A 3D finite element model of ventral furrow invagination in the Drosophila melanogaster embryo.
ABSTRACT The paper describes a mechanical model of epithelial tissue development in Drosophila embryos to investigate a buckling phenomenon called invagination. The finite element method is used to model this ventral furrow formation in 3D by decomposing the total deformation into two parts: an imposed active deformation, and an elastic passive deformation superimposed onto the latter. The model imposes as boundary conditions (i) a constant yolk volume and (ii) a sliding contact condition of the cells against the vitelline membrane, which is interpolated as a B-Spline surface. The active deformation simulates the effects of apical constriction and apico-basal elongation of cells. This set of local cellular mechanisms leads to global shape changes of the embryo which are associated with known gene expressions. Using the model we have tested different plausible hypotheses postulated to account for the mechanical behaviour of epithelial tissues. In particular, we conclude that only certain combinations of local cell shape change can successfully reproduce the invagination process. We have quantitatively compared the model with a 2D model and shown that it exhibits a more robust invagination phenomenon. The 3D model has also revealed that invagination causes a yolk flow from the central region to the anterior and posterior ends of the embryo, causing an accordion-like global compression and expansion wave to move through the embryo. Such a phenomenon cannot be described by 2D models.
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ABSTRACT: A set of equilibrium equations is derived for the stress-controlled shape change of cells due to the remodelling and growth of their internal architecture. The approach involves the decomposition of the deformation gradient into an active and a passive component; the former is allowed to include a growth process, while the latter is assumed to be hyperelastic and mass-preserving. The two components are coupled with a control function that provides the required feedback mechanism. The balance equations for general continua are derived and, using a variational approach, we deduce the equilibrium equations and study the effects of the control function on these equations. The results are applied to a truss system whose function is to simulate the cytoskeletal network constituted by myosin microfilaments and microtubules, which are found experimentally to control shape change in cells. Special attention is paid to the conditions that a thermodynamically consistent formulation should satisfy. The model is used to simulate the multicellular shape changes observed during ventral furrow invagination of the Drosophila melanogaster embryo. The results confirm that ventral furrow invagination can be achieved through stress control alone, without the need for other regulatory or signalling mechanisms. The model also reveals that the yolk plays a distinct role in the process, which is different to its role during invagination with externally imposed strains. In stress control, the incompressibility constraint of the yolk leads, via feedback, to the generation of a pressure in the ventral zone of the epithelium that eventually eases its rise and internalisation.Biomechanics and Modeling in Mechanobiology 08/2010; 9(4):451-67. DOI:10.1007/s10237-009-0187-9 · 3.25 Impact Factor
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ABSTRACT: Ventral furrow formation in Drosophila is the first large-scale morphogenetic movement during the life of the embryo, and is driven by co-ordinated changes in the shape of individual epithelial cells within the cellular blastoderm. Although many of the genes involved have been identified, the details of the mechanical processes that convert local changes in gene expression into whole-scale changes in embryonic form remain to be fully understood. Biologists have identified two main cell deformation modes responsible for ventral furrow invagination: constriction of the apical ends of the cells (apical wedging) and deformation along their apical-basal axes (radial lengthening/shortening). In this work, we used a computer 2D finite element model of ventral furrow formation to investigate the ability of different combinations of three plausible elementary active cell shape changes to bring about epithelial invagination: ectodermal apical-basal shortening, mesodermal apical-basal lengthening/shortening and mesodermal apical constriction. We undertook a systems analysis of the biomechanical system, which revealed many different combinations of active forces (invagination mechanisms) were able to generate a ventral furrow. Two important general features were revealed. First that combinations of shape changes are the most robust to environmental and mutational perturbation, in particular those combining ectodermal pushing and mesodermal wedging. Second, that ectodermal pushing plays a big part in all of the robust mechanisms (mesodermal forces alone do not close the furrow), and this provides evidence that it may be an important element in the mechanics of invagination in Drosophila.Physical Biology 02/2009; 6(1):016010. DOI:10.1088/1478-3975/6/1/016010 · 3.14 Impact Factor
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ABSTRACT: Studies carried out to determine the influence of phosphorylation and dephosphorylation of proteins in a variety of physiological events are of increasing interest. The activity of kinases and phosphatases and their respective inhibition by endogenous mediators and by pharmacological agents regulates a huge number of biochemical pathways involved in cellular proliferation, apoptosis, inflammation, hormonal activity, and gene transcription, amongother processes. This article focuses on the recently described natural products able to interfere negatively with the activity of serine/threonine and tyrosine kinases. These agents are classified, according to theirbiosynthetic origin and chemical properties in phenolics, terpenoids, alkaloids and miscellaneous substances. The nucleus of the review is preceded by a general overview on kinase activity, followed by a chapter devoted to naturally occurring kinase activators. Finally, a section concerning the advances in phosphatase inhibition research is included. The main sources of novel phenolic kinase inhibitors are tannins, coumarins, polycyclic isopentenyl isoflavonoids, and phloroglucinols. Other phenolics like flavonols or simple isoflavones are also reported, together with some reputed plant active principles such as curcumin, hypericin or resveratrol. Amongthe terpenoids, the effects of wortmannin, and thoseof certain triterpenoids like ginsenoside Rb1 or Rh1 should be mentioned. The alkaloids comprise two main groups of inhibitors: the indole alkaloids, headed by staurosporine and its derivatives, which are potent, selective inhibitors of protein kinase C, and the isoquinoline alkaloids, subdivided into aporphines, benzophenanthridines and naphtylisoquinolines. The scientific panorama regarding the inhibition of phosphatases is dominated by the polyether and cyclic polypeptide environmental toxins, although some new agents such as indole and isoquinoline alkaloids have been described.