Clarifying the mechanisms underlying shape alterations during insect metamorphosis is important for understanding exoskeletal morphogenesis. The large horn of the Japanese rhinoceros beetle Trypoxylus dichotomus is the result of drastic metamorphosis, wherein it appears as a rounded shape during pupation and then undergoes remodeling into an angular adult shape. However, the mechanical mechanisms underlying this remodeling process remain unknown. In this study, we investigated the remodeling mechanisms of the Japanese rhinoceros beetle horn by developing a physical simulation. We identified three factors contributing to remodeling by biological experiments – ventral adhesion, uneven shrinkage, and volume reduction – which were demonstrated to be crucial for transformation using a physical simulation. Furthermore, we corroborated our findings by applying the simulation to the mandibular remodeling of stag beetles. These results indicated that physical simulation applies to pupal remodeling in other beetles, and the morphogenic mechanism could explain various exoskeletal shapes.

Understanding the mechanisms underlying animal morphogenesis is challenging, particularly in exoskeletal animals with great morphological diversity. These animals grow discontinuously through molting, which enables certain hemimetabolous and holometabolous insects to undergo dramatic changes in shape, known as metamorphosis (Belles, 2020). Exoskeletal animals are covered with a rigid cuticle layer, and the undulation determines the shape of the animals. Typically, cuticle shaping is achieved as follows: the pre-existing epithelial sheet just beneath the current cuticle (outermost layer) detaches from the cuticle through apolysis in preparation for molting. Cellular (e.g. cell division) and physical (e.g. internal pressure) factors alter the epithelial and cuticle layers before and after ecdysis, resulting in different forms of the cuticle layer (Belles, 2020; Chapman, 1998; Jenkin and Hinton, 1966). However, the mechanisms controlling the shape of these layers remain poorly understood.

From a physical standpoint, the force distribution determines epithelial sheet deformation (Diaz de la Loza and Thompson, 2017; Heer and Martin, 2017; Thompson, 1942). The factors controlling the force distribution can be divided into cell-intrinsic and cell-extrinsic factors. Cell-intrinsic factors, such as the cytoskeleton and cell–cell junctions, generate short-range force patterns, whereas cell-extrinsic factors, such as extracellular matrices (ECMs), generate long-range force patterns (Diaz de la Loza and Thompson, 2017). Although the effects of cell-intrinsic factors on morphogenesis have been extensively studied in developmental biology, the effects of cell-extrinsic factors have only recently been investigated. The apical ECM protein Dumpy is an important cell-extrinsic factor controlling morphogenesis via global force. Dumpy has been reported to anchor the epithelial sheet to the overlying cuticle (Wilkin et al., 2000). Anchorage, combined with the contraction of neighboring tissues, generates long-range tension patterns, leading to elongated appendages in Drosophila (Ray et al., 2015). Dumpy also contributes to the differences in posterior lobes of Drosophila genitalia (lobed/non-lobed) by linking cell sheets to the apical ECM network (Smith et al., 2020). These studies suggest that the regulation of long-range force patterns through cell-sheet connections to ECMs (including cuticles) may play a crucial role in cell-sheet deformation. However, these studies focused on relatively simple shapes, such as wings, legs and posterior lobes, and the mechanisms regulating more complex morphologies have yet to be fully explored.

The beetle horn is one example of a complex morphology that undergoes a significant change in appearance before and after molting. The head horn of the Japanese rhinoceros beetle Trypoxylus dichotomus is four-branched at the tip and has one of the most elaborate horn shapes. It is not present on the larval surface and is formed in three steps (i.e. folded structure formation in larvae, visible protrusion formation during pupation, and remodeling in pupae), similar to other beetles (Emlen et al., 2007).

First, the cell sheet beneath the larval head capsule forms a complex folded horn primordium during the prepupal stage. We previously reported that different genetic/cellular mechanisms regulate the folding pattern and macro shape of the horn primordia (Adachi et al., 2018, 2020). In addition, gene expression analysis of this step identified 11 genes contributing to horn formation (Ohde et al., 2018), and detailed observation of the morphological changes of this step, combined with RNA-interference (RNAi) analysis, revealed the onset of horn sex dimorphism (Morita et al., 2019).

The horn primordium is then transformed into a pupal horn under hemolymph pressure during pupation. As we previously stated, the shape of the pupal horn primarily depends on the unfolding of primordial furrows (Matsuda et al., 2017). Our previous study using computer simulations revealed the relationship between primordial furrow patterns and unfolded 3D shapes (Matsuda et al., 2021).

In terms of horn remodeling, previous studies have primarily focused on thoracic horn remodeling in Onthophagus species because they show extensive remodeling via horn tissue resorption, which can magnify, reverse or remove the sex dimorphism observed in pupae (Moczek, 2006) and generate male dimorphism (Moczek, 2007). Resorption is mediated by programmed cell death at the cellular level (Kijimoto et al., 2010), and differences in the location and domain size of Distal-less expression are related to the degree of horn resorption at the genetic level (Moczek et al., 2006). Several genes have been demonstrated to contribute to remodeling; however, the effects of RNAi differ depending on species, sex, and horn location (Wasik and Moczek, 2011; Wasik et al., 2010). Detailed observations of doublesex RNAi mutants suggest that different genetic mechanisms underlie head and thoracic horn remodeling in T. dichotomus (Morita et al., 2019). Although these studies have revealed the biological aspects of horn remodeling, the remodeling process involves both biological and physical factors. Therefore, a large knowledge gap linking these biological mechanisms and the resulting transformation of the epithelial sheet remains.

The pupal and adult horns of T. dichotomus are roughly similar in shape; however, there are two prominent differences. First, the distal tips of the pupal horns are rounded, whereas those of the adult horns are sharp. Second, the stalk is cylindrical in pupae and polyhedral in adults (Fig. 1A,B). Similar to that of other molting events, the remodeling process includes epithelial detachment from the pupal cuticle, formation of the adult horn shape, and adult cuticle deposition, as shown in the schematics in Fig. 1C (Moczek, 2006). Thus, the epithelia have the same shape as the pupal cuticle immediately after pupation, and epithelial deformation generates differences. The characteristics of adult horns resemble those of tensile membrane structures, such as outdoor tarpaulins and tents, suggesting that tension patterns are involved in epithelial deformation during remodeling, similar to wing formation in Drosophila.

Fig. 1.

The surface area and inside volume of the epithelial sheet forming the adult horn decreases, remaining localized to the ventral side, during adult horn formation. (A,B) Images of a pupal horn (A) and an adult horn (B). Images of the whole pupa and adult are shown on the left. Schematics of each horn are shown on the right. (C) Schematics of the beetle horn remodeling process. The orange and black lines show the pupal and adult cuticles, respectively. The gray and purple dotted line shows the epithelial sheet. (D-F) Visualization of the pupal and adult epithelial sheet using the CoMBI method. Section images of proximal (D), middle (E) and distal (F) parts of the horn are shown. The green, yellow and blue panel outlines correspond to the colors of the arrowheads in A, indicating the estimated sectioning position. Upper panels show the raw data, and lower panels show the corresponding schematics (yellow area, pupa; orange area, adult: red line, the estimated area of the epithelia–cuticle adhesion). D, dorsal; L, left; R, right; V, ventral. (G) Comparison of the surface area (left) and the inside volume (right) of pupal and adult horns (n=3). Scale bar: 10 mm (A,B); 5 mm (D-F).

Fig. 1.

The surface area and inside volume of the epithelial sheet forming the adult horn decreases, remaining localized to the ventral side, during adult horn formation. (A,B) Images of a pupal horn (A) and an adult horn (B). Images of the whole pupa and adult are shown on the left. Schematics of each horn are shown on the right. (C) Schematics of the beetle horn remodeling process. The orange and black lines show the pupal and adult cuticles, respectively. The gray and purple dotted line shows the epithelial sheet. (D-F) Visualization of the pupal and adult epithelial sheet using the CoMBI method. Section images of proximal (D), middle (E) and distal (F) parts of the horn are shown. The green, yellow and blue panel outlines correspond to the colors of the arrowheads in A, indicating the estimated sectioning position. Upper panels show the raw data, and lower panels show the corresponding schematics (yellow area, pupa; orange area, adult: red line, the estimated area of the epithelia–cuticle adhesion). D, dorsal; L, left; R, right; V, ventral. (G) Comparison of the surface area (left) and the inside volume (right) of pupal and adult horns (n=3). Scale bar: 10 mm (A,B); 5 mm (D-F).

Therefore, we focused on adhesion and shrinkage in the horn remodeling of T. dichotomus, during which a cylindrical pupal horn transforms into a polyhedral adult horn, and developed a physical simulation to reproduce this transformation in this study. First, we identified the shrinkage ratio of each part of the horn, volume change, and area of epithelia–cuticle adhesion through detailed observation of the formation process and RNAi analysis of dumpy in pupae. Next, we developed a physical simulation based on these data and demonstrated that simple physical simulations can reproduce pupal horn remodeling. As the physical simulation could also reproduce the mandibular remodeling of a stag beetle to some extent, it may serve as a general model for pupal remodeling in beetles.

Positional and morphological relationship between the pupal horn and the adult horn

An adult beetle horn is formed inside the pupal horn and is almost complete at eclosion. Thus, we initially observed the position and shape of the epithelial sheet in pupae using the correlative microscopy and block-face imaging (CoMBI) method (Tajika et al., 2017), in which serial section images were acquired by capturing the block-face images of a frozen block during frozen sectioning using a digital camera. Fig. 1D-F shows sectional block-face images and schematics of the proximal, middle and distal parts of the horn (the window colors correspond to the colors of the arrowheads in Fig. 1A, indicating the estimated sectioning position). The results showed that the pupal horns were rounded in all sections, whereas the adult horns were flattened in the distal region and more polygonal with a dorsal ridge in the proximal region. The ventral side of the adult epithelial sheet was located near the pupal cuticle, suggesting that the ventral region was the site of adhesion to the pupal cuticle (Fig. 1D-F, red lines).

Furthermore, micro-CT 3D mesh reconstructions (Fig. S1) revealed that the adult mesh model had approximately 50% of the surface area of the pupal mesh model and about 20% of its volume (Fig. 1G, n=3).

RNAi analysis of dumpy, which contributes to epithelia–cuticle adhesion

Given the images that suggested ventral epithelia–cuticle adhesion (Fig. 1D-F), we investigated the effect of adhesion on epithelial sheet deformation by knockdown analysis of dumpy, which has been reported to be involved in epithelia–cuticle adhesion in Drosophila (Ray et al., 2015; Wilkin et al., 2000). We injected dsRNA for dumpy RNAi into pupae and observed how the horn formation process and its final shape varied depending on the presence of adhesions.

To observe the formation process in the same pupa, we observed it by transmitting light from the dorsal and left sides (Fig. 2, Fig. S2). Fig. 2A shows the changes over time in the control and in dumpy mutants. During adult horn formation, the distal tips of the dumpy mutants detached and gradually moved toward the proximal side (Fig. 2A, blue arrowheads), whereas those of the control individuals remained at the distal tips of the pupal horn (Fig. 2A).

Fig. 2.

RNAi analysis of dumpy reveals two types of adhesion and uneven shrinkage ratios between the proximal and distal parts. (A) Visualization of the horn formation process in control individuals (top) and dumpy RNAi mutants (bottom) with light transmission from the dorsal side. Days after pupation are indication. Blue arrowheads indicate the distal tip of the adult horn in each image. (B,C) Visualization of the pupal horn, which includes the adult horn (at day 20; just before eclosion), of control individuals (B) and dumpy RNAi mutants (C) with light transmission from the dorsal and left side. The blue arrowheads point to the distal tip of the adult horn, and the red lines show the estimated area of ventral adhesion (where the adult horn surface is close to the pupal cuticle). The schematic in C shows the traced adult horn (black) and pupal horn (yellow), rescaled so that the length from the root of the horn to the bottom of the central groove (first branching point) of the pupal horn is the same as that of the adult horn.

Fig. 2.

RNAi analysis of dumpy reveals two types of adhesion and uneven shrinkage ratios between the proximal and distal parts. (A) Visualization of the horn formation process in control individuals (top) and dumpy RNAi mutants (bottom) with light transmission from the dorsal side. Days after pupation are indication. Blue arrowheads indicate the distal tip of the adult horn in each image. (B,C) Visualization of the pupal horn, which includes the adult horn (at day 20; just before eclosion), of control individuals (B) and dumpy RNAi mutants (C) with light transmission from the dorsal and left side. The blue arrowheads point to the distal tip of the adult horn, and the red lines show the estimated area of ventral adhesion (where the adult horn surface is close to the pupal cuticle). The schematic in C shows the traced adult horn (black) and pupal horn (yellow), rescaled so that the length from the root of the horn to the bottom of the central groove (first branching point) of the pupal horn is the same as that of the adult horn.

Fig. 2B,C shows the control individual and dumpy mutant on day 20 when the remodeling process was complete. The adult horn in control individuals was stretched over the entire horn region, whereas the distal end of the dumpy mutants was located near the stalk region (Fig. 2B,C, blue arrowheads). However, the adult horn was biased toward the ventral side of the pupa in both the control and dumpy mutants (Fig. 2B,C, red lines), indicating that ventral adhesion was less susceptible to dumpy knockdown. We also estimated the distribution of horn shrinkage in dumpy mutants. The traced pupal and adult horns (yellow and black, respectively, in the schematic in Fig. 2C) after the lengths of the stalks (defined as the part from the root of the horn to the bottom of the central groove of the first branching point) were matched using rescaling showed that the distal area of the horn displayed a higher level of shrinkage than the proximal area (Fig. 2C, schematic). These data suggested an uneven shrinkage of the epithelial sheet.

Physical simulation settings

The results of biological experiments are summarized in Fig. 3A. We identified three factors involved in adult horn formation: epithelia–cuticle adhesion, uneven shrinkage, and volume reduction. The first factor can be divided into distal dumpy RNAi-sensitive and ventral dumpy RNAi-insensitive adhesions. In addition to these factors, we introduced smoothing effects into the simulation, as pupae have a few wrinkles and adults do not. This is based on the idea that surfaces of epithelial cell are actively smoothed (Fig. 3B). Based on these factors, we developed a physical simulation to investigate whether deformation could be reproduced from the pupal mesh model, which describes the pupal horn shape as a curved 2D surface, discretized as a triangular mesh (Fig. S1). See Materials and Methods for further details.

Fig. 3.

Summary of the experiments and development of the physical simulation. (A) Summary of findings from the experiments. From the experimental data, we extracted three factors: ventral adhesion (yellow area) and Dumpy-mediated adhesion at the distal tips (orange circles); uneven shrinkage of the epithelial sheet (white arrows outlined in black); and volume reduction (blue arrows). The corresponding figures are shown near each factor. (B) The fourth factor we introduced to the simulation: smoothing effects of a cell sheet. Smoothing is probably due to the return of protruding cells or their elimination (e.g. by apoptosis). (C) The fixation area in the simulation. We extracted the fixation area (blue area) from the pupal mesh (transparent gray area) by comparing it with the adult mesh (red area). (D) The proximodistal axis in the simulation. rs (see Eqn 1; the ratio of triangle shrinkage) in the red area was set to be smaller than that in the blue area. See Supplementary Materials and Methods for details of the simulation settings.

Fig. 3.

Summary of the experiments and development of the physical simulation. (A) Summary of findings from the experiments. From the experimental data, we extracted three factors: ventral adhesion (yellow area) and Dumpy-mediated adhesion at the distal tips (orange circles); uneven shrinkage of the epithelial sheet (white arrows outlined in black); and volume reduction (blue arrows). The corresponding figures are shown near each factor. (B) The fourth factor we introduced to the simulation: smoothing effects of a cell sheet. Smoothing is probably due to the return of protruding cells or their elimination (e.g. by apoptosis). (C) The fixation area in the simulation. We extracted the fixation area (blue area) from the pupal mesh (transparent gray area) by comparing it with the adult mesh (red area). (D) The proximodistal axis in the simulation. rs (see Eqn 1; the ratio of triangle shrinkage) in the red area was set to be smaller than that in the blue area. See Supplementary Materials and Methods for details of the simulation settings.

Distal and ventral adhesions were implemented as fixation of the vertices. The fixation area was set by calculating the distance between the pupal and adult mesh models and by manual selection based on the projection from the dorsal side (Fig. 3C, Figs S3, S9-S12, Supplementary Materials and Methods). We introduced the proximodistal axis into the simulation for uneven shrinkage, and rs was set to be smaller in the distal area than in the proximal area so that the distal area shrunk more strongly (Fig. 3D, Fig. S13, Supplementary Materials and Methods).

The physical simulation revealed each factor's contribution and the generality of the model

To investigate the role of each factor in remodeling, we varied the parameters (rs, shrinkage ratio of the triangle area; ka, bending rigidity of the surface; kn, intensity of the negative pressure) and settings (fixation area) in the simulation to observe shape changes (Fig. 4A-E). Without shrinkage, the final shape exhibits large folds and lacks a polyhedral structure (Fig. 4A, leftmost). When the entire mesh shrank uniformly, the resultant shape gradually flattened, particularly in the distal region, with stronger shrinkage (Fig. 4A, left to right). However, uniform shrinkage did not generate a sloped dorsal ridge structure in the stalk region. Uneven shrinkage along the proximodistal axis did result in a sloped dorsal ridge structure (Fig. 4B). With a fixed distal shrinkage ratio, the size and slope of the dorsal ridge structure became slimmer and gentler, respectively, as the proximal part shrunk more strongly (Fig. 4B, left to right). Without ventral adhesion (only the distal tips were fixed), the final shape was elongated and cylindrical without the typical adult polyhedral structure (Fig. 4C). The intensity of negative pressure was also varied. An arch structure instead of a ridge structure appeared in the stalk region in the absence of negative pressure (Fig. 4D, leftmost). A ridge structure appeared on the dorsal surface, which gradually became sharper as the negative pressure increased (Fig. 4D, left to right). The last factor that was varied was the bending rigidity of the sheets. When the sheet was soft, small folds appeared, especially in the stalk region, although the shape of the ridge was roughly similar to that of an adult. The folds disappeared as the bending rigidity of the sheet increased, and only the dorsal ridge structure remained (Fig. 4E, left to right).

Fig. 4.

The simulation reveals each factor's contribution to the shape determination and the generality of the simulation. (A-E) Shape changes when the parameters and settings were varied. (A,B) Simulated horns with various shrinkage ratios. (A) Simulated horns with uniform shrinkage ratios (rs: position independent). The value of rs is shown under each horn. (B) Simulated horns with uneven shrinkage ratios (rs: proximodistal position dependent). The values under each horn are the values of rs in the most distal (D) and proximal (P) areas, respectively. (C) Simulated horn without ventral fixation (i.e. only the distal tips were fixed). (D) The intensities of negative pressure were varied. The values of kn in Eqn 2 are shown under each horn. (E) Shape changes with various bending rigidity of the sheet. The values of ka in Eqn 1 are shown under each horn. (F) Simulated (top) and actual (bottom) adult horns were compared from various angles. (G) Validation of the simulation with the mandible formation of the stag beetle D. hopei. The leftmost image shows the 3D data of a stag beetle. The pupal mandible mesh model was extracted from the mesh (boxed area). The simulated result was compared with the actual adult mandible (rightmost) of a different individual.

Fig. 4.

The simulation reveals each factor's contribution to the shape determination and the generality of the simulation. (A-E) Shape changes when the parameters and settings were varied. (A,B) Simulated horns with various shrinkage ratios. (A) Simulated horns with uniform shrinkage ratios (rs: position independent). The value of rs is shown under each horn. (B) Simulated horns with uneven shrinkage ratios (rs: proximodistal position dependent). The values under each horn are the values of rs in the most distal (D) and proximal (P) areas, respectively. (C) Simulated horn without ventral fixation (i.e. only the distal tips were fixed). (D) The intensities of negative pressure were varied. The values of kn in Eqn 2 are shown under each horn. (E) Shape changes with various bending rigidity of the sheet. The values of ka in Eqn 1 are shown under each horn. (F) Simulated (top) and actual (bottom) adult horns were compared from various angles. (G) Validation of the simulation with the mandible formation of the stag beetle D. hopei. The leftmost image shows the 3D data of a stag beetle. The pupal mandible mesh model was extracted from the mesh (boxed area). The simulated result was compared with the actual adult mandible (rightmost) of a different individual.

We also evaluated the effects of these factors on the shape by quantifying the pupal and adult mesh models, and the simulated results (Fig. S4). The results showed that the surface shrinkage was the main influence on the surface area and volume of both the proximal and distal regions, whereas the bending rigidity and negative pressure had relatively minor effects. Moreover, the effect of surface shrinkage on the area and volume differed between the proximal and distal regions, suggesting uneven shrinkage along the proximodistal axis. The relationship between negative pressure and the stalk section index also showed that negative pressure plays a significant role in the transition of the proximal region from an arch to a polyhedral shape. Therefore, surface shrinkage was the essential parameter for determining the size change, negative pressure was an important parameter for making the stalk polyhedral, and the influence of bending rigidity was low.

Based on these data, the simulator successfully reproduced the adult horn shape from the pupal horn shape (Fig. 4F, Fig. S5). The simulated and actual adult horns were similar in that they were flattened in the distal region and had a ridge structure with a slope on the dorsal side of the stalk (Fig. 4F). The surface area and volume of the proximal and distal regions, and the stalk section index were quantified and compared using pupal, actual adult and simulated adult horns (Fig. S5). The results showed that the volume and surface area tended to be slightly larger in the simulated adult horns; however, the values for the simulated adult horns were close to those of the actual adult horns.

Finally, mandible formation in the stag beetle Dorcus hopei was reproduced using the simulation (Fig. 4G) to determine its applicability to other beetles. The 3D data of the pupae were acquired using a 3D scanner (Fig. 4G, leftmost image), from which the pupal mandibular mesh model was extracted. After the proximodistal axis and the fixation area were manually set (Fig. S6), a physical simulation was applied to the mesh model, successfully reproducing the adult form (Fig. 4G, center and rightmost images).

In this study, we investigated the mechanisms of horn remodeling in T. dichotomus using physical simulations that were applied to the horns of T. dichotomus and the mandibles of D. hopei. Many insects have polyhedral parts; for instance, many other beetles have polyhedral-like horns. In general, insects have polyhedral-like claws, as exemplified by the 3D data on the claws of mole crickets provided by Zhang et al. (2019). Because morphogenesis by adhesion and shrinkage (of both volume and surface) can generate polyhedral shapes, it might underlie their morphogenesis. The simulation developed in this study could aid in investigating this.

When only the distal parts were fixed and the intensity of the negative pressure was low relative to the surface shrinkage, the simulations produced sharp protrusions (Fig. S7). The polyhedral shapes and sharp protrusions generated by the ‘adhesion and shrinkage’ mechanism complement the rounded structures caused by the ‘furrow formation and unfolding’ mechanism, indicating that both are needed to explain various exoskeletal shapes.

Previous studies have investigated the remodeling process from a biological perspective. However, studying this solely from a biological perspective is challenging because it involves both biological and physical factors. In this study, we focused on epithelial sheet deformation and organized the contributing factors to provide insights for future biological research. Among these factors, epithelia–cuticle adhesion and uneven shrinkage can be studied biologically and will be studied in more detail in the future.

Adhesion mechanisms

Our RNAi data suggest Dumpy-dependent adhesion at the distal tips (Fig. 2), comparable with Dumpy expression in the Drosophila leg and antennae formations (Ray et al., 2015). In contrast, dumpy RNAi-insensitive ventral adhesion suggested other mechanisms. In addition to the difference in the expression levels of Dumpy, other ECM proteins (e.g. Obstructor) may explain this phenotype. Zhu et al. reported that each member of the chitinase-like protein family exhibits different functions and distinct expression patterns, including variations in molting stages (larval-larval molting, pupation and eclosion) and tissue specificity (Zhu et al., 2008). Therefore, the spatiotemporal regulation of apolysis may also contribute.

Regarding the pattern of adhesion, differences in location and domain size of Distal-less expression in Onthophagus are related to the degree of horn resorption during remodeling (Moczek et al., 2006); and a similar mechanism might underlie horn remodeling in T. dichotomus and relate to the regulation of ventral or distal tip adhesions.

Shrinkage mechanisms

Similar to the complete resorption of the pupal horn in Onthophagus binodis and Onthophagus taurus (Kijimoto et al., 2010), programmed cell death might cause epithelial shrinkage in T. dichotomus. Although programmed cell death can partly explain the shrinkage in T. dichotomus, it is different from that in O. binodis and O. taurus in that shrinkage is not complete resorption. Data from this study suggested the mechanical regulation of resorption patterning. The phenotype of dumpy RNAi (Fig. 2) showed that the epithelial sheet undergoes stronger shrinkage without distal tip adhesion. Because the ventral adhesion remained in the mutants, it was difficult to estimate the ability of the epithelial sheet to shrink. In contrast, a protrusion surrounded by gentle ridges appeared when we created new adhesion patterns using a magnetic force on the pupae (Fig. S8). These data suggested that mechanisms other than those involving the proximodistal axis, such as surface-tension patterns, also affect shrinkage.

Our series of studies have implications for genetic research on beetle morphogenesis. Moczek demonstrated the importance of developmental processes in understanding the evolutionary diversity of beetle horns because dimorphism can change during development (Moczek, 2006, 2007). Therefore, considering the biological processes that determine morphology is crucial. Based on the results of this and our previous study (Matsuda et al., 2017), beetle horn morphogenesis is primarily derived from the ‘furrow formation’ and ‘adhesion and shrinkage’ processes. Previous studies have identified several genes involved in beetle horn formation. For example, wing- and limb-patterning genes are involved in prothoracic horn formation in Onthophagus species (Hu et al., 2019; Moczek and Rose, 2009). Kijimoto et al. and Ito et al. have reported the function of doublesex in beetle horn dimorphism development in Onthophagus species and T. dichotomus, respectively (Ito et al., 2013; Kijimoto et al., 2012). Ohde et al. also identified 11 genes contributing to the horn formation (Ohde et al., 2018). Several genes that contribute to remodeling have been identified (Wasik and Moczek, 2011; Wasik et al., 2010). If our model is applicable to various horns, these genes contribute to some of the factors in the model, and the variation in the corresponding molecules/genes to the factors causes various horn shapes, which results in the differences in sensitivity to RNAi. Therefore, further investigation into where, when and how these genes influence morphogenesis will be important for improving our understanding of beetle morphogenesis, such as the detailed analysis of the effect of RNAi timing on morphology (Morita et al., 2019).

When comparing the morphogenetic mechanisms of the head horn of T. dichotomus with those of the Drosophila leg and wing, the formation and unfolding of furrows, followed by the generation of tension via adhesion, are common features. However, their underlying biological mechanisms differ. Unfolding furrows is mainly a physical process (internal hemolymph pressure) in beetles (Matsuda et al., 2017), whereas it is primarily a biological process in Drosophila: cell shape change (columnar to cuboidal) contributes to wing (Fristrom, 1969) and leg expansion (Mandaron, 1970; Poodry and Schneiderman, 1970) and cell rearrangement is involved in the leg elongation process (Fristrom, 1976; Fristrom and Fristrom, 1975). The source of tension is thought to be the contraction of neighboring tissues in Drosophila (Ray et al., 2015), whereas contraction of the sheet is important in beetles. Regarding adhesion, both Drosophila and T. dichotomus use the same anchoring protein, Dumpy; however, different mechanisms may mediate ventral adhesion during head horn remodeling. Because the mechanical mechanisms of ‘unfolding furrows’ and ‘tension generation by adhesion’ are common, they may be universally applicable to exoskeletal animals despite the differences in biological mechanisms.

In morphogenesis by adhesion and shrinkage, 2D adhesion patterns in the epithelial sheet control the 3D shape after shrinkage. This mechanism is similar to morphogenesis by unfolding furrows, in which 2D furrow patterns control the 3D shape after unfolding. Thus, both mechanisms link 3D morphogenesis with known genetic patterning mechanisms.

Insects

Beetle larvae were purchased and kept according to our previous studies (Matsuda et al., 2017; Adachi et al., 2020). Briefly, commercially purchased last instar (third instar) larvae of the Asian rhinoceros beetle Trypoxylus dichotomus were kept individually in 1 l or 800 ml plastic bottles filled with rotting wood flakes at 10-15°C to suspend their development. Larvae were moved to 25°C to restart their development before the experiments and/or observations. Bottles were checked daily in order to record the date of pupation. Pupae were weighed before each experiment.

Larvae of stag beetle Dorcus hopei were purchased from Tsukiyono-kinoko-en (Gunma, Japan) and were kept in an 800 ml Kinshi bottle (Tsukiyono-kinoko-en, Gunma, Japan) until pupation. The male pupa was fixed with formalin-acetic acid-alcohol for 3 h and replaced with 70% ethanol.

Acquisition of 3D data with micro-CT

3D information of a pupa just before eclosion was obtained by micro-CT, because the epithelial sheet in the pupa had cuticles on the surface, causing a clear contrast in CT values, and was less susceptible to deformation by freeze-drying.

Frozen samples of pupa were freeze-dried. Then, dried samples were scanned using a micro-CT scanner (Skyscan1172, Bruker, USA) following the manufacturer's instructions. Serial images were processed with ImageJ (Fiji) (Schindelin et al., 2012). From the serial images, meshes were reconstructed with 3D slicer software (Fedorov et al., 2012).

Acquisition of 3D data of a pupal stag beetle with a 3D scanner

3D data of fixed samples was acquired with a 3D scanner (SOL 3D scanner, Global Scanning, Denmark). The mesh was reconstructed with SOL software (Scan Dimension, version 21.07.13.1511).

Observation of a pupa with CoMBI

Because the epithelial sheet before secretion of the cuticles (several days after pupation) is susceptible to artifacts from drying and fixation, we employed the CoMBI method. In the method, serial section images were acquired by capturing the block-face image of a frozen block with a digital camera during frozen sectioning. Because biological samples were directly frozen and the 3D information was acquired from the serial section images, the effect of artifacts was reduced.

As preparation, pupae were anesthetized on ice before dissection. The dissected pupal head was mounted in OCT compound (Sakura Finetek) and frozen in liquid nitrogen. The frozen block was sectioned with a cryostat (Leica CM1850, Leica Microsystems), and images of the block surface were automatically taken using a digital camera (Nikon D810) after every section (20 μm). The chamber temperature was set at −15°C.

Gene knockdown by RNAi

We searched for the ortholog mRNA sequence from the RNAseq database of T. dichotomus (PRJDB6456) using D. melanogaster sequences as a query via the tblastn program (Morita et al., 2019). Amplification of target gene sequence for making the template, synthesis of dsRNA and injection of RNAi were performed as described in our previous study (Adachi et al., 2020); 5 µg of dsRNA of each target gene was injected into pupae. The primer sequences for amplifying the target gene sequence were: F-ACCTGTCGACCAGAACCAAC, R-GCAGGAACAAGAAGCCTGTC.

Mesh processing

The acquired mesh was cleaned with MeshLab (Cignoni et al., 2008). After cleaning, the mesh was processed with the Poisson remeshing filter with MeshLab, to generate a single-layered mesh with no holes or tunnels. Then, meshes were processed with the Quadric Edge Collapse Decimation filter, to reduce the number of vertices and triangles. The details of each mesh are shown in Table S1.

Physical simulation

To simulate the development of an adult horn, energy minimization was performed with respect to the vertex position using the steepest descent method, as described in our previous papers (Matsuda et al., 2017, 2021). The numerical calculation was performed with sundials (Hindmarsh et al., 2005).

In the simulation, the energy U was calculated for the mesh model as follows:
(1)
where the elastic energy was calculated for each edge length l, triangle area s, and dihedral angle θ (kl, ks and ka denote the coefficient for each elastic energy), and and denote the initial state of the ith edge length and triangle area, respectively. was set as 0 radian (because this bending rigidity calculation depends on the triangle size, the effects of triangle size on the simulated results were checked; see Supplementary Materials and Methods, Figs S14, S15). To express the epithelial sheet shrinkage, and were multiplied by rl and rs (rl, rs<1). Based on the energy settings, the movement of the ith vertex, for which the position vector at time t was denoted by ri, was calculated using the following equation:
(2)
where γ is a friction coefficient. The first and second terms on the right-hand side represent the energy minimization and negative pressure for volume reduction, respectively. In the second term, AdjT(i), kn and nj represent the adjacent triangles of the ith vertex, the coefficient for negative pressure (kn≤0) and the normal vector of the jth triangle, respectively. The third term represents the smoothing effects. It was implemented as a force on each vertex based on Laplacian smoothing, moving in the direction of the barycenter of the connecting vertices. AdjV(i) and refer to the adjacent vertices of the ith vertex and the number of vertices, respectively (we introduced smoothing effects into the simulation based on biological observation, but the effects of this term can be theoretically absorbed by the edge shrinkage; see Supplementary Materials and Methods, Figs S16, S17, Tables S3, S4 for the details of the simpler simulations).

The details of the settings of the proximodistal axis and the fixation area are given in Supplementary Materials and Methods. The simulated data were visualized with ParaView (Ahrens et al., 2005). The parameters for each simulation are shown in Table S2.

Usage of generative AI and AI-assisted technologies

During the preparation of this work, DeepL, ChatGPT and Grammarly were used to improve the clarity and grammatical usage of English. After using these services, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

We thank Dr S. Morita for his advice in the beads injection into pupal horns. We also thank Editage (www.editage.jp) for English language editing.

Author contributions

Conceptualization: K.M., S.K.; Methodology: K.M.; Software: K.M., Y.I.; Investigation: K.M., H.A., H.G.; Resources: H.A., H.G.; Writing - original draft: K.M., S.K.; Writing - review & editing: K.M., H.A., H.G., Y.I., S.K.; Supervision: S.K.; Funding acquisition: K.M., H.G., Y.I., S.K.

Funding

This work was supported in part by KAKENHI grants from the Japan Society for the Promotion of Science (JSPS) (15H05864 and 20A306 to H.G., Y.I. and S.K.; 22J10710 to K.M.). K.M. was supported by a Grant-in-Aid for JSPS Fellows (DC2) and the ANRI Fellowship. H.A. was also supported by Grant-in-Aid for JSPS Fellows (DC2).

Data availability

Codes used in this work are available on Bitbucket (https://bitbucket.org/kMatsuda_klab/remodelingsimulator/src/main/).

The peer review history is available online at https://journals.biologists.com/dev/lookup/doi/10.1242/dev.202082.reviewer-comments.pdf

Special Issue

This article is part of the Special Issue ‘Uncovering developmental diversity’, edited by Cassandra Extavour, Liam Dolan and Karen Sears. See related articles at https://journals.biologists.com/dev/issue/151/20.

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Competing interests

The authors declare no competing or financial interests.

Supplementary information