Anti-icing properties of polar bear fur

Abstract

The polar bear (Ursus maritimus) is the only Arctic land mammal that dives into water to hunt. Despite thermal insulation provided by blubber and fur layers and low Arctic temperatures, their fur is typically observed to be free of ice. This study investigates the anti-icing properties of polar bear fur. Here, we show that polar bear fur exhibits low ice adhesion strengths comparable to fluorocarbon-coated fibers, with the low ice adhesion a consequence of the fur sebum (hair grease). Lipid analyses reveal the presence of cholesterol, diacylglycerols, anteisomethyl-branched fatty acids, and the unexpected absence of squalene. Quantum chemical calculations predict low ice adsorption energies for identified lipids and high adsorption for squalene, suggesting that sebum composition is responsible for the observed anti-icing properties. Our work enhances understanding of polar bears and their interactions with their environment and builds on Inuit knowledge of natural anti-icing materials.

Polar bears are able to minimize ice accumulation thanks to their hair oil.

INTRODUCTION

The polar bear (Ursus maritimus) has become a global icon for climate change in large part due to its interaction with its diminishing sea ice habitat. As a marine mammal living in one of the coldest climates in the world, polar bears dive and swim in regions where air temperatures can drop below −40°C. Key to polar bear survival under such conditions is the thermal insulation provided by blubber and fur layers. Such is the quality of the thermal insulation provided by these layers that the surface of polar bear fur is typically close to that of the air temperature (1–3). However, despite their semiaquatic lifestyle and the cold climate of their habitat, polar bear fur is typically observed to be clean and free of ice accumulation, suggesting that the fur may have anti-icing characteristics (4, 5). While there have been many studies of the thermal, structural and even optical properties of polar bear fur (1–3, 6–8), as well as several studies of specific contaminants (e.g., mercury, organohalogens, and crude oil) and hormones present in polar bear hairs (9–12), a study of the anti-icing properties of polar bear fur has not yet been reported. A systematic scientific study of the anti-icing properties of polar bear fur will not only enable a better understanding of how this iconic animal interacts with its surroundings, but it will cement and build upon the existing indigenous knowledge relating to polar bear fur that has developed through generations of native Arctic peoples. Moreover, the identification of key physical and chemical characteristics of polar bear hair that enable anti-icing properties promises to inspire the development of more sustainable and environmentally friendly anti-icing materials and surfaces to address the major challenge of icing in global industrial infrastructure.

Nature has inspired advances in material performance across a wide range of technologies from lotus leaf–inspired hydrophobic surfaces to protein-based water filtration membranes (13, 14). Recently, polar bear fur has inspired the development of thermally insulating textiles based on aerogels that can outperform conventional down jackets. While the emergence of biomimetic thermally insulating materials based on polar bear fur is a relatively recent enterprise, indigenous knowledge of the thermally insulating properties of polar bear fur has existed for generations. Unlike the thermal properties of polar bear fur, studies of anti-icing properties have not previously been reported. The absence of such studies in the literature opens up the possibility for the emergence of bioinspired anti-icing surfaces based on a newfound understanding of the interactions of polar bear fur with ice. Recent advances in bioinspired anti-icing materials based on anti-icing proteins and penguin feathers provide further motivation (6, 15, 16). For example, the anti-icing behavior of penguin feathers has been attributed to the intricate hierarchical structure of the feather, which has guided the development of structured synthetic anti-icing surfaces (16–18). A variety of other synthetic materials have also been explored for anti-icing applications to date including superhydrophobic surfaces, slippery liquid–infused porous surfaces (SLIPS) (15, 19, 20), low-interfacial toughness materials (21), dynamic anti-icing materials (22), and functionalized graphene coatings (23, 24). In this work, we show the important role of the fur sebum (hair grease) in the anti-icing properties of polar bear fur, which generates further avenues to develop bioinspired environmentally friendly synthetic anti-icing materials based on components of polar bear fur sebum. Moreover, a clearer picture of the anti-icing properties of polar bear fur provides a fresh perspective on Arctic ecology. For example, polar bear fur has long been used for a wide range of applications by native Arctic peoples, and the specificity of its use in a given application has not always been clear. The low adhesion of ice to polar bear fur reported in this work provides more context for the use of polar bear fur by natives of the Arctic region and allows us to consider indigenous knowledge and indeed the behavior of the polar bear itself through a new lens.

Several aspects of polar bear behavior indicate the utility of anti-icing characteristics. Firstly, polar bears are known to slide on snow and ice (Fig. 1A). An early account of this behavior is given by the Inuk hunter and artist Jakob Danielsen (1888 to 1938). He writes: The (polar bear) mother plays a lot with her young. We see in the mountains that they have made slides on the snow slopes down which they go on their tail all in the same track (25) (p. 317).

Fig. 1. Properties of polar bear fur used in the wild.

(A) Polar bear sliding down a snow slope at Sallyhamna, Spitsbergen Island, Svalbard, Norway. (B) Infrared image showing the temperature of the polar bear fur and the surrounding snow taken with an FLIR E75 24o (FLIR Systems OÜ, Estonia) Svalbard Archipelago, Norway. (C) Adult female polar bear shakes water from her fur after climbing out of the water onto sea ice. Olgastretet, Barents Sea, Svalbard Archipelago, Norway. (D) An adult male polar bear cleans his fur by rolling and rubbing against snow-covered sea ice. Arctic Ocean, near 81° N, north of Svalbard Archipelago, Norway. Image credits: (A) P. Souders, Getty Images; (B) J. Aars, Norsk Polarinstitutt; and (C) and (D) J. E. Ross, LifeOnThinIce.org.

Secondly, the polar bear is the only Arctic land mammal that deliberately dives into water as part of its hunting strategy to cool down in warmer weather and to clean debris from fur (4). As mentioned above, polar bears are so well insulated that the temperature of the dry fur closely matches that of the surroundings, meaning that ice could accumulate quickly (26). Thermal imaging (Fig. 1B) illustrates this point, where the fur exhibits little contrast with the surroundings. Observations in the field indicate that after emerging from water, polar bears first shed water by shaking (Fig. 1C) before rolling in snow (Fig. 1D). Rolling in snow may help freeze any remaining water, which can then be shed from the fur as ice (5, 27). In addition, Stirling (4) has also noted that polar bears will slide on their abdomens on ice while “still hunting” where minimal friction between fur and ice would help to prevent alerting nearby seals. One early report of Indigenous knowledge also points to the possible anti-icing properties of polar bear fur. Ethnologist Erik Holtved (1899 to 1981) described how snow and ice can easily be brushed off trousers made from polar bear fur (nanut) (28) (based on notes from stays with the Inughuit, the northernmost Inuit people, from 1935 to 1937 and 1946 to 1947). Moreover, Inughuit hunting stools used on sea ice have also been shod with polar bear fur, mimicking the strategy of polar bears lying on ice when still hunting as highlighted above (28). The indigenous knowledge and bear behavior described here indicate that polar bear fur is likely to exhibit anti-icing properties.

In this work, we report a systematic study of the anti-icing properties of polar bear fur. Specifically, we establish that polar bear fur exhibits low ice adhesion strengths that are similar to fluorocarbon-coated mohair pads. These pads are used as ski skins in backcountry skiing and cross-country skiing where low-ice adhesion is critical to performance. Furthermore, we found that the polar bear fur sebum is key to achieving the observed low ice adhesion strength, marking the anti-icing properties of polar bear fur as distinct from cold-climate penguin feathers whose anti-icing properties are derived from the feather structure rather than the preen oil coating (16–18). To better understand the role of sebum composition in anti-icing properties, we have analyzed the lipid distribution in the sebum, in so doing completing the first major study on polar bear sebum composition. Sebum is produced by sebaceous glands near the root of the hair. While human sebum is well studied (29, 30), less is known about the seba of other mammals. A recent report has found that sebum composition has only been characterized for 29 living mammal species (31). For these mammals, the sebum serves a variety of purposes, including the repulsion of water and pathogens (32, 33). It also plays an important role in thermoregulation as issues with sebum secretion or contamination alter the thermal properties of fur leaving mammals at risk of heat stroke and hypothermia (34, 35). Sebum has not yet, to the best of our knowledge, been investigated for its role in anti-icing properties. In our study, we identify the distribution of lipids present in polar bear sebum harvested from hair of wild polar bears. We then use quantum chemical calculations to predict adsorption energies for prominent components of the sebum guiding us to key components that support low ice adhesion. Notably, squalene, a compound present in seba of other mammals living in aquatic environments as well as in humans, is absent from polar bear sebum. We confirm here that washed polar bear hair, human hair, and squalene-coated substrates all exhibit high ice adhesion values in marked contrast to sebum-coated polar bear fur.

Our results improve our understanding of polar bears and their interactions with their environment while providing important context to indigenous knowledge of natural anti-icing materials present in the Arctic region. Furthermore, information about the composition of polar bear sebum presented here will help to guide the development of bioinspired anti-icing materials supporting divestment from environmentally harmful fluorocarbons.

RESULTS

Anti-icing properties

The anti-icing properties of polar bear fur were characterized by measurements of ice adhesion strength, hydrophobicity, and freezing delay times. The ice adhesion strength is a measure of how well ice sticks to fur. Adhesion strengths below a threshold of 100 kPa are indicative of a substrate that can be considered icephobic; however, lower adhesion strength is generally required for ice to be shaken off under its own weight (36, 37). At lower ice adhesion values of 30 kPa, ice may be passively removed by wind (38). Evaluation of hydrophobicity was achieved through measurements of water contact angle on individual hair fibers and indicates how well liquid water sticks to hairs. A hydrophobic hair surface would allow liquid water to be shed before freezing can take place. Freezing delay time is a measure of the time required for a droplet of water to freeze on a hair at a specific temperature. While not as crucial as a low ice adhesion to preventing ice accumulation, a longer freezing delay time can reduce ice accumulation by allowing liquid water to be shed before freezing ensues (37, 39).

The anti-icing properties of polar bear fur were compared to two types of fluorocarbon-treated ski skins sourced from Colltex AG and human hair samples. Ski skins are hairy fabrics, in our case mohair, attached to a substrate that is stuck onto skis using an adhesive. The hairs are oriented so as to allow the skis to easily slide forward on snow but provide increased friction in the opposite direction to support travel uphill and are used in Nordic skiing. The ski skins used here are fluorocarbon treated, but Colltex has since discontinued fluorocarbon coatings for environmental reasons. Fluorocarbon coatings enhance the ski skin performance, so these particular ski skins were selected to represent the state of the art in synthetic fibrous anti-icing materials. Measurements of ice adhesion on human hairs were also conducted as human hair sebum is rich in squalene like many mammals that are native to damp or aquatic environments, including the sea otter, beaver, and sea lion (40–42). Given the similar aquatic lifestyle of the polar bear, we might expect squalene to be present in the polar bear sebum. Human hair also has structural similarities to polar bear hair (fig. S5), making it a good candidate for comparison. To determine the importance of the polar bear sebum in imparting anti-icing properties, samples of polar bear fur were washed with 20% SDS solution to remove the sebum. Such a surfactant solution is known to be effective at dissolving lipid membranes, and most commercially available shampoos typically contain 5 to 25% SDS (43, 44). Comparison of anti-icing properties of washed and unwashed fur, thus gives us a means to determine the importance of sebum in producing the observed anti-icing properties.

Ice adhesion strength was measured using the maximum shear force required to remove a block of ice of known contact area from a surface, and this force was then divided by the contact area to obtain ice adhesion strength (Fig. 2B). The ice adhesion of unwashed polar bear fur was found to be similar to race-level ski skins and an average of about 40 kPa lower than standard ski skins. At 50 kPa, it falls well below the often accepted threshold for icephobicity of 100 kPa (36, 37) although not quite at the levels required for passive ice removal by wind (30 kPa) (38). Ultralow ice adhesion values below 20 kPa are typically reported for planar surfaces rather than fibrous materials like polar bear fur (19, 45).

Fig. 2. The main anti-icing results and testing setups.

(A) Ice adhesion measurements of unwashed (PB) and washed (WPB) polar bear fur compared with unwashed (HH) and washed (WHH) human hair and racing (RSS) and non-racing (NRSS) ski skins. (B) A 2 cm–by–2 cm–by–2 cm block of ice in a mold on the polar bear fur sample before removal of this ice to characterize ice adhesion strength. (C) Water contact angle measurements for individual PB, WPB, HH, WHH, and fluorocarbon-treated RSS and NRSS samples. (D) An example of a water droplet on an unwashed polar bear hair. Error bars in (A) and (C) represent the SD of measurements for each sample type. Raw measurements are shown as gray diamonds on the plots.

Next, the effect of polar bear hair sebum (hair oil) on ice adhesion was investigated. Washed (sebum-free) fur was observed to have a much higher ice adhesion than unwashed fur, with the ice adhesion strength of washed fur at least 100 kPa greater than unwashed fur. Furthermore, in all tests, it was very difficult to displace ice from washed fur once it had formed. As a result, the maximum force applied was used to make a conservative estimate of the ice adhesion pressure, but the actual ice adhesion likely exceeds this value as the ice was not fully dislodged. The adhesive strength of the ice on washed polar bear fur was generally greater than either the shear strength of the ice or the adhesive strength of the clamp used to mount the fur. Similarly, the human hair investigated in this study displayed a strong adhesion to ice, comparable to that of the washed polar bear fur. Both the unwashed and washed human hair displayed a high ice adhesion of more than 150 kPa on average. Our results suggest that components of polar bear sebum ascribe an anti-icing advantage over human sebum.

To better understand the role of wetting on polar bear fur, hydrophobicity was investigated through water-contact angle measurements on individual hairs where an increased contact angle indicates a more hydrophobic surface. For this purpose, we designed a custom-built microscope capable of reaching 50× magnification (fig. S15), which uses functionalized micropipettes (46) to deliver suitably sized water droplets with diameters in the range of 50 to 150 μm to individual hairs (Fig. 2D). The ski skin fibers had slightly greater static water contact angle than polar bear hairs. However, this is not overly notable as the contact angle hysteresis measurement (fig. S6) displayed similarity in their advancing and receding contact angles. The static contact angles can vary in value with the advancing and receding contact angles acting as a maximum and minimum, respectively, so the small difference in contact angle between these samples is not notable. The washed and unwashed polar bear hairs exhibited similar water-contact angle values as did human hair samples. The similarity in the water contact angles aligns with the similarity in the root mean square (RMS) roughness of all the hair samples studied, shown in the Supplementary Materials, which makes sense given that water contact angle depends on roughness (47, 48).

Delayed ice formation or freezing delay is another important characteristic of anti-icing surfaces. By increasing the time for ice nucleation on a surface, water may be shed before freezing occurs. Hydrophobic surfaces in particular would benefit from longer freezing delay times allowing them to shed water before freezing. We measured the onset of freezing on individual hairs and observed a large spread of freezing times. The median freezing delay time was in the range of 70 to 120 s, but freezing times of more than 600 s were observed for some unwashed human and polar bear hair. Particulate matter on unwashed hairs can account for this variation as particles on otherwise smooth surfaces can provide a point of ice nucleation (49) with particles in Arctic air and water thought to be especially important for Arctic ice nucleation (50–52). More detail on freezing delay measurements can be found in the Supplementary Materials.

Our measurements of anti-icing properties of polar bear fur highlight the crucial role of the sebum. In the presence of sebum, the ice adhesion is comparable to fluorinated ski skins, but after the sebum is removed, the ice adhesion strength increases almost fourfold. The low ice adhesion imparted by the sebum appears to be critical to passive shedding of ice on polar bear fur as neither the hydrophobicity nor freezing delay time differed greatly between the polar bear, human, and ski skin samples. Given the important role of the sebum in the provision of anti-icing properties, we next explored the composition of the sebum to aid in the identification of anti-icing components that might enable the development of anti-icing coatings.

Sebum analysis

To determine the molecular composition of polar bear sebum, we obtained fur samples from six wild polar bears and adopted a two-phase extraction protocol to collect lipids and other hydrophobic molecules from polar bear hair. Three different methods were used to analyze the lipid isolates—gas chromatography–mass spectrometry (GC-MS) (53), liquid chromatography tandem MS (LC-MS/MS), and nuclear magnetic resonance (NMR) (54, 55). GC-MS involves separating unesterified core fatty acyls (for example, fatty acids, fatty alcohols, and hydrocarbons), sterols and prenols by GC, and detection by MS. GC-MS provides molecular details on branching and unsaturation positions on fatty acids, and when combined with fractionation of total extracts (for example, by solid phase extraction), GC-MS can provide information on the fatty acid composition of lipid classes. The second method, LC-MS/MS, involves separating molecular species by LC before detection by MS. This approach can analyze complex intact lipids. Our LC-MS/MS setup matches exact molecular masses to a lipid species database and reconstructs each fraction’s molecular nature in a manner consistent with the detected signals (54). The advantage of this approach is that, for each major group of glycerolipids, waxes, and other lipid species, we are provided with a semiquantitative profile of each compound’s fatty acid moieties. Last, in support of both techniques, NMR provides an at-a-glance overview of the mixture of molecules present in the samples and can also provide quantitative information for the various components of the sebum.

GC-MS, LC-MS/MS, and NMR data were in broad agreement with respect to the relative abundance of lipid classes: primarily steryl esters, wax esters, free sterols, triacylglycerols, and diacylglycerols, with the data suggesting that the waxes and glycerol species constitute the bulk of the lipids in the sebum (Fig. 3 and table S4). GC-MS also indicated the presence of wax diesters, given the occurrence of hexadecan-1,2-diol. GC-MS and LC-MS/MS provided somewhat different fatty acid carbon chain lengths; GC-MS results suggest chains ranging from 9 to 26 carbons, with 16:0, 18:0, and 18:1(9Z) being most abundant, with the abundancies shown in tables S2 and S3. LC-MS/MS revealed fatty acids ranging from 10 to 30 carbon atoms long, with up to five sites of unsaturation as shown in fig. S16. Unsaturations and carbon chain length may both influence the forces of interaction between the lipid molecules and ice, thereby affecting ice adhesion. The role of chain length and unsaturation is considered in quantum chemical calculations, which are presented later in this text.

Fig. 3. Box plots of lipid quantification of sebum.

(A) GC-MS in microgram of fatty acids (FAs) per gram of hair and (B) NMR in micromole per gram of hair. Acylglycerols represent the sum of mono-, di-, and tri-acylglycerols, whereby 1,2 diacylglycerol are the dominant class (also shown in plot). (C) Total fatty acid composition of the sebum as identified by GC-MS. The central line indicates the median, and the whiskers extend to the most extreme data points that are not considered outliers. Outliers are plotted individually.

Characterization of sebum isolates by NMR revealed a total sterol molar content of 0.3 to 1.5 μmol per gram of hair (Fig. 3B). As suggested by GC-MS, cholest-5-en-3β-ol represented more than 90% of sterols detected, but cholesta-4,6-dien-3β-ol cholest-3,5-diene and cholesta-3,5-dien-7-one were also detected. Hydrocarbons, including squalene, were not detected by GC-MS. The absence of squalene and phospholipids was also confirmed by 13C and 31P NMR, respectively (fig. S9). The absence of squalene is notable when compared to other studies of seba of other aquatic mammals. Previous studies of mammals living in damp or wet environments have all shown some fraction of squalene present in seba. The absence of squalene in polar bear fur sebum is especially unexpected in this context given the polar bear’s aquatic lifestyle (40–42).

GC-MS analysis revealed the occurrence of a series of methyl-branched saturated fatty acids, with the methyl branching occurring in the “anteiso” position (ω-2, third carbon from the terminal end). Anteiso fatty acids were detected as prominent fatty acids in all samples and fractions analyzed but were most abundant as triacylglycerol (TAG) fatty acids [up to 53% of TAG FAME (fatty acid methyl ester)]. 18-methyleicosanoic acid (18-MEA) and 20-methyldocosanoic acid (20-MDA) were the most abundant anteiso fatty acids detected (Fig. 3). These structural details were used to inform the choice of molecules for quantum chemical calculations by first-principles density functional theory (DFT) with the more abundant molecules such as triglycerols, diglycerols, cholest-5-en-3β-ol, and eicosanoic acid chosen for calculations of adsorption energy on ice.

DFT calculations

Having identified abundant components of the polar bear sebum, we next considered which components of the sebum might play the most important role in reducing ice adhesion. DFT calculations allowed us to evaluate the adsorption energy (E_ads) of the most prominent components of the sebum on ice: triglycerides (TGs), diglycerides (DGs), and cholesterol, as well as, for comparison, polyfluoroalkyl substances (PFAS) previously used extensively to increase the anti-icing performance of ski wax and squalene, a prominent compound in human sebum and other aquatic/damp-environment mammals. Complete information regarding the computational methodology adopted in this study, as well as the construction of the ice surface model, can be found in the “Computational details” section.

Graphical representations of the saturated adsorbed structures are shown in Fig. 4 (A to G). The TG, DG, wax, PFAS, and cholesterol molecules are amphipathic (having both hydrophobic and hydrophilic parts). Although the structural details of animal sebum are far less understood than those of lipid membranes, with several metastable polymorphic phases coexisting below the melting point, some evidence suggests that TGs in the sebum adopt a reverse micellar orientation, (56) with the polar heads toward the skin or hair’s keratin surface to prevent water from going inside the skin (57). In the case of animal sebum, in particular, for aquatic mammals such as the polar bear, it is also well established that the oily sebum present on the fur acts as a protecting wax and makes the fur more hydrophobic, reducing the friction with ice and making the animal’s fur waterproof (31, 58). We investigated here the two possibilities of the molecular assembly on the ice surface: with the hydrophilic head (polar domain) oriented away from the ice surface, forming reverse micelles aggregates and pointing toward it (59). Results for the former are reported in Fig. 4 and for the latter are reported in fig. S12. Overall, we can observe a similar trend with respect to the adsorption energies obtained here when comparing both configurations, with stronger binding observed when the polar head is pointed toward the ice surface. Therefore, drawing from the literature and our simulation analysis, the reverse micellar configuration (Fig. 4, A to F) is the most appropriate representation for a low ice adhesion system and hence was selected as the computational model to represent the molecule-ice interactions. The exception is squalene, which does not contain polar head groups and only contains carbon and hydrogen atoms in its structure (Fig. 4G).

Fig. 4. Molecular structures analyzed and adsorption energies to ice.

Schematic of the fully saturated structures of (A) TG, (B) DG, (C) cholest-5-en-3β-ol, (D) wax, (E) PFAS, (F) eicosanoic acid, and (G) squalene adsorbed on ice. These are among the most relevant molecular species in sebum analysis, and their adsorption energy is plotted in (H). The star index “*” denotes the presence of a methyl group in the anteiso position of the respective carbon chain.

The molecular model of TG was constructed on the basis of our experimental results in which the three ester groups connect 14, 16, and 18 carbon atom chains. According to the analysis reported in previous sections, the DGs have much longer carbon chains of 24 and 27 atoms. To allow a more direct comparison of the adsorption energy values, we assume the DG, wax, and PFAS models to have the same carbon atom chain lengths as the TG model (14 and 16). The experimental sebum analysis also indicated the presence of the sterol variant cholest-5-en-3β-ol, and this form was adopted in our calculations. For the representation of the PFAS, we substituted the hydrogen atoms for fluorine atoms in the wax structure.

The influence of the number of unsaturations present in the TG and DG structures on adsorption energy at an ice surface was also analyzed (fig. S11B). Experimental lipid analyses in the previous section showed that both the TG and DG species in sebum varied in their degree of unsaturation. Here, we include double bonds in each alkyl chain of the structures, e.g., one unsaturation refers to one double bond considered in all three carbon chains of the TG. The completely saturated TG showed the most negative adsorption energy value of the TGs considered, being strongly adsorbed on the surface, and the adsorption energy monotonically becomes more negative with an increasing number of unsaturations. On the other hand, we observed that an increase in the number of unsaturations in the DG structure has little effect on the adsorption energy; increasing the unsaturations between one and five resulted in a negligible difference in adsorption (E_ads remains at approximately −29.00 kJ mol⁻¹).

The experimental sebum analysis showed that the TG and DG contain one and four double bonds, respectively, and corresponding calculated adsorption energies for DG (14:4/16:4) and TG (14:1/16:1/18:1) were −28.94 and −57.89 kJ mol⁻¹, respectively. Our experimental results in the previous section revealed an abundance of saturated branched structures, in which a methyl group is present in the anteiso position, which is hereafter denoted by a star index “*” in the respective carbon chain in this discussion. We analyzed the effect of the presence of methyl groups on the ice adsorption energy for the TG and eicosanoic acid, and results are shown in fig. S11C. For the TG, the presence of a methyl group in the anteiso position of the carbon chains, TG (14:0*/16:0*/18:0*), led to the adsorption energy becoming slightly less negative by 11%, relative to the non-branched TG (14:0/16:0/18:0). The same behavior was observed for eiconsanoic acid, in which the presence of the methyl group in the anteiso position caused the ice adsorption energy to become marginally (10%) less negative, with the E_ads values for eicosanoic acid (20:0) and (20:0*) being −22.19 and −20.26 kJ mol⁻¹, respectively.

Figure 4H shows a comparison of the adsorption energies for the molecules present in the sebum. We included the adsorption energy of PFAS for comparison, and we also included the values for the branched and non-branched variants of saturated eicosanoic acid (20:0* and 20:0, respectively) and TG (14:0*/16:0*/18:0* and 14:1/16:1/18:1, respectively). The branched TG considered is fully saturated, correlating with what was found in the previous sebum analysis. PFAS and eicosanoic acid (20:0*) have the lowest ice adhesion with the latter being less attracted to the ice surface, with its adsorption energy being 1.92 kJ mol⁻¹ higher than PFAS. The cholest-5-en-3β-ol, DG (14:4/16:4) and wax (14:0/16:0) have low ice adhesion, comparable with PFAS and eicosanoic acid, evidenced by adsorption energy values of −24.12, −28.94, and −31.84 kJ mol⁻¹. Squalene has stronger adhesion on the ice surface with an adsorption energy of −102.27 kJ mol⁻¹. When comparing the adsorption energy of the molecules in Fig. 4 with the alternative orientation of the hydrophilic head toward the ice surface, we find that all adsorption energy values, apart from the TG molecules, were less negative (meaning having a weaker binding with ice) than squalene (fig. S12H). Furthermore, apart from PFAS, adsorption energy values were more negative than the values in Fig. 4H. Nevertheless, our quantum chemical calculations indicate a correlation between the low ice adhesion of polar bear fur and the high abundance of eicosanoic acid (20:0*) and cholest-5-en-3β-ol in the sebum, regardless of the group (hydrophobic or hydrophilic) oriented toward the ice surface, as well as the notable absence of squalene.

DISCUSSION

This study sought to understand what properties, if any, allow the polar bear to live in the icy conditions of the Arctic without noticeable ice accumulation on its fur. Ice adhesion testing with and without sebum, which was removed by washing, showed the importance of the hair sebum in achieving low ice adhesion. Consequently, ice adhesion measurements were followed by analysis of the sebum composition by GC-MS, LC-MS, and NMR, which highlighted that glycerols and waxes made up the bulk of the sebum. Cholest-5-en-3β-ol was the major sterol ester present with the most common carbon chain lengths for the fatty acids being 16, 18, and 20 carbon atoms. The most prominent lipid features in the sebum were then analyzed for their adsorption energy on ice using DFT methods to determine which components may contribute the most to the observed low ice adhesion strength. The calculations show that eicosanoic acid, DG, and cholest-5-en-3β-ol adsorbed weakly on ice and were comparable to PFAS, which are commonly used in anti-icing materials. The comparable ice adsorption energies of these natural materials and PFAS indicate that these candidate molecules could be used as environmentally friendly replacements for PFAS in future low ice adhesion surfaces.

Anti-icing properties

The discovery of the critical role of polar bear sebum in generating the anti-icing properties of polar bear fur represents the major outcome of this study. It may at first seem counterintuitive that unwashed fur exhibits a substantially lower ice adhesion than washed fur despite both having similar wetting properties (hydrophobicity). However, previous reports have shown that hydrophobic surfaces only provide low ice adhesion strength if they have a structure that allows air to be trapped beneath the ice layer (60, 61). Furthermore, there is no direct correlation between wettability and ice adhesion strength (62). The measured RMS surface roughness of polar bear hair is low (fig. S2), which suggests that there is limited air trapping at the interface between an individual hair and ice. Our results show that the working principle of polar bear hair resembles that of SLIPS materials (15, 19, 20, 63). SLIPS materials can exhibit low ice adhesion similar to polar bear fur; however, the low ice adhesion of synthetic SLIPS materials is known to degrade over time because of loss of oils present in the SLIPS layer (64–66). Ice adhesion of polar bear fur also showed similar behavior. Ice adhesion strength increased considerably once the oils of the sebum were removed. It is clear from the results presented here that the key factor in the anti-icing behavior of polar bear fur is the secreted sebum, which allows the fur to operate in a manner similar to a SLIPS surface.

The low ice adhesion appears beneficial for the polar bear. It is more important than a delayed freezing time here as the hairs are not overly hydrophobic, meaning that even if freezing onset was delayed, it is unlikely that the bear would be able to shed all the water off before freezing. Instead, it appears that the polar bear can remove some water before freezing and shake off the rest as ice after freezing (Fig. 1). This mechanism appears to explain why polar bears are not observed to suffer from ice accumulation on the fur.

Distinctive molecular properties of polar bear sebum

Ice adhesion data in this study suggest that the sebum excreted by polar bears help the bear to maintain a low ice adhesion on its fur. By removing the sebum coating through washing, we observed that the ice adhesion increased. The role of sebum as a water-repellent coating on hair is well known (67, 68). The contribution of each sebum component to water repulsion is not fully understood; however, as sebum consists of water-repelling waxes, glycerols, and other lipids, it can be assumed that all components contribute to some degree. While the role of sebum in water repulsion is well known, its role in anti-icing properties has not been reported. Our analysis of polar bear sebum highlighted the abundance of eicosanoic acid and cholest-5-en-3β-ol. Subsequent simulation results highlighted the reduced ice adsorption energies of both of these components on the ice surface with adsorption energies comparable to PFAS. The low adsorption energy suggests low adherence to ice allowing it to be easily shed from fur.

Our lipid analyses and DFT calculations suggest that the lack of squalene is another key factor influencing the anti-icing properties of sebum. Cholesterol is a biochemical derivative of squalene, where squalene monooxygenase is rate limiting (69). Squalene is present in the seba of animals native to relatively warm and moist environments, e.g., sea otters and moles (40–42). Given that the polar bear, like the otter, spends prolonged periods in water, we may expect squalene to be present in its sebum. Cholesterol, on the other hand, is commonly present in other furred animals such as rats, mice, hamsters, and sheep (32, 33, 70). Squalene is interesting from an abrasion point of view, where synthetic seba with high squalene content has been reported to provide surfaces with higher friction (71). It appears that modulating the conversion of squalene to cholesterol in secreted sebum constitutes a route to influence the ice-adhesion of fur, which is reflected by the low ice adsorption energy of cholest-5-en-3β-ol compared to squalene in our calculations. This finding is supported by our observation that isolated squalene has a high ice adhesion strength similar to that of unwashed human hair (fig. S10). It should be stated though that sebum needs to fulfil several distinct needs, and its properties are reflected in the sum of its numerous components rather than single molecules.

The presence of unsaturations, methyl-branching, and very long carbon chain lengths on fatty acid species, as well as TG-to-DG ratios and the total amount of lipids, may also be important for explaining the anti-icing properties of polar bear sebum. Our calculations support the notion that DGs are important as they have low E_ads values on ice. Moreover, methyl-branched anteiso fatty acid species were notable lipid species in our analyses. 18-MEA is a major component of mammalian hair fibers, including polar bear hair, being covalently bound to protein via thioester bonds (72–74). 18-MEA is also a major component of noncovalently bound lipids in sheep’s wool (75), notable for its water-repellent properties. 20-MDA has been reported as a prominent fatty acid in wool and in meibomian gland excreta (76) but, to the authors’ knowledge, has not been reported in mammalian sebum or hair fibers. Our simulations indicate a minor reduction in E_ads when comparing branched and unbranched lipid species, suggesting that branching may provide weaker hair-ice interaction. Simulations also suggest that saturated versus unsaturated species can contribute, although TG and DG behave differently in this regard. TG shows a relatively clear trend in that saturation leads to lower E_ads. It is possible that branching and saturation effects can be additive and dependent on exact positioning of these modifications in a way that would strongly favoring deicing.

These findings have a promising number of potential applications. The low calculated ice adsorption energies of eicosanoic acid and cholest-5-en-3β-ol compared to PFAS suggest that these materials could aid development of anti-icing surface coatings, e.g., in SLIPS surfaces acting as the lubricant in place of fluorinated compounds. They could even be used in ski skins such as the ones tested in this study by replacing the fluorinated coating currently used to treat the skins.

Arctic ecology

Recent behavioral research has shown that one of the polar bears main hunting strategies (more than 80% in the summer) is still hunting: Here, the polar bear lies motionless beside a breathing hole on sea ice waiting for seals to surface (Fig. 5A) (4). Still hunting frequently develops into an aquatic stalk with the polar bear using its hind paws to slide into the water to pursue its prey (Fig. 5B). The lower the ice adhesion, the less noise generated while still hunting and the faster and quieter the slide. Seals have impressive hearing (77, 78) that would aid detection of polar bear movements. The expected benefit of low ice adhesion in still hunting together with the ice-shedding drying procedure (Fig. 1) reveals anti-icing properties of fur as a hitherto unrecorded trait that contributes crucially to the survival of polar bears in the Arctic.

Fig. 5. Inuit artifacts and polar bear hunting behavior.

(A) Adult male polar bear still hunting. Sea ice on Hudson Bay, Manitoba, Canada. (B) Adult male polar bear setting out on an aquatic stalk. Note the marks from the hind paws indicating how the polar bear slides into the water. Sea ice near 81° N, Arctic Ocean north of the Svalbard Archipelago, Norway. (C) Inghuit hunting stool (nikorfautaq). According to the original inventory, it is made of driftwood with polar bear fur wrapped around the ends of the legs. Cordage of de-haired seal skin. Collected by T. Thomsen during a visit to North Star Bay, north of Kap York, Uummannaq (Thule) district, 1909. It is stated in the inventory that the stool used to belong to Manigosok. (National Museum of Denmark, inventory number L. 4326). (D) and (E) Inughuit sandals (tuterissat) for ice hunting, 29 cm by 12 cm. Made from polar bear fur and attached to the soles of the boots (kamiit) by straps of de-haired seal skin. The fur side is turned downward, the hair direction pointing backward. Image credits: (A) and (B) J. E. Ross, LifeOnThinIce.org; (C) L. E. Hansen, Nationalmuseet; (D) and (E) donation from D. Rasmussen (wife of polar explorer K. Rasmussen) 1935. National Museum of Denmark (inventory number L17.9). Nationalmuseet. R. Fortuna, National Museum of Denmark.

Our findings also provide further insight into human Arctic ecology. The use of polar bear fur in clothing among Inuit communities and the Inuit hunting method of waiting at a breathing hole for seals to surface have been discussed in the literature on multiple occasions (28, 79–84) but only with the anti-icing perspective can we understand the subtlety of the steps taken by Inuit people to optimize hunting strategies to mimic the polar bear method of still hunting. Figure 5C shows an Inughuit hunting stool. According to Holtved (28) (p. 98), it has been shod with polar bear fur on the feet to avoid noise when moving on the ice (see fig. S12). The hunting stool is used together with polar bear “sandals,” (see Fig. 5, D and E) to make it possible to move in almost complete silence across the ice (28) (p. 46). Sitting on a hunting stool shod with polar bear fur and wearing polar bear trousers and polar bear sandals, the hunter ensures that his entire contact area with the ice is covered in low ice adhesion polar bear fur for optimal noise reduction—perfect still hunting. Notably, the traditional Inuit preparation method protects the sebum on the fur by ensuring not to clean the hair-covered side of the skin. (28) (p. 136–137). This is unlike, for example, a fox skin, which would traditionally be cleaned by rubbing the hair side with soapstone or dry clay (28) (p. 138–139).

There are some limitations to this study that should be noted. Future studies should perhaps look at other bear species to determine any shared properties with other bears. This is a study on the components of bear sebum and their anti-icing properties. It could be that other bears share some of these sebum properties.

Here, we present experiments showing that polar bear fur has unique anti-icing properties with an ice adhesion comparable to that of fluorinated fibers. By washing the fur, we show that the low ice adhesion is a result of the polar bear hair grease (sebum).

Through a combination of anti-icing measurements, sebum analysis, and DFT calculations, we are able to attribute the low ice adhesion of polar bear fur to the large amounts of cholesterol, DG, and long-chain fatty acids present in the polar bear sebum. There appears to be a complex relationship between lipid ratios and their degrees of methyl branching and unsaturation, which may be rationalized with further investigation. This opens exciting perspectives for the development of environmentally friendly anti-icing lubricant formulations.

This study represents one of the very few systematic investigations of animal sebum. Our work provides further context for polar bear behavior when considered through the lens of anti-icing properties of the fur. Future research should also include the investigation of other types of bears to clarify whether the polar bear sebum composition is an adaptation to the Arctic environment (i.e., squalene developing into cholesterol) or if anti-icing is an inherent trait, which enabled the bear to colonize the Arctic region. Other polar animal furs and feathers should also be investigated. Inuit knowledge tells us that different types of fur behave very differently when exposed to ice. For example, according to Danielsen, the fur of a dead polar fox will freeze onto the ground if it is left in the trap for too long (25) (p. 238), unlike polar bear fur, which does not freeze even after hour-long contact with the ice.

Our research also provides insight into how the properties of polar bear fur are utilized by native Arctic people. We hope that this paper can serve as inspiration for future material science research projects related to Arctic cultures through investigation of cultural heritage objects as well as through the collection of information directly in Arctic communities.

MATERIALS AND METHODS

Sample collection

Polar bear hair samples from six polar bears, three males and three females with ages in the range of 4 to 14 years, were collected from the Svalbard polar bear population between March and April of 2022 by personnel from the Norwegian Polar Institute (table S1). The samples were collected as part of a yearly monitoring campaign, a capture-recapture programme of the Barents Sea population in the Svalbard (Norwegian Arctic) area. The polar bears were immobilized by remote injection of the drug Zoletil or a mix of Zoletil and Medetomidine using a dart fired from a helicopter, following standard procedures (85). Hair samples were cut from each sedated specimen from a patch 10 to 20 cm lateral to the base of the tail. The hair samples were immediately transferred to sterilized 50-ml Falcon tubes, marked with bear ID and date, and kept on ice in a Styrofoam box until the helicopter returned to the research base, and the tubes were stored in a freezer room at −20°C. The samples were later transferred in freezer at −20°C to the University of Tromso and from here distributed to different partners with the cooled conditions maintained (see the Supplementary Materials), which also contains a schematic overview of the sample collection and analytical work undertaken.

In addition, one polar bear skin sample (20 cm by 20 cm from the neck) was sampled by employees at the Norwegian Polar Institute from a sub-adult 3-year-old male polar bear, shot in a bear-human self-defense situation in Svalbard. The sample was collected a day after the bear had been put down, with the bear had been kept in a freezer room before this. The skin sample was carefully sampled and packed in a way to prevent hairs from being greased by the underlying fat and kept frozen at all times during storage and later transport.

Anti-icing properties measurement

Washing

The fur and individual hairs from both polar bear and humans were washed with a few drops of SDS (20%, Sigma-Aldrich, Merck KGaA, Darmstadt, Germany) to remove the lipids for the tests on washed hairs. They were then rinsed three times with large amounts of deionized water and allowed to dry. To ensure that no damage was done by this process, the washed and unwashed hairs were compared using scanning electron microscopy (SEM) imaging and their tensile strengths were measured (Supplementary Methods).

Ice adhesion methods

All ice adhesion tests were conducted using a custom-built apparatus consisting of an icing chamber, freezing plate, and force gauge (86). The icing chamber was cooled by a chiller set to −40°C for all ice adhesion tests that caused internal temperature of the icing chamber to be around −23°C. Purpose-built three dimensionally (3D) printed cuvettes (2 cm by 2 cm by 2 cm) were filled with deionized water and placed within the chamber. The ski skin pads were cut into 3 cm–by–3 cm areas for all tests, and the fur was cut into approximately the same size with some limitations as it was harder to cut. The samples, either ski skin or polar bear fur, were placed on top of the cuvette with the hairs facing toward the water. The samples were placed on top of the cuvette, rather than the cuvette being placed on top of the samples as is typical for ice adhesion experiments. This alternative method prevented water from spilling out of the cuvette onto the sample as the fur is an uneven surface. The ice block was allowed to freeze over 2 hours, and, once frozen, the block and sample were inverted so that the block was on top of the sample. The sample was attached to the stage for ice adhesion testing. The adhesion force was measured using the force gauge, and the maximum force required to remove the block from the sample was divided by 4 cm² to determine a pressure value. Eight measurements were taken for each sample type to get this average. The 3 cm–by–3 cm pieces of ski skin and unwashed polar bear were tested twice at most, except for the washed bear samples that were used four times as there was a limited number of samples.

For ice adhesion measurement of human hair, a full head of hair was shaved after 6 days without washing. All the human hair samples tested were sourced from the lead author of this work with informed consent after 6 days of not washing the hair. The hair was fixed onto a 4 cm–by–4 cm area 3D-printed polylactic acid substrate using Loctite 3421 two-part epoxy adhesive (Henkel Corp., USA). Twelve samples were made and left for the epoxy to harden over 36 hours in a dark sealed box. Six were washed with SDS using the same method applied to the hairs before. Both sets of samples, washed and unwashed, were tested for ice adhesion strength as before.

Contact angle measurement

Contact angle measurement was performed on single hair samples. A specially built microscope apparatus was used to observe the water droplets on the hair. This consisted of an light-emitting diode source, two condenser lens, an adjustable aperture, movable stage, and complementary metal-oxide semiconductor camera (Thorlabs) with a 50× magnification objective lens (Mitutoyo BD Plan Apo 50×). Hairs were suspended between two mounts, and microdroplets were administered using specially made micropipettes attached to a syringe of deionized water. Contact angle values were measured using the ImageJ contact angle plugin and recording the ellipse best fit angle, with four measurements taken for each of the six bear samples totaling 24 altogether, 20 for the human hair and 10 for the ski skin fibers, respectively.

SEM imaging

All SEM samples were coated with a layer of gold-palladium before imaging using a Cressington Sputter Coater 108 auto (Cressington Scientific Instruments, UK). SEM micrographs were acquired using a Zeiss ULTRA plus (Carl Zeiss AG, Germany) operating at an accelerating voltage of 5.0 kV using the 30-μm aperture.

Sebum analysis

Solvent and chemicals for lipid extraction were acquired from Millipore Sigma (St Louis, MO, USA). Dichloromethane was purchased from Thermo Fisher Scientific (Massachusetts, USA). Fifty-milliliter tubes were opened, and the hair was weighed before solvent extraction of lipids. Weight of the hair samples is included in table S1. The sampled hair was washed two times with 10 ml of organic extraction mixture (dichloromethane/methanol 3:1 v/v). The extraction mixture was collected, and water was added to a 2:1 (organic:water) ratio. Next, isopropanol was added until the mixture was uniphasic and transferred to a separation funnel. To this, dichloromethane was added until two phases appeared. After time for equilibration, the denser organic phase containing the lipid solutes was collected. The collected solvent was removed by rotary evaporator and freeze-drying, leaving films of lipid material on the glassware.

Gas chromatography–mass spectrometry

Total lipid extracts were spiked with 10 μg of both 5alpha-cholestane (Thermo Fisher Scientific Acros) and nonadecanoic acid (Merck Supelco). A 20% aliquot of lipid extracts was directly transesterified using 0.5 M methanolic HCl (Thermo Fisher Scientific Acros, reacted at 70°C for 45 min) and analyzed by GC-MS (described below). Separately, a second aliquot representing 60% of the total lipid extract was fractionated by solid phase extraction according to established protocols (53). Briefly, aliquots of total extracts were loaded onto a 500-mg aminopropyl solid phase extraction (SPE) cartridge (Waters, USA). Neutral lipids were eluted with 5 ml of chloroform, and two separate more polar lipid fractions were eluted with acetone and 6:1 (v/v) methanol:chloroform, respectively. Only results from neutral lipid fractions are included for discussion here. Neutral lipids were further fractionated using a second 500-mg aminopropyl SPE cartridge by elution with 5 ml each of the following solvents: F1 with n-hexane, F2 with 88:10:2 (v/v) n-hexane:dichloromethane:chloroform, F3 with 5:95 (v/v) hexane:ethyl acetate, F4 with 15:85 (v/v) hexane:ethyl acetate, and F5 with 2:1 (v/v) chloroform:methanol. Using this approach, hydrocarbons, wax esters, and steryl esters elute in F1; triacylglycerols elute in F2; and diacylglycerols and free sterols elute in F3. GC-MS analysis was performed using a 30-m polyethylene glycol stationary phase capillary column (DB-WAX, 30 m–by–250 μm inner diameter × 0.25-μm film thickness; Agilent J&W, USA) installed in an Agilent 7890A gas chromatograph hyphenated to an Agilent 5975 mass spectrometer. GC conditions were as follows: 50°C for 1 min, 5°C min⁻¹ to 200°C, 3°C min⁻¹ to 230°C, and finally hold for 25 min. MS scan ranges were 50 to 600 Da. Data analysis was performed using Chemstation (Version E02.01). Quantification of lipid classes was performed by reference to the internal standards. A 37-component FAME reference standard (Supelco CRM47885, Merck Sigma, USA) was run with each sequence to assist in identifying the position of double bonds in monounsaturated fatty acids and to monitor instrument performance.

Liquid chromatography tandem MS

LC-MS/MS was run according to previously published protocols (54). Briefly, samples for LC-MS/MS were prepared by reconstituting freeze-dried lipid material from the extraction step described above into a mixture of methanol:ethanol (50:50, v/v). The analytes were separated on a UPLC HSS C18 column (1.8-μm particle size, Waters, USA) at a rate of 0.4 ml/min; an injection volume of 5 μl was used. Mobile phase A consisted of 40% acetonitrile and 60% water, mobile phase B consisted of 10% acetonitrile and 90% isopropanol, and both phases were supplemented with 10 mM ammonium acetate. Data processing was done by using previously in laboratory writing script in Matlab 2020b with updated libraries available at Github (87). Targeted searches were done for TAG, DAG, free fatty acids, squalene, wax esters, cholesterol, and cholesterol esters using predictive fragmentation collected from literature (54, 88, 89).

Nuclear magnetic resonance

Samples for NMR were prepared by reconstituting freeze-dried lipid material from the final steps in the lipid extraction process described above. These films were suspended in deuterated chloroform, with 0.03% tetramethylsilane serving as a chemical shift reference and internal standard for protons. All NMR experiments were acquired at 300 K on a 600-MHz Avance NEO 600 Spectrometer fitted with a 1H/13C/15N/31P QCI cryogenic probe. The NMR instrument was equipped with a temperature-controlled SampleJet, which ensured that samples were stored at 4°C before and between use. 31P NMR experiments were acquired as described earlier (54, 55). Briefly, protons were decoupled using inverse gating, and 2560 transients were acquired with a recycling delay of 8 s and a p1 pulse duration of 40 μs. No phospholipids were detected in this manner. For proton and 13C spectra, 64 and 1024 scans were summed, respectively. The spectra were processed in Topspin 4.0.6 (Bruker, Berlin, Germany) using line broadening and baseline correction, and peaks were deconvoluted and peak areas assigned to glycerols, waxes, and sterols used to determine amounts of these lipids in a manner analogous to the approach of Jakubec et al. (54). Peaks were assigned using literature values (33, 90, 91).

Computational details

DFT calculations were carried out within the exchange correlation functional parameterized by Perdew-Burke-Ernzerhof (92) as implemented in the CASTEP program (93, 94). Long-range dispersion effects were included in our calculations by adopting the Tkatchenko-Scheffler correction scheme (95). The calculations were performed at the Γ-point and an energy cutoff value of 400 eV was adopted. The ultrasoft pseudopotentials of Vanderbilt were used for the treatment of core electrons (96). The forces were converged to 0.025 eV Å⁻¹, and tolerance for the self-consistency field calculations was set to 1 × 10^–6 eV.

The ice surface was constructed by cutting a three-layer thick slab along the (010) plane from the proton-ordered P-ice bulk model (space group Pna2₁), (97, 98), derived from the proton-ordered (ferroelectric) ice XI (space group Cmc2₁) (99). This model was chosen because of the P-ice having a null dipole moment in the (010) surface, with one dangling hydrogen and oxygen atoms (100). The primitive surface unit cell was expanded to a periodically repeated (4 × 3) cell, which was adopted for investigation of the models of TG, DG, and wax, whereas a larger (5 × 3) cell was used for the adsorption of cholesterol and squalene. A vacuum of 20 Å was considered in the nonperiodic axis to avoid interactions among images. Overall, three water layers were considered in all calculations with only the adsorbate allowed to relax.

The adsorption energy of each molecule on the ice surface was evaluated by the equation E_ads = E_{molecule + ice} − E_ice − E_molecule, in which E_{molecule + ice} is the total energy of the respective adsorbed species, E_ice is the energy of the bare ice (010) surface, and E_molecule refers to the energy of the isolated molecule. The isolated molecules were optimized in a cubic box of 40 Å and using the same computational parameters discussed for the surface systems.

Supplementary Materials

This PDF file includes:

Supplementary Materials and Methods

Supplementary Results

Specialist Apparatus

Tables S1 to S4

Figs. S1 to S19

References