A comprehensive model of Drosophila epithelium reveals the role of embryo geometry and cell topology in mechanical responses

Abstract

Understanding physical mechanisms underlying morphogenesis requires the knowledge of the mechanical properties of embryonic tissue. Despite a long-standing interest in this subject, very few in vivo measurements are currently available. Here, using the early fly embryo as a model, we describe a novel cantilever-based technique for measuring material properties of embryonic tissues. A major advantage of our approach is the ability to exert large (nanonewton-range) forces with subcellular spatial precision: our technique improves signal to noise by approximately an order of magnitude compared to previous methods. This advance allowed us to demonstrate that deformation caused by force applied to a single cell edge spreads across the whole embryo on a time scale of seconds and that the mechanical response is dominated by system-size effects, and not friction between the tissue and its environment. Based on these measurements, we estimate the Young's modulus of the cellular edges in the early embryo.

A scaling law for epithelial tissue rheology

“…Using these values, fitting a 1/2 power law to measurement data from Fig. 1, we obtain an estimate of k ≈ 23 nN/µm, which is in excellent agreement with our independent measurements from (2). Note that our value for k basal therein is relevant to long-time dynamics and therefore corresponds to the 20 % of total actin that does not turn over; for this reason, a correction factor of 5 is in order for a more direct (semi-)quantitative comparison.…”

“…Subsequently, in a stereotyped sequence of folding events called gastrulation, the embryo becomes multilayered. Recent experimental studies examined material properties of embryonic tissues during the blastula stage (1)(2)(3). Strikingly, when constant concentrated force was applied to the cellular layer, displacement followed a power law with an exponent of 1/2.…”

The Geometric Basis of Epithelial Convergent Extension

“…This suggests that rapid force equilibration makes the apparent tissue flow approximately adiabatic (see also Refs. [37,40]). Second, we assume that mechanical stress in the epithelium is primarily carried by the adherens-junctional cytoskeleton, which resides on cell interfaces.…”

“…whether they are active or passive. Importantly, tension-isogonal decomposition is based on the same assumptions as tension inference which has been validated extensively in previous literature [34, 35, 42, 43].…”

“…Together, the adherens junctions define a tissue-wide mechanical structure, capable of (i) generating locally controlled internal tension and (ii) adaptively remodelling its architecture. The Drosophila blastoderm lies on top of a fluid yolk [41] which exerts negligible drag forces on tissue motion on the surface [42], suggesting that all forces are balanced within the epithelial layer. Concentration of tension in interfaces tightly links force balance with the readily observable geometry of cell-cell interfaces.…”