The role of mural mechanics on cephalopod palaeoecology

Abstract

Cephalopods transformed the molluscan shell into a buoyancy device that must be strong enough to resist external water pressure. Historically, unique features of the shell have been interpreted on the basis that the strength of the shell presents a hard limit on maximum habitat depth. One such feature is the mural flap, which is a semi-prismatic layer deposited on the inner surface of some coleoid septa that has been suggested to strengthen the shell and permit colonization of deeper waters. We test this hypothesis by constructing finite-element models that show how mural modifications affect the response of the shell to hydrostatic pressure. The mural flaps are found to have no notable structural function. Another mural modification discovered here is the adapical ridge flap that initially seemed to have a potential function in shifting peak stress away from the attachment site of the septum; however, the irregular distribution of this feature casts any functional interpretation in doubt. Ecological separation of belemnites and decabrachians is likely not mediated by the presence/absence of mural flaps. This work illustrates a potential caveat that not all unique septal features formed in response to increasing hydrostatic pressure and deeper habitats.

1. Introduction

Cephalopods are unique among molluscs for having evolved a septate shell whose chambers are all connected via an organic strand, the siphuncle, which extends from the rear of the body through the septa to the first formed chamber (protoconch). The siphuncle allows the animal to exchange fluid and gas within the chambers thereby providing the mechanism by which cephalopods turned the shell into a buoyancy device. However, as a result of this innovation, the phragmocone is filled with gas at near atmospheric pressure [1,2] and thus has to be able to withstand the pressure differential between the internal chambers and the external water pressure. This is true regardless of whether the shell is internal or external.

Unlike externally shelled nautiloids and ammonoids, coleoids internalized the phragmocone thus removing the defensive function of the shell but retaining its buoyancy function. The internalization of the phragmocone seemingly occurred sometime in the Carboniferous (298–358 Ma) with the early coleoid group Hematitida being among the first to show this internalization [3,4]. The initial internalization of the shell may have allowed the animal to repair damage to the phragmocone as well as expanding the animal's sensory surface, while further stages of internalization would have contributed to increases in manoeuvrability by decreasing the distance between the animal's centres of mass and volume [5]. This internalization of the shell also coincided with the transition from nacreous septa present in nautiloids and ammonoids, including the extant Nautilus and Allonautilus, to lamello-fibrillar septa [6] that are also present in extant Spirula spirula (figure 1). In some cases, such as in Spirula and Sepia, the primary shell wall (conotheca) also lost the nacreous layer although this layer was retained in some coleoid groups such as belemnites [7]. Another difference between Decabrachia, the group that includes both Spirula and Sepia—the only two extant coleoids that retain a fully formed and functional phragmocone, and belemnites is how the septum attaches to the shell wall.

Figure 1.

Polished light microscopy image (a) of the septum/shell wall attachment zone in Spirula spirula. Cryo-fractured (b,d,e) and polished SEM (c) images of a septum. The lamello-fibrillar septum is composed of thin lamellae (b,c) that themselves are composed of aragonitic rods that tend to be parallel within a lamella (d). The orientation of these rods shows significant variation between lamellae (d,e). Scale bars represent: (a) 128 µm (b) 100 µm; (c,d) 2 µm; (e) 3 µm.

Decabrachians like Spirula exhibit a specific feature of the septal/shell wall attachment zone called a mural flap [8,9], which appears as an extension of the shell wall that overlays a portion of the internal face of the septum (figure 2) and is formed sometime after the septum has been mineralized but prior to the formation of the next septum. The mural flap is an autapomorphy of the group consisting of the extinct coleoid Longibelus and Decabrachia with the lack of this feature in sepiids interpreted as a secondary loss [10]. Belemnites, however, lack this feature and this morphological variation between the shells of decabrachians and contemporaneous belemnites has contributed to interpretations of ecological separation between the two groups on the basis of depth partitioning [8,10,11]. In this view, belemnites are typically considered to live in shallower water, up to 250 m water depth [12], while some decabrachians, such as Groenlandibelus rosenkrantzi and Naefia neogaeia, would possess a similar habitat range as S. spirula, whose lower habitat range limit extends to the upper Bathyal zone [8,11,13], 700 m for adults with juveniles as deep as 1750 m [14]. This interpretation of the mural flap as an adaptation to strengthen the shell [10] and permitting deep water colonization is in line with the classical trend that additional morphological ‘complexity’ increases a shell's resistance to higher water pressure, a trend that can be traced back to the work of William Buckland in the 1830s [15].

Figure 2.

A modelled median section through the simulated shell (a) made by mirroring the finite-element model geometry. Colourized close-ups of the septa/shell wall attachment zone (b–d) to illustrate the location and morphology of three mural modifications: the mural flap (red), adapical ridge (blue) and the adapical ridge flap (purple).

The interpretation of septal modifications in relation to hydrostatic pressure is exemplified in the study of ammonite septa. Ammonites were a diverse group of cephalopods that evolved, from the Devonian through the Mesozoic, complexly folded septal morphologies that have classically been interpreted as being adaptations towards increasing water depth, meaning that forms with more complexly folded septa could live at deeper water depths [15–20]. However, this idea has been criticized and there is a growing body of research potentially arguing against it [21–24]. This represents an interesting case since, in light of the classical description, many other septal features, both in ammonites and in other cephalopods, have been interpreted as serving a potential function relating to water pressure and habitat depth. This includes features such as the septal lobe of lytoceratid ammonites [17] that forms from the attachment of the internal septal lobe to the surface of the preceding septum [25] as well as the previously discussed mural flaps of some decabrachians. If ammonite septa did not necessarily serve a function to strengthen the shell against increasing water pressure then perhaps this ‘hydrostatic’ functional interpretation of these other septal features was similarly overemphasized.

This paper focuses on testing the potential function of the aforementioned mural modifications seen in coleoids. In order to test the potential role these mural flaps might have on the shell's internal stresses and strains due to water pressure, we first need two things: the geometry of the shell, and the material properties of the ultrastructures.

The ultrastructure of the aragonitic Spirula shell is similar in structure to other fossil coleoids, such as Longibelus and Cyrtobelus. The lack of nacre may be a defining feature of Decabrachia [10,26,27] meaning the wealth of mechanical data on nacre, while potentially applicable to nacre bearing coleoids, is not transferable to this group. The shell wall of Spirula is largely composed of two prismatic layers (figure 3), a uni-layered conotheca and a secondary outer layer, while the septa have a lamello-fibrillar structure [28,29], sometimes referred to as lamello-fibrillar nacre or nacre type II. It is worth noting, however, that the lamello-fibrillar structure is distinct from ‘true’ nacre both in structure, being composed of aragonitic rods rather than hexagonal tablets, and likely in its governing mineralizing conditions [26,30–32] and is, therefore, not considered here to be a type of nacre. The orientation of these rods is said to change between the lamellae [33], potentially indicating a mechanical gradient through the septal thickness due to mechanical anisotropy observed in other mollusc shell components [34,35]. On a higher scale, the interaction between the lamello-fibrillar septa and the prismatic shell wall along the sutural attachment zone is important as stress tends to be concentrated along this zone under hydrostatic pressure [24]. Nanoindentation was used to collected material properties [36], namely reduced modulus and indentation hardness, from both the prismatic shell wall and from the lamello-fibrillar septa of Spirula, while computed tomography (CT) scans of Spirula were used as a guide to construct a finite-element (FE) model of a theoretical coleoid shell both with and without mural flaps.

Figure 3.

Polished (a) and cryo-fractured SEM images (b,c) of the shell wall of Spirula. The shell wall is composed of two prismatic layers with the outer prismatic layer being secondary and not homologous to any of the shell layers in non-coleoids (i.e. the outer spherulitic-prismatic layer in Nautilus). The boundary between these two layers (b), a close-up of this boundary (c). Scale bars represent: (a) 50 µm; (b) 30 µm; (c) 10 µm.

A second modification of the mural region observed in Spirula that was, as far as the authors are aware, undescribed before is the adapical ridge flap (figure 4). The adapical ridge itself, also known as the mural ridge or septal ring [10], is an annular ring about the inner circumference of the shell wall that is in contact with the convex, adapical, mural edge of the septum (figure 3d). The mural ridge is also present in Nautilus where it is formed prior to the formation of the septum and serves as an attachment point for the septal mantle so it can begin calcifying the new septum [37]. The chamber formation cycle has not been directly observed in Spirula but the adapical ridge might perform a similar role in septal formation. The adapical ridge flap is observed as a small extension of the edge of the adapical ridge that extends around the curvature of the septum. It is unclear when this structure might form or what function it might serve.

Figure 4.

CT datasets of the entire Spirula animal (a) and higher resolution data from an isolated Spirula shell (b–e). An overview of the extent of the higher resolution dataset (b), the area of which is represented by the box in (a), that comprises the final few formed chambers of the shell. A magnified view of the septa/shell wall attachment zone (c,d) showing the mural flap (mf), which is a portion of the shell wall (light grey) that overlays the interior face of the septum (dark grey). Note the lack of the mural flap on the final formed chamber. The second modification of this attachment zone is the adapical ridge flap (arf) that appears to be an extension of the adapical ridge (d,e). Scale bars represent: (b) 1.2 mm; (c) 0.18 mm; (d) 0.25 mm; (e) 0.18 mm.

A functional benefit for the adapical ridge itself has been suggested, unsurprisingly this function is related to reducing stress from hydrostatic pressure [38]. This reduction of stress in the FE models is not surprising considering that without the adapical ridge, the area where the septum meets the shell wall forms a sharp, re-entrant angle and the adapical ridge then becomes a fillet leading to a reduction of stress. One might be cautious, however, in interpreting the actual magnitude of stress reduction shown in these models considering the well-known problems finite-element analysis (FEA) has with resolving stress at re-entrant angles. In order to test the potential function of the adapical ridge flap, additional FE models are constructed both with and without this flap to test their contribution to stress and strain distribution when the shell is loaded under simulated water pressure.

2. Material and methods

2.1. Specimens and imaging

The final quarter whorl of a S. spirula shell was embedded in poly(methyl methacrylate) and cut along the median plane of the shell and diamond polished. Cryo-fractured samples were immersed in liquid nitrogen, broken using a hammer and then mounted for scanning electron microscopy (SEM) imaging. SEM images were made of this polished median section using an FEI Quanta 600 in low vacuum mode with a voltage of 5.00 kV and a current of 0.10 nA. Electron backscatter diffraction analysis was performed on a cross-section of S. spirula using an EDAX Hikari Super electron backscatter diffraction (EBSD) system using 12.00 kV and 0.8 nA. EBSD data were collected through the thickness of a single septum.

The final three chambers of a Spirula shell (figure 4b) were scanned at the Department of Operative and Preventative Dentistry of the Charité, Berlin, using a Skyscan 1172 (Bruker, Kontich, Belgium). The shell was scanned at 70 keV with a 0.3 step size over a 360° rotation resulting in an isotropic voxel size of 4.9 µm. Raw data were reconstructed with NRecon (v. 1.7, Brucker microCT, Kontich, Belgium). The reconstructed image stack was then visualized and volume rendering produced with Avizo (Material Science, v. 9.7, http://www.vsg3d.com/).

CT data of the Spirula shell are available from Morphosource (https://www.morphosource.org/Detail/SpecimenDetail/Show/specimen_id/28511). CT data of the Spirula animal are from [39]. Spirula shells used for indentation and scanning are beach collected specimens both of which lack the protoconch. Additional observations are taken from CT data of the Spirula animal (with the protoconch preserved).

2.2. Nanoindentation

Nanoindentation experiments were performed in a Triboscan TI 950, with a Berkovich diamond tip. The indentation was performed with a maximum load of 1000 µN with a load function consisting of a 10 s loading segment, a 10 s holding segment and a 10 s unloading segment. Nanoindentation experiments were performed on polished sections of the median plane of the shell of S. spirula along the shell wall, the septa and at the attachment point of a septum to the shell wall. Reduced modulus (E_r) and hardness data were collected from 20 indent × 20 indent grids (electronic supplementary material, table S1), with a 5 µm spacing, over a space of 100 × 100 µm for each section of the shell. Indentation contour plots were produced by interpolating the raw indentation data using the akima package [40] for R [41].

2.3. Finite-element modelling and analyses

FE models and FE analyses were completed using Abaqus (2016; Dassault Systèmes Simulia; http://www.3ds.com/products-services/simulia/products/abaqus/). Two-dimensional models of a septum and three different shell wall models were made based on measurements taken from Spirula. The resulting septa models were, therefore, domic, reflecting the morphology of interest expressed in coleoid shells [42,43]. Three variants of the shell wall were produced: the unmodified shell wall (figure 2b); the shell wall with mural flaps (figure 2c) and the shell wall with both mural flaps and ridge flaps (figure 2d). Each shell model was composed of one version of the shell wall that possessed four septa (figure 2a). The attachment zone was closely modelled after the attachment zone in Spirula so as to avoid problems arising from the simplification of this area [38]. All FE models of the shell were axisymmetric with the symmetry axis of shell parallel to the long axis of the cylinder and composed of six-noded triangular axisymmetric elements, to take advantage of the rotational symmetry of the shell. For these models, the siphuncle was ignored. The septum and shell wall models are available as igs files (doi:10.6084/m9.figshare.11841930). Material properties for the shell wall and septum were taken as averages of the indentation data taken from those respective regions (electronic supplementary material, table S1). Both the shell wall and septa were modelled as linear elastic with an isotropic elastic modulus of 80 GPa, and 36 GPa, respectively. The Poisson ratio of both materials was 0.3, the typical value used for mollusc shells [44].

The mechanical properties of the shell are simplified in the model; the material properties applied to the FE model have been averaged so features such as the mechanical gradient of the septa and differentiation between the two prismatic layers of the shell wall are not included. The applied material properties are also based on the average values for reduced modulus rather than a calculated elastic modulus though this is not expected to have any significant impact because the proportional difference between the two layers is the same since both are expected to have the same Poisson ratio.

Two load cases were investigated: a ‘lateral pressure’ case (electronic supplementary material, figure S1a) with a pressure loading along the exterior surface of the shell wall of 1 MPa and a ‘hydrostatic pressure’ load case (electronic supplementary material, figure S1b) that included the lateral pressure along the shell wall as well as an additional 1 MPa pressure along the model equivalent external face of the last formed septum. This load case is a more accurate simulation of the hydrostatic pressure the shell would be exposed to underwater as the last formed septum in the shell is exposed to water pressure while the internal septa are only exposed to lateral pressure through the shell wall. The septa were constrained against translation along the x-axis at the axis of symmetry for both load cases, while the adoral-most and adapical-most face of the shell wall (parallel to the x-axis) was constrained against translation in the y-direction for the lateral pressure load case. For the chamber pressure load case, the adoral-most y-direction constraint on the shell wall was removed to reflect the fact that this edge in the animal is not fixed.

Meshes of the modelled geometries were created by applying an element size gradient, 0.1–0.001, from the axis of symmetry to the attachment zones in order to maximize the number of elements in this region of interest. An additional edge seed was applied to the outermost shell wall of size 0.01. All models possessed similar final sizes ranging from 1 818 676 to 1 893 172 nodes. Mesh convergence was judged on two parameters at selected nodes: theoretical stress values from the shell wall and hoop (tangential) stress along the mural flap (being the thinnest component of the model). Theoretical hoop stress was calculated using the standard equation for hoop stress in a thin-walled pressure vessel:

$${\sigma }_{\mathrm{h}}=\frac{Pr}{t},$$ 2.1

where σ_h is hoop stress, P is the applied pressure, r is the radius—here measured as the distance from the symmetry axis to the external shell face and t is the thickness of the shell wall. The theoretical radial stress is equal to the applied pressure (1 MPa) at the surface the pressure is applied. Theoretical hoop stress along the wall was calculated at 25 MPa, compared to the hoop stress from FEA, the error ranged from −2% (24.5 MPa) to 1.6% (25.4 MPa). The error between radial stresses ranged between −7% (0.93 MPa) and −1% (0.99 MPa). Furthermore, hoop stress on the mural flap was considered converged when it fell within 0.5 MPa (2%) between different sized meshes. Transect paths were made through the thickness of the septa and shell wall at three locations: the tip of the septal attachment zone, the mid-region and the base (adapical) of the attachment zone. Stresses were taken at 60 evenly spaced intervals along each path and stress linearization was performed to calculate membrane stresses (electronic supplementary material table S2) with an out-of-plane correction equal to the outer most radius of the shell, 3.125.

3. Results

Nanoindentation results show an average difference between the prismatic shell wall and lamello-fibrillar septa of 44 GPa (figure 5). Both the outer and inner prismatic layers have a similar range of modulus values. The prismatic layers of Spirula possess overlapping reduced modulus values compared to the columnar (prismatic) layer of Nautilus pompilius, though the upper boundary is higher for Spirula, ranging roughly from 90 to 100 GPa, while N. pompilius ranges roughly from 80 to 90 GPa. The boundary between the shell wall and septa shows a sharp, rapid shift in stiffness. There is a persistent gradient through the septal thickness on the order of 10 s of GPa. Textural analysis using EBSD reveals co-alignment of the crystallographic c-axes with the growth direction, with the a- and b-axes oriented within the plane of the lamellae but no regular textural gradient that would correlate to the observed mechanical gradient (figure 6). However, there is clear variation in orientation both between and within lamellae.

Figure 5.

Finite-element model geometry (a) with representative locations (b′, c′ and d′; not to scale) of the respective indentation grids (b, c and d). Contour maps of the reduced modulus (E_r) measured via nanoindentation on the shell of Spirula. Three areas of interest were measured: the shell wall (b), here the blue area partially represents the embedding medium that transitions to the outer prismatic layer. The septum (c) shows a gradient in reduced modulus from the edges towards the centre. The interface (d) between the shell and septum, which shows a relatively sharp boundary. Contour maps were made by extrapolating the raw 20 × 20 indentation grid with a 5 µm spacing between each indent.

Figure 6.

Crystallographic analysis of a median section through a single septum of Spirula (the yellow box in the inset image) showing the crystallographic orientations of the lamello-fibrillar septal ultrastructure. The inverse pole figure is colour coded relative to: the axis perpendicular to the polished surface (a), the axis approximately parallel to the septal lamellae (b) and the axis approximately perpendicular to the septal lamellae (c). The (001) plane normal of aragonite is generally aligned parallel to the growth direction (c). The (010) and the (100) plane normal do not show a clear gradient from the edge of the septum to the centre that can be easily correlated to the mechanical gradient seen in the indentation data (figure 4b). The yellow arrow is the approximate growth direction of the inset; the septum grows in thickness in the direction perpendicular to the lamellae planes. The scale bar represents 4 µm.

3.1. Mural flap

FE models were composed of two linear elastic materials, the shell wall (80 GPa) and the septa (36 GPa). The mural flaps were modelled as parts of the shell wall using the same material properties. Comparisons between stresses (figure 7) and strains (electronic supplementary material, figure S2) show that the mural flaps have no appreciable effect on the structures' response to either lateral pressure, applied only to the external surface of the cylinder, or hydrostatic pressure (figure 8), which includes the lateral pressure and an additional pressure load on the external face of the final septum. Under both loading cases, the average out-of-plane stress component (hoop stress) is the most significant at the attachment zone. Under lateral pressure, the in-plane shear stress is the least significant. The average longitudinal stress is the smallest in the hydrostatic load case with a single exception in the model with no mural modifications. Here, the radial stress in the middle region of the septum is smaller in magnitude than the other measured stresses. Measurements of line paths through the thickness of the septa and shell at the attachment zone show a general trend of increasing stresses from the rear of the attachment zone to the tip (adapical to adoral) while under lateral pressure. While under hydrostatic pressure, the mid-region of the final septum shows peak average and membrane stresses, approximately 2–5 MPa higher than at the tip or base regions, regardless of the presence or absence of any mural modifications.

Figure 7.

Stress contours comparing attachments zones without the mural flap (a–d) and with the mural flap (e–h). The models were loaded with a lateral pressure on the external surface of the shell of 1 MPa. Stress maps, like the strain maps (electronic supplementary material, figure S2), show no appreciable differences between the two models suggesting that the mural flaps play no significant role in resistance to hydrostatic pressure. The radial stress is stress parallel to the x-axis (radius of the cylinder), the longitudinal direction is parallel to the y-axis (long axis of the cylinder) and hoop stress is the out-of-plane stress.

Figure 8.

Maximum principal stress (a–c) and strain (d–f) for the three modelled geometries: non-modified geometry (a,d); the mural flap model (b,e) and the mural and ridge flap model (c,f). These models are under the ‘hydrostatic’ pressure load case, with a constant pressure of 1 MPa against the shell wall and the adoral surface of the final septum. As with the lateral pressure load case (figure 7) the presence of the two mural modifications does not cause any appreciable change in stress or strain.

Comparisons of the stresses extracted from the measured line paths demonstrate nearly identical values of both hoop and longitudinal stress across all morphologies. Only radial stresses have small variations between models and largely in magnitude rather than stress or strain contour pattern differences. Magnitude differences are also not consistent, for example, radial stress due to lateral pressure in the geometry without mural modifications has values near identical to the mural flap model at the base of the attachment zone while the ridge flap model develops lower magnitude values; at the mid-region the unmodified model generates the lowest magnitude stress near to the surface of the septum; the highest values at the tip of the unmodified model are induced near the septal surface.

3.2. Ridge flap

The presence of a ridge flap does show a repeated pattern across both load cases. Analyses of peak stresses and strains in the confined area around the ridge flap and adapical attachment zone show the presence of this flap regularly migrates the peak stresses and, to a lesser extent, some in-plane strains away from the septa–shell wall attachment site and onto the shell wall (figure 9). Under lateral pressure, certain values, such as maximum principal stress, longitudinal stress and longitudinal strain increase in the ridge flap model while peak von Mises and maximum principal strain decrease. These patterns are largely the same under hydrostatic pressure though the peak von Mises stress remains the same.

Figure 9.

Maximum principal stress (a,c) and strain (b,d) contour plots showing the redistribution of these parameters resulting from the addition of a ridge flap to the adapical part of the septa/shell wall attachment zone (c,d). The models are subject to lateral pressure as in figure 7. In the absence of the rear flap (a,b), the peak stresses lie on the point of attachment of the septa onto the shell wall. The rear flap migrates the peak stresses to the stiffer shell wall as well as causing a very slight decrease in peak strain.

4. Discussion

While the mural flap is a well-documented morphological feature, the adapical ridge flap is not. Therefore, it is unclear if this feature is limited to Spirula but it is interesting to note that even in Spirula this feature is difficult to find. Using CT data to visualize the three-dimensional structure of this region, it is clear why it is difficult to find the ridge flap in cut sections. The extent of mineralization along the adapical ridge is highly heterogeneous and this flap is created by a slight increase in mineral deposition potentially during the formation of the adapical ridge itself (figure 10). These structures appear to be primary structures rather than secondary mineral deposits, like the infillings seen in Nautilus by Grégoire [45], and they appear to be continuous with the shell wall rather than the laminated septa (figure 10a). It is worth noting, however, that both the CT data and SEM images are based on beach strandings where the shells have a potential for alteration. However, the heterogeneous structure of the adapical ridge that gives rise to the adapical ridge flap are seen in other specimens including the CT data from the Spirula animal [39]. The ridge flap could not be visualized in individual orthoslices due to the relatively low resolution of the scan and the very small size of the flap. The dimensions of the modelled mural and ridge flaps were based on two Spirula specimens, being the most complete specimens available, meaning that potential variation in the relative proportions of this region that might be present in other groups is not accounted for here.

Figure 10.

Cryo-fractured SEM image (a) showing the adapical ridge flap, here the septum has detached from this portion of the shell wall. Volume renderings of the CT data (b) show the region about the adapical ridge flap possess a high variability in the amount of mineral deposition along the curvature of the septum. An orthoslice along the blue line (c) shows no adapical ridge flap while an orthoslice along the red line (d) shows the adapical ridge flap. The ridge flap is, therefore, a non-continuous structure along the mural zone.

4.1. Material mechanics

The shell wall and septa of Spirula exhibit a large average difference in reduced modulus of around 44 GPa, compared to N. pompilius that shows a difference of around 10–20 GPa between the outer prismatic and nacre layer. As stated previously, the septa of Spirula show a reduced modulus gradient through their thickness of roughly 10–15 GPa. The septa are described as being composed of aragonitic rods whose orientation changes in each successive lamellae [33]; the change in orientation of these rods was hypothesized to cause the observed mechanical gradient. EBSD data show the variation of the crystallographic axes both between and within lamellae; however, no clear gradient in the orientations was seen that could be directly correlated to the measured mechanical gradient. While the diversity of crystallographic orientation could account for some of the measured mechanical variation, more controlled and higher resolution tests would be needed to measure the effect of orientation of the aragonite components on the measured modulus of the septa. Another possible explanation of this gradient could be variations in organic content from the edge to the centre of the septum.

Characterization of the reduced modulus values of the Sepia cuttlebone show similar trends as those seen in Spirula. A measured difference between the cuttlebone's dorsal shield and the dorsal zone of the septa is, on average, 45 GPa though the average difference between the outer shield and the ventral zone of the septa is only around 20 GPa [46]. North et al. [46] also show a gradient in modulus and hardness values in a Sepia septum though this is related to a change in ultrastructure from a prismatic structure to a lamello-fibrillar structure. No such change in ultrastructure is seen in Spirula septa.

The relative difference between the modulus of the shell wall and septa is relatively low, despite the high value compared to Nautilus, such that this interface is unlikely to be effective at acting to stop crack propagation [47]. Though failure was not specifically tested, cracks formed during sample cutting and polishing show multiple cracks that travel directly through the septa/shell wall thickness, cracks localized to the septa/shell wall attachment zone, as well as apparent delamination of the septal lamellae. Prior research has suggested a relationship between the ratio of reversible/irreversible deformation to the ratio of a materials indentation hardness/indentation modulus with higher ratio values indicating an increasing dominance of reversible deformation [48], which is particularly useful in materials whose yield strength is unknown. Hardness/modulus ratios of the Spirula shell wall are calculated at an average of 0.057 while the septa have an average ratio of 0.042 indicating a higher potential for the shell wall over the septa to undergo elastic deformation.

4.2. Finite-element analysis

FEA results show that the presence of the mural flap has no appreciable change in the stress or strain developed around the septal/shell wall attachment region. Under hydrostatic pressure, neither magnitude nor contours appear affected by the mural flap and contours that are continuous across the shell wall and septa also become continuous through the added mural flap. Under hydrostatic pressure, the stress and strain contours both with and without the mural flaps remains essentially identical. One difference is that, under hydrostatic pressure, the mural flap does seem to concentrate maximum principal stress though the stress contours developed on the septum are largely unchanged. However, the increase in maximum principal stress in the mural flap is not accompanied by an increase in maximum principal strain.

The ridge flap does show some potentially beneficial effect by redirecting the peak stresses and strains away from the linear attachment area and onto the shell wall (figure 9) for both loading cases. The value of the peak stresses and strains show little change with the addition of the ridge flap. This redirecting of stress is beneficial if the shell wall does have a greater tendency for elastic deformation over the septa and a potentially higher tensile/compressive strength than the septa that would delay failure at higher water pressures. Elasticity indices of the shell and septa have been calculated but the material strengths are currently unknown so it cannot be said to what degree the presence of the flap may delay failure. Increasing the applied pressure by 1.5–2.0 times increases the peak stresses in the model with the ridge flap to the same peak values as the model without the ridge flap. This increase in pressure is approximately equivalent to an increase of 50–100 m water depth; however, this increase also doubles the peak von Mises stress on the shell wall. This potential function is further complicated by the fact that the ridge flap is non-continuous and irregular in morphology further limiting any potential functional interpretation.

4.3. Palaeoecology

The initial hypothesis, that the mural flaps are an adaptation to deeper water habitats in the clade consisting of Longibelus and Decabrachia, is not supported by the simulations presented here. The mural flap does not seem to present any notable mechanical benefit under any tested load case, though the ridge flap does seem to potentially protect the adapical region of the attachment zone by shifting stresses away from it. The presence of mural flaps does not seem to be a valid character to indicate a transition into deeper water habitats in and of themselves.

Based on the biogeographic distribution of Longibelus, in inner and outer shelf deposits, and septal strength calculations [11], Fuchs et al. [10] proposed an ecological separation between epipelagic belemnites (that do not possess mural flaps) and mesopelagic Longibelus. The presence of ridge flaps may help support this separation but it is unknown if Longibelus possesses such structures. Moreover, the ridge flaps are irregular extensions of the adapical ridge and this irregularity casts some doubt on a functional origin and may instead indicate that they are a fabricational artefact or possibly diagenetic due to the limited availability of suitable specimens and observations.

The septal strength calculations are subject to a large potential for error based on the radius of curvature taken during the calculations as shown for Spirula where different parameters for the same specimen can lead to variations of more than 200 m in calculated maximum depth [24]. While including this error, the calculated 580 m depth still potentially separates Longibelus from the calculated depth range, 100–250 m, of belemnites [11]. The potential depth separation of these groups based on these calculations is much smaller than stated when taking the calculation error into account.

The mural flap may still possess a function related to shell failure. The apparent morphology of this region, with the mural flap essentially seeming to secure the septum in place could logically help prevent failure at very high water depths. Failure was not tested here and much more material information would be needed to properly simulate this kind of loading; however, it is important to recognize that the mural flap is formed at an indeterminate point after the septum itself is formed. Meaning that for some period of time the final formed septum exists without the mural flap at all, meaning that it must be capable of withstanding both lateral pressure and the pressure on the septal face from the body chamber even without the mural flap. Once a new septum is constructed and the previous septum ‘secured’ with the mural flap the pressure loading from the body chamber is, of course, gone and the older septum is now only loaded via lateral pressure. This means that the force on the septum decreases and the resulting stresses also decrease [24]. It is unclear why then the septum would structurally need the mural flap only after the largest loading forces have been removed. This argument makes some assumptions on the timing of formation of the mural flap, which is currently not known as the chamber formation cycle in Spirula is not as well documented as the chamber formation cycle in Nautilus. However, we can draw on analogy to the Nautilus chamber formation cycle to propose a potential developmental sequence.

Ward et al. [37] summarized the chamber formation cycle with four general processes: apertural growth, forward movement of the body, septal secretion and finally removal of cameral liquid from the newly formed chamber. The formation of the mural ridge (equivalent to our adapical ridge) in Nautilus occurs very early in this process, prior to the separation of the septal mantle from the previous septum. It is possible that the mural flap on the previous septum forms at the same stage as the formation of the next chamber's adapical ridge. This would mean there would be some period of time in which the mural flap is exposed to the hydrostatic pressure, though it is unknown how long this period of time would be or what depth this process would occur at. It is also reasoned then that the formation of the mural flap would occur after the chamber emptying process has begun. The adapical ridge flap would then form either during the formation of the adapical ridge itself or during the initial stages of septal mineralization.

5. Conclusion

Material characterization of the shell of Spirula and computational mechanical simulations of shell geometries have revealed that a major mural modification that characterizes the group consisting of Longibelus and Decabrachia does not appear to have a definable function in terms of accommodating hydrostatic pressure. The adapical ridge flap does appear to divert the peak stresses and strains away from the attachment site and onto the shell wall. While this is potentially beneficial as nanoindentation results from the shell of Spirula indicate that the shell wall is a stiffer material with a greater tendency for reversible deformation compared to the laminated septa, tomographic analysis of the posterior mural zone shows the ridge flaps are discontinuous along the septum and may more likely arise from variable mineral deposition in this region rather than any functional pressure.

The results presented here do not support the idea that the mural flap evolved to help improve the shell's resistance against hydrostatic pressure to facilitate a deeper habitat for this group. Moreover, prior mechanical analyses may have overestimated the depth stratification of Longibelus and belemnites. It is unclear if the mural flaps are functional features, constructional features or indicative of clade-specific suites of biomineralizing conditions that precipitate this additional shell layer on top of the septum. The limitations of this study highlight the need for further mechanical data for cephalopod ultrastructures in order for more accurate simulations that can help elucidate the relationship between structure, mechanics and palaeoecology of these marine organisms.

There is a notable historical trend in the palaeontological literature where many features of cephalopod septa are interpreted as adaptations to strengthen the shell against increasing water pressure [15,16,18,42]. The evolution of complexly, near fractal, folded septa in ammonites is perhaps the best example of this trend [49]. This interpretation has become increasingly controversial [22–24]. The evolution of mural flaps was similarly suggested, in line with this historical tradition, to increase resistance to water pressure and the failure of the mural flaps to demonstrate this function in the analyses presented here can be seen as a critique to the general, ‘go-to’, interpretation of septal modifications as adaptations to deep water.

Data accessibility

CT data of Spirula spirula is available from Morphosource (https://www.morphosource.org/Detail/SpecimenDetail/Show/specimen_id/28511).

Geometry used to construct the finite-element models is available as part of the electronic supplementary material.

Two figures and two data tables with FEA and nanoindentation data are provided as supplementary material.

Authors' contributions

R.L. planned the study, constructed the digital geometries, carried out the finite-element analyses and generated three-dimensional renderings as well as manuscript preparation and editing. D.S. designed and performed EBSD analyses and SEM data collection. I.Z. assisted in experimental planning, nanoindentation analyses and manuscript editing. P.Z. collected computed tomography data and assisted in manuscript editing. D.F. provided the original impetus for the study and assisted in study design as well as manuscript editing.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by the Deutsche Forschungsgemeinschaft through grant LE 4039/1-1. I.Z. and D. S. were supported by the Bundesministerium für Bildung und Forschung through grant 03Z22EN11.