Remodeling Tissue Interfaces and the Thermodynamics of Zipping during Dorsal Closure in Drosophila.

Dorsal closure during Drosophila embryogenesis is an important model system for investigating the biomechanics of morphogenesis. During closure, two flanks of lateral epidermis (with actomyosin-rich purse strings near each leading edge) close an eye-shaped opening that is filled with amnioserosa. At each canthus (corner of the eye) a zipping process remodels the tissue interfaces between the leading edges of the lateral epidermis and the amnioserosa. We investigated zipping dynamics and found that apposing leading edge cells come together at their apical ends and then square off basally to form a lateral junction. Meanwhile, the purse strings act as contractile elastic rods bent toward the embryo interior near each canthus. We propose that a canthus-localized force contributes to both bending the ends of the purse strings and the formation of lateral junctions. We developed a thermodynamic model for zipping based on three-dimensional remodeling of the tissue interfaces and the reaction dynamics of adhesion molecules in junctions and elsewhere, which we applied to zipping during unperturbed wild-type closure and to laser or genetically perturbed closure. We identified two processes that can contribute to the zipping mechanism, consistent with experiments, distinguished by whether amnioserosa dynamics do or do not augment canthus adhesion dynamics.

Cell ingression and apical shape oscillations during dorsal closure in Drosophila.

Programmed patterns of gene expression, cell-cell signaling, and cellular forces cause morphogenic movements during dorsal closure. We investigated the apical cell-shape changes that characterize amnioserosa cells during dorsal closure in Drosophila embryos with in vivo imaging of green-fluorescent-protein-labeled DE-cadherin. Time-lapsed, confocal images were assessed with a novel segmentation algorithm, Fourier analysis, and kinematic and dynamical modeling. We found two generic processes, reversible oscillations in apical cross-sectional area and cell ingression characterized by persistent loss of apical area. We quantified a time-dependent, spatially-averaged sum of intracellular and intercellular forces acting on each cell's apical belt of DE-cadherin. We observed that a substantial fraction of amnioserosa cells ingress near the leading edges of lateral epidermis, consistent with the view that ingression can be regulated by leading-edge cells. This is in addition to previously observed ingression processes associated with zipping and apoptosis. Although there is cell-to-cell variability in the maximum rate for decreasing apical area (0.3-9.5 µm(2)/min), the rate for completing ingression is remarkably constant (0.83 cells/min, r(2) > 0.99). We propose that this constant ingression rate contributes to the spatiotemporal regularity of mechanical stress exerted by the amnioserosa on each leading edge during closure.

Quantifying dorsal closure in three dimensions.

Dorsal closure is an essential stage of Drosophila embryogenesis and is a powerful model system for morphogenesis, wound healing, and tissue biomechanics. During closure, two flanks of lateral epidermis close an eye-shaped dorsal opening that is filled with amnioserosa. The two flanks of lateral epidermis are zipped together at each canthus ("corner" of the eye). Actomyosin-rich purse strings are localized at each of the two leading edges of lateral epidermis ("lids" of the eye). Here we report that each purse string indents the dorsal surface at each leading edge. The amnioserosa tissue bulges outward during the early-to-mid stages of closure to form a remarkably smooth, asymmetric dome indicative of an isotropic and uniform surface tension. Internal pressure of the embryo and tissue elastic properties help to shape the dorsal surface.

Impulse penetration into idealized granular beds: behavior of cumulative surface kinetic energy.

We report a particle dynamics based simulational study of the propagation of delta function mechanical impulses in idealized three-dimensional hexagonal close packed lattices of monosized Hertz spheres. This paper presents five key results on the kinetic energy of grains at the surface of a granular bed after the generation of a normal impulse into the bed. (i) We find that the time integrated or cumulative average kinetic energy per surface grain, kappa, drops as an impulse penetrates into the bed. The minimum value of kappa, say kappa(0), is reached at some time t=tau after the impulse has been generated. (ii) This value, kappa(0), depends upon the restitutional losses at the grain contacts and kappa(0) increases as restitutional losses at granular contacts increase in magnitude. (iii) The asymptotic value of kappa is denoted by kappa(final) . Our data show that increasing the area across which an impulse is generated, A, leads to kappa(final) proportional to A(-1/2) . (iv) If we assign random masses to our monosized grains, kappa(final) grows quadratically as a function of the range of mass variation about a mean mass. We find that at large times, i.e., t>>tau , kappa proportional to (1-exp [k (1-t/tau)]) , where the constant k is roughly independent of restitution for the typical values of restitution encountered. (v) Our data suggest that at early times, the backscattering process carries signatures of ballistic propagation of the mechanical energy while at late times, the backscattering process is reminiscent of vibrations of an essentially ergodic system. Given the ballisticlike propagation of mechanical energy into granular beds, we conclude that a wave equation based description of mechanical energy propagation into granular beds may not always be appropriate.

Complete canthi removal reveals that forces from the amnioserosa alone are sufficient to drive dorsal closure in Drosophila.

Drosophila's dorsal closure provides an excellent model system with which to analyze biomechanical processes during morphogenesis. During native closure, the amnioserosa, flanked by two lateral epidermal sheets, forms an eye-shaped opening with canthi at each corner. The dynamics of amnioserosa cells and actomyosin purse strings in the leading edges of epidermal cells promote closure, whereas the bulk of the lateral epidermis opposes closure. Canthi maintain purse string curvature (necessary for their dorsalward forces), and zipping at the canthi shortens leading edges, ensuring a continuous epithelium at closure completion. We investigated the requirement for intact canthi during closure with laser dissection approaches. Dissection of one or both canthi resulted in tissue recoil and flattening of each purse string. After recoil and a temporary pause, closure resumed at approximately native rates until slowing near the completion of closure. Thus the amnioserosa alone can drive closure after dissection of one or both canthi, requiring neither substantial purse string curvature nor zipping during the bulk of closure. How the embryo coordinates multiple, large forces (each of which is orders of magnitude greater than the net force) during native closure and is also resilient to multiple perturbations are key extant questions.

How hertzian solitary waves interact with boundaries in a 1D granular medium.

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.