Over the past century, many marine organisms have served as a source for the design of bioinspired robots and other structures. For example, designs of grasping devices have been inspired by octopus arms and suckers (Laschi et al., 2009; Margheri et al., 2012; Xie et al., 2020), digging mechanisms by clams (Winter and Hosoi, 2011), and swimming robotic systems have been produced based on principles of tuna locomotion (Zhu et al., 2019; White et al., 2021). Sharks have been a particularly important group stimulating the manufacture of biomimetic materials, specifically due to the unique structures on their skin: dermal scales or denticles. Shark denticles are tooth-like structures, cover the surface of all shark species, and vary in their shape, size, and surface characteristics including the presence/absence of ridges, ridge height, and ridge spacing (Rief, 1985; Castro, 2011; Motta et al., 2012; Ankhelyi et al., 2018; Popp et al., 2020; Gabler-Smith et al., 2021). Although dermal denticles likely have various functions (e.g., abrasion reduction, parasite deterrence, protection from predators), the ability of these microscopic structures to reduce drag and enhance thrust during aquatic locomotion has been of considerable interest in the biomimetic and bioinspiration community for years (Bechert et al., 1985; García-Mayoral and Jiménez, 2011; Wen et al., 2014; Domel et al., 2018a; Suprapaneni et al., 2022). If inspiration from the design of shark skin can be applied to fabricated and engineered materials, then application of such bioinspired materials to the hulls of both surface and underwater vehicles could assist in reducing the energetic cost of moving through water.

But how well do current engineered or fabricated materials match the characteristics of shark skin? Fabric designed for competition swimsuits has achieved some notoriety by increasing the speed of swimmers (Takagi and Sanders, 2000; Hutchinson, 2008; Oeffner and Lauder, 2012), and shark skin-inspired engineered riblet surfaces have been applied to wind turbines (Chamorro et al., 2013; Sareen et al., 2014; Leitl et al., 2020), and tested for drag reduction properties (Bechert et al., 2000; Zhao et al., 2012; Ibrahim et al., 2018). Do these current applications, generally inspired by shark skin, possess quantitatively accurate three-dimensional (3D) surface characteristics that match shark skin? Previous efforts to compare engineered surfaces to shark skin have been largely qualitative, and such comparisons have been limited due to the lack of information on the 3D profiles of shark skin denticle surfaces (see Wainwright et al., 2017; Ankhelyi et al., 2018). Scanning electron microscopy (SEM) is the technique most often used for imaging shark skin, but SEM images do not generally provide information on height variation across the denticle surface and on the shape and distribution of the longitudinal ridges that characterize denticle crown surfaces. Recently, 3D profilometry techniques have been applied to image the surface of biological materials (Wainwright et al., 2017; Wainwright and Lauder, 2018; Wainwright et al., 2019), allowing the measurement of shark denticle ridge heights, as well as profiles of ridges across the shark skin surface. Therefore, the goals of this paper are: (1) to determine if there is a difference in denticle surface microstructure between two locations within individual sharks: the midbody and tail regions; (2) to assess the extent to which cross-sectional profiles of denticle surfaces differ among sharks with differing ecological habitats; and (3) to quantitatively compare how surface ornamentation and microstructure of engineered riblets and competition swimsuit materials compare to biological denticles.

All surfaces imaged in this study had ridges present ( Figure 2 ), with the exception of the angelshark ( Table S1 ), which has skin with individual thorn-like denticles lacking ridges. All other shark species had denticles with well-defined, regularly spaced, ridges on their crown surfaces ( Figures 2A, B ). Profiles across the denticle surface show distinct ridges varying in height from 2.9 to 25.7 µm and ridge spacing between adjacent peaks from 29.6 to 151.7 µm among the sharks sampled. Competition swimsuit fabrics ( Figures 2C, D ) displayed much more irregular surface profiles with less distinct ridge peaks that ranged in height from 3.7 to 87.6 µm. Profiles across individual fabric surface elements projecting from the surface (the closest equivalent to denticle ridges) did not show distinct riblet patterns, but the magnitude of surface variation approached that of shark denticles ( Figure 2D ). 3D-printed shark denticles (Domel et al., 2018b) revealed a shark-like ridge pattern but with many fewer ridges that are much larger in height than those of sharks ( Figure 2E ).

Some measured variables differed between the midbody and midcaudal locations within individual sharks. Mean denticle crown width was larger at the midbody location (mean 374.7 ± 49.8 µm) compared to tail surfaces (mean 322.6 ± 43.6 µm, Table S1 , Paired t-test: p = 0.009). Mean denticle crown aspect ratio was smaller at the midbody location (mean 1.3 ± 0.1) compared to the midcaudal (mean 1.5 ± 0.1, Table S1 , Paired t-test: p < 0.001), suggesting that midbody denticles are squatter and squarer compared to those on the tail, which are more triangular. Due to some statistical differences between the two locations, both values were used in subsequent analyses.

Denticle features also differed when shark species were grouped according to habitat category (e.g., benthic, demersal, pelagic; Figures 3A ; Figure S1 , Table S1 ). Denticle crown width was higher in benthic species (mean 371.1 ± 33.0 µm, ANOVA: p = 0.01) compared to pelagic (mean 212.7 ±17.5 µm, Bonferroni: p = 0.009) but not demersal species (mean 331.6 ± 63.9 µm, Bonferroni: p = 1.0, demersal-pelagic p = 0.4). Crown length was also higher in benthic species (mean 548.2 ± 51.7 µm, ANOVA: p = 0.002) compared to pelagic (mean 252.9 ± 22.2 µm, Bonferroni: p = 0.001) but not demersal species (mean 383.9 ± 78.7 µm, Bonferroni: p = 0.8, demersal-pelagic p = 0.4). Crown aspect ratio was also higher in benthic species (mean 1.5 ± 0.1, ANOVA: p = 0.003) compared to demersal (mean 1.1 ± 0.1, Bonferroni: p = 0.03) and pelagic species (mean 1.2 ± 0.1, Figure 3A , Bonferroni: p = 0.01). There was no difference in crown aspect ratio between demersal and pelagic species (Bonferroni: p = 1.0).

There were also considerable differences in the surface characteristics among the three classes of materials imaged. Crown aspect ratio differed among the materials (Kruskal-Wallis: p = 0.007): the engineered material (mean 1.1 ± 0.1) had a lower mean aspect ratio compared to the biological shark skin (mean 1.4 ± 0.04 Bonferroni: p = 0.04), while shark skin and swimsuit values (mean 1.0 ± 0.03, Bonferroni: p = 0.1) and engineered and swimsuit values were similar ( Figure 3B ; Table 1 , Bonferroni: p = 1.0). Mean engineered material ridge height (mean 987.0 ± 738.0 µm) was higher than the other materials ( Figure 3C ; Table 1 , Kruskal-Wallis: p < 0.001, engineered-swimsuit Bonferroni: p < 0.001, engineered-biological Bonferroni: p < 0.001), while swimsuit (mean 21.4 ± 16.6 µm) and shark skin (mean 8.9 ± 0.8 µm) were similar (Bonferroni: p =1.0). Ridge spacing also differed (Kruskal-Wallis: p < 0.001): biological shark skin (mean 73.2 ± 5.4 µm) and swimsuit materials (mean 271.0 ± 234.0 µm) were similar (Bonferroni: p = 0.3), while engineered material ridge spacing (mean 1031.0 ± 473.0 µm) was higher than the other materials ( Figure 3D ; Table 1 , engineered-biological Bonferroni: p < 0.001, engineered-swimsuit Bonferroni: p = 0.003). Ridge aspect ratio was higher in engineered materials (mean 0.6 ± 0.1) compared to the other materials ( Figure 3E ; Table 1 , Kruskal-Wallis: p < 0.001, engineered-biological Bonferroni: p < 0.001, engineered-swimsuit Bonferroni: p = 0.007). Ridge bumpiness was similar between the biological shark skin (mean 0.03 ± 0.003) and swimsuit material (mean 0.07 ± 0.04, Kruskal-Wallis: p < 0.001, Bonferroni: p = 1.0); however, engineered material (mean 0.4 ± 0.1) had higher ridge bumpiness compared to both the shark skin and swimsuits ( Figure 3E ; Table 1 , engineered-biological Bonferroni: p < 0.001, engineered-swimsuit Bonferroni: p = 0.008).

Overall, biomimetic shark skin materials did not closely replicate the surface ornamentation of actual shark skin. Measured three-dimensional (3D) surfaces of engineered riblets differed from shark skin in the height, pattern, and spacing of the ridged surfaces ( Figure 2 ). Most competition swimsuit fabrics more closely matched shark skin surface metrics across the variables measured ( Figure 3 ) but did not possess the distinct parallel longitudinal ridges that are characteristic of shark skin denticles ( Figures 2A, B ). The many challenges involved in quantifying the complex surface geometry of shark skin and the common use of two-dimensional imaging approaches such as scanning electron microscopy have limited the data available to engineers and swimsuit manufacturers needed to match the 3D surface structure of shark skin.

Surface profilometry techniques have been applied to many biological surfaces, enabling 3D data collection of surface metrics on shark skin (Wainwright et al., 2017; Baeckens et al., 2019; Wainwright et al., 2019; Popp et al., 2020). One advantage of gel-based 3D surface profilometry is that no coating needs to be applied to the surface, the technique is non-destructive, and even reflective or damp surfaces can be imaged with accuracy approaching 1.0 um (Wainwright et al., 2017). However, even with 3D data from shark skin, current manufacturing technology faces challenges in producing engineered surfaces that replicate the intricate details of shark skin surfaces at relevant size scales. Additive manufacturing (3D printing) at resolutions that match the size scale of shark denticles is extremely challenging with current technology, as is the ability to manufacture sufficiently large surface areas with appropriately patterned biologically-sized denticles for testing and application to underwater systems. Due to the overhanging conformation of denticle crowns (Reif, 1985; Motta et al., 2012; Ankhelyi et al., 2018), even molding the shark skin surface does not fully replicate 3D skin surface characteristics.

Riblet structures are well known to reduce drag by altering skin friction at the fluid-surface interface (Bechert and Hage, 2007; Dean and Bhushan, 2010; García-Mayoral and Jiménez, 2011; Raayai-Ardakani and McKinley, 2017; Raayai-Ardakani and McKinley, 2019; Suprapaneni et al., 2022). But to date, both computational and experimental estimates of forces on riblet samples have been conducted on rigid elements, and not on surfaces undergoing rhythmic movement as occurs when the skin surface of sharks oscillates during undulatory locomotion (Lauder et al., 2016). Flow over moving skin surfaces can differ considerably from rigidly mounted surfaces, and engineered surfaces would likely experience improved performance if their surface riblet characteristics more closely matched to those of shark skin.

We noted differences in denticle surface characteristics among the three habitat types that we assigned to each of the 17 shark species studied, suggesting that denticle surface characteristics may be related, at least in part, to mean swimming speeds of sharks ( Figures 3A ; S1 ). Some benthic shark species (e.g., chain catshark, Scyliorhinus retifer) spend considerable time sedentary on the ocean floor with limited open water locomotion (see Compagno, 2001). Other open ocean pelagic sharks such as the white shark (Carcharodon carcharias), which undertake long migrations, are nearly constantly in motion and the skin surface is thus subjected to continuous water flow where drag reduction and reduced energetic costs may be at a premium (Compagno, 2001). Domel et al. (2018b) compared mako shark, white shark, and leopard shark skin surfaces and showed differences in overall surface texture patterning and ridge spacing: mako and white sharks have smaller denticles with small-scale surface ridge patterning compared to leopard sharks. In the current study, we also documented that denticle crown aspect ratios are larger in benthic sharks than in demersal or pelagic species, and pelagic species also tend to have smaller denticle surface ridges which are more tightly packed across the skin surface ( Supplemental Tables 1 , 2 ; Figure S1 ). The functional effect of differences among denticle surface textures that correspond to different shark habitat types is still unknown, and new research is needed to specifically address how different shark surface textures affect drag and lift forces on the skin surface.

Although shark skin surfaces have been shown to increase swimming performance, by both reducing drag and enhancing thrust (Oeffner and Lauder, 2012; Lauder et al., 2016), there are few data published on hydrodynamic flow patterns over shark skin. Du Clos et al. (2018) studied flow patterns over mako shark skin in fixed samples, but flow dynamics over shark skin surfaces moving in a biomimetic undulatory manner remains largely unknown (Anderson et al., 2001). Future experiments measuring flow over shark skin with different surface textures (e.g., Figures 3A , S1 ), especially under dynamic conditions, will be a key next step in understanding the effect of shark skin-inspired designs on aquatic propulsion.

The original contributions presented in the study are included in the article/ Supplementary Material . Further inquiries can be directed to the corresponding author.

All work followed institutional ethical guidelines, and valid scientific collecting permits were used to obtain shark tissues.

MG-S and GL conceptualized the project idea. MG-S collected and analyzed the data. MG-S and GL both contributed to the writing of the manuscript. All authors agree to be held accountable for the content herein and approve the final version of the manuscript.

This work was funded by an NSF PRFB1907211 grant to MG-S, and NSF IOS-2128033 to GL.

We would like to thank Diego Bernal at the University of Massachusetts Dartmouth for supplying some of the shark skin tissue and Andrew Williston at the Harvard Museum of Comparative Zoology for help with tissue accession from the ichthyology collection. We would also like to acknowledge Dylan Wainwright, Madeleine Ankhelyi, and Meghan Popp for prior collaborative research that generated some of the GelSight images used for analyses in this paper.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.