Stiffness gradients facilitate ovipositor bending and spatial probing control in a parasitic wasp

For many insects, it is essential that they can locate and reach resources hidden in substrates. Examples are mosquitos searching for blood vessels (Choumet et al., 2012), hemipterans probing for plant vasculature (Pollard, 1973), and parasitic wasps finding host larvae living in fruits or wood (Leyva et al., 1991; Vincent and King, 1995). Although the drilling mechanism is relatively well understood, it is still uncertain how these animals steer their probes in the desired direction.

Female parasitic wasps use slender, needle-like ovipositors to search for hosts hidden in various substrates (Cook and Rasplus, 2003; Pennacchio and Strand, 2006; Vilhelmsen et al., 2001). At least some species can actively steer their ovipositors, sometimes in complex trajectories in a single insertion (Cerkvenik et al., 2017; Elias et al., 2012; Quicke et al., 1995). One of these species, the braconid wasp Diachasmimorpha longicaudata (Fig. 1A), can explore a wide area of the substrate from a single puncture point in any direction with respect to its body orientation, and can achieve highly curved insertion trajectories (Cerkvenik et al., 2017). How this and other insect species accomplish such curvatures is not completely understood, but for D. longicaudata, the insertion curvature clearly correlates with configurational changes of the ovipositor (Cerkvenik et al., 2017).

As in most wasps, the ovipositor of D. longicaudata consists of multiple elements (valves) – one dorsal and two ventral valves (Fig. 1B,C) (Quicke et al., 1994; Smith, 1970) – and has an asymmetric tip in the dorsoventral direction. The ventral valve tips bear backward-facing serrations, while the dorsal valve tip has a prominent bulge. Additionally, the ovipositor is S-shaped proximal to the tip when the valves are aligned (Fig. 1B; Movie 1). The valves are interconnected with tongue-and-groove linkages (Fig. 1C; Movie 1) that allow for sliding, but prevent separation of the valves (Smith, 1969; Vincent and King, 1995). Generally, the valves slide back and forth during probing in stiff materials (Cerkvenik et al., 2017), which is thought to reduce the overall net pushing force on the ovipositor in the process and limits the risk of buckling (Vincent and King, 1995).

Kinematic analysis of the probing behaviour of D. longicaudata showed that insertion with predominant protrusion of the ventral valves leads to curved trajectories (Movie 2; Cerkvenik et al., 2017). When protracted, the ventral valves curve towards the dorsal side of the ovipositor (Fig. 1D; Cerkvenik et al., 2017). The dorsal curving of the ventral valves upon protraction is also observed outside a substrate, which implies that it occurs without external forces and is thus initiated from within the ovipositor (Movie 3). In contrast, the dorsal valve remains approximately straight when it is protracted inside a substrate (Fig. 1D; Movie 2; Cerkvenik et al., 2017). In addition to the changes in the very tip of the ovipositor, protraction of either the dorsal or the ventral valves results in a straightening of the S-bend region just proximal to the tip (Cerkvenik et al., 2017).

Because all the muscles that operate the valves are located in the animal's abdomen (Fergusson, 1988; Quicke et al., 1994; Scudder, 1961), we expect that the shape and curvature changes of the ovipositor tip occur only as a result of longitudinal shifts of the valves with respect to one another. It is therefore likely that the valve structural and material properties play an important role in such configurational changes, although external forces may enhance the overall effect.

One possible mechanism of induced bending has been described for parasitoids of the genera Zaglyptogastra and Pristomerus and relies on the differential sclerotization of the valves (Fig. 1E; Quicke, 1991). These wasps have ovipositors characterized by a series of intermittent arches and nodes near the tip (El-Heneidy and Quicke, 1991; Rousse and Van Noort, 2015). The arches are regions of sclerotized cuticle and are presumably stiffer than the nodes in between (Quicke, 1991). When the valves are aligned at their tips, the arches and nodes of the dorsal and ventral valves also align. Protraction of one of the valves aligns the arches with the nodes on the other valve. This causes bending of the ovipositor as the nodes in each of the valves conform to the shape of the arches of their adjacent valves (Quicke, 1991). This mechanism can lead to bending of up to 180 deg, but is considered to be unsuitable for piercing hard substrates, which implies that these wasps only exploit existing holes in the substrate to access their hosts (Quicke, 1991).

Based on the anatomical characteristics of the ovipositor in D. longicaudata, and specifically the S-shaped region and the bulge on the dorsal valve, it is plausible that these wasps rely on a steering mechanism similar to the one described above. In the case of D. longicaudata, we hypothesize that the thickened portion of the dorsal valve might act as a stiff region and the S-shaped region as a deformable soft region. The stiff region will probably be highly sclerotized, whereas the part undergoing deformation, the S-shaped region, is exposed to repetitive strains and we therefore expect it to be adapted to minimize potential damage. A good candidate for mitigating harmful effects of loading in insect cuticle is resilin, an elastic protein that can undergo considerable strain without damage (Weis-Fogh, 1960). Resilin is commonly found in highly deformable and high load-bearing structures such as jumping legs of locusts and fleas (Burrows et al., 2008; Rothschild and Schlein, 1975), wings of beetles and dragonflies (Appel et al., 2015; Haas et al., 2000), beetle tarsal setae (Peisker et al., 2013), and sound-producing organs of cicadas (Bennet-Clark, 1997).

To determine whether stiffness variations in the ovipositor of D. longicaudata are present, we measured the bending stiffness along its length with small-scale three-point bending tests. This measured bending stiffness is determined by the shape (structure) of the ovipositor and its material properties. The second moment of area along the ovipositor length, describing the structural bending stiffness, was obtained from histological cross-sections and high-resolution synchrotron X-ray microtomographs. The material composition of the ovipositor was qualitatively determined with confocal laser scanning microscopy, and estimated by dividing the bending stiffness by the cross-sectional area. This gave us insight into the distribution of bending stiffness along the ovipositor of D. longicaudata and confirmed that there is a mechanism of flexible and stiff zones which can be aligned to induce flexion. This provides a better understanding of how steering of probes can be achieved, and how it contributes to the probing versatility of parasitic wasps and potentially other probing insects. In addition, these findings also indicate how steering without intrinsic motors can be achieved in man-made probes.

Diachasmimorpha longicaudata (Ashmead) were taken from the breeding colony at the Experimental Zoology Group at Wageningen University. The rearing protocol was the same as described in Cerkvenik et al. (2017). All animals were anaesthetized with CO₂ and then decapitated immediately prior to fixation or experimentation.

For histological sectioning, the abdomen with the intact ovipositor was dissected from the body and fixed with a mixture of 0.1 mol l⁻¹ sodium cacodylate buffer (dimethylarsenic acid sodium salt trihydrate; Merck, Darmstadt, Germany), 2% (w/v) paraformaldehyde (Merck) and 2.5% (v/v) glutaraldehyde (EMS, Hatfield, PA, USA) on ice (0°C) for 2.5 h. The sample was washed with the 0.1 mol l⁻¹ cacodylate buffer twice at 0°C, dehydrated in a series of ethanol solutions of increasing concentration from 50% to 100%, and transferred to epoxy resin (epon; Embed-812 Embedding Kit, EMS) through a sequence of solutions: a mixture of ethanol and propylene oxide (PO), pure PO, a series of 3:1 and 1:1 mixtures of PO and epon, and finally pure epon. The samples in epon were put in moulds and left to harden overnight at 60–65°C.

Semi-thin sections of 1 and 2 µm thickness were cut using a Reichert Ultracut S ultramicrotome (Leica Microsystems GmbH, Wetzlar, Germany) and stained with a mixture of 1% Toluidine Blue (VWR, Radnor, PA, USA) and 1% borax (disodium tetraborate decahydrate; Merck) dissolved in distilled water. The sections were photographed with a Leica DFC 450 C camera (5 megapixels) mounted on a Leica DM6b microscope (Leica Microsystems) with 40× or 100× objective. The images were stored as tiff files for further analysis.

We removed the ovipositor from a single collection specimen of D. longicaudata obtained from the Naturalis Biodiversity Center (Leiden, The Netherlands) and mounted it on a pin using beeswax such that it could rotate around its longitudinal axis.

We scanned ∼600 µm of the distal part of the ovipositor in two consecutive scans with 30 µm overlap at the TOMCAT beamline X02DA of the Swiss Light Source (Paul Scherrer Institute, Villigen, Switzerland) with a 14 keV monochromatic X-ray beam. Projection images were recorded over an angular range of 180 deg with an angular step of 0.1 deg with a PCO Edge 5.5 sCMOS camera (exposure time of 100 ms), using a 5 µm thick FEE Tb:LSO scintillator and an optical magnification of 40×, resulting in an effective pixel width of 162.5 nm at a propagation distance of 9 mm. The scans were reconstructed using the gridrec reconstruction algorithm (Marone and Stampanoni, 2012) in conjunction with propagation-based phase contrast (delta/beta ratio=100) as described by Paganin et al. (2002).

Seg3D 2.2.1 (University of Utah; http://www.seg3d.org) was used for segmentation of the reconstructed μCT slices and histological images. Manually adapted thresholds were applied to roughly isolate the exoskeleton from the background. Masks were further manually adjusted, converted to binary images, and rotated such that the dorsal valve was on top. Histological sections were aligned manually, while the µCT slices were rotated by the average angle (169.66±3.68 deg) measured from 16 slices spread equally along the length of the dataset.

To obtain more accurate estimates of the second moment of area, we recalculated the cross-sections perpendicular to the central axis along the full length of the µCT scan. The points along the axis served as centres of rotation for freely rotating planes. The orientation where these planes had the minimal cross-sectional area of the 3D reconstructed structure was considered perpendicular to the longitudinal axis of the scanned ovipositor. To avoid merging of the segmented valves, we applied an erosion algorithm on the entire reconstruction before determining the minimal cross-sections, followed by a dilation algorithm with the same parameters. This algorithm performed well and produced few artefacts that were omitted in further analysis (see Results).

The histological and µCT datasets were combined to form a full-length dataset. To correct for size differences between ovipositors, we calculated two scaling factors based on a randomly chosen set of animals (n=33) from our breeding colony. The ovipositors were dissected in phosphate buffer (pH 7.5; 136.9 mmol l⁻¹ NaCl, 2.7 mmol l⁻¹ KCl, 1.5 mmol l⁻¹ KH₂PO₄ and 8.1 mmol l⁻¹ Na₂HPO₄·2H₂O in deionized water) to prevent desiccation, and were photographed using an Olympus DP50 camera (5 megapixels; Olympus, Tokyo, Japan) mounted on the Zeiss Stemi SV-11 stereomicroscope with a 1.6× objective (Zeiss, Jena, Germany). The length of the ovipositor, its tip length (distal point of the dorsal valve to the apex of its enlargement) and the ovipositor width at two tip lengths from its distal vertex were measured using analySIS FIVE software (Olympus). We correlated both these measures with the overall length of the ovipositor (Fig. 2A,B). The slopes of the major axis regression lines were used to calculate the sample lengths based on their tip length. This allowed us to express the measurement locations (distances along each sample) as percentages of the sample length.

To compute the correction factor for calculating the second moment of area of differently sized samples, we assumed isometric scaling of the ovipositors and we considered the ovipositor to be a hollow cylinder, the dorsal valve a hollow half-cylinder, and each ventral valve a hollow quarter-cylinder. Formulas for the calculation of the second moment of area of these shapes differ only in their constants, which cancel each other out when deriving the correction factor, so we present here only the derivation for hollow quarter-cylinders.

For the bending tests, the sheaths surrounding the ovipositor were removed, and the ovipositors were cut close to their base at the abdomen. Subsequently, the ovipositors were kept submerged in physiological (Ringer's) insect buffer solution (Barbosa et al., 2014) at all times to prevent desiccation and to minimize changes in the material properties of the cuticle. To avoid damage to the ovipositor, we manipulated the samples only at the side opposite to the one intended for measurements. In total, we sampled data from 23 individuals. In 10 cases, the ovipositor valves were separated by carefully sliding them off each other. In most samples, the stiffness of their distal part was measured, but five ovipositors were measured at their proximal part. The dissected ovipositors or individual valves were clamped into a custom-made clamp that kept the samples horizontal and prevented them from twisting when mounted in the experimental setup (Fig. 2D).

The setup (Fig. 3A) was positioned on a vibration isolation table TS-150 (Table Stable, Zwilikon, Switzerland) to avoid external interference. It consisted of three parallel carbon steel razorblades (FA-10; Feather): two on the bottom pointing up and one on the top pointing down. The bottom razorblades were glued in the centre of a square Petri dish, more than 10 times the diameter of the ovipositor apart from each other (distances of 350.48 µm or 357.90 µm; averages obtained from multiple measurements under the microscope). The horizontal position of the top blade was located exactly in between them. The Petri dish was fixed onto a Hexapod micro-motion positioning system (Physik Instrumente, Karlsruhe, Germany) that allowed translations in all directions with sub-micrometre resolution. To prevent sample desiccation during measurements, the Petri dish was filled with physiological (Ringer's) buffer solution for insects (Barbosa et al., 2014), which was degassed to avoid air bubbles forming on the sample surface.

The top razor was mounted onto a force transducer (FORT10g, dynamic range 10 g, resolution <0.01 mN; World Precision Instruments, Sarasota, FL, USA) fixed on a clamp stand and connected to a PC via a MP100WSW data acquisition system (Biopac Systems Inc., Goleta, CA, USA). The measurements were recorded with AcqKnowledge 3.7.0 software (Biopac System Inc.). The force transducer was calibrated by hanging a mass of 1655.3 mg on the lever of the force transducer with the attached razorblade. Because the transducer behaved linearly within its dynamic range, a single weight was sufficient to calibrate it (Fig. S1).

Using the micromanipulator, the sample was placed perpendicular to the longitudinal axis of the razors and parallel to the bottom of the Petri dish. The Petri dish with the two razor blades was moved upwards in at least four steps (deflections) of 10 µm with inter-step intervals of several seconds (variable in number). The bending was done at 4–6 locations along each tested sample, depending on its length and the location of the clamp. The most distal part of the ovipositor (tip), which measures approximately 200 µm, could not be measured because it was too short to fit between the razorblades in the experimental setup. The most distal measurement of each sample that could be obtained was within the S-shaped region. This S-shaped region spans approximately 200 µm and could always be positioned accurately in between the bottom two razorblades. The reaction forces on the top razorblade during bending were continuously recorded at a sampling frequency of 200 Hz.

All three-point bending tests were monitored with a camera (Basler piA1900-32g, Basler Vision Technologies, 2 megapixels and 5 frames s⁻¹) mounted on a stereomicroscope and controlled with StreamPix 5 (NorPix Inc.) software. Light was provided by a cold light source isolated from the vibration isolation table. The recorded videos were used to determine the location of the measurements along the length of the samples and to monitor slippage of the samples on the razorblades. We did not observe any slippage of the samples off the razorblades, although it is possible that minute and limited slippage occurred during bending, which were undetectable because of the uniform geometry and the lack of landmarks along the length of the samples. Our results might therefore slightly underestimate the actual stiffness of the ovipositor and its parts.

Analysis of the signal-to-noise ratio with AcqKnowledge 3.7.3 software showed low values in highly flexible regions of the ovipositor such as the dorsal valves and the S-shaped region of the ventral valves (Fig. 3B). Low signal-to-noise recordings were filtered with an infinite impulse response (IIR) band-stop filter (frequency 50 Hz, Q=0.1) to remove electrical noise and improve curve fitting in further analyses. Application of the IIR filter did not affect the accuracy of the fits (Fig. 3B).

Data were corrected for stiffness of the experimental setup, which was determined by pressing two perpendicular razor blades against each other with 1 µm steps and analysing the obtained data in the same manner as described above.

The maximum dimensionless curvature of the whole ovipositor during natural probing is 0.048 (Cerkvenik et al., 2017). This value was adjusted to the size of ventral and dorsal valves by multiplying it by the diameter ratios of the ventral valve and dorsal valve, respectively, to the whole ovipositor. The same valve diameters were used as above. The dimensionless curvature induced in the first full deflection in three-point bending experiments was similar to the one observed during kinematic experiments, whereas the second and third full deflection step usually induced higher curvatures than found in nature (Fig. 4B–D; Cerkvenik et al., 2017). The effective stiffness of the ovipositor and its valves were therefore estimated from the first full deflection step; that is, the deflection step after omitting the deflection where the razorblades were not in contact with the sample throughout the bending.

To assess the effects of clamping and of the pre-bent beam shape of the S-curve on our results, we used finite element (FE) simulations using Abaqus/CAE 2017 (Simulia, Dassault Systemes). Because this assessment does not require a complete description of geometrical and material valve properties, we simulated solid cylindrical beams. To reduce the computational time, we took advantage of the lateral symmetry of the bending simulation and longitudinally halved the model and assumed lateral symmetry in the cut plane. The beam was therefore modelled as a half cylinder (length 5 mm, radius 7.5 µm). Bending was simulated such that it closely resembled the experimental conditions; one end of the beam was clamped and the razorblades were modelled as rectangular pins with rounded corners (width and height 5 µm, depth 8 µm; Fig. 5A). The pins were positioned perpendicular to the beam and parallel to each other – the bottom two pins were 350 µm apart and the top one was positioned in the middle. The middle pin was located on top of the beam, with the outer two pins on its bottom side. One end of the beam and the top pin were fixed in all three dimensions, while the bottom two pins were only allowed to move upwards and rotate in the vertical plane that cut the beam in half. The pins were modelled as non-deformable rigid bodies, thus resembling steel razorblades of much greater stiffness than the ovipositor. Additionally, we assumed frictionless contact between the beam and the pins and only considered the normal forces. As in the experiment, the bottom two pins were pushed towards the top one in three 10 µm steps. The vertical reaction forces (i.e. those in the bending direction) in the pins and at the fixed end of the beam were extracted for each deflection.

To determine the effect of the mesh size on the model output, we performed multiple simulations where the mesh size was varied, while keeping all other parameters constant. The mesh grid size was varied between 0.5 and 2 µm in steps of 0.5 µm along both the length of the beam and its perimeter. In these simulations, the bending location was kept at 4 mm from the clamp, the stiffness of the beam (E) was 10 GPa and its Poisson's ratio (ν) was 0.3. The mesh size had little effect on the simulation output and therefore a mesh grid size of 1 µm was used in subsequent simulations (Fig. 6A).

For the effect of clamping, we used homogeneous material properties with a Poisson's ratio (ν) of 0.3, while the Young's modulus (E) was varied and set at 0.1, 1 and 10 GPa. Both parameters are within the range of their estimated values for insect cuticle (Vincent and Wegst, 2004). The effect of clamping was negligible on beams with E=0.1 GPa (Fig. 6B) and therefore simulations on beams with E<0.1 GPa were not performed.

The clamp effect was estimated by bending the beam at several distances from its fixed end, namely 1, 2, 3 and 4 mm from the clamp. Clamping had little effect on soft beams (E≤1 GPa), whereas at higher beam stiffness (E=10 GPa and presumably above), the recorded forces strongly increased with a decreased distance to the clamp (Fig. 6B). If the force in the top pin differed by more than 5% compared with the measurements done at the location farthest away from the clamp, we considered the force measurements to be inaccurate. To obtain the distance from the clamped end at which this threshold was reached, we interpolated the data for a 10 GPa beam using a cubic spline. The threshold distance was 1.87 mm (Fig. 6B). We therefore omitted all data points that were obtained at distances ≤1.87 mm from the clamp from our experimental dataset.

To determine the effect of the S-shape near the tip of the ovipositor, we created a cylinder with a similar S-shape located 4 mm away from the clamped end (Fig. 5B). The ovipositor geometry was estimated from the micrographs obtained with confocal laser scanning microscopy (n=4; for details, see below). The S-shaped FE model beam consisted of a proximal bend in the dorsal direction of 10 deg from its longitudinal axis, followed by a 20 deg bend in the ventral direction and a 10 deg bend in the dorsal direction again. The bends were spaced 100 µm apart and were rounded (r=150 µm) to avoid structural discontinuities and the associated stress accumulation. The beam was assigned E=10 GPa and ν=0.3.

The material composition of the ovipositor was qualitatively assessed by visualizing autofluorescence with a confocal laser scanning microscope (ZeissLSM 700, Zeiss) with 10× and 20× objective lenses (Zeiss Plan-Apochromat; numerical apertures of 0.45 and 0.8, respectively). We applied the method established by Michels and Gorb (2012), which provides reliable information on the presence of resilin in insect cuticles. The ovipositors were put on a glass slide, embedded in glycerin, and covered with a cover glass. The sample was left under the microscope for half an hour to stabilize in the medium before scanning. Zeiss Efficient Navigation (ZEN) software (Carl Zeiss MicroImaging GmbH, Jena, Germany) was used to record the autofluorescence and create maximum intensity overlay images. We used excitation lasers of 405, 488, 555 and 639 nm and recorded the Z-stacks of autofluorescence using a 420–480 nm band-pass filter and ≥490, ≥560 and ≥640 nm long-pass filters, respectively. Before every scan, the laser power and detector gain of each laser were manually adjusted in live view at the scanning speed that was also used for the acquisition of the final image. We first increased both parameters until observing pixel saturation. Afterwards, the two parameters were carefully reduced to obtain an image with a minimal number of saturated pixels, before taking the micrographs. In the final image, the fluorescence light emissions were assigned to blue, green, red (50% intensity) and red (50% intensity) channels, respectively, according to the colour code of Michels and Gorb (2012).

The ovipositor of D. longicaudata is a slender structure that connects to the musculoskeletal apparatus at its base (Fig. 7A; Fergusson, 1988). The three valves it consists of form a cylindrical structure approximately circular in cross-section, which encloses the egg canal (Fig. 7B,C). The unloaded shaft of the ovipositor is slightly curved, making it dorsally concave. An S-shaped region is present just proximal to the distinct ovipositor tip (Fig. 7A inset, Fig. 7C). For most of its length, the dorsal valve is crescent shaped in cross-section, while the ventral valve cross-sections resemble a quarter of an ellipse (Fig. 7B,C). The dorsal valve connects to each ventral valve with a tongue-and-groove linkage that is ‘mushroom shaped’ in cross-section (Fig. 7B).

The cross-sectional area of the ovipositor varies little along most of its length (similar to Fig. 7B2), except at its base (Fig. 7B1) and the morphologically distinct tip (Fig. 7B3–5). The base of the ovipositor is enlarged and polygonal in cross-section. While the dorsal valve base is approximately 5 times wider than most of the ovipositor shaft, the ventral valves are only slightly enlarged compared with their cross-sectional size along the shaft (Fig. 7B1). At the tip, distal to the S-shaped region, the dorsal and ventral valves both possess a bulging area before tapering towards the vertex (i.e. the point furthest away from the base). Additionally, the cross-sectional area of the tapered tips changes shape towards the tip vertices. The bulge on the dorsal valve changes from rectangular to oval, while that of the ventral valves changes from approximately oval to approximately triangular (Fig. 7B4,5).

The second moment of area varied along the ovipositor length in accordance with the above-described anatomy (Figs 7A,B and 8A; for full comparison and statistics, see Table S1). The I_x of both the whole ovipositor (I_x,ov; grey data in Fig. 8A) and the dorsal valve (I_x,dv; light blue data in Fig. 8A) sharply decreased from the base to the shaft, varied little along the shaft, and sharply increased at the location of the bulge of the dorsal valve, which was followed by a steep decrease towards its vertex. To illustrate, at the base (at 6.9% of the ovipositor length, OL), I_x,ov was 12.8×10⁴ μm⁴, which diminished to about one-quarter of this value along the shaft (lowest values around 3.64×10⁴ μm⁴ at 66% OL), and increased at the bulge on the ovipositor tip (highest value of 19.93×10⁴ μm⁴ at 96.8% OL), before decreasing to 0 at the end of the tip. The extreme values for the dorsal valve (I_x,dv) occurred at comparable locations, showed a similar pattern, but were smaller (4.51×10⁴ μm⁴ at 6.9% OL, 0.14×10⁴ μm⁴ at 68% OL and 3.06×10⁴ μm⁴ at 96.9% OL).

The I_x of the ventral valves (I_x,vv) varied little along their entire shaft and increased only at their tip (dark blue data in Fig. 8A). The values ranged from 0.60×10⁴ μm⁴ at 6.9% OL to 0.80×10⁴ μm⁴ at 63.6% OL, and were highest at 96.7% OL at 1.61×10⁴ μm⁴. The dorsal valve in the dorsoventral direction was thinner than the ventral ones along most of their length, except for the base (<10.5% OL; Fig. 8A, left) and the bulge on the tip (>96.6% OL; Fig. 8A, right).

The contribution of the individual valves to the second moment of area of the complete ovipositor (i.e. when computed with respect to the centroid obtained from whole ovipositor cross-sections; see Fig. S2) was considerably higher than the values given here, but showed a similar pattern. Here, we show the data with respect to the centroid of the object of interest, because they link directly to the bending stiffness measured in the three-point bending experiments discussed below.

Bending stiffness (E_effI_x) along the length of different parts of 23 different ovipositors was obtained with three-point bending experiments in which one end of the sample was clamped. We excluded values obtained close to the clamp (see Materials and Methods) and some additional measurements because twisting of the samples occurred during the bending tests, which resulted in erroneous force estimates. Values for bending stiffness reported here (for full comparison and statistics, see Table S2) were all determined for curvatures within the observed natural range (see Materials and Methods).

The shaft (<93% OL) of individual ventral valves was stiffer than the dorsal valve shaft (compare dark and light blue data points in Fig. 8B). The mean recorded stiffness of the shaft of the whole ovipositor (15.72×10⁻¹¹ N m²) was approximately 3.6 times greater than the mean shaft stiffness of the isolated ventral valves (4.40×10⁻¹¹ N m²) and more than 17 times greater than the mean stiffness of the shaft of the isolated dorsal valve (0.9×10⁻¹¹ N m²).

The stiffness of both the ovipositor and the ventral valves was significantly lower in the S-shaped region between 93% and 96% OL (Table S2). The mean recorded value in the S-shaped region for the whole ovipositors (5.12×10⁻¹¹ N m²) is approximately one-third (30.8%) of the mean value of the shaft. Similarly, the stiffness of the S-shaped region of the isolated ventral valves (1.57×10⁻¹¹ N m²) is also approximately one-third (28.0%) of the mean stiffness of their shafts. FE studies showed that an S-shaped morphology compared with a straight beam resulted in only a 7% (−0.43 mN versus −0.46 mN) reduction in measured reaction forces in a three-point bending experiment, indicating that the differences in stiffness between the shaft and S-bend region cannot be explained by the S-bend shape alone.

The variation in the dorsal valve data was high and we did not observe significant differences between the shaft and the S-shaped region (0.90×10⁻¹¹ N m² versus 0.88×10⁻¹¹ N m²; Table S2). This variation was caused at least partially by the limited accuracy of the force transducer (see Materials and Methods).

The bending stiffness measured in our experiments depends on the second moment of area and the material properties of the ovipositor and the valves. We were able to estimate the material properties of these structures and express them as the effective modulus of elasticity (E_eff) by dividing the bending stiffness by the second moment of area. The effective modulus of elasticity showed the same variation along the length of the ovipositor as seen for the bending stiffness (Fig. 8C). The effective elasticity of the ovipositor, and ventral and dorsal valves was significantly lower in the S-shaped region than in the shaft (Table S2). For the whole ovipositor, the effective modulus of elasticity of the S-shaped region was almost 4 times lower than that of the shaft (0.92 versus 3.60 GPa), over 3 times lower in the ventral valves (1.46 versus 4.81 GPa) and only 1.6 times lower in the dorsal valve (3.7 versus 5.95 GPa).

To link the differences in effective modulus of elasticity to actual differences in material properties, we analysed the autofluorescence of the ovipositor with confocal laser scanning microscopy (Fig. 9; Fig. S3). The green (488 nm excitation) and red (555 and 639 nm excitation) autofluorescence signals indicate that the cuticle of the ovipositor is well sclerotized. The more flexible S-shaped region of the ventral valves is clearly less well-sclerotized and shows high levels of resilin (blue channel; 405 nm excitation; Fig. 9A). Other regions with high resilin content are the most lateral parts of the dorsal valve (Fig. 9B,C) and the valve inner walls forming the egg canal (Fig. 9B,D).

Parasitic wasps, mosquitoes and hemipterans are capable of inserting probes into a variety of substrates, and can even explore the substrate by steering their probes in a range of directions (Cerkvenik et al., 2017; Choumet et al., 2012; Leopold et al., 2003). Hitherto, very little was known about how these animals induce a shift of the probing direction. The kinematic analysis of ovipositor insertions in the parasitic wasp D. longicaudata indicates that the reciprocal sliding movements of its valves may be important for both insertion (Vincent and King, 1995) and steering (Cerkvenik et al., 2017). In D. longicaudata, the protraction of the ventral valves over the dorsal one induces a clear shape change in the ovipositor tip that leads to a curved insertion trajectory (Movie 2; Cerkvenik et al., 2017).

We hypothesize that the ovipositor of D. longicaudata employs the same principle of differentially sclerotized (and therefore differentially stiff) valves as suggested for the arched ovipositors of Zaglyptogastra sp. and Pristomerus sp. (Quicke, 1991). For this mechanism to work, both soft and very stiff regions must be present. Analysis of the bending stiffness of the D. longicaudata ovipositor as a whole indeed showed an approximately 67% lower bending stiffness in the S-shaped region than in the rest of the shaft. This reduction in stiffness is mainly caused by a change in material properties (effective modulus of elasticity). Structural properties of the S-shaped region even counteract the drop in stiffness as can be seen from the increased second moment of area in that region (Table S1). The reduced stiffness also cannot be explained by the curved morphology as this only results in a 7% decrease in stiffness compared with a straight morphology with the same material. That the S-shaped region is composed of softer materials than other regions along the ovipositor is substantiated by the confocal laser scanning microscope images, which show a stronger fluorescence signal indicative of the presence of relatively soft resilin at that location.

The derived effective moduli of elasticity of the ovipositor and its valves in D. longicaudata (Fig. 8C; Table S2) are in agreement with those previously reported for other wasp ovipositors and the intromittent organs of beetles, which range from 0.6 to 10 GPa (Kundanati and Gundiah, 2014; Matsumura et al., 2017; Vincent and King, 1995). The reported Young's modulus of resilin, which is present in the S-shaped region of the ovipositor in D. longicaudata, is approximately 1 MPa (Vincent and Wegst, 2004; Gosline et al., 2002) – this is much smaller than our derived stiffness estimates of the sclerotized cuticle. Thus, the decreased stiffness of the S-shaped region of the ovipositor is likely to be due to the presence of resilin in the ventral valves at that location. However, the effective elasticity of the samples reported in Fig. 8C and Table S2 is presumably influenced (reduced) by the possible sliding of the valves along each other during the three-point bending experiments or by possible minute slippage of the samples on the razorblades. However, the effect of sliding valves was not estimated in this study.

Although areas of increased stiffness were not directly measured, it can be assumed that the tip of the ovipositor is stiffer than the rest of the ovipositor. We observed a dramatic increase in second moment of area of the whole ovipositor at the location of the dorsal bulge, where the mean second moment of area was 2 times greater than that in the shaft (Table S1; Figs 7 and 8A). Because the autofluorescence of the materials of the shaft and the tip did not differ, we can assume that the material properties are the same, and that the twofold increase of the second moment of area at the bulge results in a twofold increase in bending stiffness of the ovipositor. This is mainly due to the bulge in the dorsal valve, which has a 6 times greater second moment of area than the dorsal valve shaft. The slight thickening of the ventral valve at the same location only leads to a very small increase in second moment of area (Table S1).

According to the steering hypothesis described above, alignment of flexible and stiff areas should lead to configurational changes of the ovipositor distal end. In the ovipositor of D. longicaudata, this occurs when the S-shaped region of either the dorsal or the ventral valve aligns with the morphologically distinct tip of the opposite valve. The S-shaped region and the bulge area of the tip have approximately the same length (3% OL; Figs 1B and 7A,C; Table S1), which facilitates an accurate alignment. The movement of the valves occurs via a complex mechanism of chitin plates in the abdomen (Eggs et al., 2018; Smith, 1970), the description of which is outside the scope of the present study. An in vivo study of probing kinematics has shown that D. longicaudata can displace the valves over a distance of 200 µm (Cerkvenik et al., 2017), which is sufficient for aligning the valve tip with the S-shaped region of their neighbours. Below, we describe how the alignment of the different parts may lead to these configurational changes and, consequently, to a change in probing direction. We consider two valve configurations: (i) protraction of the ventral valves and (ii) protraction of the dorsal valve (Fig. 10).

Protraction of the ventral valves moves them from their rest position (Fig. 10A) forward, such that their less-stiff S-shaped regions align with the stiff bulge of the dorsal valve tip (Fig. 10B). At the same time, the dorsal S-shaped region aligns with the shaft of the ventral valves. Because of the difference in stiffness, the dorsal valve bulge straightens the S-shaped region of the ventral valves as observed by Cerkvenik et al. (2017) (Movie 2). Similarly, the S-shaped region of the dorsal valve is presumably straightened by the shaft of the ventral valves (Fig. 8B; Table S2). We expect that after straightening of the S-shaped region, the natural angle between the S-shaped region and the tip region remains, which causes the dorsal curving of the ovipositor (Fig. 10A,B; Cerkvenik et al., 2017). While probing in stiff substrates, the substrate reaction forces presumably prevent the bending of the long ovipositor shaft, but allow the curving of the short tip. Additionally, the bevel shape of the ventral valve tips (Figs 1 and 10B) generates asymmetric substrate reaction forces that potentially enhance the curving of the tip during insertion of the ovipositor, and may explain the high curvatures observed during probing (Cerkvenik et al., 2017).

Although this pattern seems straightforward, it is difficult to predict what happens upon protraction of a single ventral valve. The resulting bending moments on the ovipositor tip would in this case be asymmetric and could lead to local twisting of the valves. However, this is hard to substantiate experimentally and is outside the scope of this paper.

Dorsal valve protraction aligns the relatively soft S-shaped region of the dorsal valve with the stiffer ventral valve tips, which also possess a small bulge near their tips (Figs 1D and 8; Table S1). This presumably straightens the S-shaped region of the dorsal valve. The ventral S-shaped region in this case aligns with the shaft of the dorsal valve, and also straightens out (Figs 1D and 10C; Cerkvenik et al., 2017). The straightening of both S-shaped regions should lead to dorsal curving of the ovipositor tip as explained above. This does occur when the ovipositor is outside a substrate (Movie 3) but was not observed during natural probing (Movie 2; Cerkvenik et al., 2017). We hypothesize that substrate reaction forces acting on the bevelled dorsal valve tip counteract any dorsal bending moments originating from the straightening of the S-shaped regions. Protraction of the dorsal valve inside a substrate therefore results in an approximately straight path, but in dorsal curving of the tip outside the substrate. Because the forces acting on the bevel counteract the bending moments within the ovipositor, we expect that protracting the dorsal valve by more than its tip length leads to ventral curving. However, such large protraction amplitudes seem to be outside the natural probing range (Cerkvenik et al., 2017).

In both ventral and dorsal valve protraction, the S-shaped region of the ovipositor undergoes continuous deformation and is subjected to repetitive strains of about 9% (see Materials and Methods), which could lead to damage due to material failure. The strains are larger in the thicker and stiffer ventral valves, compared with those in the relatively thin and flexible dorsal valve. It is unlikely that the expected strains in the ventral valves induce damage to their outer walls, because of the presence of resilin (Fig. 9A). Resilin is known for its high resilience (≥ 92%) and its high maximum strain of 1.9 (Gosline et al., 2002). Therefore, we expect that it will not be damaged during probing with the anticipated strains. The presence of resilin presumably makes the sclerotized cuticle tougher and reduces the likelihood of damage (e.g. Haas et al., 2000).

Interestingly, resilin-containing regions were also found in the inner walls of the valves around the egg canal and in the lateral sides of the dorsal valve (Fig. 9B–D). These softer central regions could facilitate the passage of ‘oversized’ eggs during the egg-laying process (Austin, 1983; Austin and Browning, 1981; Bronner, 1985; Fulton, 1932; Whiting, 1967). Additionally, having softer lateral sides could be important in terms of the wasp’s ability to explore the substrate in an approximately half-ellipsoid without rotating its body (Cerkvenik et al., 2017), by facilitating lateral bending or twisting of the ovipositor.

Although the functional principles of ovipositor bending are similar among D. longicaudata, Zaglyptogatra sp. and Pristomerus sp., the implementation of the mechanism in D. longicaudata differs from that in the other two species. Whereas Zaglyptogastra and Pristomerus possess a series of stiff (arches) and flexible (nodes) ovipositor regions, the ovipositor of D. longicaudata has only a single flexible area near its tip. This difference might be linked to the fact that D. longicaudata probes in solid substrates such as citrus fruits (Leyva et al., 1991), while Zaglyptogastra and Pristomerus cannot (Quicke, 1991).

The modulus of elasticity of orange peel estimated for freshly harvested fruits ranges between 3.5 and 4.3 GPa (Fidelibus et al., 2002). It is likely that fruits infested with fruit-fly larvae are softer, although the stiffness of such fruits is not known. Nevertheless, D. longicaudata is capable of puncturing artificial gels with a stiffness of at least 0.2 GPa (Cerkvenik et al., 2017). We argue that this is presumably facilitated by the low number of stiff and flexible regions in the ovipositors of D. longicaudata. Although the flexible S-shaped region in the ovipositor of D. longicaudata may still bend when axial loading is applied, a small offset of the valves can potentially strengthen this region without inducing strong ovipositor curvature that would hinder puncturing. The low number of flexible and stiff nodes might come at a price as it is likely that the S-shaped ovipositors cannot bend as much as the arched ones. We therefore hypothesize that the ovipositor S-shaped region is a morphological adaptation for probing and steering in solid substrates such as fruits that occurs in D. longicaudata. Interestingly, S-shaped ovipositors also occur in species closely related to D. longicaudata (Van Achterberg, 1999; Wharton et al., 2012), which might face similar functional demands during probing.

Here, we show that the structural and material properties of the ovipositor vary across its individual elements. This, together with the kinematics of individual elements (Cerkvenik et al., 2017), leads to controlled shape changes of the probe tip and therefore offers a degree of control over spatial probing of the animal. The probing principles found in parasitic wasps presumably also apply to other insect probers including mosquitoes and hemipterans. These animals also explore a variety of substrates with multi-element probes (Gordon and Lumsden, 1939; Pollard, 1973) that are moved reciprocally during substrate exploration (Choumet et al., 2012; Pollard, 1970). This kinematics indicates that these insects use similar principles of buckling avoidance and steering to those described for parasitic wasps. It would be interesting to see whether a steering mechanism similar to that described here is also found in other insect groups. This would add to our understanding of the convergent evolution that led to the widespread use of slender, multi-element probes capable of independent and reciprocal element movements and steering. Furthermore, it also indicates that such probes are highly effective for substrate exploration and studying their working principles may also be beneficial in the design of slender man-made probes.

Slender, multi-element probes inspired by parasitic wasp ovipositors have been developed and can be steered without placing actuators inside the probe and without axial rotation (Ko et al., 2010; Scali et al., 2017). The individual elements of such probes slide along each other and therefore form an adjustable bevel tip (Ko et al., 2011; Scali et al., 2017). The probe is steered by taking advantage of the substrate reaction forces acting on the adjustable bevel. Consequently, the amount of curving in such probes heavily depends on the material properties of the substrate and the probe. The steering mechanism described here is not dependent on the substrate interaction, although it can be enhanced by it. Therefore, application of a mechanism using stiff and deformable regions as described here will presumably result in probes that are less susceptible to substrate differences. The steering mechanism can be implemented by adjusting either the material properties or the cross-sectional area of the probe S-shaped region which would not compromise the diameter of the probe. Such a design would therefore propel further miniaturization of man-made probes.

We acknowledge the Paul Scherrer Institut, Villigen, Switzerland for provision of synchrotron radiation beam time at the TOMCAT beamline X02DA of the SLS and would like to thank Christian Schlepütz for invaluable assistance. We thank the Naturalis Biodiversity Center (RMNH; Leiden, The Netherlands) and collection manager Frederique Bakker for help and for providing the specimen used for CT-scanning. We also acknowledge the National Institute of General Medical Sciences of the National Institutes of Health for their role in the development of the Seg3D software (grant number P41 GM103545-18) for segmentation purposes. We thank Henk Schipper and Frank van den Berg for their help with histological sections of the ovipositor; Karen Leon-Kloosterziel for technical support, animal care and help with ovipositor scaling analysis; and the user committee of the Netherlands Organization for Scientific Research Division Applied and Engineering Sciences (NWO TTW/NWO AES) WASP project and the members of the research group for their useful discussions.