Dermal Denticle Diversity in Sharks: Novel Patterns on the Interbranchial Skin

Synopsis Shark skin is covered in dermal denticles—tooth-like structures consisting of enameloid, dentine, and a central pulp cavity. Previous studies have demonstrated differences in denticle morphology both among species and across different body regions within a species, including one report of extreme morphological variation within a 1 cm distance on the skin covering the branchial pouches, a region termed “interbranchial skin.” We used gel-based profilometry, histology, and scanning electron microscopy to quantify differences in denticle morphology and surface topography of interbranchial skin denticles among 13 species of sharks to better understand the surface structure of this region. We show that (1) interbranchial skin denticles differ across shark species, and (2) denticles on the leading edge of the skin covering each gill pouch have different morphology and surface topography compared with denticles on the trailing edge. Across all species studied, there were significant differences in denticle length (P = 0.01) and width (P = 0.002), with shorter and wider leading edge denticles compared with trailing edge denticles. Surface skew was also higher in leading edge denticles (P = 0.009), though most values were still negative, indicating a surface texture more dominated by valleys than peaks. Overall, leading edge denticles were smoother-edged than trailing edge denticles in all of the species studied. These data suggest two hypotheses: (1) smoother-edged leading edge denticles protect the previous gill flap from abrasion during respiration, and (2) ridged denticle morphology at the trailing edge might alter water turbulence exiting branchial pouches after passing over the gills. Future studies will focus on determining the relationship between denticle morphology and water flow by visualizing fluid motion over interbranchial denticles during in vivo respiration.

Shark skin is covered in dermal denticlestooth-like structures consisting of enameloid, dentine, and a central pulp cavity. Previous studies have demonstrated differences in denticle morphology both among species and across different body regions within a species, including one report of extreme morphological variation within a 1 cm distance on the skin covering the branchial pouches, a region termed "interbranchial skin". We used gel-based profilometry, histology, and scanning electron microscopy to quantify differences in denticle morphology and surface topography of interbranchial skin denticles among 13 species of sharks to better understand the surface structure of this region. We show that 1) interbranchial skin denticles differ across shark species, and 2) denticles on the leading edge of the skin covering each gill pouch have different morphology and surface topography compared to denticles on the trailing edge. Across all species studied, there were significant differences in denticle length (P=0.01) and width (P=0.002), with shorter and wider leading edge denticles compared to trailing edge denticles. Surface skew was also higher in leading edge denticles (P=0.009), though most values were still negative, indicating more valleys than peaks. Overall, leading edge denticles were smoother-edged than trailing edge denticles in all of the species studied. These data suggest two hypotheses: 1) smoother-edged leading edge denticles protect the previous gill flap from abrasion during respiration, and 2) ridged denticle morphology at the trailing edge might alter water turbulence exiting branchial pouches after passing over the gills. Future studies will focus on determining the relationship between denticle morphology and water flow by visualizing fluid motion over interbranchial denticles during in vivo respiration.
Translated by Elsa Goerig, postdoctoral fellow -Harvard University

Introduction:
One of the most remarkable aspects of shark biology is the structure of their unique skin. The skin of sharks is covered in many thousands of dermal denticles, which are tooth-like structures comprised of enameloid and dentine outer layers and a central pulp cavity. Denticles have a characteristic form, which consists of a flattened crown and an elongated neck that extends to an expanded base embedded into the dermis. Though all shark denticles have a generally similar structure, there is considerable diversity in denticle shape, size, and density within and among shark species (Ankhelyi et al., 2018;Bigelow and Schroeder, 1941;Díez et al., 2015;Lang et al., 2011;Motta et al., 2012;Oeffner and Lauder, 2012;Raschi and Tabit, 1992;Reif, 1985a;Reif, 1985b).
Along with studies on the diversity of denticle morphology, there have been many proposed functions of dermal denticles, including abrasion reduction, protection from predators and ectoparasites, and use of denticles during feeding and mating (Pratt and Carrier, 2001;Raschi and Tabit, 1992;Southall and Sims, 2003;Tricas and Le Feuvre, 1985;Whitenack and Motta, 2010). One function that has been an important focus for research is the role of denticles in support of locomotion, as many extant shark species have denticles with morphologies that improve swimming performance. Fluid dynamic studies have revealed that denticles can improve swimming performance by enhancing thrust, reducing hydrodynamic drag, as well as changing the boundary layer characteristics of water flow over the body (DuClos et al., 2018;Lang et al., 2012; Lauder et al., 2016;Oeffner and Lauder, 2012). Hydrodynamic studies using foils covered in real pieces of shark skin or 3D-printed shark skin models have offered an additional understanding of how denticles may function in flow (Domel et al., 2018;Lauder et al., 2016;Oeffner and Lauder, 2012;Wen et al., 2014;Wen et al., 2015).
However, denticles are morphologically diverse and there is still uncertainty as to how changes in denticle morphology may affect function and performance. In part, this lack of knowledge remains due to the challenging nature of both understanding patterns of the three dimensional morphology of shark surfaces and experimentally examining flows over denticle surfacesboth body deformation during swimming coupled with the need for a very small field of view to observe flow over small patches of denticles makes visualizing natural flows difficult.
Although connecting denticle diversity with in vivo flows in sharks is challenging, a recently published image of denticles on a segment of skin between gill slits (the "interbranchial" or "branchial" skin) provides hope in that regard. In that report, a single image taken from the interbranchial skin of a smooth dogfish (Mustelus canis; Ankhelyi et al., 2018) shows a dramatic gradient in denticle shape. Specifically, rounded, smoothedged denticles were found along the leading edge of the branchial skin, and more triangular denticles with surface ridges were found along the trailing edge, all over a distance of just a few millimeters. Interestingly, the diversity observed in only a few millimeters at the interbranchial skin seems to replicate the diversity of denticle forms that have been observed around the entire body in other species. For example, in species like the smooth dogfish and thresher shark, denticles from the leading edge of the tail and fins tend to be flattened, more rounded, and have reduced ridges compared to the denticles on the trailing edges, which are triangular with multiple ridges (Ankhelyi et al., 2018;Popp et al., 2020;Reif, 1985b). If denticle diversity is similar on the interbranchial skin of other individuals and species, the interbranchial region may be an interesting target for simultaneously imaging surface flows above denticles of different morphology. Moreover, substantiating the discovery of denticle diversity at the interbranchial region in sharks would add to our growing knowledge about comparative patterns of denticle diversity across shark bodies and species. Unfortunately, current data on the interbranchial skin is very limited -several studies describe the general morphology of internal denticles within the mouth cavity and on gill rakers (Nelson, 1970;Paig-Tran and Summers, 2014), but just the single aforementioned study (Ankhelyi et al., 2018) shows data for the interbranchial skin, and just from a single image of one species.
Flow over the interbranchial skin would likely be dominated by respiratory flows.
During respiration, high volumes of water are taken in through the mouth and are expelled through the gill slits while the interbranchial skin located between adjacent gill slits undergoes considerable deformation as a result of the regular expansion and compression of the branchial chambers by constrictor muscles (Liem and Summers, 1999). Flow exiting the gills then passes over denticles located on the interbranchial region between gill slits. The pumping of water across the gills is a common behavior for most sharks and is called active ventilation. This is contrasted with ram ventilation, where a shark swims forward with enough speed to pass flow through the mouth and across the gills (Graham et al., 1990;Wegner et al., 2012). Some shark species are obligate ram ventilators, but most are active ventilators, especially at zero or low swimming speeds (Barker et al., 2011;Ferry-Graham, 1999;Roberts, 1975;Tomita et al., 2018;Wegner et al., 2012). Because even stationary sharks experience regular respiratory flows, the interbranchial skin may be a tractable system for studying fluid flow in live sharks due to the relative ease of visualizing boundary layer and near-skin flows when the shark is not swimming. Future studies may then find it possible to experimentally measure flow in the interbranchial skin region and correlate patterns with denticle morphology, particularly in sedentary, benthic species.
Therefore, there are two main goals of this study. First, we imaged and quantified surface topography of interbranchial skin denticles across 13 different shark species to determine if the gradient in denticle morphology observed previously occurs in a diversity of shark species. These shark species also exhibit a range of ecologies (e.g., benthic, demersal, pelagic, suspension-feeding), respiratory modes (e.g., active and ram ventilation), and locomotor modes (e.g., sedentary and active; Barker et al., 2011;Dolce and Wilga, 2013;Graham et al., 1990;Roberts, 1975;Thomson and Simanek, 1977;Tomita et al., 2018;Wegner et al., 2012). In doing so, we describe denticle morphology and provide quantitative measurements of surface topography from branchial skin denticles from multiple species at multiple locations around the gills and body. Second, we investigated potential differences in denticle morphology and surface topography between the leading edge and trailing edge denticles on the interbranchial skin in an effort to elucidate morphological patterns across species and the possible functional roles for differences in denticle morphology on interbranchial skin. Perhaps differences in surface topography (rough versus smooth surfaces) between the leading and trailing edges may influence fluid dynamic drag. Since the branchial region experiences routine oscillatory flow (Ferry- Graham, 1999), any change in denticle morphology and surface characteristics could suggest functional differences between leading and trailing edge locations and generate testable ideas for future experimental work.

Study animals
Data for this study were obtained from fish caught from fishing surveys ( frozen), and one white shark (Carcharodon carcharias, stored in 70% ethanol, MCZ Ichthyology #171013). Unless otherwise noted, all individuals were subadults or adults.
We also categorized the general habitat and ecology of our sampled species to see if there are ecologically-related patterns in interbranchial skin denticle morphology.
We defined four broad categories: benthic, demersal, pelagic and suspension.
Additionally, since the current study is focusing on the interbranchial skin where respiration occurs, we also wanted to consider each group's ventilatory behavior along the axis from active suction ventilation to ram ventilation (see Dolce and Wilga, 2013 Suspension feeders are large-bodied, slow-swimming sharks (basking shark) and are likely ram ventilators. We placed suspension feeders in their own category due to their modified gill anatomy as a result of their feeding strategy, which entails swimming slowly and passing a large amount of water over the gills (Paig-Tran and Summers, 2014).

Surface profilometry
Our goal was to explore differences in denticle morphology and surface texture on the interbranchial skin and surrounding body skin among shark species and assess the extent to which denticles on interbranchial skin vary in morphology. To meet this goal, we collected data from five general regions near the gill openings: the interbranchial skin between gill openings (either between gill openings 2-3 or 3-4) including leading edge (LE) and trailing edge regions (TE), the region anterior to the first gill opening (AG), the region posterior to the last gill opening (PG), and the body (B) region on the lateral side of the body ventral to the first dorsal fin (Figure 1). We sampled 13 species across a diversity of shark clades (see Study animals) but in some cases were unable to sample all five selected regions on an individual due to incomplete specimens (see Supplemental Table 1 for details). Samples used for surface profilometry were obtained either by removing sections of skin approximately 4 cm x 4 cm in size or by collecting data with the skin in situ on the specimen. We used gel-based profilometry to image these five regions in order to collect data on denticle morphology and surface texture.
Gel-based profilometry involves pressing a deformable clear elastomer gel with a painted bottom surface onto a region of interest (GelSight Incorporated, Waltham, MA).
The painted-side of the gel conforms to the surface and then photographs are taken at six different illumination angles. Images are then processed with GelSight software into 3D, topographic surfaces. Following previous methodology (Ankhelyi et al., 2018;Popp et al. 2020;Wainwright et al. 2019;, surface metrology variables were quantified and three-dimensional (3D) skin surface topography was described.
After we acquired the topographic images, 3D-surfaces were processed using MountainsMap (v. 7 Digital Surf, Besançon, France). Within each image, three spatially separate 800 m 2 areas were cropped and analyzed, providing nested measurements for each topographic image (see Statistical Analyses below). Large-scale background curvature was removed from the surfaces, and we measured several metrology variables on each cropped image, including root-mean-square roughness (Sq), skew (Ssk), and kurtosis (Sku). We also quantified denticle morphology by measuring average length, average width, and aspect ratio (length/width) of five denticles for each of the five regions ( Figure 1) using ImageJ (NIH, Bethesda, MD). Ridge spacing and height were not measured in these samples as data for many of the species analyzed in the current paper have had denticle ridge spacing and height previously documented (see Ankhelyi et al., 2018;Domel et al., 2018;Popp et al., 2020).
The surface metrology variables we used are standard parameters to report when describing surfaces and we describe them briefly here (see also ISO 25178-2). in denticle morphology across the interbranchial region, so we focused our histological analysis on this one species, although we would expect similar histological results in other shark species since interbranchial denticles exhibit all major features of body skin surface denticles.

Statistical Analyses
Nested ANOVAs with individual as a nested random effect were used to determine if the five regions studied show differences in denticle length, aspect ratio (length/width), or root-mean-square roughness in either smooth dogfish (n = 3 individuals) or porbeagle (n = 3 individuals) specimens. In addition, we pooled LE and TE data across all species and used nested ANOVAs with species and individual as nested random effects to determine if LE and TE measurements are different across the 13 species of sharks.
We also pooled LE and TE data into groups according to our ecological categories (benthic, demersal, pelagic, and suspension-feeding) and again used nested ANOVAs with individual and species as nested random effects to determine whether ecological groups have any effect on denticle morphology between the LE and TE. For all comparisons, where applicable, post-hoc tests were used to determine differences between groups. All analyses were conducted using the statistical software R (ver. 4.0.1, "See Things Now"; R Foundation for Statistical Computing, Vienna, Austria).
Test values were considered significant at P < 0.05.

Results:
First, we present general morphological data on denticles from the interbranchial and surrounding regions in the leopard shark. These data will demonstrate the variation in denticle surface topography within an individual at the five regions sampled in this study. The leopard shark was chosen because the specimen is small enough to allow the entire interbranchial skin surface to be imaged in one Figure (Figure 2A). We then begin each sub-section with results from one individual species before broadening the analysis to include data from multiple shark species.

Morphology and surface characteristics of denticles around the gills
Surface images from the five regions of interest in a leopard shark are shown in Figure   2 with their corresponding height maps and surface profiles shown in Figure 3. These images illustrate differences in denticle shape, size, and surface topography between the leading (LE) and trailing edges (TE) of the interbranchial skin surface as well as differences in other skin regions (AG = anterior to gill slit 1, PG = posterior to gill slit 5, and B = body ( Figures 2B-F). A gradient in denticle morphology is clearly seen across the entire surface of the branchial gill skin (Figure 2A). Variation in denticle surface ornamentation, size, and shape are evident across all regions ( Figures 2B-F, Figure 3).
Qualitatively, leopard shark LE denticles are smooth-edged and spatulate, and lack any type of ridge ( Figure 2B, Figure 3B). In contrast, TE denticles are more triangular, with multiple ridges ( Figure 2C, Figure 3C).
To better understand how denticle morphology varies across our five sampled regions, we compared measurements of morphology across regions in two representative species: the porbeagle shark and smooth dogfish (Figure 4). In particular, we compared measurements of denticle length, denticle aspect ratio (length/width), and surface roughness (Figure 4). We did not observe any significant differences in denticle length among all five regions on porbeagle sharks (nested ANOVA: F(4, 58) = 0.8972, P = 0.47); however, we found differences in denticle length among different regions in smooth dogfish (nested ANOVA: F(4, 68) = 115.50, P < 0.0001). In particular, we found that in smooth dogfish the B region (ventral to the dorsal fin, Figure 1) had the longest denticles, followed by the AG region. Next in length were PG denticles, grouped together with the region at the TE of the interbranchial skin, and then the denticles at the LE of the interbranchial skin as the shortest in length (all indicated pairwise comparisons, P < 0.05).
Higher values of denticle aspect ratio indicate more elongate denticles, and we found significant differences among regions for both the porbeagle (nested ANOVA: F(4, 58) = 3.17, P = 0.02) and smooth dogfish (nested ANOVA: F(4, 68) = 111.52, P < 0.0001). The patterns in denticle aspect ratio were different in each species and the differences among regions were much weaker in the porbeagle ( Figure 4); in the porbeagle shark, B region denticles had a lower aspect ratio (stouter in shape) than the PG and TE regions (pairwise comparisons, P < 0.05), with AG and interbranchial skin LE regions intermediate and indistinguishable from all groups (pairwise comparisons, P > 0.05). In the smooth dogfish, B region denticles had the highest aspect ratio (are more elongate in shape) than the other four regions. The high aspect ratio of B region denticles is followed by the AG region, followed by a group containing both PG and interbranchial skin TE regions, and finally the interbranchial skin LE region with the lowest aspect ratio values (indicated pairwise differences P < 0.05).

Measurements of roughness for porbeagle and smooth dogfish surfaces also
showed different patterns for the two species (Figure 4). There were differences among regions for the porbeagle samples (nested ANOVA: F(4, 32) = 24.58, P < 0.0001) with the interbranchial skin LE region having a higher denticle surface roughness compared to the other four regions (indicated pairwise comparisons P < 0.05). There were also differences among regions for the smooth dogfish samples (nested ANOVA: F(4, 38) = 11.32, P < 0.0001), but in this species the B region had a higher roughness compared to the other four regions (indicated pairwise comparisons P < 0.05).
General differences in denticle morphology and surface topography are also observed among shark species examined and across all skin regions. Roughness values range from 3.0 m at the PG region in the mako shark to 35.7 m at the B region in the sand tiger (  1). All skew values in the sand tiger shark are positive, meaning that these denticles have more peaks than valleys. Sand tiger shark denticles are also the largest in size ranging from 306 m (LE length) to 522 m (B width), compared to the short-fin mako with the smallest denticles ranging from 131 m (TE width) to 147 m (TE length; Table   1).

Differences in leading and trailing edge denticle morphology among species
The histological structure of interbranchial skin denticles was also investigated with the aim of comparing their anatomy to previously published descriptions of denticles from other body regions, and to establish the relationship of interbranchial denticles to underlying muscle and cartilage. Similar to dermal denticles found on the body, the interbranchial skin denticles also have a crown, neck and base embedded in the epithelium ( Figure 5). The smooth-edged LE denticles can be distinguished from the trailing edge denticles based on the curvature at the crown ( Figure 5A and B). The interbranchial skin denticles also contain a pulp cavity ( Figure 5C and D). Histological sections of the interbranchial region demonstrate a thick layer of collagen fibers underlain by bundles of striated muscle and branchial cartilage ( Figure 5C and D).
Morphological differences between LE and TE denticle crown surfaces and profiles in the chain catshark are demonstrated using individual denticles ( Figure 6).
The profile of the LE denticle exhibits fewer surface features than the TE denticle ( Figure 6C and F). The LE denticle has a small ridge in the center ( Figure 6A-C), while the TE denticle has three ridges ( Figure 6D-F). Further, the distal crown margin of the TE denticle has three posteriorly-directed tines (i.e. prongs or sharp points), whereas the LE edge denticle is smooth-edged ( Figure 6). A dramatic gradient in denticle morphology and surface topography of interbranchial skin is visualized in chain catsharks using scanning electron microscopy ( Figure 7A). Even over a short distance of 10 denticles or less, denticle shape changes from smooth-surfaced with rounded trailing edges to elongate with prominent posterior tines and surface ridges (Figure 7).
The LE denticles ( Figure 7B) on the interbranchial skin in the chain catshark are rounder and have less prominent ridges compared to the TE denticles ( Figure 7C). This transition in denticle morphology occurs even between adjacent denticles ( Figure 7E).
We also observed the presence of denticles erupting through the epidermis on interbranchial skin ( Figure 7D).
The LE and TE denticles on the interbranchial skin differ qualitatively in morphology among all species of sharks studied (Figure 8). For example, in most species ( Figure 8A, B, D and F), LE denticles are rounder with few to no ridges. By pooling data across individuals and species for the LE and TE regions, we quantitatively investigated how denticle morphology and skin texture differed between these two regions ( Figure 9). We found significant differences in denticle morphology between LE and TE interbranchial skin regions, with the LE region having shorter denticles (denticle length nested ANOVA: F(1, 170) = 6.60, P = 0.0111), wider denticles (denticle width nested ANOVA: F(1, 170) = 9.39, P = 0.0025), and denticles with a lower aspect ratio (nested ANOVA: F(1, 170) = 48.97, P < 0.0001) compared to the TE region ( Figure 9, Table 1).
We also found significant differences in surface texture between the LE and TE interbranchial skin regions, with the LE having higher skew values (more peaks and other positive surface features) compared to the TE (nested ANOVA: F(1, 94) = 7.08, P = 0.0092; Figure 9, Table 1). The patterns for roughness and kurtosis approached significance but were not significant at the 0.05 level (nested ANOVA for roughness: F(1, 94) = 3.77, P = 0.0551; nested ANOVA for kurtosis: F(1, 94) = 3.88, P = 0.0519).
The general pattern for these two variables was that LE surfaces tended to have a higher roughness and lower kurtosis (less extreme values) compared to the interbranchial skin TE surfaces.
When grouping LE and TE data by ecological categories (e.g., benthic LE vs. benthic TE vs. demersal LE, etc.), there were statistical differences in denticle morphology and surface texture between the LE and TE regions in different ecologies (nested ANOVA for denticle length: F(7, 164) = 11.98, P < 0.001; Figure 9). Pairwise post-hoc comparisons show that demersal and benthic species have shorter LE denticles compared to TE, whereas pelagic species have longer LE denticles than TE denticles. Suspension feeders have LE and TE denticles of similar lengths. Pelagic species also have LE denticles that are wider than their TE denticles, while all other ecological groupings have LE that are similar in width to the TE denticles (nested ANOVA for denticle width: F(7, 164) = 6.64, P < 0.0001). Aspect ratio in all groups except for suspension feeders is lower in LE denticles than TE (LE denticles are less elongate in the anteroposterior direction); suspension feeders have aspect ratios similar between LE and TE denticles (nested ANOVA for aspect ratio: F(7, 164) = 12.14, P < 0.0001). Roughness and skew values showed similar trends with demersal and benthic species having equal LE and TE denticle values, pelagic LE denticles having higher values compared to TE, and LE denticles having lower values than the TE denticles in suspension feeders (nested ANOVA for roughness: F(7, 88) = 13.13, P < 0.0001 and nested ANOVA for skew: F(7, 88) = 7,89, P < 0.0001). Kurtosis values also differed among the ecological groups (nested ANOVA for kurtosis: F(7, 88) = 10.00, P < 0.0001), with pelagic species having lower kurtosis at the LE, suspension-feeders having higher kurtosis at the LE, and benthic and demersal species having indistinguishable kurtosis at LE versus TE regions.
Denticles were also observed on the medial surface of the interbranchial skin ( Figure 10). In all species of sharks studied, denticles were present on the outer edges of the medial gill flap surface. Though morphological and surface metrology measurements were not collected, these denticles resemble the LE denticles on the lateral surface of the interbranchial skin as they are smooth-edged and lack ridges on the crowns ( Figure 10B-F).

Discussion:
This is the first comparative study of denticle morphology and surface topography on the interbranchial skin in a wide diversity of shark species. We show that the interbranchial skin region exhibits a considerable transition in denticle shape and ornamentation over just a short distance, and that denticle variation in this one small region is the equivalent of that seen around the body as a whole (Ankhelyi et al., 2018;Reif, 1985b). Our statistical results show that when leading and trailing edge (LE and TE) sites are pooled across species, we see significant differences in denticle length, width, aspect ratio, and surface skew, along with results that are approaching significance in surface roughness and kurtosis. In particular, LE denticles tend to be shorter in length, broader in width, less elongate, and have higher skew (tend to have more peaks on their surface) compared to TE denticles from the interbranchial skin region. An additional novel result from the current study was the discovery of smoothedged and ridge-less denticles on the inner (medial) surface of interbranchial skin patches ( Figure 10).

Morphological diversity of denticles on the interbranchial skin in shark species
While the diversity of shark denticles on the body is well-described in the literature (e.g., Ankhelyi et al., 2018;Bigelow and Schroeder, 1941;Díez et al., 2015;Lang et al., 2011;Motta et al., 2012;Oeffner and Lauder, 2012;Raschi and Tabit, 1992;Reif, 1985b), as researchers continue to explore shark skin surfaces, some surprising features of denticle diversity have emerged. Denticle morphology has been shown to differ across shark bodies, with quantifiable and repeated differences in denticle form between LE and TE locations on the body and fins of multiple species (Ankhelyi et al., 2018;Motta et al., 2012;Popp et al., 2020;Raschi and Tabit, 1992;Reif, 1985b). Additionally, the recent addition of three-dimensional imaging methods (e.g., gel-based profilometry, micro computed-tomography) has provided a richer understanding of quantitative denticle morphology and surface diversity across species and body locations (Ankhelyi et al., 2018;Domel et al., 2018;Popp et al., 2020;. New discoveries continue to be made about shark denticle diversity and form; recently, Tomita et al. (2020) described denticles on the eye surface of whale sharks, and presumably these denticles function in abrasion resistance and protection of the eye.
Additionally, a single previous image demonstrated a surprising transition in denticle shape on the interbranchial skin of one shark (smooth dogfish, Mustelus canis; Ankhelyi et al., 2018). In this image, changes in denticle crown shape that normally occur across distinct body regions were observed within only a few millimetersan observation that inspired this study.
When comparing LE and TE interbranchial skin denticles, all species display a morphological transition from denticles with a spatulate shape, rounded distal margins, and either reduced or no ridges, to more elongate, ridged denticles with posterior tines.
In some species, such as the chain catshark (Figure 7), this transition is particularly dramatic and denticles within a few hundred microns can display substantially different morphology. When data were pooled between LE and TE sites across species, LE denticles have shorter and broader crown lengths and higher skew values compared to TE denticles from the interbranchial skin region. Although we find significant trends when pooling data from all species, in many cases these variables show mixed trends when looking across individual species (Figure 4, Figure 9)we discuss these different trends with respect to general ecological categories below.
Pooling LE and TE data separately into ecological groups provides a more refined perspective on how ecology and ventilation mode may affect denticle morphology at the interbranchial region ( Figure 9). We show that across ecologies, denticle shape (aspect ratio) shows consistent differences between LE and TE sites, with nearly all groups showing stouter, less-elongate denticles at the LE compared to TE. However, patterns of denticle size (length and width) are different among ecologies; for example, ram-ventilating pelagic sharks have larger LE denticles compared to TE denticles, whereas the opposite is true in active-ventilating benthic and demersal sharks. The larger LE denticles of the pelagic group may also contribute to the significantly higher roughness values at the LE versus the TE in this ecological group, whereas benthic and demersal ecologies have no significant differences in LE versus TE roughness. These differences combined with different patterns across ecologies in skew and kurtosis demonstrate that although denticle shape shows a consistent pattern between LE and TE sites across ecological groups, measurements of denticle size and surface form indicate that the ram-ventilating pelagic sharks have different patterns in LE vs TE morphology compared to active-ventilating ecological groups. These patterns strongly suggest that ventilatory ecology plays a role in shaping the morphology and function of denticles on the interbrachial skin, but that denticle shape may function in a way that is consistent across ecology or ventilatory mode.
Our single suspension-feeding species (basking shark) also shows different trends among TE and LE morphology compared to other ecological groups, and this species is notably different from pelagic sharks, despite inhabiting the same general environment. These differences in results suggest that filter-feeding, as well as the slow swimming speed of these species influences the morphology and possible function of interbranchial denticles compared to other ram ventilators (e.g., thresher and white shark; Cheer et al., 2001).
Previous studies that have measured shark skin using GelSight reported largely negative skew values, indicating that these surface textures are more dominated by valleys or pits than peak-like surface features (Ankhelyi et al., 2018;Popp et al., 2020).
Interestingly, interbranchial skin denticles from the basking shark and sand tiger have positive skew values (ranging from 0.19 to 1.6: Table 1), suggesting that these surfaces are dominated by positive surface features (i.e., peaks or features above the mean height). Other surfaces with similar positive skew values are the skin surfaces of bony fishes .

Comparing leading and trailing edge denticles beyond the interbranchial region
Previous studies (Ankhelyi et al., 2018;Motta et al., 2012;Popp et al., 2020;Reif, 1985b) have noticed that there are often repeated patterns in denticle morphology and surface texture when comparing leading and trailing edge sites on the body of sharks (nose vs tail) or on individual fins (leading vs trailing edges). Here we discuss how these patterns compare to the trends seen here on the interbranchial skin.
When our LE and TE data are separately pooled across all species, LE denticles tend to have higher roughness values compared to TE denticles ( Figure 9 and  Ankhelyi et al., 2018;Popp et al., 2020). In addition, most leading edge sites in other species have much larger denticles compared to their relevant trailing edges (Ankhelyi et al., 2018;Popp et al., 2020) we see this pattern repeated in a subset of our species here, specifically those species with a pelagic ecology. We also note that leading edge sites both on interbranchial skin and across other body regions tend to have denticles with reduced surface ridges and more rounded posterior edges (Ankhelyi et al., 2018;Popp et al., 2020).
These repeated patterns across the body, fins, and at the interbranchial skin suggest that both leading and trailing edges may share similar functional pressures across different body parts and species. Perhaps free-stream flow over the body and fins and flow passing over interbranchial skin imposes similar hydrodynamic constraints on denticle shape and surface texture. In addition, it has been postulated that the unique shape of the leading edge denticles on shark fins and tails could also provide protection to reduce damage at leading edge sites (Ankhelyi et al., 2018;Popp et al., 2020).

Functional significance of interbranchial skin denticles
The consistent differences observed between leading and trailing edge interbranchial skin denticles on a diversity of shark species suggests two non-mutually-exclusive hypotheses for how these interbranchial skin denticles might function. First, the smoothedged crowns and lack of ridges on leading edge interbranchial skin denticles may act to reduce friction from contact with the preceding gill flap. During respiration, motion of the gill flaps results in contact between neighboring interbranchial regions, particularly when gill slits are closed when buccal expansion moves water through the mouth and into the buccal cavity. In benthic sharks such as the chain catshark, active respiratory pumping involves not just a buccal pump, but also activity in muscles located within the interbranchial skin ( Figure 6) to constrict the gill pouches and force water posteriorly out of the gill slits during the branchial expansive phase of respiration (Brainerd and Ferry- Graham, 2006;Ferry-Graham, 1999). This active motion results in repeated contact of the posterior interbranchial margin with anterior denticles on the downstream interbranchial-skin segment. Reduction of ridges and the presence of smooth posterior margins on these leading edge interbranchial skin denticles could reduce friction and damage to gill flaps in the region where physical contact occurs with regularity during ram ventilation. At interbranchial regions such as TE (Figure 1), where no physical contact occurs during respiration, denticles have a more classic shape with prominent ridges and posteriorly directed pointed tines (e.g., Figure 8).
A second hypothesis about why denticles transition in morphology at the interbranchial skin region focuses on the possibility that the transition in denticle shapes on the interbranchial surface serves to reduce fluid dynamic drag resulting from respiration. Respiratory flows in species with either pulsatile or ram ventilation (Roberts, 1975;Wegner et al., 2012), likely result in interbranchial skin denticles being subjected to complex flow patterns over their surface that necessarily create drag. Drag forces could be reduced by altering flow close to the surface both near and within the boundary layer. For example, the transition from smooth to ridged denticles as flow exits the gill slits could help maintain a laminar flow condition and reduce friction. Alternatively, the transition could create turbulence to instead prevent flow separation (Smits, 2000), reducing drag forces on the posterior margins of the gill flaps which can undergo significant movement during respiration. Hydrodynamic drag has been suggested to decrease with the presence of ridges on manufactured riblets (Bechert et al., 2000;Bechert and Hage, 2007). Although water flow patterns near the interbranchial skin have yet to be studied experimentally, the rapid transition in denticle shape suggests that this area may be a fruitful location to investigate the relationship between flow and denticle shape.
To date, analyses of the relationship between denticle shape and water flow patterns in sharks have necessarily been inferential, as it has not been possible to study water movement over shark denticles in vivo in freely-swimming sharks at the resolution demonstrating the potential hydrodynamic function of dermal denticles, provide the foundation to further investigate the relationship between denticle morphology and water flow. To test hypotheses concerning the hydrodynamic effects of denticle diversity, the interbranchial gill skin of benthic sharks, like the chain catshark, may prove to be a valuable experimental model. Benthic sharks are active ventilators and will pump water over their gills when they are not swimming. This behavior combined with their sendentary nature may provide conditions where in vivo ventilatory flows in benthic sharks can be imaged and measured, even over the small (2-4 mm) segments of the interbranchial skin. Our results also show that benthic sharks, such as the chain catshark (Figure 7), exhibit dramatic gradients in denticle shape on interbranchial skin that are similar to patterns in other species, making benthic sharks potentially representative as a model in this context.
Visualization of respiratory flows exiting gill slits in laboratory experiments could help to better understand how denticle shape affects water flow patterns. For example, if the flow at the leading edge of an interbranchial segment is different than the flow at the trailing edge, this provides some support for our hypothesis that the change in denticle shape between these regions may be due to hydrodynamic effects. We can make predictions, such asdenticles that experience more complex turbulent flows may have increased surface ornamentation (ridges and posterior tines), which we can then test by correlating aspects of surface flow with the patterns in denticle diversity we have shown in this manuscript. Furthermore, advances in additive manufacturing may make it possible to use our morphological data to create models of denticles with different morphology that can then be systematically tested in different flow conditions, either physically or through computational means. These types of studies may be able to more directly connect denticle diversity and drag reduction in different flows. We hope our demonstration of denticle diversity at the interbranchial region of sharks inspires future work on the relationships between form and function in shark skin denticles.  Table 1. Comparative data on denticle surface morphology across the body from multiple shark species. Numbers in parentheses indicate sample size.