Mechanics of Drosophila wing deployment

Abstract

During their final transformation, insects emerge from the pupal case and deploy their wings within minutes. The wings deploy from a compact origami structure, to form a planar and rigid blade that allows the insect to fly. Deployment is powered by a rapid increase in internal pressure, and by the subsequent flow of hemolymph into the deployable wing structure. Using a combination of imaging techniques, we characterize the internal and external structure of the wing in Drosophila melanogaster, the unfolding kinematics at the organ scale, and the hemolymph flow during deployment. We find that, beyond the mere unfolding of the macroscopic folds, wing deployment also involves wing expansion, with the stretching of epithelial cells and the unwrinkling of the cuticle enveloping the wing. A quantitative computational model, incorporating mechanical measurements of the viscoelastic properties and microstructure of the wing, predicts the existence of an operating point for deployment and captures the dynamics of the process. This model shows that insects exploit material and geometric nonlinearities to achieve rapid and efficient reconfiguration of soft deployable structures.

Fig. 1. Geometry and pressure in the deploying wing.

a Snapshots of the wings deployment with one of the longitudinal veins highlighted in green. b (i) Microtomography of the folded wings. (ii) Micro-CT scan cross-section showing macroscopic folds, vein structure (white arrows), and internal pillars. (iii) Perpendicular section revealing the hexagonal pillars organization. The sketch summarizes the wing structure: two plates (thickness e) connected with pillars (height h, diameter d) organized in a hexagonal lattice (interpillar distance a). c Fluorescent beads (white dots, hemolymph markers) flowing in a deploying wing. d In vivo recording of the internal pressure P(t) of a newly emerged insect. Wings deployment takes place throughout the grayed-out segment at a constant pressure P^*.

Fig. 2. Unfolding and expansion.

a Veins network in the folded state (from micro-CT scans) and in the deployed state (from bright-field microscopy images). Each color represents a specific vein. b Macroscopic wing deployment Λ = L/L_F as a function of time for 3 different flies. L is the length between the two ends of the longitudinal vein highlighted in green in (a) and Fig. 1a, and L_F is the initial folded length. Dotted vertical lines correspond to the snapshots in Fig. 1a. c Arclength of deployed veins l_D versus folded veins l_F. Each color represents a vein shown in (a). Length measurements from micro-CT are represented by square markers, while veins tracked on videos are represented by circular markers (empty for females, full for males). The solid line is a linear fit of all experiments. Folded veins from micro-CT (l_F, ◼) are coming from measurement on 2 male wings, and the corresponding deployed veins (l_D, ◼) are obtained from bright-field images of 10 male wings (5 different flies), the data are presented as mean values ± max/min measurements. Veins are tracked on 6 flies deploying their wings, 3 females ○, and 3 males ●; the data are presented as mean values ±5% relative error due to video tracking.

Fig. 3. Cells stretching and cuticle unwrinkling.

a Schematic view of a wing microscopic structure: 2 monolayers of epithelial cells (green) covered by a thin rigid cuticle (red) and connected by pillars. b Cross-section following the dotted frame in (a), transmitted electron microscopy (TEM). c Wing surface scans (optical profilometer, 50 × 50 μm²). Top right inset: 3D reconstruction of the volcano-shaped wrinkle on the apical surface of an epithelial cell (spining disk confocal microscopy, Utrophin:GFP). d Epithelial cells contour (spining disk confocal microscopy, Ecad:GFP). For (b-d) top images correspond to folded wings, while bottom images correspond to deployed wings. e Evolution of the main geometric characteristics from folded (F) to deployed (D) stages (from top left to bottom right diagram): 2D epithelial cell surface area; 3D surface area integration of the cuticle; total wing thickness; and wrinkles height. Data are obtained by TEM (purple boxes, see (b)), profilometer scans (yellow, (c)), spinning disk (blue, (d)), and two-photon images (gray, see Supplementary Fig.5d). Each boxplot displays the median, the lower and upper quartiles, and the minimum and maximum values, and is obtained with the following sample sizes. Area: spinning disk (folded wing: 16 z-stacks, deploying wing: 7 z-stacks), profilometer (folded wing: 3 scans, deployed wing: 3 scans). 3D area: spinning disk (folded wing: 5 z-stacks), profilometer (deployed wing: 3 scans). Wing thickness: TEM (folded wing: 2 scans, deployed wing: 3 scans), two-photon (deploying wing: 2 scans). Height: profilometer (folded wings: 8 scans, deployed wings: 3 scans).

Fig. 4. Mechanics of wing deployment.

a Schematic of the two-scale deployment mechanism. Macroscopic scale (top): wing unfolding and expansion. Microscopic scale (bottom): cellular stretching and subsequent cuticle unwrinkling and pillar straightening. The sketch shows a cross-section of the folded (left) and deployed (right) wing structure with wrinkles and pillars under pressure. b F/S₀ versus deployment Λ = L/L_F obtained from the tensile test of the wing. c True stress σ = λF/S₀ versus true strain $ln\left(\lambda \right)=ln\left(l/l_F\right)$. Yellow line: hyperelastic Gent model (E = 200 kPa, J_m =  20). d Prediction of in-plane stretch λ (black, left axis) and pillars vertical stretch λ^p (orange, right axis) as a function of the normalized applied pressure $\overline{P}=P/E$ for a hyperelastic Gent material (model: solid lines; FEM: dashed lines). Pressure measurements normalized by a Young’s modulus of E = 16 kPa are shown as gray markers.

Fig. 5. Dynamics of wing deployment.

a Force-displacement curves obtained from nano-indentation experiments on folded wings, from slow indentation ($\stackrel{°}{F_i}=10^{-1}\mu$N/s, blue) to faster ($\stackrel{°}{F_i}=10^1\mu$N/s, red). Inset: Deformation ϵ = (δ/R)^1/2 measured over time for a creep experiment during which a constant-force F_i is applied (gray line). Experimental data (in black) are fitted with the model (yellow line). b ϵ versus normalized time t/T: both experimental data (from a, colored markers) and FEM numerical simulations of viscoelastic bilayer indentation (green dashed line) collapse on the model $ϵ={\left(t/T\right)}^{2/3}$ (black line). Inset: local strain in the indentation direction ϵ_zz from FEM simulations. c In-plane stretch λ as a function of t/τ. Experimental measurements (normalized with τ = 10 s): gray markers; model: solid line. Snapshots of FEM simulations at t/τ = 0, 5, and 25 are shown (color bar: strain in one of the in-plane directions).