotype. Embryo's 2D geometry is oriented with its dorsal side upward. The undeformed initial configuration (panel b′) corresponds to in vivo deformations at t = −10.43 min (see panel d). (c) In silico force distributions utilised to simulate invagination in b). (d) Time-trends of average radial mesodermal () and ectodermal () thicknesses of the epithelium (see schematic in Fig. 3e). (e) Time-trends of furrow's height h at the ventral side (see schematic in Fig. 3e).

Figure 5. Modelling ventral furrow invagination: armadillo-mutant genotype.

(a) Selected multi-photon images of in vivo transverse cross-sections of an armadillo-mutant embryo during ventral furrow formation. armadillo-mutant lacks strong apical junctions, and ventral indentation collapses at t = −4.22 min. The embryo is labelled with Sqh-GFP and oriented with its dorsal surface upward (Fig. 1a). The time interval between successive frames is 45 sec and instant zero was set by using apical-basal cell height profiles on the dorsal side (Fig. S2c). (b) Selected frames (columns) of in silico transverse cross-section of an arm-mutant genotype. Embryo's 2D geometry is oriented with its dorsal side upward. The undeformed initial configuration (panel b′) corresponds to in vivo deformations at t = −10.43 min (see panel d). (c) In silico force distributions utilised to simulate invagination in b). (d) Time-trends of average radial mesodermal () thickness of the epithelium (see schematic in Fig. 3e).

Figure 6. Modelling ventral furrow invagination: cta/t48-mutant genotype.

(a) Selected multi-photon images of in vivo transverse cross-sections of a cta/t48-mutant embryo during ventral furrow formation. In cta/t48-mutants apical constriction is completely abolished. Embryo is labelled with Sqh-GFP and oriented with its dorsal surface upward (Fig. 1a). Time interval between successive frames is 45 sec and instant zero was set by using apical-basal cell height profiles on the dorsal side (Fig. S2d). (b) Selected frames (columns) of in silico transverse cross-section of a cta/t48-mutants genotype. Embryo's 2D geometry is oriented with its dorsal side upward. The undeformed initial configuration (panel b′) corresponds to in vivo deformations at t = −10.43 min (see panel d). (c) In silico force distributions utilised to simulate invagination in b). (d) Time-trends of average radial mesodermal () thickness of the epithelium (see schematic in Fig. 3e).

Figure 7. Ventral furrow invagination robustness to in silico ectodermal perturbations.

The wild type mechanism of invagination (Fig. 3c) has been perturbed by switching on/off component forces acting in the ectoderm (blue and yellow lines). The figure shows that perturbing the wild type mechanism of invagination does not hinder ventral furrow formation, which is ultimately regained in a shorter or longer period depending on the typology of perturbation. It is worth noticing that the perturbation introduced in the invagination mechanism (see panels f–g) does not affect phenotypes corresponding to t<−1.5 min, which remain the same as in the wild type case (Fig. 3a′–a″). (a) Phenotypes relative to the wild type mechanism where no basal ectodermal constriction is activated. (b) Phenotypes relative to the mechanism where no radial ectodermal shortening has been activated. (c) Phenotypes relative to the mechanism where both ectodermal movements have been turned off, resulting in an inactive ectoderm. (d) Force trends utilised to simulate the wild type invagination mechanism with no ectodermal basal constriction – the component that corresponds in the graph to this movement has been suppressed (blue line). (e) Force trends utilised to simulate the wild type invagination mechanism with no ectodermal radial shortening – the component that corresponds in the graph to this movement has been suppressed (yellow line). Similarly, force trends to simulate wild type invagination with no active ectodermal forces (both basal and radial ones) have been obtained by suppressing the lines that correspond in the graph to these two movements. (f) Time-trends of average radial mesodermal () thickness of the epithelium (see schematic in Fig. 3e). (g) Time-trends of furrow's height h at the ventral side (see schematic in Fig. 3e). The blue dotted lines in panels (f) and (g) indicate that the simulation detailed in (b) (where no radial ectoderm has been activated) fully invaginates on a longer period of time with respect to that shown in figure panels.

Figure 8. Meso-radial time study.

The quantitative effects of anticipating the onset of mesodermal radial shortening with respect to the wild type case reported in Fig. 3, while keeping the remaining force trends unchanged (Fig. 3c). (a) Force trend curves labelled by , , and illustrate the case where meso-radial movement was respectively advanced at t = −3.48 min, t = −5.8 min, t = −8.12 min and delayed at t = 0.58 min with respect to the wt case (where meso-radial movement onsets at t = −1.2 min, as shown in Fig. 3c). (b–c) Changes in the onset time of this movement with respect to the others have significant impact on furrow's height h, which increases with the anticipation of the movement. The average mesodermal thickness decreases with the anticipation of the movement in that mesodermal cells start shortening earlier. (d–g) Final phenotypes (t = 6 min) corresponding to wild type with mesodermal radial movements respectively delayed by (dotted lines in panels a–c) and advanced by , and .