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.
Sneppen, K.; Lizana, L.; Jensen, Mogens H.; Pigolotti, S.; Otzen, D. Physical biology Vol. 6, num. 3, p. 036005-1-036005-10 DOI: 10.1088/1478-3975/6/3/036005 Data de publicació: 2009-05-01 Article en revista
In Parkinson's disease (PD), there is evidence that a-synuclein (aSN) aggregation is coupled to dysfunctional or overburdened protein quality control systems, in particular the ubiquitin–proteasome system. Here, we develop a simple dynamical model for the on-going conflict between aSN aggregation and the maintenance of a functional proteasome in the healthy cell, based on the premise that proteasomal activity can be titrated out by mature aSN fibrils and their protofilament precursors. In the presence of excess proteasomes the cell easily maintains homeostasis. However, when the ratio between the available proteasome and the aSN protofilaments is reduced below a threshold level, we predict a collapse of homeostasis and onset of oscillations in the proteasome concentration. Depleted proteasome opens for accumulation of oligomers. Our analysis suggests that the onset of PD is associated with a proteasome population that becomes occupied in periodic degradation of aggregates. This behavior is found to be the general state of a proteasome/chaperone system under pressure, and suggests new interpretations of other diseases where protein aggregation could stress elements of the protein quality control system.
The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-¿B). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.