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. 2017 Dec 20;3(12):eaao5469.
doi: 10.1126/sciadv.aao5469. eCollection 2017 Dec.

Penetration mechanics of a beetle intromittent organ with bending stiffness gradient and a soft tip

Yoko Matsumura  1 , Alexander E Kovalev  1 , Stanislav N Gorb  1
Affiliations

Penetration mechanics of a beetle intromittent organ with bending stiffness gradient and a soft tip

Yoko Matsumura et al. Sci Adv. .

Abstract

Hyper-elongated structures and their penetration are widespread among insects, for example, intromittent organs, ovipositors, and piercing-sucking mouthparts. The penetration of thin structures with high aspect ratio without buckling and rupturing is mechanically very challenging. However, this problem is economically solved in nature, and the solutions might be helpful for, for example, in the development of harmless catheters. We focus on the penetration process of a hyper-elongated structure of a cassidine beetle intromittent organ, termed a flagellum. We applied a three-point bending test for the flagellum to measure its bending stiffness along the entire flagellum. We demonstrated the bending stiffness gradient, in which the basal half is relatively stiff and the apical half is softer, whose good performance during copulation had been previously numerically demonstrated. The stiffness gradient is the result of the flagellum shape, which is cylindrical and tapered toward the tip. Moreover, the curved tip comprises a harder outer curve and a softer inner curve. Considering the findings of preceding studies, the flagellum works in the following way: (i) the bending stiffness gradient supports the flagellum, easily fitting to a shape of a highly coiled spermathecal duct, (ii) the stiffness property of the very tip may make the tip tougher, and (iii) the curled tip and homogeneously cylindrical shape of the organ help the very tip to fit the shape of the spermathecal duct of the female. Our study shows that the apparently simple flagellum penetration is achieved with numerous elaborate mechanical adaptations.

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Figures

Fig. 1
Fig. 1. Genital morphology of Cassida rubiginosa.
(A) A couple scanned with micro–computed tomography. (B) An enlarged image of the abdomen during copulation; different parts of the male reproductive system are shown with different colors. (C) A scheme of the flagellum inserted into the spermathecal duct. (D) The male genitalia at rest. The flagellum is highlighted with dark blue in (B) and (D). During copulation, a primary intromittent organ (aedeagus, light blue) is inserted in a female vagina, the ejaculatory duct is shortened due to contraction of longitudinal muscles, and the flagellum is propagated to the female spermathecal duct. Figures are modified from the study by Filippov et al. (14) for (C) and Matsumura et al. (25) for (A), (B), and (D).
Fig. 2
Fig. 2. Scheme of the experimental design of the bending test.
(A) Setup of the bending test apart from the manipulators and the microscope. The flagellum is sunk in the water puddle, and the left end of the flagellum is fixed on the bent tip of an insect pin. The fork is set perpendicular to the flagellum and is moved toward the direction of the arrow on the fork. The glass capillary is set perpendicular to the fork and flagellum. The glass capillary is movable in the direction of the arrows on the glass capillary. (B) An enlarged scheme of the bent flagellum. The insect pins at a distance of 300 μm from each other compose the fork. The glass capillary is set behind the flagellum and was movable forward (the arrow) to bend the flagellum.
Fig. 3
Fig. 3. Bending experiment.
The images (A) and (B) were taken from the bottom of the setup of the bending test shown in Fig. 2. The glass capillary with the glass sphere was moved from the upper to the lower side of each image. (A) A glass capillary terminated with a glass sphere (S) produces a load (Fl) on a fragment of the male flagellum (mf), which rests on a fork (fl, fork left; fr, fork right). (B) The trajectory of the sphere motion is shown with a thick light gray line. The flagellum at different loads is shown as a series of the gray lines. (C) Theoretical (solid line, calculated according to Eq. 1) and experimental (dotted line) deformation curves of flagellum deformation at 2.56 μN loading force. w (y axis) represents the deformation at position x.
Fig. 4
Fig. 4. Flexural rigidity of the flagellum of C. rubiginosa.
Individual values of flexural rigidity are shown as asterisks. The smoothed values of flexural rigidity are shown as a black solid line within the range, where the SE was calculated (SE is shown as a gray area), and outside that range as a dark gray line . The effective Young’s modulus calculated from the smoothed flexural rigidity curve is shown in the inset as a solid black line. A dashed line in the inset corresponds to a constant effective Young’s modulus (independent on the location), the value of which was used to calculate the flexural rigidity curve shown as a black dashed line in the main figure.
Fig. 5
Fig. 5. The flagellum measurements of C. rubiginosa with representative SEM images.
The upper values in the graph represent the diameters of the flagellum on an average, and the lower values represent the wall thickness of the flagellum on an average. The material situated on the inner wall of the flagellum at the subbasal region is likely debris of sperm.
Fig. 6
Fig. 6. CLSM image of the flagellum tip of C. rubiginosa.
We assigned colors blue, green, red, and red to emitted wavelengths of 420 to 480, ≥490, ≥560, and ≥640 nm, respectively.
Fig. 7
Fig. 7. SEM images of the flagellum of C. rubiginosa.
(A) Map of the images below, the tip of the flagellum. (B to E) Enlarged images of the flagellum corresponding to the squares in (A). The pink-colored areas in (B) and (C) represent shrunk surfaces. The scale bar in (B) is applicable for (C) to (E).
See this image and copyright information in PMC

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