We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstrain. 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.

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains' masses and the striker mass. Numerical calculations and experiments corroborate these findings.

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.

Laser microsurgery and computer tracking of embryo structures indicate that the morphogenetic process of Drosophila dorsal closure requires only forces generated by the amnioserosa tissue. Forces generated by both “zipping” of epidermal tissue at the canthi corners and the resulting actomyosin purse string curvature are not necessary for closure.

Experiments show that perturbation by an incident striker can generate solitary wave trains in unloaded, monodispersed elastic sphere alignments (Lazaridi A. N. and Nesterenko V. F., Prikl. Mekh. Tekh. Fiz., 3 (1985) 115). We report the first dynamical studies in the elastic regime that confirm and extend upon the results obtained in existing experiments and define the conditions for which controlled generation of solitary wave trains may be possible.

Energy partitioning and impulse dispersion in the decorated, tapered, strongly nonlinear granular alignment: A system with many potential applications

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.

The three-dimensional surface of dorsal-closure-staged Drosophila embryos is indented by two purse strings that surround an eye-shaped amnioserosa tissue. The amnioserosa forms a remarkably smooth, asymmetric dome that bulges outward due to the embryo’s internal pressure. Quantitative analysis with Laplace’s formula indicates that the elastic properties of the amnioserosa are isotropic and uniform.