From the knitting shop: the first physical and dynamic model of the taenioglossan radula (Mollusca: Gastropoda) aids in unravelling functional principles of the radular morphology

Abstract

The radula is the structure used for food processing in Mollusca. It can consist of a membrane with stiffer teeth, which is, together with alary processus, muscles and odontophoral cartilages, part of the buccal mass. In malacology, it is common practice to infer potential tooth functions from morphology. Thus, past approaches to explain functional principles are mainly hypothesis driven. Therefore, there is an urgent need for a workflow testing hypotheses on the function of teeth and buccal mass components and interaction of structures, which can contribute to understanding the structure as a whole. Here, in a non-conventional approach, we introduce a physical and dynamic radular model, based on morphological data of Spekia zonata (Gastropoda, Paludomidae). Structures were documented, computer-modelled, three-dimensional-printed and assembled to gather a simplistic but realistic physical and dynamic radular model. Such a bioinspired design enabled studying of radular kinematics and interaction of parts when underlain supporting structures were manipulated in a similar manner as could result from muscle contractions. The presented work is a first step to provide a constructional manual, paving the way for even more realistic physical radular models, which could be used for understanding radular functional morphology and for the development of novel gripping devices.

1. Introduction

The radula is an important autapomorphy of the Mollusca and probably one reason for the phylum's success, because it enables the foraging of a wide range of food types. This food gathering and processing structure can consist of a chitinous membrane or ribbon [1,2] with small, tightly embedded teeth, which can be mineralized in some [3–7], but not in the majority of taxa [8–10]. Tooth cusps function as an interface between the organism and ingesta (food, substrate, everything that is taken in) and as consequence of this interaction the teeth can show signs of wear [11–15]. However, the radula and its components are constantly secreted by epithelia in the zone of formation or radular sack, become maturated before they enter the working zone (where teeth actually interact with ingesta), and finally break loose in the degenerative zone [16–20]. The radula is part of the buccal mass, which also comprises various radular muscles, underlain odontophoral cartilages and alary processus.

In malacology, it is a common practice to relate radular tooth morphology, documented using scanning electron microscope (SEM), to ingesta and/or potential functionality of individual tooth types (scratching, gathering, etc.) [21–31]. However, this approach is rather problematic.

First, it does not take into account many extremely important variables of radular morphology and properties. For example, the direct inference simply from tooth shape [32], e.g. interpreting from a broad cusp directly its ability to loosen food items, is far too speculative, especially since experimental approaches revealed that not all teeth necessarily interact with the substrate [33], but still contribute to the overall radular function by, for example, reinforcing the spanned radula [34].

Second, the configuration of the radula during foraging is not the same as that of mounted radula [34]: molluscs are capable of bending, twisting and flapping their radula, as previously documented by studying foraging gastropods through glass surfaces [35–42] and/or by analysing feeding tracks [13,35,36,39,43–50]. However, feeding tracks are difficult to interpret and additionally, only teeth, which were pressed into the substrate forcefully, rather leave a mark and teeth that do not interact or interact with the low force do not leave tracks [34]. Experiments, making interaction of teeth with substrate clearly visible, are without doubts highly desired, as the knowledge about precise contact areas of teeth could further contribute to determining tooth functionality, because these areas function as load-transmitting regions. Unfortunately, such a designation is rather limited to feeding experiments involving the analysis of tooth wear, induced by sandpaper [33,34], due to three reasons. (i) Foraging can only be documented on rather large gastropods (obtaining sharp videos of fast moving, very small structures maybe from small, fast feeding and moving gastropods is almost impossible). (ii) With gastropods that foil the experimental set-up (e.g. species that prefer foraging at night and avoid light, feel uncomfortable by their surroundings or forage on ingesta types that cannot be offered under experimental conditions), these experiments are difficult or impossible. (iii) The experiments can be easily done on flat smooth transparent (but unnatural) glass surfaces, but not on more natural rough surfaces, because the latter ones are rather non-transparent.

To approach the topic of tooth function and adaptation to ingesta, the material properties (hardness, elasticity, breaking stress) of different types of teeth are additionally required [3–7,12,14,39,51–54]. Also, gradients of material properties contribute to, for example, stress distribution, ability to deform, resistance to structural failure, and thus to the functionality of the radula. By finite-element analysis (FEA), three-dimensional morphology can be consolidated with material property data, resulting in computer-aided simulations of an individual structure's mechanical behaviour [55]. Our approach was strictly computer-based first, but meanwhile subsequently translated into the physical world in form of breaking stress experiments on real radulae, where the shear load was applied to individual tooth cusps of the whole radula with a needle, measuring simultaneously the breaking force and documenting behaviour of teeth (bending, twisting and relying on other teeth) [56,57]. These experiments partially verified the previous computer-based FEA simulations, but additionally, we discovered that significantly higher force was needed to break wet teeth than dry ones, even though wet biological materials are usually softer than dry ones. The unexpected breaking stress result was due to the interactions of neighbouring teeth: wet teeth were capable of relying on teeth of adjacent rows, enabled by the shape, mechanical property gradient and softer embedment in the radular membrane, leading to a higher force resistance due to a ‘collective effect’. Several hypotheses on interacting radular parts, resulting in a specific stress distribution, were previously proposed after examination of mounted radulae with SEM [2,32,58–62] and were confirmed by our biomechanical experiments.

In addition to this ‘collective effect’ of teeth, experiments on wear, induced by abrasive sandpaper, revealed that more mechanisms preventing the structural failure of the radula seem to be present [33,34]. The radular supporting structures (buccal mass muscles with underlain odontophoral cartilages) were assumed as contributors for failure prevention and as main radular components enabling its proper functioning. Mechanical testing of such soft, thin and complex structures is highly complicated and three-dimensional computer simulation of stress and strain distribution of such hyperelastic structures in their connection with the radula, covered with very many complex-shaped and strongly interacting structures, is also highly non-trivial from an engineering point of view. We therefore sought for a workflow to experimentally test previous hypotheses on teeth interactions and their biomechanics during scratching, gathering, etc.

In this paper, we attempted to provide a foundation for a deeper understanding of radular biomechanics, by introducing the first physical and dynamic radular model. Structures were documented using SEM and subsequently designed by putting together three-dimensional-printed teeth and distinct kinds of fabrics etc. to obtain a simplistic but realistic physical model capable of mimicking proper degrees of freedom during the motion and interaction of radular parts (teeth, alary processus) when the underlain supporting structures (buccal mass muscles with odontophoral cartilages) were manipulated. We decided to build the radula of Spekia zonata (Woodward, 1859) (Gastropoda, Caenogastropoda, Cerithioidea, Paludomidae) from Lake Tanganyika, since tooth material properties, three-dimensional morphology, tooth position on membrane and mechanical behaviour are known and stress and strain simulations have been previously performed [2,31,52–56,63]. Additionally, since this radula is taenioglossan (containing only seven teeth per tooth row), it does not contain many individual parts and is thus less complex. We were here however not able to mimic the gradients in hardness and Young's modulus that had been previously identified for Spekia zonata's teeth [52,54]; this awaits further approaches in the future. The presented work aims at providing a constructional manual paving the way for further physical models of species with a more complex buccal mass or a higher quantity of radular teeth.

2. Material and methods

2.1. Specimen studied and anatomical analysis

For the anatomical analysis of the buccal mass, four adult specimens, inventoried at the Zoological Museum Hamburg (ZMH 154652/999; collected at Lake Tanganyika in 2018 by Heinz Büscher) and stored in ethanol (70%), were used. Each gastropod was placed on its ventral side and carefully a transversal cut through the snout, followed by a longitudinal cut in posterior direction, was executed to expose the buccal mass. One large complex of buccal mass muscles surrounds the odontophoral cartilages (for morphological descriptions, see [1,64–77]); the radula, with attached alary processus to both sides, is also connected to both buccal mass muscles. Thus, all these structures together can be picked by tweezers and loosened from the surrounding tissues, connecting it with the body wall. This was first arranged on an aluminium stub with double-sided carbon tape, air dried and visualized uncoated with a Tabletop Scanning Electron Microscope TM4000Plus (Hitachi, Tokyo, Japan). To obtain images from different perspectives in SEM each buccal mass muscle with connected structures was subsequently rehydrated with 70% ethanol to loosen it from the carbon tape and rearranged. To obtain information about the inner layers of the buccal mass muscle, they were cut along their longitudinal axis and again visualized in SEM. From SEM images, schematic drawings of the anatomy were drawn employing Adobe Illustrator CS 6 (Adobe Inc., San José, USA) (figure 1). Terminology of the structures was taken from [50,78].

Figure 1.

SEM images and anatomic illustrations of the buccal mass structures. (a–c,e) Dorsal view. (d,f) Ventral view. (g,h) Lateral view during relaxation, (g) and feeding (h). Blue outline = degenerative zone, red outline = working zone, yellow outline = zone of formation. AP, alary processus; BM, buccal mass muscle; CT, central tooth; DZ, degenerative zone; FP, food particle; FZ, zone of formation; LT, lateral tooth; MO, mouth opening; MT II, marginal tooth II; MTI, marginal tooth I; OC, odontophoral cartilage; RM, radular membrane; RT, radular teeth; SE, supraradular epithelium; TB, tooth basis; TC, tooth cusp; TS, tooth stylus; TL, thin ligament; VA, ventral approximator muscle; va, part of the ventral approximator muscle complex connecting both buccal mass muscles; WZ, working zone. Scale bars: (b–d) = 0.5 mm, (e) = 125 µm.

2.2. Three-dimensional model

The computer three-dimensional models of the radular teeth were taken from [55]. In that study, radulae of Spekia zonata were extracted, cleaned from tissue and ingesta with proteinase K according to the protocol of [79], then briefly sonicated, mounted on aluminium stubs, coated with carbon and visualized with the SEM Zeiss LEO 1525 (One Zeiss Drive, Thornwood, NY) from all sides. Additionally, teeth were ripped out of the membrane manually, arranged on stubs and visualized in SEM from different perspectives. Employing the three-dimensional software Maya 2019 (Autodesk, Inc., San Rafael, USA) teeth were formed by hand comparing the model with the SEM images.

2.3. Three-dimensional printing of teeth

With the software PrusaSlicer V. 2.2.0, based on the software Slic3r (Prusa Research s.r.o., Prague, Czech Republic), models were sized (central tooth width: 2 cm, lateral tooth length: 3 cm, marginal tooth I length: 3 cm, lateral tooth II length: 3.5 cm), positioned and arranged on the print-bed, and converted from stl-files to gcode-files (with parameters: layer height: 0.15 mm, 15% infill, supporting structures only on build plate). Gcode-files were imported in the software Repetier-Host V0.95F (Hot-World GmbH & Co. KG, Willich, Germany) operating the three-dimensional printer Renkforce RF1000 (Conrad Electronic SE, Hirschau, Germany) equipped with white PLA filament of 1.75 mm diameter (Renkforce, Conrad Electronic SE, Hirschau, Germany) and printed at an extruder temperature of 200°C and a print-bed temperature of 86°C. We printed teeth for 10 tooth rows, i.e. 10 central teeth, 20 lateral teeth, 20 marginal teeth I and 20 marginal teeth II.

2.4. Materials involved

After studying Spekia's buccal mass anatomy, different structures in our physical model were designed using the following materials (figure 2). The radular membrane embedding the small teeth is rendered as non-stretchable and made of tightly woven polyester fibre fabric of 8.5 cm width, 1 mm thickness and 15 cm length. The alary processus as a stiffer structure was made of a non-elastic perforated plate of stainless steel of 4–5 cm width, 0.9 mm thickness and 5.6 cm length, with a diameter of each hole of 0.4 cm. The holes were necessary to attach the buccal-mass-muscle-mimic with the alary processus by twisted yarn (diameter is approximately 0.15 mm). The large complex of buccal mass muscles was mimicked as thin, smooth, elastic, tightly woven viscose fabric, stuffed with wadding (final dimension of the whole model: 8 cm width, 3 cm thickness, 11 cm length). The odontophoral cartilages were made of rubber balls (5.8 cm length, 4.3 cm width, density of 0.95 kg cm⁻³, 15 kg weight carrying capacity). The fibrous attachment between each tooth and the membrane was made using yarn. The ventral part of the ventral approximator muscle complex, connecting both buccal mass muscles, was made using fabric ribbon (1.0 cm width, 0.2 mm thickness), which can be shortened or extended manually.

Figure 2.

Bauplan and manufacturing of the physical model. (a–c) Bauplan from (a) dorsal, (b) ventral, (c) lateral view. (d) Three-dimensional printing of lateral teeth. (e) Materials involved in manufacturing. (f) Knitting of radular teeth onto fabric representing the radular membrane. AP, alary processus; BM, buccal mass muscle; OC, odontophoral cartilage; RM, radular membrane; RT, radular teeth; va, part of the ventral approximator muscle complex connecting both buccal mass muscles.

2.5. Assembly of parts

Initially, each marginal tooth I was placed into one larger marginal tooth II, so that the marginal tooth II embraced the smaller marginal tooth I. This is a rather natural condition, which was documented on real radulae in SEM (figure 1e). Small holes of 0.9 mm diameter were carefully drilled at certain localities of printed teeth with an antique hand drill. Into each pair of marginal teeth, three holes were drilled, into each lateral tooth—two holes and into each central tooth—two holes. The holes were always drilled into the tooth bases, so that the bases of the printed teeth could be sewn onto the fabric, representing the membrane, with yarn, always comparing the SEM images of radulae, documenting each tooth's position on the membrane, arrangement of teeth, relative space between teeth, with the model. The buccal mass muscles were built by surrounding each rubber ball with wadding and finally with fabric. Each ball was not placed in the middle of the buccal mass muscle, but rather at its medial side, as was observed by dissecting specimens' buccal masses. The fabrics of each buccal mass muscle were sewn and closed by yarn. Each alary processus was sewn to one buccal mass muscle and bent to adjust the metal plate to its curvature. Tooth membrane with teeth was sewn to the alary processus. Thus, the membrane and both buccal mass muscles are only connected by the alary processus, as had been documented in real radulae. In each buccal-mass-muscle fabric, at a similar area as documented on the specimens’ buccal mass muscle, a hole was cut and a fabric ribbon, representing the ventral approximator muscle complex connecting both buccal mass muscles, was mounted. The length of the ribbon could be shortened or stretched manually leading to either a rotation of both buccal mass muscles towards each other (in ventral direction) or from one another (in dorsal direction).

2.6. Movability of the model

The presence of the ventral approximator muscle complex in Spekia leads us to propose that both buccal mass muscles can be moved parallel towards each other spreading the teeth (distal flex; motion type 1) or folding the teeth (proximal flex; motion type 2). Motion type 3 (buccal mass muscles are rotated in contrary directions) and motion types 4 and 5 (buccal mass muscles are rotated towards anterior and posterior along with their longitudinal axes) are in the range of motion of the model. If motion types 4 and 5 are possible for living Spekia, as had been observed for Lepidochitona cinerea (Polyplacophora) [42], as well as motion type 3 awaits further investigations, in e.g. form of higher resolution footage. But potentially the latter reassembly of structures (motion type 3) is passively induced while foraging on rough target surfaces.

2.7. Documentation of the physical model

The model behaviour when manipulated was documented in form of pictures (figure 3) and videos with an iPad Pro (11 inch; Apple Inc., Cupertino, USA) equipped with a 12 megapixel wide-angle lens with 30 frames per second (electronic supplementary material, video). Videos were cut and cropped with Adobe Premiere Pro 2020 (Adobe Inc., San Jose, USA). From the pictures, the angle between teeth could be calculated (figure 3a).

Figure 3.

Physical model from different views with manipulation of buccal mass muscles in different anatomical directions. (a) The method of angle measurement. (b) The model from lateral view. (c) The distal flex (motion type 1) and proximal flex (motion type 2). (d–g) The model is shown from slightly different perspectives. (h) The motions of the buccal mass muscles in opposite directions (motion type 3). (i) Rotation along with the longitudinal axis in the anterior direction (motion type 4). LA, longitudinal axis; TA, transversal axis. Scale bar = 2 cm. Arrows indicate directions of motion.

2.8. Anatomical directions

When the radula is not used (figure 1a,b), most of the degenerative and working zone of the radular membrane/ribbon face ventrally and most of the teeth from these areas face dorsally. The degenerative zone is now anterior and the radular sack posterior. When foraging the radula, with underlain buccal mass muscles and odontophoral cartilages, and alary processus changes its position in the animal by 180°, so that the membrane faces now dorsally and the teeth ventrally. The degenerative zone is now posterior and the radular sack more anterior. To describe the anatomical directions of the dissected specimens and the model, we chose the situation when the radula is at rest and not used (figure 2).

3. Results

3.1. Radula of Spekia zonata

3.1.1. Buccal mass anatomy

The radula of Spekia zonata is taeniogloss, i.e. with seven teeth per transversal row: one central tooth, flanked to each side by one lateral and two marginal teeth (figure 1e). The central and lateral teeth show signs of wear, which is a good indicator that these teeth had intense contact with ingesta (figure 1b). All teeth are tightly embedded by chitinous fibres in the underlain radular membrane with 375 µm width. When manipulating the extracted radular membrane by tweezers, elastic behaviour enabling curling of the membrane in the zone of formation can be observed, as previously described for other molluscs. In Spekia, the membrane underlying the anterior 31 tooth rows is tightly attached to either side to one alary processus. Each of these chitinous plates in Spekia has a size of 0.95 mm length and 0.7 mm width: they (i) spread the working zone of the radula and altogether act as an antagonist to the mechanical behaviour of the radular membrane, hindering its rolling up, and (ii) tightly connect the radular membrane through different layers with the underlain buccal mass muscle (see below) as had been described for other taxa. At the outermost edge of the working zone, the alary processus are fused, and this part is again connected to the ventral part of the buccal mass muscles by a long and thin ligament probably stabilizing the radula in anterior direction while foraging (figure 1d) as in other molluscs. The buccal mass muscle is in Spekia also a complex network of muscles (as the supramedian radular tensor muscle and the ventral approximator muscle inserting at outer lateral sides of cartilages) enclosing hemolymph and both odontophoral cartilages. Between the radular membrane and the buccal mass muscles, the following layers are situated: subradular membrane, subradular epithelium and connective tissue. The connective tissue and as consequence all other layers in-between and the radular membrane are connected to each buccal mass muscle by (i) the supramedian radular tensor muscle of the buccal mass and (ii) the alary processus possessing a large contact area with the buccal mass muscle and thus a proper and stable contact between the radular membrane and buccal mass muscle (see above). The odontophoral cartilages are medially situated within each buccal mass muscle directly under the membrane. Their two main parts overlap one another, as had been previously described for Pomacea bridgesii (Gastropoda, Caenogastropoda) [78].

3.2. Physical model of the radula

3.2.1. Range of motion

Buccal mass muscles of the model can be rotated strictly parallel towards each other along the transversal axis (for the definition of axes, directions, and model view from different perspectives, see figure 3) to an angle of up to approximately 90° in dorsal or ventral direction (figure 3c). When rotated in the ventral direction (distal flex; motion type 1), the range of motion is restricted by the radular membrane, spanning between the two buccal mass muscles on the dorsal side, and the dimensions of the buccal mass muscles themselves. When rotated in the dorsal direction (proximal flex; motion type 2), the motion is restricted by the part of the ventral approximator muscle complex, connecting both buccal mass muscles ventrally, and by the dorsally situated teeth on the membrane. During this latter movement, bases of teeth approach one another until they interlock tightly. When one buccal mass muscle is rotated along with the model's longitudinal axis in ventral direction (motion type 3, buccal mass muscles are rotated in contrary directions; figure 3h), it has a range of motion of approximately 100°. This is limited by the membrane, because this structure cannot bend and deform to a greater extent, and by the row of lateral teeth, which does not rotate. During rotation, lateral teeth are approximated until each tooth relies on the adjacent one from the next tooth row. In this context the posterior edge of each lateral tooth interlocks with the anterior processus of the posterior, adjacent lateral tooth. This interlocking continues until seven of 10 laterals are interlocked; they form a stiff array that does not allow any more rotation in the ventral direction.

Buccal mass muscles can be slightly rotated towards the anterior along with their longitudinal axis (motion type 4; figure 3i). Here, the rotation of maximal approximately 75° is enabled, limited ventrally by the dimensions of the buccal mass muscles themselves and by interlocking of the central and lateral teeth from the first and second tooth rows. They interlock tightly and form a stiff array. When buccal mass muscles are rotated in posterior direction (motion type 5), a slight rotation of maximal approximately 60° is possible, limited by buccal mass muscle dimensions and by the anterior part of the radular membrane, spanning between the two buccal mass muscles.

3.2.2. Interaction of teeth

During manipulation of the buccal mass muscles of the model, the interaction and finally interlocking of the teeth can be observed and documented (figure 3; electronic supplementary material, video).

As mentioned above, the laterals are capable of interlocking and relying on one another. They slide into the following place, as a result of most rotation types: the posterior edge of each lateral tooth interlocks with the anterior processus of the posterior, adjacent lateral tooth until teeth acting together form a stiff array. The amount of laterals differs between rotation types: during distal and proximal flex (motion types 1 and 2), all 10 laterals form a stiff array. When one buccal mass muscle is rotated along the model's longitudinal axis in ventral direction (motion type 3), the anterior eight laterals form a stiff array. When buccal mass muscles are rotated towards the anterior, the anterior four laterals interlock tightly (motion type 4), and when rotated towards the posterior, no laterals interlock (motion type 5). Additionally, central teeth show some interaction during the rotation of buccal mass muscles: during distal flex (motion type 1), only the central teeth number four to seven touch, but do not form a stiff array, because teeth have space between one another (figure 3h). During this action, both posterior tips of the cusp touch the adjacent, posteriorly located central tooth cusp. Marginal teeth always interact at their bases, styli or cusps, but they never interlock or form a stiff array, since the small attachment region between the teeth and membrane allows both sliding and rotation of teeth.

When buccal mass muscles are manipulated, the teeth of different types can interact and interlock. During most rotations, the lateral processus of the central teeth interlock with the bases of the lateral teeth. During distal and proximal flex (motion types 1 and 2), laterals and centrals of all ten rows interact, but do not form such a stiff array as the lateral teeth. During distal flex (motion type 1), centrals and laterals of row four to seven interact, but do not form a stiff array. When buccal mass muscles are rotated towards anterior (motion type 4), the lateral processus of the centrals and bases of the lateral teeth from the first and second tooth rows interlock tightly and form a stiff transversal tooth row array (figure 3i). When they are rotated towards the posterior (motion type 5), centrals and laterals do not interact.

The bases and ventral parts of the styli from marginal teeth interact with the lateral edges of the lateral teeth during rotation of one buccal mass muscle along with the model's longitudinal axis in the ventral direction (motion type 3) and proximal flex (motion type 2). In the latter motion, the marginal teeth are bent, so that their cusps are located directly dorsally to the lateral tooth cusps (figure 3e,f). During distal flex (motion type 1), marginal teeth are arranged to the sides of the lateral teeth, the angle between the lateral edge of laterals and styli of marginals ranging from 50 to 90° (figure 3a).

3.2.3. Position of teeth on membrane

During proximal flex (motion type 2), marginal tooth cusps become located directly dorsally to the laterals; the centrals are then located ventrally to the laterals, are covered by lateral tooth cusps and are barely seen (figure 3e,f). During distal flex (motion type 1), marginal teeth are spread to both sides and both centrals and laterals become exposed. Lateral tooth cusps are the highest components in this configuration, followed by the marginal tooth cusps, and finally the central tooth cusps (figure 3a).

When one buccal mass muscle is rotated in a ventral direction (motion type 3), the five anterior marginal tooth cusps of the side, being rotated, are located dorsally, followed by the medial and anterior lateral tooth cusps from the same side, posterior lateral tooth cusps from the opposite side, posterior marginal tooth cusps from the opposite side, anterior central teeth, anterior lateral tooth cusps from the opposite side, anterior marginal tooth cusps from opposite side and finally posterior central teeth as the most ventrally positioned teeth (figure 3h).

3.3. Role of each component

The stiffer odontophoral cartilages, each surrounded by one buccal mass muscle, stabilize the six anterior tooth rows and their underlain membrane, additionally the medial parts of the alary processus (approx. three quarters of their area). The buccal mass muscles are more elastic and flexible. They support the alary processus and the anterior tooth rows and function as a cushion or shock absorber, when teeth interact with an obstacle. Each alary processus is connected to the membrane, at the region of the anterior five tooth rows, and to one buccal mass muscle. Their stiffer properties do not allow processus deformation during manipulation of the buccal mass muscles. They ensure that the membrane is spanned during distal flex (motion type 1) and additionally pushes marginal teeth in the position where their cusps become located dorsally to the lateral tooth cusps, during proximal flex (motion type 2). The large attachment area of the alary processus with the buccal mass muscle seems to allow a uniform stress distribution from teeth, across the membrane, alary processus, to the buccal mass muscle, when teeth interact with the substrate surface. The thick membrane can be twisted and rotated, but it is not deformable enough and therefore keeps its general shape. The stiffer, but still elastic attachment between each tooth and the membrane together with membrane properties allows the approximation, interaction and finally interlocking of teeth. As the teeth are the stiffest components of the physical model, they can form stiff arrays when interlocking tightly which is needed for interaction with ingesta.

4. Discussion

4.1. Function of radular parts

Our modelling approach allows deeper insight into the mechanics and function of radular parts, which remained rather hypothetical, but is now transferred into the real physical model allowing further experimentation. We previously stated that Spekia possess a multifunctional radula with central and lateral teeth used for scratching across a solid substrate surface, loosening algae covers attached to it, whereas the marginal teeth rather collect particles by a sweeping motion afterwards. These hypotheses were inferred from certain observations. (i) Centrals and laterals are of rather broad and thick shape, whereas the marginals are thin and slender [31]. (ii) Centrals and laterals possess a larger attachment area with the membrane and thus a more intense connection than the marginals [2]. (iii) In each tooth array, central teeth are the stiffest and hardest radular parts, followed by lateral teeth and finally marginal teeth [52–54]. Additionally, every tooth shows gradients in these properties with its cusps as the stiffest and hardest part, followed by the stylus, and finally the basis as the softest and most flexible part. Based on these findings, it was proposed that central and lateral tooth cusps can transfer forces to the ingesta, whereas the marginal teeth are able to deform, enabling a wider angle of deflection and thus covering a larger substrate area for collecting ingesta. (iv) By FEA, combining morphology and mechanical property gradients, we were able to simulate the mechanical behaviour of teeth. Our results indicate that centrals are not affected by stress and strain, marginals are highly affected, and laterals are intermediate [55]. (v) By breaking stress experiments, documenting the force needed to break teeth, we found that centrals are capable of resisting the highest stresses, followed by the laterals, and finally marginal teeth [56,57]. During these experiments, we observed that native (wet) centrals and laterals can interlock with adjacent teeth and thus resist higher stresses (collective effect), whereas the wet (native) marginal teeth are capable of twisting and bending.

Previous hypotheses were now verified by the combining approach of using SEM documentation and the physical model. The detected wear on the central and lateral teeth, but not on the marginals, depicts a frequent interaction between centrals, laterals and ingesta. In the physical model, when both buccal mass muscles are rotated parallel to each other in the ventral direction, lateral and central teeth become exposed and marginal teeth are placed to each side of the radula (distal flex; ‘radular tooth spreading/unfolding’). This allows centrals and laterals to interact with ingesta and transfer forces through the broad denticles and cusps (for the relationship between shape of a tool and its ability to transfer forces, see [80–88]; for a review, see [89]) without the involvement of marginal teeth. During the rotation of buccal mass muscles in the dorsal direction (proximal flex; ‘radular tooth folding’), marginal teeth are pushed, by the alary processus, in a position where they are placed dorsal to the laterals and centrals, thus laying on them. By this motion, they cover a large area, which allows collection of particles from the substrate. This spreading and folding of teeth (for folding, see [63]; for bending of radula, see [33,34,42,61,90,91]) is enabled by the part of the ventral approximator muscle complex connecting both buccal mass muscles, which rotates the buccal mass muscles towards one another (in ventral direction—spreading) or from one another (in the dorsal direction—folding). The motions of the buccal mass muscles also move the alary processus, which again spread or fold the membrane and push teeth into position. Additional to the transfer of motions from the buccal mass muscle to the radular membrane, the alary processus keep the anterior part of the radular membrane spread along with the radula's longitudinal axis. We are not sure to what extent motion types 3, 4 and 5 are pronounced in living gastropods; however, they are all in the range of motion of the model. For Lepidochitona cinerea (Polyplacophora), a rotation of the anterior teeth towards one another followed by the rotation of teeth towards the posterior had been observed [42]; this awaits, however, further investigations for Spekia. Motion type 3 could potentially be observed with high-resolution footage, but this form or rearrangement could also be the result of the interaction with very rough target surfaces.

By almost all manipulations of the model, we observed a tight interlocking and formation of a stiff array due to the interaction of the laterals, which is clearly a kind of ‘collective effect’ leading to a proper stress distribution and thus to the reduction of the structural failure, when interacting with ingesta (for stress distribution through the interlocking of teeth, see also [2,32,56–62]). The centrals usually do not form a stiff array with the adjacent central teeth but enable the stabilization of each transversal tooth row by lateral interlocking with the lateral teeth. Centrals, thus, are not only used for loosening of food items, but additionally act as a kind of reinforcement of the radula. However, for this model, we were not able to create teeth with gradients. Printing and modelling approaches, finally leading to the mimicry of functional gradients, are under preparation, because the gradients seem to contribute highly to tooth function. Probably the sweeping action of the marginal teeth and the collective effect of the centrals and laterals will be more pronounced when styli and bases are softer and more flexible.

The odontophoral cartilages, located within the buccal mass muscles, provide a stiff, mechanical reinforcement of the thin, chitinous radular membrane and its teeth (for information about the membrane, see [2,18,76,78,92–94]), similar to a hydrostat (see also [95]). The buccal mass muscles serve as a shock absorber or cushion element, when teeth interact with an obstacle, which can also be observed in the binocular microscope when manipulating the specimens' buccal mass muscle. This mechanism is similar to the anchorage in mammalian teeth [96,97]. The adjustable radular membrane that is made of stiffer, not extensible material keeps the teeth in place, but simultaneously allows a sliding of teeth into place and adjustment of teeth to all kinds of target surface, when the buccal mass muscles are manipulated. Thus, the membrane responds flexibly to compressive force and stiffly to tensile force [33,98]. This leads to the avoidance of both stress concentration and tissue damage; the tight connection of the membrane with the surrounding relatively soft tissues of the buccal mass muscles by the alary processus also enables proper stress distribution (see also [2,76]) and avoidance of structural failure (see also [33,34]). Buccal mass muscles are rather restricted in their degrees of freedom, which probably enables a proper functioning without the loss of energy.

4.2. Biomimetics

We here present the first physical and dynamic model of the radula with its teeth. Our approach follows the previous idea of developing a radula-inspired soft grasping robotic application, with the radula of Aplysia (Gastropoda, Heterobranchia) serving as a model system [99]. Aplysia's radula is morphologically distinct from Spekia's as it has more teeth per row (one broader central tooth and on either side approximately 20 small, isodont, hook-like teeth; e.g. [100]) and possesses plain and rather thin odontophores. However, the aims of the past studies on the soft grasper development and of subsequent research [98,101,102] were not on determining the function of radular teeth, as they were not included in the robotic design. The focus of previous biomimetic research was on the gripping and conforming to irregular materials induced by the action of the buccal mass muscles, which was mimicked by latex tubing, nylon braiding and nylon spacers. Our study provides a further step towards the development of radular-inspired gripping or/and cleaning devices in the field of biomimetics (e.g. [103–105]). Additionally, by altering the mechanical properties of the fabrics and materials used for the assembly of radular models, their effect on models' mechanical behaviour can be tested, allowing a better understanding of form–structure–function relationships in mollusc radulae by reverse biomimetics (e.g. [106]).

4.3. Outlook

In the future models, we would like to pay more attention to the natural mechanical property gradients in the teeth, as they seem to strongly influence mechanical behaviour (for the relationship of radular tooth hardness and capability of scratching, see [26,32,39,52–54]). For this purpose, radular teeth can either be three-dimensional printed with different materials or can be synthesized by transforming computer models into a negative ‘mould’ made of two compartments first, which will be then three-dimensional printed and filled with, for example, silicone locally enriched with ceramics/iron dust, resulting in gradients within each physical tooth. We encourage the performing of experiments with materials resembling the mechanical properties of teeth as closely as possible. Additionally, different fabrics or materials could be used for the modelling of the buccal mass muscles, odontophoral cartilages, radular membrane, etc. and their effects on the mechanical behaviour of the model could be studied in a systematic way. By acting with these models on artificial surfaces of different scaled up roughness, the interaction between radular teeth and substrate can be documented. We believe that this approach will strongly contribute to a profound understanding of the gastropod feeding organ as a whole.

Data accessibility

Data are included in the electronic supplementary material, video.

The data are provided in the electronic supplementary material [107].

Authors' contribution

W.K. and S.G. initiated the project. H.K. provided the three-dimensional model for this analysis. W.K. built the physical radular model and wrote the manuscript draft. S.G. discussed the data, figures and contributed to the biomechanical aspects of the manuscript. All authors contributed to the manuscript draft and approved the final manuscript for publication.

Competing interests

The authors declare no conflict.

Funding

No specific funding was received for this research.