Spine models

We used FSI to assess fluid-derived stress distributions along the length of three hypothesized spine models. All spine models are approximately 2.5 mm in length depending on the angle. Spine A and Spine B are both curved cones with diameters (at the proximal attachment point) of 0.50 mm and 0.556 mm [21], respectively. Spine C includes T-ridges, with an outer ridge diameter of 0.556 mm and inner ridge diameter of 0.50 mm, corresponding to Spines B’s and A’s diameters. All spines are hollow in cross-section with a shell thickness of 0.05 mm. Spine B allowed for testing if differences in our results between Spine A and Spine C were due to the presence of the ridges and not merely the larger diameter in those regions. Since the angles at which the spines protruded out of living Y. yukonensis are unknown, three separate angles were chosen to investigate how this angle could affect stress based on fossil specimen photographs: 0º, 10º, and 15º to the body wall. See S1 Table for full details regarding the mesh sensitivity test of the spine.

Each spine model was placed in a hexahedral flow domain, with the spine attached to the downstream face. The hexahedral dimensions of this flow domain are 4 mm x 3 mm x 4.25 mm (W x D x H). Due to computational constraints, all spine models and flow domains were bisected in the middle along the Z-X plane, and a symmetry boundary condition was also applied on this plane (S1 Fig). The post-bisection dimensions for the flow domain are 4 mm x 1.5 mm x 4.25 mm (W x D x H). For the CFD setup, the spine and associated wall were prescribed no-slip conditions with a normal inflow inlet (e.g., constant inlet velocity along its surface) on the opposing face (S1 Fig). As stated earlier, a symmetry boundary condition was applied to the bisected wall of the flow domain. Open boundary conditions were prescribed on all remaining flow domain walls, and a pressure point constraint was selected as the lower right corner of the flow domain. The fluid physics coupling to the linear structural mechanics was one way, meaning that the deformation of the solid spine did not lead to the deformation of the flow field. A symmetry boundary condition was added on the bisected face of the spine for the structural mechanics component. A fixed constraint was added at the spine-wall interface. For numerical simplification, the spine’s physical properties are assumed to be the same in all locations and were set to those reported for CaCO₃ [38]: density (ρ_s) = 2711 kg m^-3, Young’s Modulus (E) = 88.197 GPa, and Poisson’s Ratio (ν) = 0.33.

Macroscopic model

The macroscopic model of Y. yukonensis consists of four stacked porous chambers, each with a height of 3 mm cumulating to a total model height of 12 mm. A model with a total of four chambers was created based on most Y. yukonensis specimens preserving five or fewer chambers [22] and to reduce the number of meshing elements due to computational constraints. Similarly, only the outer wall of the organism was modelled to focus solely on the unique external structure of Y. yukonensis. The tumuli pores were geometrically simplified by modelling them as cone-shaped openings instead of hollow mounds to limit the presence of thin faces (as shown in Fig 1D cross-section). Two potential thorny corolla angles (Fig 1E) – one with a narrow thorny corolla (Fig 1B) and another with a wide morphology (Fig 1C) – were modelled to assess how corolla angle affected flow patterns. Mesh sensitivity tests were done on the narrow variant due to this version likely having greater interaction between the thorny corolla and outer wall. Models were placed in a hexahedral flow domain of dimensions 120 mm x 70 mm x 40 mm (W x D x H) (S2 Fig). Each model was placed in the center of the lower surface at one-third the streamwise distance from the inlet (40 mm) to prevent numerical anomalies arising from boundary conditions [39]. Similar to the FSI simulations, the flow domains and models were bisected along the Z-X center of the domain. The post-bisection flow domain dimensions were 120 mm x 35 mm x 40 mm (W x D x H). No slip conditions were applied to the Y. yukonensis model and the lower hexahedral face to which the model was attached (S2 Fig). Opposing downstream and upstream faces were prescribed outlet and fully developed inlet boundary conditions [34], respectively. All remaining boundaries parallel to the flow were prescribed as slip conditions. To reduce computational complexity, the far field domain received a coarser mesh than the near field domain and flow areas around the organism (S2 Fig). See S2 Table for mesh sensitivity test data. As with the spine FSI studies, a stationary laminar flow model was applied.

Macroscopic CFD

Our CFD results for the macroscopic model of Y. yukonensis display several key characters of flow (labelled A through E in Fig 2). In all figures, flow field velocities have been normalized to the inlet velocity for each simulation, resulting in unitless velocities. The viscous sublayer, or laminar layer (Fig 2A), is characterized by a local low velocity region that approaches 0 near the no-slip lower surface. Downstream of the model, there is a decline in normalized fluid velocity to < 0.1 (Fig 2B). Following the downstream wake, the velocity begins to accelerate above 0.1 of the inlet. Directly upstream of the thorny corolla, there is an increase in fluid velocity that is most prominent on the uppermost thorny corolla (Fig 2C) and is reduced for the lowermost thorny corolla (Fig 2D). Following the exterior curvature of the thorny corolla, fluids are partitioned vertically across chambers. In the space between the thorny corolla and the outer wall, flow is variable. For example, at the inner perimeter of the thorny corolla and outer wall, velocities are generally slow. However, at the middle of the thorny corolla (Fig 2C), there is an area of faster fluid flow that decelerates as it moves lower in the thorny corolla before interacting with the tumuli. In summary, the thorny corolla initially redirects water downwards, whereas flow above the corolla accelerates laterally to produce a pronounced vertical zonation (Fig 2).

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Fig 2. CFD results for U = 0.2 m s^-1 inlet flow on the Y. yukonensis narrow macroscopic reconstruction.

Colour corresponds to the velocity normalized to the inlet. A) Viscous sublayer; B) Downstream wake; C) Acceleration of fluid entering upper thorny corolla; D) Reduced circulation within bottom-most thorny corolla; E) Downstream deceleration around thorny corolla.

https://doi.org/10.1371/journal.pone.0347476.g002

Across all four tested velocities, there is little to no movement within the portion of the thorny corolla oriented downstream (Fig 2E; S3 and S4 Figs). This consistent deceleration is noticeable through all stacked chambers across Y. yukonensis – creating a ‘dead zone’ with normalized fluid velocities approaching ~0. For all velocities examined, this dead zone is most prominent in chambers found closer to the base of the organism (Fig 2; S3 and S4 Figs). Conversely, this dead zone becomes less pronounced in its vertical extent as the inlet velocity increases (S3 and S4 Figs).

These fluid circulation patterns were present in both the narrow (Fig 3A; S3 Fig) and wide (Fig 3B; S4 Fig) thorny corolla model simulations, however there are other differences in fluid flow velocities depending on the angle of the thorny corolla. In the upstream region of the wider corolla (Fig 3B), the increased clearance provides more room for water movement, promoting stronger circulation around the uppermost chambers. In contrast, the downstream region in the wider thorny corolla creates larger low velocities shadows (i.e., wake regions) along the outer perimeter of the thorny corolla compared to the narrow model (Fig 3). Despite these differences, corolla angle is demonstrated to have minimal effect on flow–tumuli interaction across chambers, since both the narrow and wide thorny corolla models show broadly comparable flow patterns (Fig 3).

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Fig 3. Velocity profiles with volume arrows indicating the direction of fluid flow.

All profiles are at 0.2 m s^-1 with arrows scaled at 1.5x. A) Full view of the narrow model; B) Full view of the wide model under the same conditions. The velocity profile has been normalized with the inlet velocity.

https://doi.org/10.1371/journal.pone.0347476.g003

Spine FSI

Flow fields and associated von Mises (J2) stress distributions for all spine model variants (Fig 4; S5-S10 Figs) enable identification of regions most susceptible to failure or fracture. In total, three spine morphologies were modelled: Spine A is a smooth (non-ridged) spine, Spine B is a non-ridged spine with an enlarged diameter that accounts for the diameter change when ridges are present, and Spine C is the T-shaped ridge variant. For each model, the spines were tested at 0°, 10°, and 15° angles at inlet velocities of 0.01 m s^-1, 0.03 m s^-1, 0.05 m s^-1, and 0.2 m s^-1.

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Fig 4. Fluid-structure interaction analysis results for the ridged Y. yukonensis 0° and 15° Spine C models at 0.01 m s^-1 and 0.2 m s^-1 velocities that are normalized to the inlet.

All panels show the same flow field slice, and von Mises Stress distributions (J₂) are plotted along the spine surface. Green arrows represent the direction of the fluid’s movement with length corresponding to normalized velocity: A) 0° angle spine at 0.01 m s^-1. B) 0° angle spine at 0.2 m s^-1. C) 15° angle spine at 0.01 m s^-1. D) 15° angle spine at 0.2 m s^-1. E) View of the spine’s tip at 0° and 0.01 m s^-1 velocity. F) View of the spine’s base at 0° and 0.2 m s^-1 velocity. G) View of the spine’s tip at 15° and 0.01 m s^-1 velocity. H) View of the spine’s base at 15° and 0.2 m s^-1 velocity. Scale corresponds to panels A, B, C, and D.

https://doi.org/10.1371/journal.pone.0347476.g004

The minimum and maximum inflow velocities (U = 0.01 m s^-1 and 0.2 m s^-1) for the Y. yukonensis Spine C model (Fig 4) show that, although flow speeds differ, the spines consistently impede flow regardless of angle, causing water to decelerate upon contact. At 0° and 15° (normalized inlet velocity of 0.2 m s^-1), the slowest velocities consistently occur in the downstream wake region of the spine tips (Fig 4B, D) and approach ~0. At the minimum inlet velocity (0.01 m s^-1), the 0° model (and, to a lesser extent, the 15° model) exhibits reduced velocities extending from the spine tip towards the spine base (Fig 4). The moderate spine orientation (10°) shows slightly improved circulation between the outer wall and the spine (S7 Fig). These normalized velocity flow patterns are identical for all non-ridged spines across all velocities (S5 and S6 Figs). A viscous sublayer occurs along the distal no‑slip surfaces of all spines.

The corresponding von Mises stress fields for the Spines A and B tests were plotted from their ventral, dorsal, and peripheral surfaces (S8-S10 Figs). The ventral section is the spine’s downwards facing edge, the dorsal is the opposite upwards facing edge, and the peripheral is the centre of the spine surface. Our results show a steady increase in stress along the peripheral section from the spine tip to base; however, beyond approximately 2.25 mm from the spine tip, stress decreases before rising sharply (S8 and S9 Figs). Across all velocities, the 0° angle spine experiences less stress than the steeper angles and the disparity in stress between angles remain minimal (S8 and S9 Figs). Generally, the steepest angle (15°) experiences the greatest amount of stress. Moreover, at all angles investigated, higher velocities generally resulted in increased stress (S8 and S9 Figs). At a velocity of 0.2 m s^-1 and an angle of 15°, Spine A (S8 Fig) reaches its maximum stress of ~2600 N m^-2, while Spine B’s (S9 Fig) maximum stress is ~ 2200 N m^-2. These maximum stress values are reached at the dorsal junction between the spine base and the outer wall of the organism. Ventral sections of Spines A and B also reach maximum stress at ~2.25 mm from the spine tip with values of ~1100 N m^-2 (S8 Fig) and ~650 N m^-2 (S9 Fig). For comparison, the peripheral section of Spines A and B under the same conditions reaches maximum stresses of ~340 N m^-2 and ~190 N m^-2 at ~2.25 mm from the tip, respectively. To summarize, the non-ridged spines (A and B) stress values are highest in the dorsal section and lowest in the peripheral section. As expected, stress scales with flow speed: the 0.2 m s^-1 case produces the highest stresses across all sections and angles, whereas the 0.01 m s^-1 case yields the lowest (S8-S10 Figs).

The ridged spine (Spine Model C; Fig 4; S7 and S10 Figs) also experiences stress values at the dorsal and ventral sections that are consistently greater when compared to Spines A and B. For example, at an inlet velocity of U = 0.2 m s^-1, peak values of approximately 3800 N m^-2 occur along the dorsal section where the wall-spine joint surrounding the T-shaped ridges is found (Fig 4F, H; S10 Fig). As with the non-ridged spines, the peripheral of Spine C experiences lower stress, while the highest stress is focused on the ridges at the spine base (Fig 4F, H). Across all angles, the highest inlet velocity generally produces the greatest peak stress in the dorsal and ventral sections (S10 Fig); however, stress in the peripheral section of Spine C can fall below that observed at the lowest velocities in the other spine models between ~0.5 mm to ~1.5 mm from the tip. Despite this, beyond ~1.5 mm, the stress begins to rise and quickly exceeds the maximum stress experienced by lower velocities. The maximum peripheral section stress at 15° reached by Spine C is ~ 260 N m^-2 (S10 Fig), while the maximum value for Spines A and B at the same angle and sections are ~ 340 N m^-2 and ~190 N m^-2 respectively (S8 and S9 Figs). The overall trends at Spine C’s dorsal and ventral sections at all angles closely match those seen in Spines A and B but with greater stress values (S10 Fig).

Paleoecology of Yukonensis

The presence of a thorny corolla in Y. yukonensis, which is unknown in any other archaeocyath species, implies a deviation from typical archaeocyath feeding behaviours. Based on our external reconstruction, the results (Figs 2 and 3) show tentative support for an active filter-feeding interpretation for Y. yukonensis. For passive feeding to be feasible, ambient flow must efficiently circulate into the central cavity via the tumuli and subsequently exit the organism, presumably through the osculum [29]. In contrast, active feeding involves the expenditure of energy such as the beating motion of flagellated units to pump water in and out of a sponge. In our simulations, we demonstrate that the presence of a thorny corolla accelerated flow along the thorny corolla’s inner curvature, but advected flow away from the organism’s tumuli (Fig 2C, D). Upon interaction with the thorny corolla, fluid is diverted and accelerated over the top of the structure, which then causes fluid to be redirected at high velocities downwards into the thorny corolla cup (Fig 3). These patterns were seen in both narrow and wide angled models, however, the wide model exhibited increased circulation across all velocities, likely caused by greater available space for fluid movement (S3 and S4 Figs). From these tests, there is little water transport from the thorny corolla into the tumuli; instead, most flow is channeled around the thorny corolla’s interior, which at higher velocities creates a downstream vertical uplift of fluid out of the individual thorny corolla structures (Fig 3). However, we emphasize that these paleoecological interpretations are made from models lacking internal structures and anatomy, which may alter results.

Although computational constraints preclude detailed analysis of flow within the internal chambers, our results provide a basis for informed assumptions. In fossil specimens, the intervallum of Yukonensis includes a localized lattice of cylindrical rods cross‑linked by synapticulae (i.e., short connecting bars) that occurs only at the uppermost portion of each chamber (Fig 1D) [24]. Because this framework does not extend continuously through the intervallum (Fig 1D), it likely had little influence on internal flow. The internal calcite rods and synapticulae may have provided structural support by bracing the intervallum and mechanically linking the inner and outer walls. Furthermore, they may have served as attachment sites for unfossilised soft tissues (i.e., choanocytes) that have yet to be reported in any archaeocyath fossil [19], and preclude their incorporation into the models.

Our external flow simulations show that the stacked nature of Y. yukonensis resulted in variable flow across each chamber (Figs 2 and 3). Handfield and McKinney [21] suggested that the lowermost chambers could have been metabolically inactive, with living tissue being restricted to the uppermost (distal) chambers. As shown in Handfield and McKinney [21], although rare, the intervallum and/or central cavity between chambers may be isolated by a horizontal calcium carbonate membrane vesicle (formerly called ‘dissepiment’ [8]) (Fig 1F, G), which would have inhibited internal flow between chambers [24]. Because horizontal vesicles are not ubiquitous, they may have represented pathological growths formed in response to parasitism [24,40], structural damage [24,40], or they may have functioned as a means of restricting living tissues (and associated flow) to the uppermost chambers [21]. Our simulations support this interpretation, showing strong vertical flow stratification such that chambers nearest the substrate experience near‑zero external flow (normalized velocities of ~0 in both wide and narrow thorny corolla variants) likely due to boundary‑layer effects (Figs 2A and 3). Notably, at an inlet velocity of 0.2 m s^-1, the thorny corolla creates zones of downwards accelerations and upwards deceleration (Fig 3) that increase with the height of the chamber. At slower velocities (S3 and S4 Figs), this flow pattern is weaker but remains. Ultimately, these external flow results show a hydrodynamic pattern that would be improved by passive pressure gradients, active pumping, or both.

The functional role of vesicles remains unknown due to their inconsistent presence and geographic restrictions [24], possibly alluding to an environmental control. We propose that aporous vesicles could have provided biological advantages related to feeding and fluid movement in several ways. These aporous structures could have inhibited water exchange between chambers, therefore limiting internal fluid flow to each chamber with all excurrent flow being directed outward through the external pores and not via a central osculum [19,21]. However, this would be detrimental to internal flow by blocking the entry of water. As such, it is possible that vesicles separated the upper metabolically active regions found higher in the water column from those found closer to the substrate. Handfield and McKinney [21] also report cases where vesicles in Yukonensis block only the intervallum allowing the central cavity to remain open. Vesicles in the intervallum could serve as horizontal partitions that improve efficiency in fluid movement by guiding water out of the central cavity and reducing vertical flow up the intervallum; this impact could be similar to the aporous septa (vertical partitions in the intervallum) model tested by Savarese [29]. The Savarese model demonstrated that aporous vertical partitions in the intervallum become increasingly beneficial as an archaeocyath increases in height and faces faster current velocities by improving filtering efficiency [29]. For Yukonensis, we would anticipate that vesicles should become increasingly common in upper chambers for better filtering efficiency and reducing leakage out of pores. However, across Y. yukonensis specimens, the abundance and locations of vesicles appear to be random across chambers, which is also observed in other archaeocyaths [21,24]. Consequently, the growth of these vesicles has also been attributed to intervallum or central cavity damage (either physical or by parasitism; [21,40]). Based on our simulations, the stacked body plan of Y. yukonensis benefits the upper-most chambers, and water pumping may be improved in combination with vesicles assuming that they are efficiently placed.

Functional role of ridged spines

Exceptionally preserved Y. yukonensis specimens have thorny corolla spines striated by T-shaped ridges along their length [21]. Previous hypotheses [21,41] have suggested that the T-shaped ridges and spines could redirect fluid flow, provide structural reinforcement, be used as a defence against predation, improve stability in sediment, or increase surface area to be used by photosynthetic symbionts. Although some of these hypotheses are difficult to test, our FSI simulations can help investigate if they redirected flow or allowed for greater structural rigidity. The spines reduce fluid velocity downstream of the spine’s distal tip, but the presence of T-shaped ridges appears to have little impact on redirecting fluid flow (Fig 4). For the ridges to aid in feeding, we would expect a noticeable redirection of flow between the ridges, increasing the velocity towards the ends of the spine closest to the wall attachment point (Fig 4; S10 Fig), and improving fluid delivery to the tumuli. Instead, we see that velocity patterns across the ridged and non-ridged spine models remain largely similar (Fig 4; S5-S7 Figs). The lack of velocity differences across ridged and non-ridged models suggest that the ridges have little impact on feeding.

Similarly, if the ridges were more structurally stable than the null model of a flat conical surface, we would expect lower overall stress values within and around the spine. Counterintuitively, our isolated spine simulations suggest that the ridges would instead structurally weaken Y. yukonensis spines. The reduced stress at Spine C’s peripheral transect is notable since it could be caused by increased drag from the presence of ridges (S10 Fig). However, this reduced stress only occurs in a small transect along the spine before stress increases closer to the spine base (S10 Fig). The dorsal and ventral weakening caused by ridges could lead to breakage along their lengths or at the junction with the outer wall where von Mises stresses were highest (Fig 4; S10 Fig). Thus, the presence of the ridges introduces a greater risk of potential damage likely disrupting the local flow. As such, it is unlikely that the purpose of the ridges would be either to improve flow or structural rigidity (assuming they lack non-fossilized soft tissue).

Hypothetically, the presence of soft tissue on the spines could have reduced the stress experienced by the calcium carbonate spine surface and served additional biological functions. The hollow structure of the spines suggests the presence of soft tissues that may have improved the structural integrity of the thorny corolla spines. For instance, the Cambrian sponge Lenica sp. has been described to have constructed spicules filled with organic material that were externally ornamented with grooves [42]. While archaeocyaths are aspiculate [8], the morphological similarities between the spines of Yukonensis and the spicules of Lenica are notable. Despite being independently derived, sea urchin spines also contain soft tissue that strengthens the calcite to make it more flexible despite being thin and hollow [43]. Alternatively, the T-ridges could create purposeful planes of weakness that break to prevent cracks forming throughout the entirety of the spine, thus protecting internal tissue, if present [43].

Functional interpretation of the thorny corolla

Handfield and McKinney [21] suggested that the spines could have primarily functioned as additional attachments for flagellated units, allowing for actively guided fluid flow into the recesses of the thorny corolla and the tumuli. The ridges would have further increased the surface area for attachment along the spines, permitting additional flagellated units that could have been beneficial due to the organism potentially living at greater depths, with correspondingly slower ambient current velocities [21]. The external flagellated units, in combination with the velocity acceleration from the thorny corolla (Fig 3), could have improved internal circulation – especially when combined with presumed internal flagellated cells. This hypothesis requires the presence of the connecting calcium carbonate membrane portion of the thorny corolla (Fig 1D), though we acknowledge the connecting membrane is not consistently present in all fossil specimens [21]. If the hypothesis of Handfield and McKinney [21] is supported, external flagella along each spine could result in the movement of water without the connecting membrane portion of the thorny corolla. The beating of external flagella along the spine could also prevent the pooling of water within the thorny corolla by improving circulation (Fig 3). Metabolically active chambers of Y. yukonensis would have made use of the flagellated units, spines, and connecting membranes to increase overall flow. However, in the absence of fossilized soft tissues, these hypotheses remain difficult to test.

The thorny corolla could have helped support the vertically stacked morphology of Yukonensis. In areas with soft substrate, archaeocyaths have been shown to adopt a mushroom-shaped cup that widens as it grows [19,44], where these wider cups would have increased stability. Since Y. yukonensis is interpreted as primarily inhabiting deep-water settings characterized by soft substrates, this morphology may have been developed for soft substrate settings [24], with sediment accumulating around the lowermost chambers, similar to the “snowshoe effect” seen in soft substrate-specialized brachiopods to prevent sinking [21,45,46]. This function would have favoured wider-angled thorny corolla morphologies for increased stability. Moreover, the sediment would become trapped within the cup of the corolla, and maybe between the T-ridges as well, thus increasing overall stability. As a result, the thorny corolla may have been a necessary adaptation to facilitate the unique stacked morphology of Y. yukonensis on soft substrate.