Inside the coupling of ladybird beetle elytra: elastic setae can facilitate swift deployment

Biological structures storing elastic energy for fast locomotion have been widely studied because of their diverse function (Farley et al., 1993), such as escaping from predators, catching prey and self-righting (Bolmin et al., 2019; Henry et al., 2005; Ruan et al., 2020). Compared with storing energy in tendons or skeletal structures of vertebrates, some energy storage devices in invertebrates rely on elastic structures; for example, composite structures consisting of chitinized cuticle and the elastic protein resilin in limbs of locusts (Schistocerca gregaria) (Burrows and Sutton, 2012), and a pad of resilin in the thoraxes of fleas (Archaeopsyllus erinacei) (Sutton and Burrows, 2011). A flea is able to jump 150 times its body length by releasing a large amount of elastic energy stored in resilin (Koh et al., 2013). Another example of swift locomotion can be found in the appendages of ladybird beetles (Coccinella septempunctata). The elytra of ladybirds, transformed from the forewings to serve a protective function, cover and protect the fragile hindwings. The elytra are scoop-shaped evaginations of the body integument attached by a membrane between the tergum and pleuron. The edge of the elytra is divided into three regions, namely the basal, costal and sutural (medial) edges (Frantsevich, 2012b). At the sutural edge, the elytra can be locked together by a coupling structure consisting of a mortise and tenon, where the tenon is blade-shaped and inserts into the grooved mortise structure. When the elytra are closed, the apex of the elytra, where the basal and sutural edges converge, is in contact with the tergum and a small triangular scutellum. Prior to taking off, ladybirds can sequentially deploy their elytra and intricately folded hindwings within 100 ms (Baek et al., 2020; Saito et al., 2017; Saito and Okabe, 2015) (Movie 1). Conversely, in the locked state, the elytra can be tightly closed above the folded hindwings by locking structures located between the elytra and thorax (Gorb, 1998, 1999).

Deployment of elytra in beetles is a fleeting event that seems to be actuated by a series of direct mesothoracic wing muscles (Dai and Yang, 2010; Frantsevich, 2011; Ge et al., 2007). There is a consensus on the role of muscles that originate in front of the pleural ridge and insert into the anterior edge of the tergum or onto the basalare: they open the elytra together (Beutel and Haas, 2000; Friedrich and Beutel, 2006). Before deploying the elytra, the prothorax and the metathorax are pulled downward by the elytral muscles to release the elytra-locking structure, and then the elytra opens like a lever turning about the elytra–body articulation (Frantsevich, 2012b). Compared with deployment of the hindwings, rapid deployment of the elytra may present a formidable challenge as the elytra are bulky and contain no elastic components, such as resilin (Song et al., 2020). Moreover, the elytral muscles are decentralized and parts of the muscles are short or thin, and so they may be incapable of generating sufficient power to open the elytra (Hao and Du, 2018). Surprisingly, deployment of the elytra occurs within 100 ms, but the mechanism by which such speed is achieved remains unknown. In this combined experimental and theoretical study, we investigated the biomechanics of elytra opening powered by specialized structures coupling the two elytra together. We quantified the mechanical power that elytral muscles can provide for deployment of elytra and assessed whether that alone can account for their rapid unfolding, and investigated the role of microstructures embedded in the elytra coupling in their swift deployment.

Thirty ladybirds, Coccinella septempunctata (Linnaeus 1758), were housed in an indoor terrarium at a temperature of 26°C and a humidity of 60% with a 12 h:12 h day:night cycle in Guangzhou, China (23.13°N, 113.27°E) (Fig. 1A). We weighed (Quintix35-1CN electronic analytical balance, Sartorius, Göttingen, Germany) and averaged the mass of the elytra as m_e (n=20 ladybird samples). The width and length of each ladybird sample were measured using a vernier caliper (AIRAJ 1331, AIRAJTOOLS, Yantai City, USA) (Fig. 1B), and each living ladybird was measured 3 times. The body width a and length b were the maximum distance in the abdominal plane along the short and long axes of the body, respectively, as shown in Fig. 1B.

To observe the kinematics of elytra unfolding, we used solid gum (PKTAK, Henkel, Düsseldorf, Germany) to attach the prothorax of ladybirds (n=10) to a 3D-printed fixed scaffold with a height of 5.30 cm (Fig. 1C). Then, a high-speed camera (Micro CLY310, Phantom, Wayne, NJ, USA) equipped with a macro lens (EF100mmf/2.8LISUSM, Canon, Tokyo, Japan) was used to record the kinematics of elytra deployment at 1000 frames s⁻¹, with elytra deployment being filmed twice for each ladybird (Fig. 1C). To quantify the kinematics of elytra opening, we defined a coordinate system with the scutellum at the origin o. The x-axis originated at point o and extended posteriorly, with the z-axis extending towards the abdomen, and the y-axis oriented according to the right-hand rule. Elytra kinematics were measured from changes in the angle between the elytra (t), defined as the angle between the medial borders (sutural edges) of both elytra rotating about the elytra base on the abdominal plane, over time t, thus defining the angular velocity ω(t) of elytra deployment (Fig. 1C). In order to elucidate the roles played by setae in elytra unfolding, some ladybirds (n=5) were first anesthetized by freezing to reduce trauma and facilitate handling, followed by scraping off the setae inside the coupling structures on both elytra using a scalpel under a microscope (CX33, Olympus, Tokyo, Japan). After setae removal, the insects were allowed to recover for a minimum of 30 min prior to filming, and we repeated the elytra unfolding experiments according to the procedures described above. In addition, we carried out control experiments that indicated that freezing anesthesia had no effect on the speed of elytra opening.

To estimate the rotational kinetic energy E_r required for deploying the elytra at an angular velocity ω, a single elytron was modeled as a quarter of a spherical shell of mass m_e with a radius of R₁. The surface density of the elytra ρ was defined as ρ=m_e/πR₁². The moment of inertia J_xp with respect to an axis parallel to the x-axis passing through the centroid was taken to be J_xp=m_eR₁²/3 and the rotational kinetic energy E_r was defined as E_r=J_xpω²/2.

The shape of setae, namely whether they were bent or remained straight when compressed, was visualized through a microscope (CX33, Olympus) and recorded by a camera (EOS 6D, Canon). We applied drops of superglue (Deli7146, Deli, Ningbo, Zhejiang, China) to the coupling structure of living ladybirds (n=4 ladybirds), and closed the elytra tightly for 30 s to fix the setae when the two elytra were in contact. Then we held the posterior of the elytra with forceps under the microscope and gently pulled the closed elytra away in a direction perpendicular to the medial edge of the elytra. The shape of the setae fixed by the glue was observed for each elytron, and all were intact with no fracture or other damage, thus validating our procedure for processing elytra.

Scanning electron microscopy (SEM) was used to examine the setae on the sutural edge of the elytra coupling. Each intact elytron (n=6) dissected from three live ladybirds was cut into six sections with a scalpel. These fresh elytron samples (n=36) were fixed by soaking in 2.5% glutaraldehyde at 26°C for 3 h. We cleaned the samples 3 times with 0.1 mol l⁻¹ phosphate buffer (pH 7) for 20 min, and used a series of ethanol solutions between 75% and 100% at 5% intervals over 12 h to dehydrate the samples. Samples were processed for 15 h in a freeze-dryer (AlPHA 1-2 LDplus). Then they were coated with gold palladium (50 nm in depth) and mounted on SEM stubs with graphite adhesive tape, for observation under a scanning electron microscope (Quanta 200, FEI, Brno, Czech Republic) in high-vacuum mode at 15 kV (Zhang et al., 2020). From the SEM images, we counted the total number of setae on elytra from each ladybird and measured the dimension of the setae along the x-axis as described in ‘Elytra unfolding kinematics’, above.

To reconstruct the 3D configuration of the elytra and the thorax of the ladybirds, we used an Xradia MicroXCT-400 (Xradia Inc., South Pasadena, CA, USA). The samples (n=4 ladybirds) were scanned at a voltage of 60 kV and a current of 133 μA. Ladybirds were mounted on a sample holder, and scanned with an axial resolution of 5 μm. The resulting data were then reconstructed using the software package Mimics (Materialise, Leuven, Belgium) to discern elytral muscles and measure the gap between the coupled elytra.

Atomic force microscopy (AFM) was used to characterize mechanical properties of the setae. A piece of elytron with four setae (n=5 ladybirds) was removed using a scalpel under a microscope, and then placed horizontally on a glass slide (Fig. 1D,E). Then an AFM probe (RTESPA-150, Bruker, Billerica, MA, USA) with a testing range of 50 MPa to 50 GPa was used with a Dimension Icon AFM (FastScan, Bruker) to measure the Young's modulus E of each setae (n=20 elytron samples), which was tested at three points along its length. In peak force tapping mode, the vibrating tip applied a bending force at each point and recorded the movement of the seta. By real-time analysis of the force curves, the Young's modulus at each point was obtained and averaged by fitting with the Derjaguin–Muller–Toporov (DMT) model (Li et al., 2019; Zhang et al., 2021).

For measuring the coupling force between elytra, we built an experimental platform consisting of a stepper motor and force sensor as shown in Fig. 1F (LSB200, FUTEK, Irvine, CA, USA). Living ladybirds were first anesthetized by freezing to eliminate muscle activity. Then each ladybird was mounted on the tip of a tapered plastic tube fixed on a slider that was driven by the stepper motor. We tested a total of five ladybirds, 3 times each. To make sure that the force applied on the coupling structure of the elytra was perpendicular to its edge, a string was fixed with superglue (Deli7146, Deli) midway along the length of the right part of the coupled elytra, and the other end of the string was connected to a fixed force sensor. The sampling frequency of the sensor was set to 200 Hz. In each experiment, we separated the elytra by pulling on the string, and recorded the force F_c. The coupling force F_c applied to the coupling structure of the elytra was perpendicular, i.e. parallel to the force on the setae F. According to the tip displacement of the setae δ on the elytra coupling, the energy for opening the elytra E_e by an external force was calculated as E_e=F_cδ (Dai et al., 2008).

The physiological cross-sectional area (PCSA) of a muscle is proportional to contractile force, while fascicle length reflects the length excursion of the muscle; both measures are used to determine how much work can be done by an individual muscle and how much power can be produced (Martin et al., 2020). Muscle volume V_m, fiber length L_m and pennation angle γ (n=4 muscle samples) were measured based on data obtained from digital 3D reconstructions. PCSA, which is a function of V_m, L_m and γ, was expressed as PCSA=V_mcosγL_m (Sellers et al., 2017). As values for maximum force (specific tension) in insect muscles are generally 5–35 N cm⁻² and the maximum shortening velocity for insect muscles is of the order of 3–15 lengths s⁻¹ (Josephson, 2009), we could obtain the maximum mechanical power P_m of muscles using the equation P_m=PCSA·T_s·U_m, where T_s is the muscle specific tension and U_m is the speed of muscle shorting.

Using a high-speed camera, we closely observed elytra opening in a living ladybird (Coccinella septempunctata) with intact elytra (Fig. 2A). During elytra deployment, a crevice of length L_c(t) formed over time t, starting from 0 mm and ultimately extending to the full length of the coupling, namely L_e=5.5 mm (n=10 ladybird samples) (Fig. 2B). The elytra kinematics were identified by measuring the crevice angle of the elytra (t) with respect to the duration t, defined as the angle between the medial borders (sutural edges) of the two elytra rotating about the elytra base on the abdominal plane, from which the angular velocity ω(t) of elytra deployment could be calculated. Using the region-wise mapping of angular velocity shown in Fig. 2C, the entire process of elytra deployment could be categorized into three phases, namely the initial, middle and final phases. At the end of the initial phase of elytra deployment at t=3 ms, the crevice split rapidly to L_c(3)=5.01±0.12 mm=(91.09±2)%L_e (n=10 ladybird samples), which suggested that the elytra were fully unlocked at (3)=10.03±0.94 deg (n=10 ladybird samples), and the average angular velocity in the initial phase was ω₁=3.81±1.22 deg ms⁻¹. However, in the middle phase, the ladybird required an additional 12 ms to deploy the elytra to (15)=20.47±1.87 deg (n=10 ladybird samples). The angular velocity on average during this phase exhibited the lowest value among the three phases as ω₂=0.93±0.31 deg ms⁻¹, only 1/4 that of the initial phase (Movie 1). The final phase had an average angular velocity of ω₃=1.92±0.73 deg ms⁻¹, which was only 50% of the initial angular velocity.

Such rapid movement requires high energy over a short time, but the mechanism of generating this energy remains unknown. Deployment of elytra may be actuated through movement of the hinged base of elytra driven by a limited number of direct and/or indirect elytral muscles (Frantsevich et al., 2005). Therefore, we examined the musculature involved in elytra deployment using micro-CT scanning to determine whether the swift deployment of elytra can indeed be powered by these elytral muscles alone.

The opening and closing of elytra have been previously ascribed to intrinsic muscles attached to the tergite and pleurite (Frantsevich, 2012b). Here, we used the muscle numbering principle based on anatomical characterization of the muscles and the elytral pivot (Beutel and Haas, 2000; Larsén, 1966). Specifically, elytra deployment is actuated mainly by a combination of M. 40 (M. mesonoti secundus), M. 47 (M. noto-pleuralis), M. 50 (M. episternosternalis) and M. 60 (M. noto-coxalis), which are the muscles in the mesothorax of a ladybird that abduct, elevate and extend the elytra (Fig. 3; Movie 2). The functions of M. 40 and M. 47 are to release elytral fixation (antagonist of M. 39) and the elytral base (depressor of the lateral notum), respectively. Previous descriptions suggest that muscle M. 60, which is well developed, may be the main muscle for actuating elytra opening (Ge et al., 2007). We scanned ladybird thorax morphology, especially the musculature of the mesothorax, by digital 3D micro-CT, and as shown in Fig. 3A–D, the PCSA of M. 60 could be calculated by measuring muscle volume, fiber length and pennation angle. The pennation angle has a negligible effect on the PCSA calculation, as shown in Fig. 3B,D. M. 60 may be the parallel-fibered muscle that shortens along the long axis of the fiber bundle when the muscle contracts (Martin et al., 2020). Therefore, PCSA=(0.16±0.01)×10⁵μm² (n=4 muscle samples), and the maximum power output by M. 60 was P_m=0.028±0.002 µJ ms⁻¹ (700 W kg⁻¹) (n=4 muscle samples), similar to the power output of fast insect muscle (500 W kg⁻¹) (Josephson, 1993; Josephson et al., 2001). Take into account average angular velocity of elytra opening in the initial phase, average body size R₁=2.59±0.20 mm and body mass m_e=5.02±0.23 mg (n=20 ladybird samples), the rotational kinetic energy for elytra deployment in the initial phase was E_r=0.11±0.06 μJ with a power of P_e=0.04±0.02 µJ ms⁻¹. Therefore, the elytral muscles cannot produce sufficient power for opening elytra at the observed high speed because muscle power P_m=70%P_e (Fig. 3E). In this case, ladybirds must rely on another source of power, such as elastic energy stored in the elytra. So, we combined micro-CT and SEM imaging to further examine elytra coupling.

We initially reconstructed the ladybird's elytra coupling through micro-CT imaging (Fig. 4A) and identified the tenon and mortise structures (Frantsevich, 2012a). The tenon structure is blade-shaped and inserts into the grooved mortise structure (Fig. 4B,C). SEM images showed that the length and height of the tenon were L_t=5.20±0.03 mm and H_t=44.51±0.02 μm (n=6 elytron samples), respectively (see Materials and Methods, ‘Scanning electron microscopy’, above). The mortise and the tenon unlock during rapid deployment of the elytra, as shown in Fig. 5A. At the end of the initial phase, the length of the crevice was L_c(3)=96.71%L_t at a splitting angle of (3)=10 deg. Moreover, the gap between the tenon blade and mortise groove G₀=55.82±5.24 μm (n=6 elytron samples) was greater than H_t (Fig. 5B,C), indicating that the entire coupling structure uncoupled completely by the end of the initial phase.

Notably, the SEM images showed that two rows of setae were distributed along the internal edge of the elytra coupling, namely the upper edge of the blade of the tenon and the upper edge of the ventral ridge of the mortise (Fig. 4B,C). These setae were distributed evenly along both elytra, with 126±20 (n=6 elytron samples) on each. The setae had tubular basal parts and pointed tips, and radiated toward the opposite part of the coupling structure at an angle θ (Fig. 4D). Along the x-axis, the length of the setae L_s increased from 24.77±2.83 µm to 56.25±3.31 µm (n=36 elytron samples), illustrating that the setae became longer posteriorly from the scutellum (Fig. 5D). Specifically, L_s in the proximal section of the elytra, between 0 and 5.2 mm from the scutellum, fluctuated around 28.57±2.28 µm. By contrast, L_s at locations between 5.2 and 6.4 mm from the scutellum (distal section of the elytra) rose from 28.95±1.62 µm to 56.25±3.31 µm. The angle θ varied similarly, increasing from 27.20±0.46 deg to 51.88±0.79 deg (n=36 elytron samples). To determine the configuration of setae inside a pair of coupled elytra, we measured the gap within the coupling structure H₂ from micro-CT images. The gap H₂ remained relatively stable at 0–5.2 mm from the scutellum, and then rose from 7.44±1.82 µm to 11.59±0.79 μm (n=4 ladybird samples) in the distal section of the elytra (Fig. 5E). Along the x-axis, the gap H₂ in the coupling structure was always smaller than the length of the setae H₁=L_ssinθ, indicating that setae are forced to bend by the internal surface of the coupling structure when the elytra are coupled. To further explore the shape of the setae in the closed elytra, we developed a technique by which the setae in the closed position of elytra were fixed with glue (see Materials and Methods, ‘Fixing setae in closed elytra’, above). Fig. 5E shows deflection of setae in the fixed samples, verifying that the setae are bent in the closed elytra coupling structure. These observations suggested that elastic energy stored in the compressed setae may contribute to swift opening of elytra in their initial phase of deployment.

In order to elucidate the roles played by setae in elytra unfolding, living ladybirds in which all the setae inside the elytra coupling had been scraped off were filmed at a frame rate of 1000 frames s⁻¹. Fig. 6 shows typical events and corresponding kinematics of elytra deployment in the absence of setae. During the initial phase of elytra opening, average angular velocity was 0.79±0.05 deg ms⁻¹ (n=5), which was only 1/5 that for elytra with setae, consistent with setae compression contributing to more rapid elytra deployment in the initial phase (Movie 3).

We built a mathematical model to evaluate the impact of compressed setae on elytra deployment. AFM measurements (see Materials and Methods, ‘Atomic force microscopy’, above) showed that the Young's modulus of the setae was E=300 MPa. When the elytra were coupled together, a load F perpendicular to the substrate was applied to the tip of each seta (Fig. 1G). SEM imaging showed that the average normal displacement was =H₁−H₂=10.36±0.88 μm, and the setae had an average length =28.56±2.27 µm and angle =38.38±2.22 deg. The average elastic potential energy stored in the compressed setae was calculated as E_s=4.27×10⁻² μJ, with the power available from the elastic potential energy being P_s=1.42×10⁻² μJ ms⁻¹. Mathematical modeling suggested that setae release provides 38.9% of the rotational kinetic energy E_r of elytra deployment, supplying 35.6% of its power P_e. Therefore, the energy stored in setae may play an essential role in swift deployment of the elytra.

We can derive the elastic energy E_s for setae of different lengths L_s and angles θ based on the theory proposed above (see Materials and Methods, ‘Mathematical modeling of energy storage in setae’). Fig. 7A shows that E_s increases with θ, but decreases with L_s for setae of constant radius, so that stored elastic energy is greater in shorter setae deflected by a higher angle (yellow regions in Fig. 7A) and is reduced in longer setae at lower angles (blue regions). For a given θ, E_s reaches a maximum for L_s between 30 and 35 μm, consistent with the actual length of setae (indicated by the region outlined in orange). As beam buckling may occur when θ turns more than 60 deg, we only consider deflection angles smaller than this critical value. For constant L_s, E_s reaches a maximum at θ=60 deg; however, excessive elastic energy storage may break the elytra-to-body interlocking. The average coupling force of elytra was measured to be F_c=16.50±0.25 mN; thus, the critical energy required for opening the elytra by an external force can be estimated as E_e=F_cδ=0.17 μJ (Fig. 7B). Fig. 7B clarifies that when θ>54 deg, the elastic energy of setae (actual L_s=30 μm) reaches E_s=0.16 μJ≈E_e (purple horizontal line in Fig. 7B), which suggests that under these conditions, the elytra may lose the ability to close tightly. When θ becomes smaller than 35 deg, E_s=2.54×10⁻² µJ, which is only 23% of the rotational kinetic energy of elytra E_r, uncovering that E_s is in that case insufficient for swift elytra deployment. Thus, the effective range of the setae angle θ lies between 35 and 54 deg, indicated by the pink shaded area in Fig. 7B, and consistent with anatomical microstructure corresponding to the region outlined in red in Fig. 7A. Therefore, the optimized length and angle are 30 μm and 54 deg, respectively, consistent with postmortem examination and indicated by the region in Fig. 7A outlined in both red and orange, which suggests a trade-off for ladybirds between swiftness of elytra opening and stability of elytra locking.

The unfolding kinematics of elytra have revealed three phases that are characterized by different angular velocities. The initial phase is the most energetically challenging as the tightly locked elytra have to be unlocked, and the energy required to open them may be much higher than during the following phases (Frantsevich, 2012a). Surprisingly, the insect generates an ultra-fast deployment with a maximum angular velocity in the initial phase that is 4 times that of subsequent phases, comparable to that of the ant lion's (M. crudelis) mouthparts in a strike (Lambert et al., 2011). To explore how this enormous energy is produced, we examined the musculature involved in elytra deployment. Muscles produce a broad range of motions in living animals. Some of the most powerful and rapid movements occur during locomotor behaviors such as flying and leaping, and this power is usually generated by muscle contraction (Camp et al., 2015). However, quantification of the power output of elytral muscles suggests that they are insufficient to produce sufficient power for opening elytra at such high speed. Thus, ladybirds may also utilize a less apparent actuation mechanism. To overcome the energetic limitations of muscle contraction when propelling both swift and powerful locomotion, many insects use elastic structures that can store energy (Burrows et al., 2008; Burrows, 2003; Wan et al., 2016). For instance, during take-off, locusts (S. gregaria) very rapidly accelerate to an initial speed of 3 m s⁻¹ in 30 ms through releasing energy stored in two bow-shaped semi-lunar processes at the femorotibial joint (Cofer et al., 2010). The champion jumpers in nature, namely froghoppers (Philaenus spumarius), can jump at a velocity of 4 m s⁻¹ by releasing energy stored in a strengthened thoracic cuticle (Burrows, 2003). To explore whether ladybirds utilize the same strategy, the elytra coupling structure was closely examined. We found that setae on the internal edge of the elytra coupling structure store energy by functioning as springs, and play an important role in rapid elytra movement during the initial phase of deployment. These setae are evenly distributed along the elytra coupling, and become longer posteriorly from the scutellum. As elytra gradually unfold from more posterior positions, the increases in both the size of the gap between elytra and the length of setae may serve to maintain deformation of the setae across the entire interdigitated suture. Our mathematical model explains the effect of seta length and angle on the energy storage capacity of setae and the tightness of elytra locking, showing that the setae are characterized by lengths and angles that may represent a trade-off for ladybirds between swiftness of elytra opening and stability of elytra locking.

Compared with locusts or froghoppers that release concentrated energy through a single elastic structure, the distributed actuation pattern in ladybirds that stores energy in setae evenly distributed along each elytron has the advantage of both morphological feasibility and functional adaptation. In order to further consider potential mechanical advantages of coupling elytra through linear arrays of setae, we examined the following scenarios involving a single seta. (1) Assuming that a ladybird stored energy for elytra deployment in only one 30 μm-long seta at an angle of 50 deg, it would have to be 21.59 μm in diameter, 4 times the measured value, to store the same amount of energy as evenly distributed 5.5 µm-diameter setae. Furthermore, a 21.59 µm-long seta would not fit in the coupling gap H₂, which is only 11.59 μm wide when the coupling structure is fully interlocked. (2) Alternatively, energy could be stored in one seta of diameter 5.5 µm at the experimentally measured angle of 39 deg. The length of the seta L_s would then have to be 4.80 μm, only 1/6 of the actual value. In this case, the seta would undergo no bending because the height of the seta H₁ would be smaller than H₂, so the seta in the closed elytra would not be able to store energy. (3) Most of the morphological adaptations for energy storage in insects are composite structures consisting of resilin and chitinous cuticle (Burrows et al., 2008). Hard materials (chitinous cuticle) can store more energy under less deformation but are liable to fracture, whereas elastic materials (resilin) can prevent fracture during bending or other distortion of the hard cuticle (Burrows and Sutton, 2012). Given the requirement for stable coupling of the elytra when closed and sufficient energy storage for deployment upon opening, and assuming energy storage in a seta of the same dimensions as that measured experimentally, the Young's modulus of a single seta would have to be 60 GPa (cf. 0.3 GPa experimentally), close to that of aluminium (68 GPa), which would result in the seta fracturing as it is bent during elytra closing.

In addition, this distributed actuation pattern allows for more gradual stable energy release, which may help to alleviate damage to the muscles involved in fast movements of the dome-like shell (Dai and Guan, 2012; Hu et al., 2018). Furthermore, as beetle flight muscles that actuate the high-frequency vibration of hindwings are well developed and kinematically complicated, using elastic energy stored in setae to open elytra may not require a large number of muscles, which may provide additional space for flight muscles (Haas and Beutel, 2001; Josephson et al., 2000). This specifically distributed actuation pattern along a ladybird's elytra may inspire the next-generation lightweight origami mechanisms capable of fast and efficient deployment.

We thank Dr Li Gong from Instrumental Analysis & Research Center of Sun Yat-sen University for assistance in measuring the Young's modulus of elytra. We thank Dr Leonid Frantsevich from the Schmalhausen-Institute of Zoology (UkrNAS) for his valuable comments on the experimental part. We sincerely thank Dr Hamed Rajabi from London South Bank University for his comments on the experiments and revision of the draft. We thank Caixia Gao and Xiaowei Qin from Institute of Zoology, Chinese Academy of Sciences, for CT scanning and freeze-drying.