Diverse set of Turing nanopatterns coat corneae across insect lineages

Artem Blagodatski; Anton Sergeev; Mikhail Kryuchkov; Yuliya Lopatina; Vladimir L. Katanaev

doi:10.1073/pnas.1505748112

Edited by Jeremy Nathans, Johns Hopkins University, Baltimore, MD, and approved July 17, 2015 (received for review March 23, 2015)

Significance

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.

Abstract

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).

Fig. 1.

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.

Fig. S1.

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.

Fig. S2.

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.

Fig. S3.

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.

View this table:

Table S1.

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).

Fig. 2.

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.

Fig. 3.

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 a_v and b_u 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 a_v and b_u 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).

Fig. S4.

Simulations of Turing pattern formation. (A) Step-wise changes in the a_v and b_u parameters produce Turing patterns within the boundary conditions; a_v and b_u 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 D_u and D_v produce nipple-type Turing patterns, with increasingly hexagonal packing upon increasing D_u within the boundary conditions. (D) Step-wise changes in the diffusion parameters D_u and D_v produce maze-type Turing patterns, with increasingly ordered parallel orientation of ridges obtained upon increasing D_u 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.

Fig. S5.

Analysis of the parameter space of Turing modeling. Parameters D_u and D_v (A), f_u and g_v (B), and f_v and g_u (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.

View this table:

Table S2.

Parameters used to model the Turing patterns shown on Fig. 3 and Fig. S4

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 a_v and b_u 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 D_u 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 D_v leads to increase in the cross section of the nanostructures (nipples or ridges, respectively, in Fig. S4 C and D).

Fig. 4.

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.

Methods

Insect Specimens.

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).

Atomic Force Microscopy.

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).

Turing Modeling.

The 2D patterns were made using the software RDsimJ.jar (16) with the parameter values listed in Table S2.

SI Text

Detailed Description of Diverse Corneal Nanostructures Order by Order.

Trichopteran eye surfaces reveal merged nipples and a maze-like structure.

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).

Dipteran eye surfaces reveal nipples merging into parallel strands and mazes.

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 related orders Mecoptera and Siphonaptera carry distinct corneal nanostructures.

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.

Megaloptera, Raphidioptera, and Neuroptera carry irregular nipples with partial merging and size variation.

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).

Coleopteran eyes show smooth surface or maze-like structures of different proportions as well as dimples.

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).

Corneal nanocoatings of Hymenoptera demonstrate a dimple-to-maze transition.

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).

Hemipterans demonstrate a broad set of transitional nanostructural patterns.

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.

Eyes of other insect and even arachnid orders are either smooth or covered by nanocoatings of the patterns described above.

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).

Turing Modeling of Corneal Nanopatterns.

The Turing reaction–diffusion system of differential equations was used,∂u∂t=F(u,v)+DuΔu∂v∂t=G(u,v)+DvΔv[S1]where u and v are concentrations of the two interacting morphogens: activator (u) and inhibitor (v) (Fig. S4B). Although, in typical Turing applications, morphogen production and degradation are analyzed, we here presume that both types of molecules are produced and secreted into the lens by the cone cells in a preset manner, and it is the ability of these molecules to aggregate/polymerize that is controlled by the Turing-type mechanisms.

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 D_u and D_v. 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:fu=∂F∂u,fv=∂F∂v,gu=∂G∂u,gv=∂G∂v.[S2]In the subsequent analysis, we set f_u > 0 (activator stimulates its own aggregation); f_v < 0 (inhibitor suppresses aggregation of the activator); g_u > 0 (activator stimulates activity of the inhibitor); g_v < 0 (inhibitor depolymerizes); and D_v > D_u (inhibitor diffuses faster than activator). This presetting allows forming the diffusion-driven instability through the activator–inhibitor scheme (20); the other scheme [substrate depletion (20)] is not considered here.

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 asG(u,v)=avu+bvv+cv−dvvF(u,v)=auu+buv+cu−duu. [S3]Two further parameters, d_u and d_v, are present in Eq. S3 and in the modeling used in our paper to produce patterns on Fig. 3 and Fig. S4. Substitutingbv′=bv−dvau′=au−du[S4]and simplifying b_v′ and a_u′, the F(u,v) and G(u,v) functions gain the easier formF(u,v)=auu+buv+cuG(u,v)=avu+bvv+cv. [S5]Finally, the initial reaction–diffusion set of Eqs. S1 becomes∂u∂t=auu+buv+cu+DuΔu∂v∂t=avu+bvv+cv+DvΔv.[S6]Schematically, these parameters of the Turing model are presented in Fig. S4B.

Using Eq. S2, one can see that fu=au,fv=bu,gu=av,gv=bv. In the current system, the concentrations u and v have the dimensions of [(number of molecules)/length³]. The parameters a, b, and c represent the rates of the respective reactions, and thus dimensions of a and b are [time⁻¹], and of c – [(number of molecules)/(time × length³)]. The diffusion coefficients D have the dimensions of [length²/time].

The solution of the system of Eqs. S6 can be given, following ref. 20, as the sum of general solutions,w∝eλt⁡sin(kx)[S7]where λ is the solution eigenvalue with a particular wavenumber k. The wavenumber k determines the size of the patterns, whereas λ determines the speed of increase or decrease of harmonics with the given k. Because the periodic structures with the negative eigenvalue will dampen with time, whereas those with the positive one increase with time, a stable Turing structure should typically has positive λ. Miura and Maini (20) have shown that the maximal λ can be obtained ifk2=−DuDv(fu−gv)+(Du+Dv)−DuDvfvguDuDv(Dv−Du) .[S8]Following ref. 34, the wavelength ω can be then calculated asω=2πk .[S9]To determine the order of magnitude of the parameters of our system, we assume that the diffusion coefficients have the same order, as do the rate constants. We set them, respectively, as D and f. Using Eq. S8 and reducing the similar terms, we conclude thatk2∝fD,⇒ω∝10Df .[S10]As the period of the final structure in the patterns (i.e., cross section of the nipple or dimple or ridge in mazes and strands) will be of the same order as the wavelength corresponding to the maximal positive eigenvalue of the system of equations, we can determine the order of magnitude of the diffusion coefficients and the reaction rate constants.

BecauseD∝ω2100f, [S11]the diffusion constants become proportional to the reaction rate constants. Given that the nanopatterns we describe are of the order of 10⁻⁵ cm, the relation above becomesD∝10−12f ,[S12]dimensions of diffusion coefficients being square centimeters per second, and reaction rate constants being per second.

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):

View this table:

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 ω_max, corresponding the maximal eigenvalue λ, from the parameters (D_u, D_v), (f_u, g_v), and (f_v, g_u). 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.

Acknowledgments

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.).

Footnotes

↵¹To whom correspondence may be addressed. Email: vladimir.katanaev{at}unil.ch or bswin2000{at}gmail.com.

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.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1505748112/-/DCSupplemental.

Freely available online through the PNAS open access option.

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Proceedings of the National Academy of Sciences: 112 (34)

Table of Contents

Submit

[1] ↵
Gilbert SF
(2014) Developmental Biology (Sinauer Assoc, Sunderland, MA), 10th Ed
.

[2] Gilbert SF

[3] ↵
Stavenga DG,
Foletti S,
Palasantzas G,
Arikawa K
(2006) Light on the moth-eye corneal nipple array of butterflies. Proc Biol Sci 273(1587):661–667
.
OpenUrl Abstract/FREE Full Text

[4] Stavenga DG,

[5] Foletti S,

[6] Palasantzas G,

[7] Arikawa K

[8] ↵
Bernhard CG,
Miller WH
(1962) A corneal nipple pattern in insect compound eyes. Acta Physiol Scand 56:385–386
.
OpenUrl CrossRef PubMed

[9] Bernhard CG,

[10] Miller WH

[11] ↵
Bernhard CG,
Miller WH,
Moller AR
(1963) Function of the corneal nipples in the compound eyes of insects. Acta Physiol Scand 58:381–382
.
OpenUrl CrossRef PubMed

[12] Bernhard CG,

[13] Miller WH,

[14] Moller AR

[15] ↵
Bernhard CG,
Gemne G,
Sällström J
(1970) Comparative ultrastructure of corneal surface topography in insects with aspects on phylogenesis and function. J Comp Physiol A 67(1):1–25
.
OpenUrl

[16] Bernhard CG,

[17] Gemne G,

[18] Sällström J

[19] ↵
Kryuchkov M, et al.
(2011) Analysis of micro- and nano-structures of the corneal surface of Drosophila and its mutants by atomic force microscopy and optical diffraction. PLoS One 6(7):e22237
.
OpenUrl CrossRef PubMed

[20] Kryuchkov M, et al.

[21] ↵
Sukontason KL, et al.
(2008) Ommatidia of blow fly, house fly, and flesh fly: Implication of their vision efficiency. Parasitol Res 103(1):123–131
.
OpenUrl CrossRef PubMed

[22] Sukontason KL, et al.

[23] ↵
Watson GS,
Myhra S,
Cribb BW,
Watson JA
(2008) Putative functions and functional efficiency of ordered cuticular nanoarrays on insect wings. Biophys J 94(8):3352–3360
.
OpenUrl CrossRef PubMed

[24] Watson GS,

[25] Myhra S,

[26] Cribb BW,

[27] Watson JA

[28] ↵
Dewan R, et al.
(2012) Studying nanostructured nipple arrays of moth eye facets helps to design better thin film solar cells. Bioinspir Biomim 7(1):016003
.
OpenUrl CrossRef PubMed

[29] Dewan R, et al.

[30] ↵
Peisker H,
Gorb SN
(2010) Always on the bright side of life: Anti-adhesive properties of insect ommatidia grating. J Exp Biol 213(Pt 20):3457–3462
.
OpenUrl Abstract/FREE Full Text

[31] Peisker H,

[32] Gorb SN

[33] ↵
Huang YF, et al.
(2007) Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures. Nat Nanotechnol 2(12):770–774
.
OpenUrl CrossRef PubMed

[34] Huang YF, et al.

[35] ↵
Nalwa HS
Palasantzas G,
De Hosson JTM,
Michielsen KFL,
Stavenga DG
(2005) Optical properties and wettability of nanostructured biomaterials: Moth eyes, lotus leaves, and insect wings. Handbook of Nanostructured Biomaterials and their Applications in Nanobiotechnology, ed Nalwa HS (Am Sci Publ, Valencia, CA), Vol 1, pp 273–301
.
OpenUrl

[36] Nalwa HS

[37] Palasantzas G,

[38] De Hosson JTM,

[39] Michielsen KFL,

[40] Stavenga DG

[41] ↵
Blagodatski A, et al.
(2014) Under- and over-water halves of Gyrinidae beetle eyes harbor different corneal nanocoatings providing adaptation to the water and air environments. Sci Rep 4:6004
.
OpenUrl PubMed

[42] Blagodatski A, et al.

[43] ↵
Fröhlich A
(2001) A scanning electron-microscopic study of apical contacts in the eye during postembryonic development of Drosophila melanogaster. Cell Tissue Res 303(1):117–128
.
OpenUrl CrossRef PubMed

[44] Fröhlich A

[45] ↵
Turing AM
(1952) The chemical basis of morphogenesis. Philos Trans R Soc B 237(641):37–72
.
OpenUrl Abstract/FREE Full Text

[46] Turing AM

[47] ↵
Kondo S,
Miura T
(2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(5999):1616–1620
.
OpenUrl Abstract/FREE Full Text

[48] Kondo S,

[49] Miura T

[50] ↵
Nakamasu A,
Takahashi G,
Kanbe A,
Kondo S
(2009) Interactions between zebrafish pigment cells responsible for the generation of Turing patterns. Proc Natl Acad Sci USA 106(21):8429–8434
.
OpenUrl Abstract/FREE Full Text

[51] Nakamasu A,

[52] Takahashi G,

[53] Kanbe A,

[54] Kondo S

[55] ↵
Sick S,
Reinker S,
Timmer J,
Schlake T
(2006) WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism. Science 314(5804):1447–1450
.
OpenUrl Abstract/FREE Full Text

[56] Sick S,

[57] Reinker S,

[58] Timmer J,

[59] Schlake T

[60] ↵
Raspopovic J,
Marcon L,
Russo L,
Sharpe J
(2014) Modeling digits. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science 345(6196):566–570
.
OpenUrl Abstract/FREE Full Text

[61] Raspopovic J,

[62] Marcon L,

[63] Russo L,

[64] Sharpe J

[65] ↵
Miura T,
Maini PK
(2004) Speed of pattern appearance in reaction–diffusion models: Implications in the pattern formation of limb bud mesenchyme cells. Bull Math Biol 66(4):627–649
.
OpenUrl CrossRef PubMed

[66] Miura T,

[67] Maini PK

[68] ↵
Tardieu A
(1988) Eye lens proteins and transparency: From light transmission theory to solution X-ray structural analysis. Annu Rev Biophys Biophys Chem 17:47–70
.
OpenUrl CrossRef PubMed

[69] Tardieu A

[70] ↵
Miura T,
Maini PK
(2004) Periodic pattern formation in reaction–diffusion systems: An introduction for numerical simulation. Anat Sci Int 79(3):112–123
.
OpenUrl CrossRef PubMed

[71] Miura T,

[72] Maini PK

[73] ↵
Chipman AD, et al.
(2014) The first myriapod genome sequence reveals conservative arthropod gene content and genome organisation in the centipede Strigamia maritima. PLoS Biol 12(11):e1002005
.
OpenUrl CrossRef PubMed

[74] Chipman AD, et al.

[75] ↵
Ishiwata K,
Sasaki G,
Ogawa J,
Miyata T,
Su ZH
(2011) Phylogenetic relationships among insect orders based on three nuclear protein-coding gene sequences. Mol Phylogenet Evol 58(2):169–180
.
OpenUrl CrossRef PubMed

[76] Ishiwata K,

[77] Sasaki G,

[78] Ogawa J,

[79] Miyata T,

[80] Su ZH

[81] ↵
Boseman A,
Nowlin K,
Ashraf S,
Yang J,
Lajeunesse D
(2013) Ultrastructural analysis of wild type and mutant Drosophila melanogaster using helium ion microscopy. Micron 51:26–35
.
OpenUrl CrossRef PubMed

[82] Boseman A,

[83] Nowlin K,

[84] Ashraf S,

[85] Yang J,

[86] Lajeunesse D

[87] ↵
Meyer-Rochow VB,
Stringer IA
(1993) A system of regular ridges instead of nipples on a compound eye that has to operate near the diffraction limit. Vision Res 33(18):2645–2647
.
OpenUrl CrossRef PubMed

[88] Meyer-Rochow VB,

[89] Stringer IA

[90] ↵
Clay Smith W,
Butler JF
(1991) Ultrastructure of the Tabanidae compound eye: Unusual features for Diptera. J Insect Physiol 37(4):287–296
.
OpenUrl CrossRef

[91] Clay Smith W,

[92] Butler JF

[93] ↵
Parker AR,
Hegedus Z,
Watts RA
(1998) Solar–absorber antireflector on the eye of an Eocene fly (45 Ma). Proc R Soc B 265(1398):811–815
.
OpenUrl Abstract/FREE Full Text

[94] Parker AR,

[95] Hegedus Z,

[96] Watts RA

[97] ↵
Anderson MS,
Gaimari SD
(2003) Raman-atomic force microscopy of the ommatidial surfaces of Dipteran compound eyes. J Struct Biol 142(3):364–368
.
OpenUrl CrossRef PubMed

[98] Anderson MS,

[99] Gaimari SD

[100] ↵
Chu H,
Norris DM,
Carlson SD
(1975) Ultrastructure of the compound eye of the diploid female beetle, Xyleborus ferrugineus. Cell Tissue Res 165(1):23–36
.
OpenUrl PubMed

[101] Chu H,

[102] Norris DM,

[103] Carlson SD

[104] ↵
Mishra M,
Meyer-Rochow VB
(2006) Eye ultrastructure in the pollen-feeding beetle, Xanthochroa luteipennis (Coleoptera: Cucujiformia: Oedemeridae). J Electron Microsc (Tokyo) 55(6):289–300
.
OpenUrl Abstract/FREE Full Text

[105] Mishra M,

[106] Meyer-Rochow VB

[107] ↵
Dey S,
Dkhar B
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Diverse set of Turing nanopatterns coat corneae across insect lineages

Significance

Abstract

Methods

Insect Specimens.

Atomic Force Microscopy.

Turing Modeling.

SI Text

Detailed Description of Diverse Corneal Nanostructures Order by Order.

Trichopteran eye surfaces reveal merged nipples and a maze-like structure.

Dipteran eye surfaces reveal nipples merging into parallel strands and mazes.

The related orders Mecoptera and Siphonaptera carry distinct corneal nanostructures.

Megaloptera, Raphidioptera, and Neuroptera carry irregular nipples with partial merging and size variation.

Coleopteran eyes show smooth surface or maze-like structures of different proportions as well as dimples.

Corneal nanocoatings of Hymenoptera demonstrate a dimple-to-maze transition.

Hemipterans demonstrate a broad set of transitional nanostructural patterns.

Eyes of other insect and even arachnid orders are either smooth or covered by nanocoatings of the patterns described above.

Turing Modeling of Corneal Nanopatterns.

Acknowledgments

Footnotes

References

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Significance

Abstract

Methods

Insect Specimens.

Atomic Force Microscopy.

Turing Modeling.

SI Text

Detailed Description of Diverse Corneal Nanostructures Order by Order.

Trichopteran eye surfaces reveal merged nipples and a maze-like structure.

Dipteran eye surfaces reveal nipples merging into parallel strands and mazes.

The related orders Mecoptera and Siphonaptera carry distinct corneal nanostructures.

Megaloptera, Raphidioptera, and Neuroptera carry irregular nipples with partial merging and size variation.

Coleopteran eyes show smooth surface or maze-like structures of different proportions as well as dimples.

Corneal nanocoatings of Hymenoptera demonstrate a dimple-to-maze transition.

Hemipterans demonstrate a broad set of transitional nanostructural patterns.

Eyes of other insect and even arachnid orders are either smooth or covered by nanocoatings of the patterns described above.

Turing Modeling of Corneal Nanopatterns.

Acknowledgments

Footnotes

References

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Article Classifications

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