Edited by Jeremy Nathans, Johns Hopkins University, Baltimore, MD, and approved July 17, 2015 (received for review March 23, 2015)
Corneal surfaces of some insects are coated with nipple-like nanostructures reducing the light reflection. Here we provide an extensive analysis of corneae across insect groups. Using atomic force microscopy, we discover a striking diversity of corneal nanocoatings, omnipresent in arthropods. These fascinating bionanostructures replicate the complete set of the Turing patterns—shapes resulting from the reaction−diffusion modeling underlying many examples of patterning in biological and physicochemical systems. Our work, verging on the interface of nanotechnology and zoology, evolution and biophysics, and ecology and genetics, sheds light on the molecular origin and evolutionary diversification of a beautiful diversity of insect corneal nanostructures. It also describes, to our knowledge, the first-ever biological example of Turing nanopatterns.
Nipple-like nanostructures covering the corneal surfaces of moths, butterflies, and Drosophila have been studied by electron and atomic force microscopy, and their antireflective properties have been described. In contrast, corneal nanostructures of the majority of other insect orders have either been unexamined or examined by methods that did not allow precise morphological characterization. Here we provide a comprehensive analysis of corneal surfaces in 23 insect orders, revealing a rich diversity of insect corneal nanocoatings. These nanocoatings are categorized into four major morphological patterns and various transitions between them, many, to our knowledge, never described before. Remarkably, this unexpectedly diverse range of the corneal nanostructures replicates the complete set of Turing patterns, thus likely being a result of processes similar to those modeled by Alan Turing in his famous reaction−diffusion system. These findings reveal a beautiful diversity of insect corneal nanostructures and shed light on their molecular origin and evolutionary diversification. They may also be the first-ever biological example of Turing nanopatterns.
Biological patterning at the microscale and macroscale levels has been under intensive investigation by developmental biology, and its fundamental principles, such as the concept of the morphogens, have become textbook knowledge (1). In contrast, nanoscale biological patterning is not well studied and understood. Among the rare known examples of biological nanopatterns are the 3D nanostructures covering insect corneal surfaces (2). They were described in moths and butterflies and later some Dipterans as pseudoregularly spaced nipple-type protrusions, up to 200 nm in height and width (3⇓⇓⇓–7). These nanostructures may carry antireflective, dirt-removing/self-cleaning, and hydrophobic/antiwetting functions (2, 8⇓⇓⇓–12). Later, some other insects were found to possess a very different type of corneal nanocoating, such as the antireflective maze-like 30-nm-high evaginations covering corneae of the overwater eyes of Gyrinidae beetles (13). An attempt to analyze the variety of corneal nanocoatings throughout the insect class was made in the classical study by Bernhard et al. (5). However, the scanning electron microscopy technique of that time was mostly performed on platinum replicas of the insect samples and was compromised by the partial collapse of the nanoprotrusions. It permitted reliable identification of 50- to 250-nm-high nipple-type protrusions in Lepidoptera, some Dipterans, Trichopterans, and, interestingly, the primitive Thysanuras, but not identification of other types of corneal nanocoatings (5).
To use the corneal nanocoatings as the model to study nanoscale biological patterning, a comprehensive investigation across insect lineages using modern techniques must be performed. We recently applied atomic force microscopy (AFM), providing nanometer and subnanometer resolution of undamaged biological material, to investigate different types of corneal nanostructures of some Dipteran and Coleopteran insects (6, 13). Here we expand this analysis to 23 insect orders and some noninsect arthropods, describing a striking richness and beauty of the corneal nanocoatings (Fig. 1, Figs. S1–S3, Table S1, and Detailed Description of Diverse Corneal Nanostructures Order by Order). These nanostructures can be grouped as follows. (i) Nipple-like structures (Fig. 1A and Fig. S1) include the regularly packed protrusions of Lepidopterans (Fig. S1A), irregular packaging in Dipterans (Fig. S1B), and irregular packaging of irregularly shaped nipple-like protrusions in a range of other orders: Trichoptera (Fig. 1A), Mecoptera (Fig. S1C), Megaloptera (Fig. S1D), Hemiptera (Fig. S1 E and F), Psocoptera (Fig. S1G), Thysanura (Fig. S1H), Raphidioptera (Fig. S1I), Neuroptera (Fig. S1J), Orthoptera (Fig. S1K), and Odonata (Fig. S1L). (ii) Maze-like nanocoatings (Fig. 1B and Fig. S2) can be observed in Coleopterans (Fig. S2 A and B) but also in other orders such as Trichoptera (Fig. 1B) and Hymenoptera (Fig. S2C), and in some arachnids (Fig. S2 D and E). (iii) Parallel strands/ridges (Fig. 1C) formed by fusion of nipple-type protrusions can mostly be seen in Dipterans (Fig. 1 F and G) and, interestingly, in true spiders (Fig. 1C). (iv) Novel dimple-type nanocoating (Fig. 1D and Fig. S3) can be seen in different orders: Siphonaptera (Fig. S3A), Coleoptera (Fig. S3B), Hymenoptera (Fig. S3C), Hemiptera (Fig. S3 D and E), Blattodea (Fig. S3F), and Dermaptera (Fig. 1D), and, interestingly, in centipedes (Fig. S3H). We also see various transitions between these major forms: (v) nipples-to-maze transition (e.g., in Plecoptera, Fig. 1E); (vi) maze-to-strands transition (e.g., in Diptera, Fig. 1F); (vii) nipples-to-strands transition (e.g., in Diptera, Fig. 1G); and (viii) dimples-to-maze transition (e.g., in Hymenoptera, Fig. 1H).
The diversity of corneal nanostructural patterns among arthropod groups: (A and B) Corneal nanostructures of Trichoptera. Merged as well as undersized nipples in an irregular nipple array of the Phryganeidae family (A) and maze-like nanocoating of the Limnephilidae family (B). (C) Clearly expressed parallel strands in a true spider. (D) Dimpled nanopattern of an earwig (Dermaptera). (E) Nipples merging into maze on stonefly (Plecoptera) corneae. (F and G) Merging of individual Dipteran nipples into parallel strands and mazes: full merging of nipples into strands and mazes on the entire corneal surface in Tabanidae (F); partial merging of nipples in the center of Tipulidae cornea into elongated protrusions and then complete fusion into an array of parallel strands near the ommatidial edge (G). (H) Merging of individual burrows and dimples into a maze-like structure on bumblebee (Apidae, Hymenoptera) corneae. All image dimensions are 5 × 5 µm, except for H, which is 3 × 3 µm. Surface height in nanometers is indicated by the color scale shown next to 2D images.
The diversity of corneal nanostructural patterns among insect orders: nipple-type nanocoatings. (A) Regular hexagonal nipple array typical for butterflies (here fam. Nymphalidae). (B) Individual pseudoregular nipples in Culicidae. (C) Mecopteran corneal surface carries irregular, partially merged nipples. (D) Megalopteran corneal surface, partially merged nipples with residual segmentation can be seen. (E) Irregular nipples of a Miridae family bug (Stenodema viris) merging into maze-like structures. (F) Irregular nipples of a Miridae bug Leptopterna dolabrata. (G) Irregular, partially split nipples of booklouse (Psocoptera). (H) Irregular nipple-type nanocoating in the primitive Thysanura. (I and J) Raphidiopteran (I) and Neuropteran (J) corneal surfaces, respectively. Partially merged nipples with residual segmentation can be seen. (K) Orthopteran corneae: disordered merging nipples in the grasshopper (fam. Tettigoniidae). (L) Irregular, partially merging small nipples in Odonata. Image dimensions are 5 × 5 µm, except for B, F, K, and L, which are 3 × 3 µm. Surface height in nanometers is indicated by the color scale shown next to 2D images.
The diversity of corneal nanostructural patterns among insect orders: maze-type nanocoatings. (A) Maze-like structures on a Staphylinidae eye, with an unusual broadness of ridges of ca. 500 nm. (B) Angular maze-like structures of Coccinellidae (Coleoptera) with a variation of broadness seen in different regions. (C) Corneae of a sand wasp (fam. Crabronidae) show an almost smooth surface in the center of ommatidia and maze-like reticulations near the edge. (D and E) Analysis of some arachnid simple eye corneae reveals maze-like nanostructures in a Phalangium harvestman (order Opiliones, family Phalangiidae) (D) and spaghetti-like structures in a scorpion (E). Image dimensions are 5 × 5 µm, except for B (3 × 3 µm) and C (10 × 10 µm). Surface height in nanometers is indicated by the color scale shown next to 2D images.
The diversity of corneal nanostructural patterns among insect orders: dimple-type nanocoatings. (A) Surface of Siphonaptera is speckled by irregularly distributed dimples. (B) Dimpled pattern on corneae of a beetle from Carabidae family. (C) Irregular dimples in ichneumon wasps (Ichneumonidae, Hymenoptera); note the unusually large interdimple distances. (D) Dimples in a spittlebug (fam. Aphrophoridae). (E) A maze-to-dimple transition in a bug from Pyrrhocoridae family. (F) Cockroaches (Blattodea) demonstrate corneal dimples. (G) A dimple/maze pattern in the cricket Gryllus bimaculatus. (H) Dimpled corneal nanocoating in a brown centipede (class Chilopoda, order Lithobiomorpha). Image dimensions are 5 × 5 µm, except for E, which is 3 × 3 µm. Surface height in nanometers is indicated by the color scale shown next to 2D images.
Characteristics of corneal nanostructures of representatives of different insect families studied in our work are provided, along with a few selected citations of previous studies when they describe nanopatterns different from those typically found in the respective families by us
The rich diversity of these nanostructures and the easiness with which the corneal nanopatterns merge one into another in closely related orders and even within the orders (Fig. 2 and Detailed Description of Diverse Corneal Nanostructures Order by Order) is striking and permits posing questions on the underlying molecular, developmental, and evolutionary mechanisms. Developmentally, the nipple-type protrusions were proposed to originate, during eye development, from secretion by the regularly spaced microvilli of the cone cells (5, 14). However, this idea could appear plausible when the ordered Lepidopteran nipple arrays were studied but, with the current diversity of nanostructures and transitions among them, sometimes within the same lens (Fig. 1G), is not satisfactory. Instead, we propose that certain mechanisms of patterning at the nanoscale are in place, and the diverse arthropod corneal nanostructures we describe here represent a model to study such nanopatterning. Further, we notice that this diversity of corneal nanostructures is remarkably similar to the complete set of the Turing patterns (Fig. 3).
Distribution of basic and intermediate nanopatterns among insect orders. Each pattern type is represented by a circle of a certain color on the diagram; double-colored circles correspond to transitional nanopatterns. Orders of which no representatives were analyzed in the present study are marked as N/A. The data on insect phylogenetic relationship are based upon ref. 24.
The insect corneal nanostructural diversity replicates Turing patterns. Mathematically modeled Turing patterns (in black and white) and their insect counterparts. (A and A′) Irregular nipples of various sizes, characteristic e.g., for Hemipteran corneal nanocoatings. (B and B′) Highly ordered nippled nanoarrays (Lepidoptera). (C and C′) Strands merging into a maze (Diptera, Tabanidae). (D and D′) Parallel strands (Diptera, Tipulidae). (E and E′) Nipples merging into a maze (Plecoptera). (F and F′) Typical maze-like structures (Coleoptera, Gyrinidae). (G and G′) Angular maze-like structures (Coleoptera, Coccinellidae). (H and H’) A typical dimpled pattern (Dermaptera). A′ is a fragment of Fig. S1F; B′ is an image from a Pterophoridae butterfly; C′ is a fragment of Fig. 1F; D′ is a fragment of Fig. 1G; E′ is a fragment of Fig. 1E; F′ is an image from a Gyrinus beetle [overwater eye (13)]; G′ is a fragment of Fig. S2B; and H′ is a fragment of Fig. 1D. Modeling parameters are given in Table S2. (I) Simulations of Turing patterns formation. Step-wise changes in the av and bu parameters within the boundary conditions produce different Turing patterns: dimples (yellow zone), mazes (blue zone), and nipples (green zone). See Fig. S4A for more detailed representation.
In his seminal paper in 1952, Alan Turing provided a system of differential equations describing the reaction−diffusion system of two reacting morphogens—a slowly diffusing activator and a fast diffusing inhibitor—which can model various biologic, chemical, and physical patterns (15, 16). Applicability of this model to biological pattern formation has been shown in several recent examples, such as formation of colored stripes in zebrafish (17), hair follicle spacing in mice (18), and digit specification in limbs (19). The insect corneal nanopatterns we describe here differ from these examples, as they reproduce not just one of the many possible forms produced by the reaction−diffusion model but a thorough set of possible variants including the intermediate forms (Figs. 1 and 3). This remarkable completeness of coverage of the possible set of Turing structures by the arthropod corneal nanopatterns strongly argues in favor of the hypothesis that these nanopatterns are indeed a consequence of the Turing reaction−diffusion mechanisms.
We hypothesize that the Turing mechanism-based reaction−diffusion processes patterning the nanocoatings are mediated by organic components of the lens, possessing different diffusion properties and mutually influencing each other’s abundance/polymerization/aggregation, the outcome of this being the stereotypical formation of the nanostructures. In previous applications of the Turing principles to biological processes, patterning at the microscale was modeled (17⇓–19). Formal mathematical analysis shows how key parameters of the reaction−diffusion equations (primarily the diffusion coefficients of the two interacting morphogens) can result in the appearance of repeated developmental structures with the experimentally observed micrometer-scale wavelength (20). Our mathematical analysis (Turing modeling of corneal nanopatterns) demonstrates that nanoscale patterns are expected to form in the reaction−diffusion system acting in the colloidal or liquid crystal-type environment [which is indeed the environment of the lens of the eye (21)] where diffusion properties are reduced (compared with the liquid phase).
Although the molecular identity of the morphogens patterning corneal nanocoatings remains to be revealed, simulations of the Turing reaction−diffusion processes provide interesting hints into the potential molecular mechanisms underlying formation of different types of the nanocoatings and transitions among them (Fig. 3I and Fig. S4). Although different sets of the reaction−diffusion coefficients (like that of Table S2 used to obtain images on Fig. 3 and Fig. S4; see also Fig. S4B for schematic description of the parameters and Fig. S5 for analysis of the parameter space) can model different nanopatterns, simulations find that three of the major types of patterns we observe in insect corneae occupy defined regions within the parameter space and transit to each other as follows: dimples ↔ maze ↔ nipples (Fig. 3I and Fig. S4A). The space in these figures is populated by the incremental changes of two of the reaction−diffusion parameters av and bu describing the degree of influence of the two diffusing components (activator u and inhibitor v) on each other (Fig. S4B) (16, 22). Interestingly, transition from the dimple-type nanocoating to the maze-type and then further to the nipples occurs by increasing the absolute value of either of the two reaction−diffusion parameters (Fig. 3I and Fig. S4A). In this regard, it may be speculated that the initial reaction−diffusion nanopatterning system emerged when these parameters just exceeded the borderline, permitting the Turing patterns to appear (16, 22), and thus was likely of the dimple type. In this regard, it is interesting to note that the dimple pattern is not only seen in many insect groups but also in centipedes (Fig. S3H), which are believed to retain more characteristics of the presumed arthropod ancestor than other arthropods with sequenced genomes (23).
Simulations of Turing pattern formation. (A) Step-wise changes in the av and bu parameters produce Turing patterns within the boundary conditions; av and bu parameters outside of the boundary conditions do not result in patterns (evenly colored boxes). This pattern space is divided into the areas with dimples (colored orange and yellow), mazes (colored blue), and nipples (green). (B) Schematic representation of the Turing model used here and its parameters used throughout the text. (C) Step-wise changes in the diffusion parameters Du and Dv produce nipple-type Turing patterns, with increasingly hexagonal packing upon increasing Du within the boundary conditions. (D) Step-wise changes in the diffusion parameters Du and Dv produce maze-type Turing patterns, with increasingly ordered parallel orientation of ridges obtained upon increasing Du within the boundary conditions. (E) Parameter conditions normally producing maze-type patterning produce parallel ridges if growth starts in a nonhomogeneous environment, with nipple-type structures preoccupying part of the space. Four time points of simulations are shown; the right-most picture is a fragment of Fig. 1F. Modeling parameters for A and C–E are given in Table S2.
Analysis of the parameter space of Turing modeling. Parameters Du and Dv (A), fu and gv (B), and fv and gu (C) are varied in the ranges indicated. The colored space indicates the range of parameters where Turing patterns can be formed; the white space is where no stable patterns can appear. Colors reflect the wavelength of the patterns, from small (blue) to large (red). Points on the colored space indicate the parameters chosen to produce Turing patterns as shown on Fig. 3 A−H, as indicated. Figures are made with the matplotlib program.
In the context of phylogeny, evolutionary advanced insects were initially assumed to possess fully developed nipple-type corneal nanocoatings, whereas simpler insects were reported to mostly carry less pronounced (and less functional) nanocoatings (5). Our findings suggest that this assumption is incorrect. Indeed, our study unequivocally shows that various types of the nanostructures can be seen in various insect (and wider—Arthropodan) groups without any correlation of the predominant type of the nanocoating and the evolutionary advance of the group (Fig. 2). Instead, we can also apply the Turing modeling to get insights into the evolutionary transitions among different types of corneal nanocoatings. Increase in the absolute value of either of the two av and bu parameters allowed the dimple-to-maze transition, and the further increase allowed the maze-to-nipples transition (Fig. 3I and Fig. S4A). These considerations permit constructing a “morphogenetic tree” or “morphogramme” of these structures (Fig. 4). In this morphogramme, different types of corneal nanocoatings are placed not based on the phylogenetic hierarchy of the insect orders (24) but instead on their morphologies and transitions among them, as justified by the Turing modeling we performed. Originating from the dimple-type nanocoatings, this morphogramme then grows into the maze type and further into the nipples type (Fig. 4). We further identify parallel ridges of some Dipterans and hexagonally packed nipples of some Lepidopterans as developments of the maze- and nipples-type structures, respectively (Fig. 4). Both represent more ordered structures and can be modeled to emerge from their less ordered predecessors through increasing of the diffusion parameter of the activator component Du to the levels maximally allowed within the boundaries permitting the Turing patterns to form (16, 22) (Fig. S4 C and D). In contrast, increasing the diffusion parameter of the inhibitor component Dv leads to increase in the cross section of the nanostructures (nipples or ridges, respectively, in Fig. S4 C and D).
Transformations of corneal nanopatterns. The morphogramme depicts the likely interconversions among the nanostructural patterns found in the insect class rather than phylogenetic relationships of the patterns. Primordial dimpled nanopatterns (1, here from a Forficula earwig) can transform into various maze-type nanostructures (2–4; 2 from a Pyrrhocoris firebug, 3 from a Tabanidae fly, and 4 from the butterfly Protographium asius). The latter can further transform into disordered nipples (6, here from the fruit fly Drosophila melanogaster), which can further become orderly packed (7, here from a Pterophoridae moth). Alternatively, parallel ridges (5, here from a Tipulidae fly) can evolve either from mazes or nipples. The figure is made of reconstructed 3D AFM images fused, for the sake of visualization not in exact scale, using MATLAB.
In some Dipterans, a transition from nipples to parallel ridges can be seen within the same lens, with nipples occupying the central part of the ommatidium and merging into elongated strands away from the center (Fig. 1G). Turing modeling predicts how such structures may be formed (Fig. S4E): Seen in flies with large ommatidia and lenses, these nanocoatings are likely a result of a nipples-to-maze transition within the same lens, happening during the lens formation after initial nipples in the center of the cornea have been formed. In this predefined space, parameters otherwise giving rise to mazes induce formation of parallel ridges emanating from the nippled area (Fig. S4E).
Detailed analysis of the physical (such as antireflective and antiwetting) properties of the diverse corneal nanostructures we present here is still to be performed, but the fact that both the nipple-type and maze-type nanostructures serve the antireflective function (2, 13) suggests the functionality of the majority, if not all, of them. The variety of these nanostructures can serve as a highly promising model, obeying the Turing mechanism of pattern formation. Insect eyes, especially those of the genetically tractable model insect Drosophila melanogaster (6, 25), can therefore serve as a powerful tool to further explore the precise mechanisms of the reaction−diffusion-driven processes in living organisms, to identify the molecular components governing formation of corneal nanocoatings, and to genetically engineer novel Turing nanopatterns with novel physical properties.
The dried insect samples were obtained from a collection of the Department of Entomology, Moscow State University. Fresh specimens were collected in the woods around the town of Pushchino, Moscow region. The phylogenetic tree of the insect class was taken from Su and coworkers (24).
To prepare corneal samples, the head of an insect was cut out of the body, followed by removal of the mouth apparatus with a scalpel, splitting of the head into the two hemispheres, and careful extraction of the brain tissue with forceps. Next, the cornea was cleared from the head capsule tissue as well as the underlying brain material with a scalpel. The sample was attached to a glass slide for AFM by means of two-sided scotch tape. AFM scanning of the corneal surfaces was performed with the Integra-Vita microscope (NT-MDT). For the semicontact procedure, the nitride silicon cantilever NSG 03 (NT-MDT) was used. The parameters of the cantilever were: length, 100 µm; resonant frequency, 62–123 kHz; radius, 10 nm; and force constant, 0.4–2.7 N/m. For the contact procedure, the cantilever CSG 10 (NT-MDT) was used, with the following parameters: length, 250 µm; resonant frequency, 14–28 kHz; radius, 10 nm; and force constant, 0.03–0.2 N/m. The choice between the semicontact and the contact measuring procedures was dictated by the size and curvature of the studied surface of the sample but provided essentially identical results. In each AFM experiment, several scans were made to check the reproducibility of images and the absence of possible surface damages. Measurements of height and width of the corneal nanostructures were performed by the Nova software (NT-MDT).
Lepidopteran corneal nanostructures were the first to be studied and remain the most studied (2⇓⇓–5). With a few exceptions (Table S1 and ref. 26), the corneal nanocoatings of moths and butterflies are built of seemingly ordered hexagonal nipple-type protrusions of ca. 150 nm in width and >200 nm in height (Fig. S1A). The closest relatives of this order are Trichopterans (caddisflies, Fig. 2). In the 1970 study by Bernhard et al. (5), they were reported to possess nipple-like nanostructures similar to those of the moths. Our examination confirms such structures of the height of about 50 nm in the Phryganeidae family of Trichoptera. Being somewhat similar to the Lepidopteran nipple arrays, however, they display some differences. First, the nipple arrangement is highly irregular compared with Lepidoptera; second, we could observe multiple merged nipples, forming blob-like structures among the normal single nipples. Third, some nipples show diminished height of about 35–40 nm and diminished broadness of ca. 50 nm compared with ca. 250 nm for normal nipples (Fig. 1A). Another caddisfly family, Limnephilidae, revealed the corneal nanocoating of a completely different type: a complex irregular maze-like structure with height of about 40 nm (Fig. 1B).
Our previous analysis of Drosophila corneal nanocoatings (6) demonstrated a pseudoregular nipple array with the average height of nipples of about 30 nm. Similar structures, somewhat higher (65 nm) with nipples less broad (170 nm), are now described in the Culicidae family (Fig. S1B). In other Dipteran families, similar nipple-type structures were seen, as well as ridges organized in a parallel manner or forming maze-like structures (7, 27⇓–29). We provide further analysis of the Dipteran families Tipulidae, Tabanidae, and Syrphidae. Here we also see parallel strands/ridges (Fig. 1 F and G). Interestingly, in Tipulidae and Syrphidae, these ridges are found in combination with single nipples, such that the nipples (mostly of the central part of the ommatidium) are merging into elongated strands away from the center (Fig. 1G). In Tabanidae, individual nipples are almost totally extinct from the entire eye surface, totally replaced by strands that further show a tendency of mixing into mazes (Fig. 1F). The average broadness of the observed strands is about 200–230 nm, and the height is significantly lower (from 15 nm in Syrphidae to 20 nm in Tabanidae) than is typical for individual nipples in Diptera (Table S1).
The scorpion flies (Mecoptera) are an order phylogenetically close to Diptera (24) (Fig. 2). Analysis of corneal surfaces in Mecopterans does not reveal any novel nanostructures: They carry ordinal irregular nipples, heterogeneous in size (Table S1) and often merging into blobs (Fig. S1C). Surprisingly, despite the phylogenetic relationship between fleas (Siphonaptera) and Mecoptera, the corneal analysis of a flea eye has shown a previously undescribed nanostructural pattern (Fig. S3A). The flea corneal nanocoating can be characterized as a flat surface speckled by dimples of about 5–20 nm in diameter and 10–20 nm in depth. The distances between individual dimples may vary from 200 nm to ≤5 nm when the dimples actually merge into small burrows.
The corneal nanostructures of the orders Megaloptera and Raphidioptera (snakeflies) consist of partially merged nipples with highly uneven distribution of height and broadness (from 15 nm to 40 nm and from 100 nm to 300 nm, respectively). Interestingly, many nipples are partially merged into proreticular formations showing a residual segmentation (Fig. S1 D and I). A similar picture can be observed in the related order of Neuroptera (net-winged insects, Fig. S1J).
Beetle (Coleoptera) is the order most closely related to the ones described just above. Many of the beetles examined in our study do not show any corneal nanostructures at all (Table S1 and Fig. 2), agreeing with some previous observations (5, 30). On the other hand, corneae of the pollen-feeding beetle Xanthochroa and the whirligig beetles Gyrinus and Orectochilus were previously seen to be covered with maze-like nanostructures (13, 31). Here we additionally describe the maze-type nanocoatings in beetles of the Coccinellidae and Staphylinidae families. The maze ridges in Staphylinidae are ca. 500 nm broad, thus notably outmatching all other studied specimens (Fig. S2A and Table S1). Nanostructures in Coccinellidae have an unusual angular pattern with a high variation of broadness (Fig. S2B and Table S1). An additional dimpled pattern of corneal nanocoatings is found in Carabidae (Fig. S3B).
Representatives of the order Hymenoptera, just like the Coleopterans, often demonstrate a total absence of eye nanostructures; e.g., honey bees (Apis melifera) have completely smooth corneae (Table S1 and Fig. 2). For Hymenopteran specimens possessing nanostructures, they often can be observed only close to the ommatidial edge, gradually disappearing in the direction of the center of the ommatidium (Fig. S2C). However, corneae of sand wasps (family Crabronidae) and bumblebees (fam. Apidae) show fairly recognizable nanostructures on their surface. These nanostructures can be interpreted as a transition from the irregular dimples, such as those observed in fleas, into maze-like structures described above in beetles and caddisflies; in this transition, individual dimples and burrows can be seen in many regions, but their partial fusion into maze-like structures is easily recognizable (Fig. 1H). In ichneumon wasps (fam. Ichneumonidae), this transition appears not to have started, as corneae are speckled by irregular dimples with uneven distribution and uncommonly large distances between individual holes, up to 1 µm (Fig. S3C).
The largest diversity of nanostructural patterns is observed by us in the order Hemiptera (true bugs). They possess the full spectrum of nanostructures described for other insect orders. The bugs of the Miridae family carry on their corneae irregular nipples, sometimes merging into small blobs (Fig. S1 E and F) and therefore resembling the Trichoptera, Mecoptera, and Neuroptera, whereas the spittlebugs (fam. Aphrophoridae) possess the dimple-type nanopattern (Fig. S3D) that further transforms into the dimple/maze-type in the families Scutelleridae and Pyrrhocoridae (Fig. S3E and Table S1). We have also studied the eyes of plant lice (Aphidoidea superfamily), scorpion bugs (fam. Nepidae), and pondskaters (fam. Gerridae), but they demonstrate a total absence of the eye nanostructures (Table S1 and Fig. 2). This could be explained by the fact that the latter two families are water-dwelling insects, whereas plant lice eyes are structureless due to their small size and the absence of hard cuticle. The large diversity of the Hemipteran eye nanocoatings can reflect an exclusive genetic and ecological diversity of this taxon.
The lice order (Phthiraptera) does not reveal any eye nanostructures, which may be explained by their parasitic way of life (Table S1 and Fig. 2). Indeed, the eyes in the related booklice order (Psocoptera) represented by free-living insects demonstrate a rather familiar nipple nanostructure. The nipples are 200 nm broad and 25–40 nm high, partially consisting of incompletely merged smaller segments (Fig. S1G).
The Mantises (Mantodea) do not reveal nanostructures (Table S1 and Fig. 2). Of the orders closely related to them, termites (Isoptera) do not either, whereas cockroaches (Blattodea) demonstrate corneal dimples (Fig. S3F).
Stoneflies (Plecoptera) reveal a striking nipple-to-maze nanostructural pattern with the height of 30–50 nm (Fig. 1E). Earwigs (Dermaptera) possess at least two different types of corneal nanocoatings, even in closely related species: Our analysis reveals the dimpled nanostructure, similar to that of the fleas, in Forficula auricularia (Fig. 1D), whereas a previous study in another Forficula species claimed to describe nippled nanocoating (32).
Orthopterans reveal diverse nanocoatings, as we see the dimple/maze pattern in the cricket Gryllus bimaculatus (Fig. S3G), whereas irregular nipples are seen in grasshoppers (Fig. S1K and ref. 33). We do not find nanostructures in the stick insects (Phasmatodea) (Table S1 and Fig. 2).
Corneal nanostructures in dragonflies (Odonata) could only be observed by means of high-resolution analysis. They are represented by irregular, partially merging small nipples (≤15 nm, typically 5–10 nm in height, ca. 100 nm broad, Fig. S1L). We were unable to find any eye nanostructures in mayflies (Ephemeroptera), which are closely related to dragonflies (Table S1 and Fig. 2).
In the Thysanura order of simple insects, we find irregular nipple-type nanocoatings (Fig. S1H), recapitulating the findings of Bernhard et al. (5).
Importantly, a brief analysis of corneal surfaces of noninsect arthropods also reveals diverse nanocoatings, such as the dimpled nanopattern in a centipede (Fig. S3H), maze nanostructures in a harvestman (Fig. S2D), “spaghetti”-type maze nanostructures in a scorpion (Fig. S2E), and parallel strands in the Araneae (true spiders) order (Fig. 1C).
The Turing reaction–diffusion system of differential equations was used,
The concentrations u and v depend on two components: (i) the F(u,v) and G(u,v) functions that describe the reaction kinetics (aggregation/polymerization, disassembly/depolymerization, and interactions between the morphogens) and (ii) the component describing the diffusion of the two morphogens with the respective diffusion coefficients Du and Dv. This second component brings about the diffusion-driven instability, which is required for the unequal distribution of the morphogens and thus patterning.
Following ref. 20, we introduce the following denominations:
We further use the derivative of the basic model of ref. 16, as it allows easy obtaining of a large set of patterns. In this derivative, the functions F(u,v) and G(u,v) are given linearly as
Using Eq. S2, one can see that
The solution of the system of Eqs. S6 can be given, following ref. 20, as the sum of general solutions,
Because
The table below provides a wide set of reaction rate constants for biological reactions, starting from the higher limit of 106 characteristic for fastest enzymatic reactions to lower values characteristic, e.g., for protein aggregation/polymerization (35):
As for the diffusion coefficients, the nanopatterning we study takes place in the developing lens, which can be considered a colloid or liquid crystal (21). For colloids, diffusion coefficients can range from 10−6 cm2/s to 10−15 cm2/s (36), whereas, for liquid crystals, the diffusion coefficient was estimated around 10−8 cm2/s (37).
We thus conclude that Turing nanopatterns with the wavelength of the order of 100 nm are likely to form in the colloidal system with reduced diffusion parameters, with the aggregation/polymerization and the disassembly/depolymerization of the interacting molecules being the underlying mechanisms of patterning.
To adequately select the parameters used to perform the Turing modeling as on Fig. 3 and Fig. S4, we first investigate different ranges of parameters and their influence on formation of Turing patterns. Using the equations provided above, we could investigate the dependence of the wavelength ωmax, corresponding the maximal eigenvalue λ, from the parameters (Du, Dv), (fu, gv), and (fv, gu). The results are shown as Fig. S5.
We have thus performed modeling that quantitavely shows the feasibility of the Turing nanopatterns to form in the environment of a developing lens.
We thank Gennadiy Enin for the atomic force microscopy technical assistance, Anastasia Ozerova for providing several Lepidopteran samples, Alexey Koval for help with Fig. 4 and for fruitful discussions, Gonzalo Solis and Oleksii Bilousov for critically reading the manuscript, and the Dynasty Foundation School of Molecular and Theoretical Biology for supporting the initiation of this work. This work was funded by Grant DP-B-14/13 from the Dynasty foundation (to A.B.) and by the Scientific & Technological Cooperation Program Switzerland-Russia (V.L.K.).
Author contributions: V.L.K. designed research; A.B., A.S., and M.K. performed research; A.S. and Y.L. contributed new reagents/analytic tools; A.B., A.S., M.K., and V.L.K. analyzed data; and A.B. and V.L.K. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
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