The mineralization and transformations during maturation in the dominant lateral tooth (termed lateral tooth II in this study) of iron and non-iron minerals were very well investigated in the last decades [see e.g. 13, 18, 42, 43, 44, 53, 54, 55, 56, 57, 58, 59]. It was previously determined that after the secretion and formation of the three-dimensional alpha-chitin matrix with the associated proteins, which are possibly involved in the biomineralization process , various iron oxide phases are incorporated into the matrix [see also 61]. First ferrihydrite (Fe3+10O14(OH)2) is deposited in the junction zone and the margins of the tooth, before it also occurs in the leading part [13, 18, 40, 54, 56, 62]. During maturation it is replaced by iron oxides and iron oxyhydroxide minerals, usually by magnetite [63, 64], in the cusps’ leading part [9, 54, 57, 65, 66]. But in some taxa small proportions of lepidocrocite (γ-FeOOH) [12, 13, 40, 56, 67, 68; 69, 70, 71, 72], goethite (alpha-FeOOH) [55, 73], or hydrated iron oxides (limonite)  were detected.
The distribution of magnetite seems to be taxon specific, in Chiton and Acanthopleura the posterior part of the dominant lateral tooth cusp is composed of magnetite whereas the anterior part is composed of apatite [12, 13, 56, 67, 71, 75, 76, 77]. In Cryptochiton, Cryptoplax, and Chaetopleura magnetite covers both posterior and anterior cusps’ surfaces [51, 57, 75, 78] whereas the core is either composed of amorphous iron phosphate [79, 80], apatite [9, 70, 73], or iron and/or magnesium phases [40, 72].
For Lepidochitona, due to our methodology, we are not capable of differentiating between the different iron oxide phases, since we were only able to determine the elemental distribution. But,  described that ferrihydrite deposition in the matrix is accompanied by colour change to red/brown and magnetite deposition by a change to glossy black. For Lepidochitona we would thus propose that from row 8 to 9 ferrihydrite is present and from row 10 on magnetite is dominant.
In Lepidochitona, the distribution of iron, observed in the dominant lateral tooth cusps, is rather similar to the pattern observed in Cryptochiton, Cryptoplax, and Chaetopleura [51, 57, 75, 78], as iron covers both the anterior and posterior parts of the cusp. Potentially, the occurrence of iron only in the posterior part is an apomorphic character of the Chitonida (for systematics of Polyplacophora, see ) and on anterior and posterior part is plesiomorphic. However, this awaits further investigations and a broader taxon-sampling.
In past studies about the radular tooth ontogeny, the dominant lateral tooth was in focus. As described by , ferritin is present in the haemolymph and delivered to the superior epithelia cells of the radular sack, which covers the dominant lateral tooth cusps. Afterwards a pore is penetrated into the cusp and stylus [77, 83]. Thus, the stylus canal may potentially serve as a biomineralization delivery pathway . The first depositions of iron were detected in the ‘junction zone’, the part between cusp and basis [51, 52], and therefore it was postulated that this region serves as repository for ions, which migrate during ontogeny to the cusp [56, 70, 72, 77, 84]. For Lepidochitona, we observed a slightly different pattern: in native radulae we found that the cusps are mineralized with iron first (0.38 ± 0.59% in row 6). In row 7, the cusps still contain the highest iron proportions (0.52 ± 0.38%), followed by the stylus (0.15 ± 0.05%), and finally the basis (0.14 ± 0.13%). These gradients in the iron distribution with the cusps, containing the highest proportions, followed by the stylus, and finally the basis continued until the tooth is mature in rows 28 or 29.
The ontogenetic changes of the iron proportions were previously documented for Acanthopleura [56, 70, 71], Ischnochiton, Onithochiton, Plaxiphora , Cryptoplax , and Clavarizona . In all of these taxa, iron proportions increase dramatically within very few rows in the magnetite region of the cusps and the junction zone. The junction zone sometimes loses its iron content during ontogeny again, whereas the anterior core region, the central/posterior core region, and the tooth basis rather increase their iron content gradually. For Lepidochitona, we were, due to the smallness of these teeth and our EDX methodology, which involved rather larger areas, not capable of clearly differentiating between the magnetite region, the anterior core region, and the central/posterior core region [terms from 71]. Our points of measurements rather cover areas of all three zones in the cusp altogether. During ontogeny we determined a steady increase of iron content in the cusps. The stylus [which is equivalent to the ‘tooth basis’ in 71] and the basis also show a steady increase of iron, which is for the stylus in congruence with the previous results of  and .
In previous studies, iron contents of mature dominant lateral teeth were determined for (1) Acanthopleura with 59.2%  or 62% [56, 71] or few percent , (2) Plaxiphora with 86.6%  and 17–27% or 66% , (3) Cryptochiton 51.8%  or up to 69% , (4) Ischnochiton with 62% , (5) Onithochiton with 66% , (6) Cryptoplax with ~90 weight % in the cap, ~30 weight % in the core, junction zone, and basis , and (7) Chiton with 97% . We detected for mature Lepidochitona teeth iron proportions (atomic ratio, atomic %) of ~30% in the cusps. However, it is rather difficult to compare percentages between studies, since in some publications weight percentages were studied, whereas in others atomic ratios were determined. Besides, methodology, sample preparation, and the analysed sample itself (whole radula or individual radular parts) strongly vary between individual studies.
The cores of the dominant lateral tooth, the region underneath the iron-containing tooth caps, can contain, besides of the organic matrix being present in the mineralized parts of teeth , some amount of phosphorus [51, 53, 71, 72, 86] as iron phosphate [40, 79, 80] or as apatitic calcium phosphate [9, 70, 72, 73, 75, 87], magnesium [71, 72], and fluor related to calcium [67, 87, 88]. It was reported that this tooth part is the least mineralized one in ontogeny . In the posterior core region, calcium (max. ~30 elemental %) and phosphorus proportions (max. ~18 elemental %) increase dramatically within few rows, whereas calcium (max. ~30 elemental %) and phosphorus (max. ~20 elemental %) content in the anterior core region increases gradually during ontogeny in Acanthopleura [70, 71] and Onithochiton . In Acanthopleura and Onithochiton, calcium and phosphorus content also increase dramatically within few rows in the anterior core region, whereas magnesium content of all tooth areas, calcium and phosphorus content of the basis (termed here ‘stylus’) of Acanthopleura, the anterior core region, the central/posterior core region, and the basis (termed here ‘stylus’) of Ischnochiton and Plaxiphora increase their content gradually . Additionally, silicon had been previously detected in the core, where the tooth also contains iron and phosphorus [9, 51, 71, 75]. In the junction zone, iron, phosphorus, and calcium were detected in higher proportions for Acanthopleura, Ischnochiton, Onithochiton, and Plaxiphora early in ontogeny (from row 8 on)  and at very low proportions before teeth become orange in colour . Sulphur, deposited in ontogeny earlier than iron (before the onset of mineralization) in the junction zone and probably responsible for the yellow colour of teeth, was also previously detected . It seems to be associated with the appearance of proteins and the tanning of the organic matrix . Additionally,  detected zinc, potassium, fluorine, sulphur, sodium, and chlorine in radular segments of Clavarizona,  - calcium, phosphorus, magnesium, sulphur, sodium, zinc, potassium, aluminium, copper, and silicon in radulae of Acanthopleura and Plaxiphora, and  - magnesium (with max ~5.5 weight % in the basis), potassium (with max ~1.0 weight % in the basis), sodium (with max ~2.0 weight % in the basis), silicon (with max ~1.0 weight % in the basis), aluminium (with max ~0.5 weight % in the basis), and sulphur (with max ~0.8 weight % in the junction zone) in Cryptoplax. Calcium proportions of ~5% were detected in the cusps of mature dominant lateral teeth of Lepidochitona: proportions decrease gradually from cusp across stylus to basis. All other elements occurred only in very small proportions. This altogether highlights that species can differ in their radular tooth chemistry which could potentially be used as tool for taxonomy .
For the central, lateral teeth I, marginal teeth, no gradients in iron, calcium, or any other inorganic components could be detected, thus these teeth are regarded as non-mineralized, similar to most gastropods and limpets [90, 91, 92].
By comparing treated and native radulae, we found that iron seems to be tightly bonded within Lepidochitona radular teeth, as it was not washed out by EDTA, whereas calcium and all slightly distributed elements do not seem to be tightly bonded. In the native specimens, reduction in the calcium proportion from row 25 on was detected. Potentially, under native conditions, calcium is washed out by surrounding fluids, either by passive diffusion or possibly by the salivary fluids. However, this awaits further investigations.
Young’s modulus and hardness
Biological materials are generally composites displaying material heterogeneities or property gradients, which are important for the function of particular structure due to improved load bearing capacity or contact damage resistance [for comprehensive reviews, see 93, 94]. Functional material gradients have been investigated in numerous biological structures, such as e.g. Nereis jaws , crustacean exoskeleton [96, 97], pangolin scales [98, 99], wood stems [100, 101, 102], and chiton and gastropod radular teeth [18, 24, 30, 57]. Analyses of the material properties and their distribution complement morphology and enable the assignment of functions. The parameter Young’s modulus (E) indicates the stiffness of a solid material and describes the relationship between tensile stress and axial strain. It correlates with the ability of the material (and structure) to transmit force [e.g. 103, 104, 105, 106], which is important to understand the puncturing behaviour and failure resistance [e.g. 107, for review on puncture mechanics, see 108]. The hardness (H) is the measure of the resistance to local plastic deformation induced by indentation or abrasion.
In molluscs, the ontogenetic change in these parameters (E and H) was well investigated for the dominant teeth of Patella (Gastropoda). Here, the hardness increases dramatically from row 60 to 110 (~150 rows in total) [45, 46]. For Lepidochitona, we observed a rather gradual increase in hardness and elasticity modulus for most tooth parts. Only in the styli of the lateral teeth II, their E and H values increased rather exponentially from row 15 to row 22.
Overall, hardness and elasticity values vary between studies and molluscan taxa.  analysed the mature dominant lateral tooth regions by nanoindentation in Cryptochiton and revealed that the leading edge has a hardness of 10.2–10.4 GPa and a Young’s modulus of 128.5–130.8 GPa, the trailing edge - H=7.5–8.2 GPa and E=97.6–114.8 GPa, and the core - H=1.5–1.6 GPa and E=28.6–29.4 GPa.  determined H=3.6 GPa and E=86 GPa for the core, comparable to vertebrate enamel . For mature limpet tooth cusps (Gastropoda), E=16 GPa in dry state and E=8 GPa in wet state was measured by nanoindentation for Megathura . However, for Patella cusps, E=120 (up to E=140 GPa) and H=4.9 GPa was reported [19, 21]. For paludomid gastropods, E=8 GPa and H=0.4 GPa were measured for the tooth cusps [24, 27, 30]. For the stylus of polyplacophoran teeth, H=0.2–1.8 GPa and E=7–30 GPa  or from E=18 GPa (for upper stylus) to E=12 GPa (basis)  were previously determined. Here the walls of the stylus canal and the core of the upper stylus are rather soft and flexible, whereas the outer parts are stiffer and harder [109, 111].  identified a hardness of 0.6 GPa and a Young’s modulus of 10.5 GPa for the stylus leading edge. The stylus becomes first softer (hardness: 0.55 GPa, Young’s modulus: 9.5 GPa) and then again harder and stiffer (hardness: 0.60–0.65 GPa, Young’s modulus: 11–12 GPa) towards the stylus canal. The stylus is both the hardest and stiffest at its outer layer of the trailing edge (hardness: 0.6–0.7 GPa, Young’s modulus: 12–14 GPa); both parameters decrease around the stylus canal (hardness: 0.55 GPa, Young’s modulus: 11 GPa) .
For Lepidochitona, we detected graded values of hardness and Young’s modulus for every individual tooth type, which is in congruence with the previous studies on Polyplacophora, but also with analyses of radular teeth from paludomid gastropod species that forage on algae attached to rocks [24, 27, 30]. The cusps were always the stiffest and hardest elements, followed by the stylus, and finally the basis. This probably enables the cusps to puncture or interact with the ingesta with possible formation of local stress. The tooth styli and bases enable the avoidance of structural failure or heavy abrasive wear, as it had been observed for paludomid gastropods [24, 27, 30]. Due to the smallness of the analyzed structures we were not able to differentiate between the core and the cusp edges in Lepidochitona, but values of the mature cusps of the dominant lateral teeth are comparable to cores of Cryptochiton  and the values of the styli are comparable to the values detected in other polyplacophorans [109, 111, 112]. The hardness and elasticity moduli of the central, lateral teeth I, and marginal teeth are comparable to the values detected for the limpet Megathura .
Breaking force and stress
For proper functioning, failures of biological structures must be avoided or reduced and studies on various biological structures, as e.g. insect wings and their components [113, 114, 115, 116, 117, 118, 119, 120], mammal teeth [121, 122, 123, 124, 125, 126, 127, 128, 129], or bones [130, 131, 132, 133, 134, 135, 136, 137], depict the multiple origins of failure prevention. As biological structures are adapted to certain functional loads, the analysis of forces leading to the structural failure could lead to the detection of e.g. functional specialisations.
For radulae, mechanisms contributing to the avoidance of structural failure were already in focus of research [e.g. 26, 36, 37, 138, 139]. A proper stress distribution, reducing high local stress, is probably enabled by the inner structure of the tooth, i.e. fibre orientation [49, 139], and the radular membrane itself [3, 26, 139, 140], as the wet membrane enables a higher bending capability of the tooth [26, 28].
Teeth also contribute to the prevention of failure by their mechanical behaviour, which is based on their individual morphology, arrangement in particular arrays, mechanical properties, and water content. Tooth morphology can enable the tooth to rely on adjacent teeth of the adjacent rows or to bend and slip away leading to the resistance of higher forces, which were previously termed ‘collective effect’ [26, 28]. The strong ability to bend, enabling a higher range of motion for tooth cusps, including the ability to deform and twist, when shear force is applied, was observed for long, slender, and thin teeth of paludomid gastropods [25, 26, 28, 35] and is also observed for the marginals, lateral teeth I, and centrals of Lepidochitona. However, this capability is only possible, when teeth are loaded under wet condition. In dry condition, the thin teeth break at their bases or stylus. The wet lateral teeth II of Lepidochitona are also capable of bending [see also 109]; here the basis and stylus bend in contrast to the stiff and hard iron-containing cusp, leading to structural failure underneath the junction zone. The lateral teeth II are in Lepidochitona the only teeth that are capable of relying on the stylus of the adjacent lateral tooth II, resulting in the resistance to high forces. This ability is, however, not as pronounced as in paludomid gastropods [26, 28]. Under dry condition, lateral teeth II are not capable of bending and break, when loaded, directly at the junction zone.
A stiffer part (higher E) of the tooth rather transfers forces, when e.g. interacting with the ingesta, whereas more flexible regions (lower E) enable the structure to bend. Previous breaking stress experiments in paludomid gastropods revealed that tooth failure usually occurred at the softest and most flexible part of the tooth (stylus and basis), whereas the hardest and stiffest parts (cusps) are not as prone to failure under applied shear force. The same pattern is also observed for Lepidochitona as teeth usually break at their soft and flexible parts.
The hardness and stiffness of wet biological materials are lower than those of dry ones. Additionally, dry materials have lower fracture toughness [e.g. 114, 115, 141, 142, 143, 144, 145, 146, 147, 148]. This was also previously reported for chiton radular teeth with wet teeth having 15% reduction in Young’s modulus and hardness . However, previous breaking stress experiments on teeth of paludomid gastropods showed that wet teeth are capable of resisting higher stresses than dry ones due to the increased flexibility of teeth and membrane [26, 28]. This distributes the stress from the tooth cusps to the radular membrane [3, 14, 22, 32, 33, 34, 112, 149]. The same pattern was observed in Lepidochitona, as wet radular structures were capable of resisting higher stresses than the dry ones.
Lepidochitona teeth were capable of resisting higher forces than teeth of paludomid gastropods [26, 28]. Here the wet and mature central teeth of the species, foraging on algae attached to stone, showed the highest degree of collective effect, allowing the teeth to resist 754 ± 406.62 mN. The wet and mature lateral teeth II of Lepidochitona resisted to 1150 ± 143 mN, whereas the wet and mature marginals, centrals, and lateral teeth I resisted to much lower forces (Ct: 379 ± 75 mN; Lt I 360 ± 134 mN; Mt: 94 ± 18 mN). These latter values are rather comparable to the breaking forces of wet and mature teeth of paludomid species foraging on mixed feeding substrate (plant surface, sandy surfaces, and occasionally on rocky surfaces) . We would, thus, assume that centrals, lateral teeth I, and marginals of Lepidochitona are capable of occasional, but not regular interaction with the solid feeding substrate (rock).
Origins of the mechanical property gradients and the behaviour
In biological materials, functional gradients and heterogeneities can have their origin in geometry, chemistry, and/or structure [for review on the origins of gradients and heterogeneities see 93]. E.g. in abalone shells gradients are induced by the arrangement of structures [150, 151, 152], in the cephalopod sucker ring by their distribution [153, 154], in crustacean exoskeletons by their dimensions [96, 97, 155], in pangolin scales by their orientation [98, 99], in tarsal setae of ladybird beetle gradients are induced by the distribution of the protein resilin and different degree of sclerotization [156, 157], in squid’s beak by a combination of the regionalization of histidine-rich proteins and the degree of hydration [158, 159, 160], in mammal teeth or bones by multiple gradient types [161, 162, 163, 164, 165, 166, 167], and in the dominant lateral teeth of chitons and limpets by the distribution of the inorganic components and the architecture of the organic components [18, 20, 57, 109, 111, 112, 168].
The here detected values of E and H in the dominant lateral teeth (lateral teeth II) of Lepidochitona highly correlate to the iron and the calcium proportions. The relationship between hardness and iron content was previously described for limpet teeth [21, 45, 46, 47] and for chiton teeth [18, 20, 57, 112], but here for Lepidochitona we are now able to determine correlation coefficients. Additionally we assume that organic components and degree of tanning have a high influence on the mechanical properties as well. Thus, the property gradients of the lateral teeth II probably have their origin in the combination of iron, calcium, and organic substances, as it had been described for Cryptochiton teeth [20, 57, 111]. In limpets, hardness seems to depend additionally on silicon content [45, 46, 47], but in Lepidochitona only small proportions of silicon were detected.
For the centrals, lateral teeth I, and marginal teeth, we detected smaller correlation coefficients between hardness, Young’s modulus, and the amount of calcium (r = 0.23–0.32) and no correlations between hardness, Young’s modulus, and the amount of iron. Thus, the measured gradients in H and E and the resulting mechanical behaviour of the teeth of Lepidochitona could be rather based on the radular organic components, as distinct folding or bounding conditions of the chitin due to tanning , a mixture of both, or/and fibre size, arrangement, distribution, and/or density [19, 20, 23, 68, 78, 109, 168, 169, 170]. As the fibre orientation contributes highly to the mechanical behaviour of teeth and to the self-sharpening effect [47, 168, 170, 171, 172], this should be investigated for Lepidochitona in the future.
For Lepidochitona, we demonstrated relationship between the breaking force of the central teeth (and the lateral teeth II) and the mean iron and the mean calcium contents. The breaking force of the lateral teeth I strongly correlates with the mean calcium content and less strong with mean iron content. The breaking force of the marginal teeth strongly correlates with the mean calcium content. For the breaking stress similar patterns were observed. Thus, calcium content seems to have a high influence on the biomechanics of all teeth. In breaking stress experiments, we observed that wet and treated radulae resisted to higher forces. This indicates that the degree of mineralization with calcium hinders the tooth from bending, but the reduction of this element enables a higher collective effect under wet conditions. A very high bending amplitude had also been detected for the unmineralized teeth of paludomid gastropods [26, 28].
Function of radular structures
During foraging, a rotatory scraping action of the dominant lateral teeth, followed by inward sweeping action, enabled by the bending of the radula, can be observed in chitons (2, 31, 111, 173, 174]. For this purpose, the membrane must be flexible and capable of changing its shape, but it must also be strong and tough, to avoid failure during this action [see 44, 111]. This is in congruence with our results from the breaking stress experiments in Lepidochitona and paludomid gastropods [26, 28], where we observed that the wet membrane is flexible enough to enable the bending of embedded teeth and additionally contributes to stress distribution. The dominant lateral tooth cusps possess caps of exceptional hardness, reducing wear and contributing to a self-sharpening effect [18, 20, 48, 170, 172; see also 168 for limpets]. This, together with their high ability to resist forces (documented here) and with the previously documented foraging behaviour and observed rotating interaction of the dominant lateral teeth with the ingesta surface [2, 31, 147], depicts that these teeth loosen the food from the hard surface and transport them towards the mouth [44, 111]. The underlain softer core of the tooth seems to serve as a shock absorption and toughening mechanism , as it was observed in other biological materials [e.g. 175, 176, 177, 178].
It was previously reported that due to the specific shape of the cusp and the gradients in hardness and Young’s modulus across the tooth, tensile stress is concentrated on the leading edge and reduced in the trailing edge, reducing the ability of the tooth to bend and thus reduce the failure of the sharp tip of the tooth [20, 48]. It was also reported that the stylus enables the sweeping action during feeding [109, 111], orients the tooth to the ingesta , but also transfers force from the basis to the tooth cusp  leading to the reduction of structural failure . These mechanical behaviours, which are based on the graded mechanical property gradients, were also confirmed by breaking stress experiments in Lepidochitona.
The centrals of Lepidochitona can resist highest forces, followed by lateral teeth I, and finally marginals, even though marginal teeth have (slightly) higher E and H values than lateral teeth I and marginals. This leads to the conclusion, that centrals potentially interact more frequently with the ingesta surface, followed by the lateral teeth I. Since the marginals can resist to significantly lesser forces, these teeth may be potentially responsible for collecting the loosened particles in the sweeping motion. We also detected material property gradients in every type of teeth, with the cusps always the hardest and stiffest tooth parts, followed by the styli, and finally the bases. This may lead to the conclusion that the cusps of these teeth probably also interact, or even puncture, the ingesta with the possible formation of local stress at the cusps, whereas the softer and flexible tooth styli and bases allow the avoidance of structural failure or heavy tooth wear during scratching on the hard substrate.