Drosophila Morphogenesis: The Newtonian Revolution Dispatch

The ability of cells to change their relative positions is a fundamental process in metazoan development. Many studies have identified genes that are essential for cell and tissue movement, but their specific roles are not well understood, and the description remains mostly qualitative. This complex biological problem requires novel approaches directed at quantitative analysis. In a pioneering study, Hutson et al. [1] have combined quantitative modeling and laser microsurgery to describe the forces that drive dorsal closure of the Drosophila embryo [2,3]. During this morphogenetic event, two symmetrical epithelia move towards each other in a lateral-to-dorsal direction (Figure 1A). Within two hours, the dorsal borders of the moving epithelia — the leading edges — meet and fuse at the dorsal midline. During closure, the amnioserosa, a transient dorsal tissue, is progressively covered by the incoming lateral epithelia. When viewed from the top, the leading edges draw an eye shape, where the corners — known as ‘canthi’ — act as zippers. At the cellular level, zipping between approaching edges at the canthi is promoted by active actin protrusions which interlace at the seam [4,5]. In the initial phase of dorsal closure, a prominent actin cable is assembled in the edges, leading to the possibility that a ‘purse string’ mechanism would provide a major force for closure [6]. In order to evaluate the forces in the tissues that participate in dorsal closure, laser microsurgery and mechanical jump experiments have been used on wild-type embryos [7]. This simple approach indicates that the amnioserosa contributes positively to the movement, as its ablation induces ventralward relaxation of the leading edges. An incision in the lateral epithelium has the opposite effect, revealing a force that resists dorsal closure. The effect of cutting the actin cable, on the other hand, highlights the existence of a tension which is tangent to the leading edge. From these observations and the application of Newton’s second law, it is possible to draw a diagram of the three main forces present at the leading edge symmetry point (Figure 1B): two forces of contraction, from the amnioserosa (σAS) and the cable (Tκ , where T is the tension in the actin cable and κ is the curvature), which are opposed to the force of resistance from the lateral ectoderm (σLE). To simplify the calculations, the model focuses on describing the forces at the cable symmetry point only, and takes advantage of the fact that, during mid-to-late stages, the dorsal surface nearly lies in a plane (Figure 1A). Video recording showed that, following initiation of dorsal closure, the velocity of the leading edge is constant, at 12 ± 1.5 nanometres per second. This striking observation indicates that, once initiation is achieved, the forces driving dorsal closure are in equilibrium — that is, the sum of the applied forces, σLE – σAS – Tκ, is constant and balanced by a drag force. As it is not possible to establish the absolute force values at a given point and time, experiments involving a series of laser-induced mechanical jumps were carried out at different stages of dorsal closure to assess the relative contribution of the amnioserosa and of the tension in the cable. From these data along with simple mathematical arguments and simplifying hypotheses (see [1] for details), the contributions of the three forces (σLE:σAS:Tκ) relative to the effective force driving closure (taken as 1) were bracketed between the ratios 120:80:40 and 160:80:80. Note that the magnitude of σLE can be as much as 160 times bigger than that of the force driving closure. Two conclusions can be drawn from this determination of the force balance. First, although the tension in the cable, T, is the strongest force, its contribution to closure (Tκ) is comparatively small — because the curvature, κ, is modest — showing that, contrary to common sense, the ‘purse string’ is not contributing the major force for closure. Second, during mid-to-late closure, the largest individual force is negative, originating from the resistive force generated by the lateral ectoderm. In addition to providing a quantitative basis of the relative forces shaping dorsal closure, Hutson et al. [1] have developed a model to describe the geometry of closure. The rationale is to provide a mathematical model that is predictive, not only for wild-type embryos, but also for mechanically or genetically perturbed ones. For this purpose, the leading edges are viewed as two intersecting circular arcs (Figure 1C), the geometry of which can be described in a time-dependent manner using an empirical rate equation (for details on the mathematical formalism, see [1]). In this model, the changes in shape of the leading edges are due to fractional contributions coming from zipping at the canthi (fz) and from forces acting on the cable (fc). During normal dorsal closure, fz is ~1/3 and fc is ~2/3 (fc = 1 – fz). Strikingly, the geometric model not only describes the behavior of leading edges of wild-type embryos, but also of embryos in which fc or fz have been strongly affected by laser ablations. Current Biology, Vol. 13, R494–R495, June 17, 2003, ©2003 Elsevier Science Ltd. All rights reserved. DOI 10.1016/S0960-9822(03)00412-3