26453 articles – 20328 references  [version française]
Short view Article in peer-reviewed journal
A mathematical model for dorsal closure.
Almeida L. et al
Journal of Theoretical Biology (2010) epub ahead of print - http://hal.archives-ouvertes.fr/hal-00533785
Luís Almeida1, Patrizia Bagnerini2, Abderrahmane Habbal1, Stéphane Noselli3, Fanny Serman1, 4
1:  JAD - Laboratoire Jean Alexandre Dieudonné
CNRS : UMR6621 – Université Nice Sophia Antipolis (UNS)
Université de Nice - Sophia Antipolis U.M.R. no 6621 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France
2:  DIPTEM - Dipartimento di Ingegneria della produzione, termoenergetica e modelli matematici
Università degli studi di Genova
Universite degli Studi di Genova P.le Kenedy - Pad D 16129 Genova
3:  IBDC - Institute of Developmental Biology and Cancer
CNRS : UMR6543 – Université Nice Sophia Antipolis (UNS)
Parc Valrose 06108 Nice cedex 2
4:  ISBDC - Institut de signalisation, biologie du développement et cancer
http:// www.unice.fr/ISDBC
CNRS : UMR6543 – Université Nice Sophia Antipolis (UNS)
Centre Antoine lacassagne 33 Avenue de volombrose 06189 NICE CEDEX 2
Life Sciences/Development Biology
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.

Journal of Theoretical Biology
epub ahead of print