Sharp boundaries of Dpp signalling trigger local cell death required for Drosophila leg morphogenesis

Article available at http://dx.doi.org/10.1038/ncb1518Morphogens are secreted signalling molecules that govern many developmental processes1. In the Drosophila wing disc, the transforming growth factor (TGF) homologue Decapentaplegic (Dpp) forms a smooth gradient and specifies cell fate by conferring a defined value of morphogen activity. Thus, neighbouring cells have similar amounts of Dpp protein, and if a sharp discontinuity in Dpp activity is generated between these cells, Jun kinase (JNK)-dependent apoptosis is triggered to restore graded positional information2, 3. To date, it has been assumed that this apoptotic process is only activated when normal signalling is distorted. However, we now show that a similar process occurs during normal development: rupture in Dpp activity occurs during normal segmentation of the distal legs of Drosophila. This sharp boundary of Dpp signalling, independently of the absolute level of Dpp activity, induces a JNK—reaper-dependent apoptosis required for the morphogenesis of a particular structure of the leg, the joint. Our results show that Dpp could induce a developmental programme not only in a concentration dependent manner, but also by the creation of a sharp boundary of Dpp activity. Furthermore, the same process could be used either to restore a normal pattern in response to artificial disturbance or to direct a morphogenetic process.This work has been supported by grants from the Dirección General de Investigación Científica y Técnica (BMC 2002-00300), the Comunidad Autónoma de Madrid (08.1/0031/2001.1 and GR/SAL/0147/2004) and an Institutional Grant from the Fundación Ramón Areces. C.M. is a recipient of a Formación del Personal Universitario (F.P.U.) fellowship from the Ministerio de Educación y Ciencia.Peer reviewe

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Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings