JNK signalling controls remodelling of the segment boundary through cell reprogramming during Drosophila morphogenesis.

Segments are fundamental units in animal development which are made of distinct cell lineages separated by boundaries. Although boundaries show limited plasticity during their formation for sharpening, cell lineages make compartments that become tightly restricted as development goes on. Here, we characterize a unique case of breaking of the segment boundary in late drosophila embryos. During dorsal closure, specific cells from anterior compartments cross the segment boundary and enter the adjacent posterior compartments. This cell mixing behaviour is driven by an anterior-to-posterior reprogramming mechanism involving de novo expression of the homeodomain protein Engrailed. Mixing is accompanied by stereotyped local cell intercalation, converting the segment boundary into a relaxation compartment important for tension-release during morphogenesis. This process of lineage switching and cell remodelling is controlled by JNK signalling. Our results reveal plasticity of segment boundaries during late morphogenesis and a role for JNK-dependent developmental reprogramming in this process.

A mathematical model for dorsal closure.

During embryogenesis, drosophila embryos undergo epithelial folding and unfolding, which leads to a hole in the dorsal epidermis, transiently covered by an extraembryonic tissue called the amnioserosa. Dorsal closure (DC) consists of the migration of lateral epidermis towards the midline, covering the amnioserosa. It has been extensively studied since numerous physical mechanisms and signaling pathways present in DC are conserved in other morphogenetic events and wound healing in many other species (including vertebrates). We present here a simple mathematical model for DC that involves a reduced number of parameters directly linked to the intensity of the forces in the presence and which is applicable to a wide range of geometries of the leading edge (LE). This model is a natural generalization of the very interesting model proposed in Hutson et al. (2003). Being based on an ordinary differential equation (ODE) approach, the previous model had the advantage of being even simpler, but this restricted significantly the variety of geometries that could be considered and thus the number of modified dorsal closures that could be studied. A partial differential equation (PDE) approach, as the one developed here, allows considering much more general situations that show up in genetically or physically perturbed embryos and whose study will be essential for a proper understanding of the different components of the DC process. Even for native embryos, our model has the advantage of being applicable since an early stages of DC when there is no antero-posterior symmetry (approximately verified only in the late phases of DC). We validate our model in a native setting and also test it further in embryos where the zipping force is perturbed through the expression of spastin (a microtubule severing protein). We obtain variations of the force coefficients that are consistent with what was previously described for this setting.

Optimal Control of Propagating Fronts by Using Level Set Methods and Neural Approximations.

We address the optimal control of level sets associated with the solution of the normal flow equation. The problem consists in finding the normal velocity to the front described by a certain level set in such a way to minimize a given cost functional. First, the considered problem is shown to admit a solution on a suitable space of functions. Then, since in general it is difficult to solve it analytically, an approximation scheme that relies on the extended Ritz method is proposed to find suboptimal solutions. Specifically, the control law is forced to take on a neural structure depending nonlinearly on a finite number of parameters to be tuned, i.e., the neural weights. The selection of the optimal weights is performed with two different approaches. The first one employs classical line-search descent methods, while the second one is based on a quasi-Newton optimization that can be regarded as neural learning based on the extended Kalman filter. Compared with line-search methods, such an approach reveals to be successful with a reduced computational effort and an increased robustness with respect to the trapping into local minima, as confirmed by simulations in both two and three dimensions.

Modeling and Identification of Amnioserosa Cell Mechanical Behavior by Using Mass-Spring Lattices.

Various mechanical models of live amnioserosa cells during Drosophila melanogaster's dorsal closure are proposed. Such models account for specific biomechanical oscillating behaviors and depend on a different set of parameters. The identification of the parameters for each of the proposed models is accomplished according to a least-squares approach in such a way to best fit the cellular dynamics extracted from live images. For the purpose of comparison, the resulting models after identification are validated to allow for the selection of the most appropriate description of such a cell dynamics. The proposed methodology is general and it may be applied to other planar biological processes.