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Extreme flow simulations reveal skeletal adaptations of deep-sea sponges

Abstract

Since its discovery1,2, the deep-sea glass sponge Euplectella aspergillum has attracted interest in its mechanical properties and beauty. Its skeletal system is composed of amorphous hydrated silica and is arranged in a highly regular and hierarchical cylindrical lattice that begets exceptional flexibility and resilience to damage3,4,5,6. Structural analyses dominate the literature, but hydrodynamic fields that surround and penetrate the sponge have remained largely unexplored. Here we address an unanswered question: whether, besides improving its mechanical properties, the skeletal motifs of E. aspergillum underlie the optimization of the flow physics within and beyond its body cavity. We use extreme flow simulations based on the ‘lattice Boltzmann’ method7, featuring over fifty billion grid points and spanning four spatial decades. These in silico experiments reproduce the hydrodynamic conditions on the deep-sea floor where E. aspergillum lives8,9,10. Our results indicate that the skeletal motifs reduce the overall hydrodynamic stress and support coherent internal recirculation patterns at low flow velocity. These patterns are arguably beneficial to the organism for selective filter feeding and sexual reproduction11,12. The present study reveals mechanisms of extraordinary adaptation to live in the abyss, paving the way towards further studies of this type at the intersection between fluid mechanics, organism biology and functional ecology.

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Fig. 1: Skeletal motifs of E. aspergillum and associated flow physics.
Fig. 2: Effect of manipulations of the morphology of E. aspergillum on the flow downstream.
Fig. 3: Effect of manipulations of the morphology of E. aspergillum on helicity, enstrophy and drag coefficient.
Fig. 4: Role of the ridges in flow speed, vorticity, Q-structures and residence time within the body cavity.

Data availability

STL files for all of the models, raw data for the plots, and scripts to reproduce the figures are available on GitHub at https://github.com/giacomofalcucci/Euplectella_HPC. Additional data that support the findings of this study are available from the corresponding author on request.

Code availability

All codes necessary to reproduce results in main paper are available on GitHub at https://github.com/giacomofalcucci/Euplectella_HPC.

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Acknowledgements

G.F. acknowledges CINECA computational grant ISCRA-B IsB17–SPONGES, no. HP10B9ZOKQ and, partially, the support of PRIN projects CUP E82F16003010006 (principal investigator, G.F. for the Tor Vergata Research Unit) and CUP E84I19001020006 (principal investigator, G. Bella). G.P. acknowledges the support of the Forrest Research Foundation, under a postdoctoral research fellowship. M.P. acknowledges the support of the National Science Foundation under grant no. CMMI 1901697. S.S. acknowledges financial support from the European Research Council under the Horizon 2020 Programme advanced grant agreement no. 739964 (‘COPMAT’). G.F. and S.S. acknowledge K. Bertoldi, M. C. Fernandes and J. C. Weaver (Harvard University) for introducing them to E. aspergillum and for early discussions on the subject. A. L. Facci (Tuscia University) is acknowledged for discussions on graphics realization. M. Bernaschi (IAC-CNR) is acknowledged for discussions on extreme computing. V. Villani is acknowledged for his support with Japanese language and culture. E. Kaxiras (Harvard University) is acknowledged for early discussions that proved fruitful for the development of the present code.

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Authors

Contributions

G.F. designed the research; G.F. and G.A. wrote the original lattice Boltzmann method code; G.A. extended the code for massively parallel computation, developed the GPU version for Marconi100, and helped collect and post-process the data; P.F. realized all of the models; V.K.K. ran the validation tests and helped in post-processing and data interpretation; G.F. created the figures; G.P. and M.P. led the biological framing of the results; G.F., M.P. and S.S. supervised the research and the interpretation of the results; G.F., G.P., M.P. and S.S. wrote the manuscript. All authors contributed to analysing the results of the simulations and revising the manuscript.

Corresponding author

Correspondence to Giacomo Falcucci.

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The authors declare no competing interests.

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Peer review information Nature thanks Carlo Massimo Casciola and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Detail of the grid resolution.

The grid resolution within the small fenestrae of E. aspergillum models is 5.33 lattice spacings.

Extended Data Fig. 2 Details of the flow field.

a, Tilted view of main text Fig. 1c, detailing the flow field downstream and within the body cavity of the complete model of E. aspergillum at Re = 2,000. Colour intensity indicates the helicity magnitude, and the streak lines are coloured according to the velocity magnitude. b, Stereo view of a.

Extended Data Fig. 3 Details of the vorticity field.

a, Visualization of the vorticity magnitude, complementing Extended Data Fig. 2a, such that colour intensity indicates the helicity magnitude, and the streak lines are coloured in green, based on the vorticity magnitude. b, Stereo view of a.

Extended Data Fig. 4 Morphological manipulations of the E. aspergillum model.

ai, Details of the nine variations of the hollow cylindrical lattice with helical ridges (P2), obtained by including random defects simulating wounds and scars. The nine morphological manipulations are identified as Mark01, Mark02, …, Mark09.

Extended Data Fig. 5 Details of the vorticity magnitude fields.

ae, Comparison between the vorticity magnitudes (colour scale) for the plain cylinder (S1, left panels) and for the hollow cylindrical lattice with helical ridges (P2, right panels) at statistical steady states, for all Re simulated in the present work. Panels ae show data for Re = 100, 500, 1,000, 1,500 and 2,000, respectively.

Extended Data Fig. 6 Details of the drag coefficient.

Zoomed-out view of main text Fig. 3c, with error bars identifying the range of predicted values of the drag coefficient CD due to random morphological manipulations. These variations lead to a modest decrease, from 2.5% to 3.5% in the drag coefficient with respect to the pristine model.

Extended Data Fig. 7 Views of the skeletal system of E. aspergillum.

The model is reconstructed according to ref. 3: left, side view; right, AA and BB cross-sections from the left panel, detailing the osculum and the body cavity, respectively.

Extended Data Fig. 8 Details of the E. aspergillum complete model.

a, Front (centre panel) and side (leftmost and rightmost) views of the complete model of E. aspergillum; b, stereo views of the complete model of E. aspergillum realized with the Anaglyph algorithm.

Extended Data Fig. 9 Lift coefficient CL.

Left, time trace at statistical steady state of the lift coefficient CL for the different models (see key at right) of E. aspergillum at Re = 2,000. The range of the oscillations in the porous models is two orders of magnitude less than that of the plain cylinder S1. Right, magnified view of boxed region.

Extended Data Table 1 Accuracy assessment
Extended Data Table 2 Main physical parameters at Re = 2,000
Extended Data Table 3 Details of resource allocation

Supplementary information

Supplementary Data

This zipped file contains the STL geometry of the complete E. aspergullum, as well as the STL files to realize models S2, P1 and P2. The simple cylinder model S1 is not provided.

Video 1 Comparison of the Vorticity Field generated by S1 and P2 models.

The Video shows the vorticity field generated by S1 (left) and P2 (right) models for Re=100, 500, 1,000, 1,500 and 2,000. The video highlights the formation of a nearly quiescent region downstream the porous model, as well as the vortical patterns within the body cavity.

Video 2 Comparison of the Vorticity Field for all models at Re=2,000

The video shows the vorticity field generated by S1 (top left), P1 (top right), S2 (bottom left) and P2 (bottom right) at Re=2,000. The two porous models are characterised by a nearly quiescent region extending several diameters downstream the structure.

Video 3 Detail pf the vorticity field generated by S1 and P2 at Re=2,000.

The video highlights the vorticity field downstream S1 (top) and P2 (bottom) models, as well as within the body cavity of P2.

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Falcucci, G., Amati, G., Fanelli, P. et al. Extreme flow simulations reveal skeletal adaptations of deep-sea sponges. Nature 595, 537–541 (2021). https://doi.org/10.1038/s41586-021-03658-1

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