Morphology and biomechanics of the entire spike
The raptorial appendage of the spearer zebra mantis shrimpLysiosquillina maculata (Figure 1A) features 10 spikes of increasing size, regularly arranged along the dactyl (Figure 1B). The morphology and the external surface of distal spikes were characterized by high resolution micro-CT and SEM. Each distal spike is a tapered, thin and elongated offensive weapon (Figure 1C). In contrast to the straight needle-like shape common to many man-made harpoons[11], it has a curved form and an elliptical cross-section (Figure 1D). The local curvature of the spike varies along its length such that 3 regions can be identified: a slightly curved zone close to the base, a fairly straight segment in the middle and a region with the highest curvature before reaching the tip (Figure 1D, the length of the arrows is proportional to the local curvature k). This allows the spike to orient its sharp end at an almost right angle with respect to the dactyl within a short distance, while avoiding a large angle at the base, which may cause stress localization upon bending. A curved rather than a straight profile may be linked to the curved trajectory of the appendage during a strike [31]and could as well facilitate the parking of the spikes within dedicated holes in the propodus at resting position (Figure S1 ). In nature, the shape of puncturing systems is highly diverse and closely connected with their function [11]. A straight offensive tool such as the harpoon of the cone snail[37], the bee stinger [38]or the mosquito proboscis [39] may be used to maximize penetration depth [11], whereas highly curved devices like crustaceans claws [40] or spider fangs [41] should enable puncture along different trajectories and facilitate prey retention[35,37]. The unusual form of the spike, featuring both curved and straight zones, may be a trade-off between large penetration depth and prey grabbing. Micro-CT imaging of the spike cross-section reveals a thin highly mineralized cover bordering a less mineralized but much thicker layer with a central cavity (Figure 1D). This dual mineralization is a specific reinforcement feature of raptorial appendages used for impaling or smashing preys as well as for fighting with opponents [28,32,34–36]. In general, the electron dense region is particularly pronounced on the impact surface and much less in other region of the cuticle[9,42]. After a heavily mineralized and sharp tip, characterized by a radius of curvature of about 20 µm, which should facilitate puncture into the tough skin of the preys, the spike exhibits a spatially varying geometry. The cross-section has an ellipsoidal profile and the cross-sectional area increases gradually from tip to base, always having a pronounced eccentricity (Figure S2 ). An additional peculiarity is a small rotation (of about 15°) of the cross section around the longitudinal axis of the spike (insert in Figure 1D), resulting in a slightly twisted shape. From a biomechanical viewpoint, such a slender and eccentric hollow beam may suffer from low bending and torsional rigidity, thus questioning the ability to remain straight during a capturing event. We evaluate how cross sectional properties evolve along the longitudinal length of the spike from tip to base and we estimate the consequences for bending and torsional resistance using second area and polar moments as surrogate for mechanical properties (Figure 1F). Both maximum and minimum second moments of area (\(I_{\max}\) and \(I_{\min}\)), corresponding approximately to dorso-ventral and lateral loading, increase proximally and show a steeper slope starting at ∼90% of the spike length, where the spike begins to merge with the appendage. The polar moment \(J\) (a proxy for torsional rigidity) follows a similar trend, being bounded by\(I_{\min}\) and\(\ I_{\max}\). Despite a fairly high eccentricity, the ratio \(I_{\max}/I_{\min}\) suggests only a moderate mechanical anisotropy, with resistance to dorso-ventral loading (i.e., parallel to the prevalent hunting movement of the raptorial appendage) being in average 3.3 times higher than lateral loading. Additionally, the ratio\(I_{\max}/I_{\min}\) is fairly constant for about 60% of the spike length. Although simplified, this analysis suggests that the spike is not only very stiff along the longitudinal direction but it can also face multiaxial loading, consistent with the assumed ability of the spearing mantis shrimps to control and direct the strike[31].
The outer surface of the spike is decorated with two reinforcing serrated ridges, running all the way from tip to base (Figure 1E). Such “shark fin-shaped” serrations are part of the highly mineralized layer; with the exception of a zone close to the tip, they have fairly constant dimensions (i.e., \(\sim\)100 µm in height and \(\sim\)55 µm in length, Figure S3 ) in the first third of the spike, while their size decreases when approaching the base, suggesting that only a portion of the spike (closer to the tip) is engaged to impale preys. Serrations are prominent features in many diverse biological cutting tools, ranging from teeth to insect stingers[43], and could have a dual function: they should help to cut through the tissue of the prey by acting as local stress concentrators and, owning to their specific shape, they may prevent the prey from slipping off the spikes by interlocking with the damaged tissue[11]. In addition to the serrations, the surface of the spikes features a characteristic “grooved” pattern (Figure 1E and Figure S3). The grooves have a periodic spiral arrangement, starting and ending at two opposite serrated ridges, and have dimensions smaller than the serrations (i.e., ~5 µm in height and ~35 µm in width, Figure S3). The grooves should provide the spike surface with a controlled roughness which may increase frictional forces as an additional strategy at a smaller length scale to enhance prey retention. From a biological viewpoint, grooves should reflect the specific growth pattern of the spike outer layer, regulated by the epidermis cells which are arranged into parallel arrays.