Rheology of marine sponges reveals anisotropic mechanics and tuned dynamics

2.1. Animal care and sample preparation

Sponges were procured from Gulf Specimen Marine Laboratories (Panacea, FL, USA) and acclimated slowly to a large, 1 m depth (electronic supplementary material, S4) laboratory saltwater aquarium (T = 20°C, salinity 36 g kg⁻¹). We chose individuals with open oscula and bright tissue for preparing samples, as these characteristics indicate good health. All sponges were used within a span of several weeks and any exposure to air was minimized. We used a kitchen sponge (Medium Duty, Scotch–Brite) to determine whether living sponge rheology was distinct from that of a synthetic porous material. For branching and erect species of sponge, tissue cuts parallel to their substrate attachment area were made with a razor blade, resulting in discs of thickness 2–4 mm with axial vectors ${\hat{n}}_1$ parallel to $\hat{y}$ and perpendicular to ambient flow v as depicted in figure 1k. We also made cuts perpendicular to the substrate, so that these discs’ axial vectors ${\hat{n}}_2$ were oriented along $\hat{x}$. In species where consistent samples could not be obtained in the above fashion due to tissue being too heterogeneous (Cliona celata), compressible (I. notabilis) or brittle (pith of Tethya sp.), a biopsy device was used to punch 12–14 mm diameter cylindrical cores which were then sliced into discs of thickness 2–4 mm. Discs from different cores were thus distinctly oriented at random with respect to ambient flow v, so we denote their axial vectors , and .

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Sponges can be difficult to identify to species, and our experimental animals were obtained from a commercial supply source. All species sampled here were demosponges, and species identifications are provided to the best of our ability in working with this supply resource. In this instance, photographs of the individuals used and their spicules are included, and are the most information we have about exact species identity. Ultimately, the magnitude and quality of the differences between individuals and species are the most salient part of the present work.

2.2. Rheology

We mounted discs of live sponge tissue between parallel plates (12 mm diameter) on a rheometer (MCR 502 WESP, Anton Paar GmbH). A small amount of cyanoacrylate adhesive (Gorilla Super Glue Gel 7700104) was applied to both sides of the sample to maintain contact between it and the rheometer plates during deformation. We initialized contact with the plates by exerting a uniaxial stress σ_N ∼ 10 kPa, and the sample was then immediately rewetted with 1 ml of artificial seawater (figure 2a). We did not observe the living tissue react or degrade with the glue application, and the resulting film formed could be peeled off intact after the experiments. Therefore, the use of this adhesive does not seem to have altered any internal properties of the sponge tissue.

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After relaxation of the loading stress, we applied sinusoidal shear strain

where γ₀ is the strain amplitude and ω is the angular frequency (speed) of oscillation (figure 2b). For small γ₀ such that stress outputs are proportional to strain inputs, the shear stress in the sample τ(t) is a single sinusoid shifted by an amount δ:where τ₀ is the shear stress amplitude. The dynamic storage and loss moduli, G′(ω) and G′′(ω), quantify elastically stored and viscously dissipated energy due to oscillatory shear and describe a sample’s viscoelastic response in the linear regime. We measured G′(ω), G′′(ω), and their ratio tan δ = G′′/G′ at 12 logarithmically spaced frequencies between 0.1π and 10π s⁻¹ at ${\gamma }_0=0.05\text{\%}$. Ambient, free-stream flow v (figure 1i) in marine intertidal and subtidal environments where sponges are common typically ranges from 0.1 to 100 cm s⁻¹ [8,9]. Since the maximum speed v_θ of a disc-shaped sample subject to torsion is $v_{\theta }^{\max }=\omega a$ [15], where a is the disc radius, we chose these frequencies ω as they correspond to environmentally relevant flow speeds between 0.2 and 20 cm s⁻¹.

We interpreted the linear viscoelasticity of sponge tissue as characterized by our frequency sweep data using rheological circuit models. We considered the classical Maxwell, Kelvin–Voigt and Zener models, as well as a model with a fractional-order derivative element known as a spring-pot [16]. This fractional calculus-based model was formulated to capture precisely and without overfitting, the power-law viscoelasticity commonly seen in biological materials [16]. Fits were performed with the Julia (v. 1.5.3) package RHEOS, developed for robust optimization of linear viscoelastic data [17].

After a frequency sweep, we subjected samples to steady uniaxial strain or large-amplitude oscillatory shear (LAOS). We conducted LAOS on a subset of species by increasing shear strain γ₀ in 12 logarithmic increments from 0.1 to 10% at ω = 4π s⁻¹. To check for any pre-conditioning effects, we repeated this LAOS protocol after ten minutes of rest. We were unable to probe above γ₀ = 10% in A. polycapella and C. celata and γ₀ = 20% in Callyspongia sp., since the glue typically separated from the rheometer plates prior to any visible sample failure. Sponges in nature are not regularly observed to deform in ambient flow, so we considered γ₀ = 20% a reasonable value to qualitatively capture strains that are not readily perceptible, and above which, strains are unlikely to be physiological.

Within the nonlinear viscoelastic regime probed by LAOS experiments, higher harmonics of the driving (fundamental) frequency are excited in a material’s mechanical response. In other words, the stress output in the sample τ(t) is no longer a single sinusoid shifted in time from the input strain γ(t) but can be represented as a Fourier series taken over odd integer harmonics n due to the odd symmetry of shearing:

where $G_n^{\mathrm{\prime }}(\omega ,{\gamma }_0)$ and $G_n^{\mathrm{\prime }\mathrm{\prime }}(\omega ,{\gamma }_0)$ are now a set of trigonometric Fourier coefficients. Material measures may also be extracted from parametric plots of τ(t) versus γ(t), or elastic Lissajous–Bowditch (L-B) curves [18]. For amplitudes γ₀ within the linear regime, L-B curves are ellipses and G′(ω) and G′′(ω) are proportional to the semi-major and semi-minor axes [19]. In the nonlinear regime, L-B curves become bent shapes whose axes are no longer constant with respect to γ(t). This distortion of L-B curves is a geometrical signal that the linear moduli G′(ω) and G′′(ω) are insufficient to describe a sample’s viscoelastic nonlinearities [18].

Here, we analyse the nonlinear τ(t) signal in sponges with the minimum strain $G_M^{\mathrm{\prime }}({\gamma }_0)$ and maximum strain $G_L^{\mathrm{\prime }}({\gamma }_0)$ elastic moduli because together they describe an L-B curve’s overall concavity and, moreover, are analytically related to $G_n^{\mathrm{\prime }}(\omega ,{\gamma }_0)$ (electronic supplementary material, equation (S5)) [18–20]. We compare $G_M^{\mathrm{\prime }}({\gamma }_0)$ and $G_L^{\mathrm{\prime }}({\gamma }_0)$ to each other at every γ₀ (using the intracycle stiffening index S [18]) and also consider each as a function of γ₀. We calculated these measures of elastic nonlinearity by fast Fourier transform methods on the time-resolved strain γ(t) and stress τ(t) signals at each amplitude as described in electronic supplementary material, §VB.

Finally, on distinct samples not already subjected to LAOS, we applied steady uniaxial strain:

where l is the deformed height of the sample controlled by changes in the rheometer gap, initially at height L. Compression or extension was applied in seven linearly spaced steps between 0% and ±12% (ε < 0 in compression and ε > 0 in extension). We calculated the uniaxial stress in a sample of radius a = 0.6 aswhere F_N is the rheometer reported normal force exerted on the top plate. We superposed an oscillatory shear of ${\gamma }_0=0.05\text{\%}$ and ω = π s⁻¹ to measure the shear storage modulus G′ as a function of uniaxial strain ε. Since ε was constant within a step, we waited until σ_N and G′ relaxed to apply the next 2% gap change, averaging the last four time points of both to compute values for each ε. We calculated uniaxial moduli for distinctly oriented samples ${\hat{n}}_1$ and ${\hat{n}}_2$ in each species as the slope of linear fits to plots of uniaxial stress versus uniaxial strain, and denoted them E₁ and E₂. Comparing these as well as G′ measured at ε = 0 for each orientation, ${(G_0^{\mathrm{\prime }})}_1$ and ${(G_0^{\mathrm{\prime }})}_2$, allowed us to make general statements about mechanical symmetries in living sponges.

2.3. Dissection microscopy

After rheology, samples were removed from the rheometer, put back into artificial seawater, and allowed to rest. We blotted each of excess water, determined its wet mass m_w, and in between four layers of paper towel applied firm pressure (σ_N ∼ 1 MPa), until water could no longer be drawn into fresh, layered paper towel. This method may not remove water bound tightly to protein, but provides an adequate estimate of the mass fraction of bulk water in the tissue ${\varphi }_w=(m_w-m_d)/m_w$, where m_d is the squeeze-dried mass of the disc.

To characterize sponge skeletal architecture, we submerged individuals of each species in deionized (DI) water, causing cells to osmotically burst, and agitated gently in several washes of additional DI water to remove remaining cellular debris. Some of the species left behind stiff, fibrous skeletons after washing, while others fully disintegrated in this treatment. Intact skeletons were dried in air before being sampled into discs of distinct orientations ${\hat{n}}_1$ and ${\hat{n}}_2$ as in §2.1. We imaged these with a USB microscope (Dino-Lite AM4113T) and a stereomicroscope (Nikon SMZ800). We used the ImageJ (v. 1.53e) plugin FibrilTool to check for structural anisotropy in the skeletons at this mesoscopic scale (0.001–10 cm). FibrilTool uses a local nematic order tensor as a measure of average fibre orientation, and thus quantifies fibrillar anisotropy within a region of interest (ROI) [21]. We drew three ROIs in each image to determine whether fibre orientation depended on its position within an image or overall tissue disc orientation.

To quantify spicule content in the sponges, we first made 5 mm diameter tissue cores with a biopsy device. Thin (approx. 2 mm) core slices were placed in individual wells of a 24-well culture plate with 1 ml of 6% bleach to dissolve all organic material including the protein skeleton while preserving any siliceous spicules (electronic supplementary material, figure S6). After dissolution of tissue, the supernatant was removed with care to leave settled spicules undisturbed. We then washed the spicules three times with 1 ml of DI water, allowing them to settle before removing the wash fluid and rinsing a final time with 95% ethanol. A few drops of well-mixed solution were drawn into clean, large-bore pipettes and held vertically for about 30 s to allow sedimentation. A single drop (approx. 0.05 ml) of this sedimented aliquot was then placed on a slide and examined by light microscopy. We used the multipoint tool in ImageJ to count all whole spicules in a field of view to estimate the number density of spicules in different species.

3.1. Mechanics

These eight species (figure 1) span six orders within the largest sponge class (Demospongiae) and display an array of growth forms [22,23]. In five of them, Aplysina fulva, Callyspongia sp., A. polycapella, T. keyensis and C. apion (figure 1a,d,e,f,h), we obtained samples perpendicular ${\hat{n}}_1$, and parallel ${\hat{n}}_2$, to the assumed substrate and ambient, free-stream flow v (figure 1i). Due to various features of their biology, the other three species (figure 1b,c,g) required a slightly different sampling strategy as follows. Cliona celata tissue was dense with embedded tracts of sand (electronic supplementary material, figure S4c), which resulted in randomly oriented samples , and so on. Igernella notabilis was comparatively homogeneous but soft and collapsible upon attempted slicing (electronic supplementary material, figure S4d), so we used any mechanically stable and geometrically suitable samples (figure 1c, inset) while making note of distinct orientations. Tethya sp. had a stiff cortex that overloaded the rheometer’s normal force transducer (F_N > 50 N), barring us from rheology on the outer part of this sponge (electronic supplementary material, figure S4a). Its pith was softer but brittle with long and flexible spicules, resulting in randomly oriented samples for Tethya sp.

Sampling geometries and uniaxial stress–strain curves in each species of sponge are shown in figure 3a–h. We took slopes within the linear regime of each as an effective, uniaxial modulus E = σ_N/ε (figure 3i). The uniaxial mechanics of A. polycapella, C. apion, T. keyensis and Tethya sp. were highly dependent on sample orientation. Their tissue more strongly resisted compression along the ${\hat{n}}_1$ than along the ${\hat{n}}_2$ direction. Cliona celata curves, on the other hand, were independent of sample orientation but highly nonlinear, sharply plateauing in σ_N at ε = −6%. The ratio of uniaxial moduli measured along each direction, E₁/E₂, confirms the former sponges were about three times stiffer along ${\hat{n}}_1$ compared with ${\hat{n}}_2$ (figure 3i). By contrast, this ratio for Callyspongia sp., A. fulva and I. notabilis was much closer to one (E₁/E₂ = 1.3), a result suggesting the tissue of these three sponges contains at least one mechanically isotropic plane. The E₁/E₂ ratio in C. celata was equal to one, and therefore we conclude that this species was the most isotropic of those tested.

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The shear storage modulus G′ (measured at ω = π s⁻¹ and γ₀ = 0.05%) as a function of uniaxial strain ε is shown in figure 4. It increased with compression in C. apion, C. celata, T. keyensis and Tethya sp. Instead, in A. polycapella, Callyspongia sp., A. fulva and I. notabilis, G′ stiffened modestly in compression, and only after initially softening. Reconstituted networks of collagen and fibrin have also been shown to compression soften, while whole tissues made of these biopolymers plus cells, compression stiffen [24]. We found sponge tissue with living cells does both depending on the species. This suggests that the presence of deformable but volume-conserving cells [25] is not the biggest contributor to compression stiffening in sponges.

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In figure 5, we compare sponge multiaxial mechanics with those of mammalian tissues. G′ as a function of compressive stress |σ_N| in brain [26], liver [27] and adipose [28] is approximately linear: $G^{\mathrm{\prime }}({\sigma }_N)=m|{\sigma }_N|+G_0^{\mathrm{\prime }}$ with slopes m ≤ 1 [29]. Sponges compression stiffen linearly as well, but with m > >1, and largest in C. celata (m = 60, zoomed inset). Cliona celata also displayed a sharp discontinuity at ε = −6%, where m goes to infinity and G′ increases to 9 MPa, more than four times its initial value at ε = 0%. By complete contrast, A. polycapella, Callyspongia sp., and the spicule-less sponges, change their G′ relatively little with |σ_N|, indicating low multiaxial responsivity.

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In figure 5b, we normalize the change in G′ by $G_0^{\mathrm{\prime }}$, and see that under the significantly smaller strains we applied (ε = −12% versus ε = −40% in brain [26], for example), sponges overall accessed a larger scaled range of G′ for every scaled increment of |σ_N| than did any of the mammalian tissues. The slope produced by this approximately linear scaling also gives an estimate of the persistence length (bending rigidity [30,31]) of the biopolymers underlying these living tissues. We found the mammalian tissues at a scaling of about one (dotted line), and the sponges varied from one through five (a value typically used in silico and found in semi-flexible biopolymer gels [31]; dashed-dotted line) and upwards. This indicates a comparatively large range of bending rigidities in the spongins that make up the tissue of these species, given that larger slopes translate to smaller bending rigidities [31]. Overall, most of the sponges had larger slopes than one, and therefore spiculated spongins are more flexible than mammalian collagens but locally quite stiff. Taken together, these results suggest that spiculated spongins may be semi-flexible polymers.

We compare E with $G_0^{\mathrm{\prime }}$ in the sponges and mammalian tissues in figure 5c. Material constants in sponges would be most accurately determined from constitutive models that include dissipation from both fluid flow within the pore space [32] and viscoelastic flow (§3.2) of the solid constituents of the spiculated spongins. Here, the diversity in the measured linear elastic constants E and $G_0^{\mathrm{\prime }}$ is sufficient for comparative biology among this set of sponges, and versus brain, liver and adipose tissue. Interestingly, E was larger than $G_0^{\mathrm{\prime }}$ in all of the mammalian tissues, while the opposite was true in most of the sponges (figure 5d). These data recapitulate that mammalian tissues are incompressible (like rubber, with Poisson’s ratio ν = 1/2 [27]), while the sponges approach what is expected for extremely compressible materials, ν = −1 [33]. Negative values of ν imply auxeticity, or the tendency to contract instead of bulge transversely when compressed, and ‘spongy’ materials like re-entrant polymer foams and many honeycomb structures are auxetic [34]. Through constraints associated with the stress and strain tensors of linear elastic orthotropic materials (electronic supplementary material, §IA), we found ν take on negative values in all of the sponges (electronic supplementary material, table S1), suggesting auxeticity is possible in Poriferan body tissue.

3.2. Linear viscoelasticity

The linear viscoelastic response of sponge tissue as a function of driving frequency ω is shown in figure 6. The storage modulus G′(ω) was an order of magnitude larger than the loss modulus G′′(ω) and spanned two orders of magnitude (10⁴–10⁶ Pa) in these sponge species. Sponges with spicules (squares) were an order of magnitude stiffer than those without (diamonds). G′(ω) followed a very weak power law in all specimens, including the synthetic cellulose sponge, but interestingly, G′′(ω) also followed a frequency power law for the synthetic sponge only, and was non-monotonic and disparate among living sponges (figure 6b).

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The ratio of dissipated to stored energy in the tissue when sheared, tan δ, highlights these disparities (figure 6c). In C. apion, C. celata, Tectitethya sp. and Tethya sp., tan δ decreases at low ω, followed by a slow increase in some, or a plateau in others. Axinella polycapella, Callyspongia sp. and I. notabilis behave similarly, but tan δ takes values roughly fourfold smaller (figure 6d). In other words, the first group of sponges dissipate four times as much energy when sheared compared to the second group, and many of the sponges had dissipation minima at specific frequencies (figure 6e).

None of the classical viscoelastic circuit models that we fit provided adequate descriptions of G′(ω) and G′′(ω) (electronic supplementary material, figure S8). We also fit a model including a fractional element that reproduces the power-law behaviour associated with a continuous distribution of relaxation times in biological materials [16]. This model reproduced the power-law storage behaviour and the non-monotonicity of dissipation in the live sponges with high accuracy.

3.3. Nonlinear viscoelasticity

For increasing amplitude of oscillatory shear strain γ₀ (LAOS), sponge tissue responded nonlinearly by softening as indicated by decrease of $G_M^{\mathrm{\prime }}({\gamma }_0)$ and $G_L^{\mathrm{\prime }}({\gamma }_0)$ (figure 7a–c), defined in §2.2. We let the onset of softening γ_a (dotted vertical lines) be where $G_M^{\mathrm{\prime }}$ first decreased more than 10% from its previous value. Cliona celata began softening at a smaller γ_a and also softened more than A. polycapella and Callyspongia sp. over the course of one LAOS test. By the final amplitude, $G_M^{\mathrm{\prime }}$ had decreased by roughly 90% in C. celata (electronic supplementary material, table S2).

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Intriguingly, A. polycapella and C. celata tissue had additional shear nonlinearities arise after pre-conditioning of the first LAOS test. During the second LAOS test, the large strain elastic modulus $G_L^{\mathrm{\prime }}({\gamma }_0)$ (grey upward triangles) in these two species increases after another strain γ_c (dashed-dotted vertical lines). This was most pronounced in C. celata (figure 7c), since G′_L(γ₀) decreases markedly yet eventually increases and returns to its exact value at the end of the first round. In other words, $G_L^{\mathrm{\prime }}({\gamma }_0)$ has an inflection point during the second LAOS in A. polycapella and C. celata. Callyspongia sp. does not, despite it being sheared to a twice larger γ₀ = 20%. We made γ_c be where the numerical derivative $K_L=\mathrm{\Delta }{G}_L^{\mathrm{\prime }}/\mathrm{\Delta }{\gamma }_0$ changed sign to confirm there was no inflection point in $G_L^{\mathrm{\prime }}({\gamma }_0)$ for Callyspongia sp. during the second round of LAOS (electronic supplementary material, table S3).

The time-resolved trajectory of the shear stress τ(t) (electronic supplementary material, figure S2(ii)) in response to oscillating shear strain γ(t) (electronic supplementary material, figure S2(i)) reveals further richness in the larger strain viscoelasticity of sponge tissue. τ(t) increases nonlinearly during a single cycle from γ = 0 to γ = ±γ₀ as indicated by concave-up parametric plots of τ(t) versus γ(t) (L-B curves; electronic supplementary material, figure S2(iv)). We evaluated this stiffening at each γ₀ with the index $S=(G_L^{\mathrm{\prime }}-G_M^{\mathrm{\prime }})/G_L^{\mathrm{\prime }}$ and made its onset γ_b be where S ≥ 0.1 [18]. S = 0 signifies no stiffening within a cycle and elliptical L-B curves with well-defined semi-major and semi-minor axes (L-B curve lower insets). The more positive is S, the greater $G_L^{\mathrm{\prime }}$ compared with $G_M^{\mathrm{\prime }}$, the more upwardly concave the L-B curve, and the greater the stiffening (L-B curve upper insets) at that γ₀. This stiffening nonlinearity occurs during a single oscillation from γ = 0 to γ = ±γ₀ for γ₀ > γ_b.

The onset of stiffening γ_b (dashed vertical lines) followed the same trend as γ_a. It was about ten times smaller in C. celata compared with A. polycapella and Callyspongia sp. (electronic supplementary material, table S2). In other words ${\gamma }_{a,b}^{\mathit{\text{Cliona}}}<{\gamma }_{a,b}^{\mathit{\text{Callyspongia}}}<{\gamma }_{a,b}^{\mathit{\text{Axinella}}}$ was true. S increased monotonically with increasing γ₀ in all species and by γ₀ = 10%. C. celata had the largest and Callyspongia sp. the smallest S (figure 7d). Cliona celata shear stiffened more (more positive S) and after smaller strains than A. polycapella and Callyspongia sp. when γ(t) is increased over the trajectory of a single cycle but also softens more (more negative K_L) and at smaller strains (electronic supplementary material, table S2).

Cliona celata was also distinct from A. polycapella and Callyspongia sp. by the sign of its induced normal stress and ratio of dissipation to storage as functions of γ₀ (figure 7e,f). Due to perpendicular expansion upon shearing, positive normal stress is induced in many materials [35]. Semi-flexible biopolymer networks instead pull downward when sheared, exhibiting negative normal stress [35]. Surprisingly, sponge tissue did both: A. polycapella and Callyspongia sp. pushed upward on the top plate with a positive normal stress of roughly 5 kPa while C. celata pulled downward with negative normal stress twice as large by γ₀ = 10%. Finally, tan δ increases with γ₀ in all three species initially, but C. celata reaches a clear maximum dissipation (figure 7f). Axinella polycapella and Callyspongia sp. begin the LAOS experiment about half as dissipative as C. celata, and after increasing initially, dissipation then only marginally decreases for A. polycapella and Callyspongia sp. over this physiological range of γ₀.

3.4. Morphological and skeletal characteristics

As described in §2.3, we imaged mesoscopic features in the washed fibrous skeletons of less dense sponges (figure 8). Aplysina fulva grows as rope-like branches that hang downward. It has no spicules but a relatively stiff spongin skeleton of irregular polygons with large mesh sizes of a few millimetres. We could not distinguish ${\hat{n}}_1$ from ${\hat{n}}_2$ in A. fulva samples at this scale. Igernella notabilis, the other sponge without spicules in our dataset, has a similar skeleton (electronic supplementary material, figure S5b) and a lobe-like, branching growth form. Callyspongia sp. has hollow tissue (figure 8h), making it ultimately vase-like, but when viewed on a smaller scale by stereomicroscope (electronic supplementary material, figure S5f,g) its tissue looks like that of A. fulva and I. notabilis.

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By contrast, A. polycapella is conspicuously solid and axially arranged. This sponge forms erect, tree-like structures (electronic supplementary material, figure S3), with one central column, or trunk. Figure 8e,f shows an ${\hat{n}}_1$ (${\hat{n}}_2$) disc of A. polycapella. The red lines signifying local nematic order and thus average fibre orientation show a condensed region of axial fibres, a trait well documented in erect sponges [36,37], as well as radial and tangential fibres. Tethya sp. and T. keyensis growth forms are radially symmetric but the nematic tensors drawn with FibrilTool also reveal three principal fibre directions as in A. polycapella (electronic supplementary material, figure S4a,b). Materials such as wood [38], bone [39] and brick [40] also have three principal directions and are thus orthotropic. A point within an orthotropic material has three mutually perpendicular planes of reflection symmetry [39] and material properties are different along each principal direction. This was most obvious in A. polycapella, whose tissue does bear a striking resemblance to a tree trunk (electronic supplementary material, figure S5d), but we also found structural and mechanical signatures of orthotropy in T. keyensis and Tethya sp.

In terms of the bulk density measured by the mass fraction of water ϕ_w in the tissue, C. apion, C. celata, T. keyensis and Tethya sp. were significantly denser (ϕ_w ≤ 0.5) than A. polycapella, Callyspongia sp., A. fulva and I. notabilis (ϕ_w ≥ 0.7) (figure 9a). Multiplying the mass fraction of solids ϕ_s = 1 − ϕ_w by the total density of the sponge tissue disc m_w/V gives an estimate of the concentration of spongins c. On a log–log plot of $G_0^{\mathrm{\prime }}$ versus c in mg ml⁻¹, we find an approximate scaling of $G_0^{\mathrm{\prime }}\sim c^{11/5}$ to fit the sponge data (figure 9b). This agrees with previous results for the dependence of the network shear modulus on semi-flexible polymer concentration [41], providing further evidence for general semi-flexibility of spiculated spongins.

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The major component of the spicule population in these species was monactine (electronic supplementary material, figure S7). Tethya sp. (electronic supplementary material, figure S7d) also contained spiky spherical spicules (spherasters) in its cortex only. We did not count these since they were much more numerous than the monactine strongyloxeas found in both the cortex and pith. Axinella polycapella oxeas (figure 8d), Callyspongia sp. oxeas (figure 8g) and C. celata tylostyles (electronic supplementary material, figure S7b) were similar in size and shape: monactine and about 100 μm long and 10 μm thick, though arranged differently with respect to the softer part of the tissue. The three fibre directions in A. polycapella are spicule-reinforced [42] while spicules in Callyspongia sp. are constrained entirely within the fibres of its spongin network [43]. Cliona celata spicules are arranged and oriented densely and randomly [22], along with a surprising amount of sand (figure S6f). We observed A. polycapella, C. apion, C. celata, T. keyensis and Tethya sp. tissues dissolve slowly and vigorously in bleach (electronic supplementary material, video S1) and produce strong light scattering in culture wells (electronic supplementary material, figure S6). These observations and our estimates of spicule number density (figure 9c,d) confirm heavier spiculation in these sponges compared with Callyspongia sp. and the two species without spicules.