Structure, Function, and Self-Assembly of Single Network Gyroid (I4132) Photonic Crystals in Butterfly Wing Scales
biological meta-materials, organismal color, biomimetics, biological cubic mesophases
Small angle X-ray scattering (SAXS) was used to identify the 3D photonic nanostructures (made of chitin and air) of five butterfly species from two families (Papilionidae, Lycaenidae) as single network gyroid (<math>I4_132</math>) photonic crystals. Photonic band-gap modeling was also performed. Butterflies first develop thermodynamically favored double gyroid precursors and transform these into a single gyroid network which is optically more efficient.
Results and Discussion
A periodic variation in the refractive index on the order of visible wavelengths gives butterflies its structural colors. Pinhole synchrotron small angle X-ray scattering (SAXS) has been used to investigate natural photonic materials with mesoscale (150–350 nm) scattering features (Fig. 2). The order of the lattice constant in these cases require small scattering angles and advanced X-ray optics. Five butterflies species were tested: Parides sesostris, Teinopalpus imperialis, (Papilionidae); Callophrys (formerly Mitoura) gryneus, Callophrys dumetorum, and Cyanophrys herodotus (Lycaenidae) (Fig. 1).
Figure 2 shows SAXS patterns of these species which predict distinctly oriented crystallite domains that have also been indicated with SEM (Fig. 1 B and E). These results are consistent with the size of the X-ray beam (15 × 15 μm). The unit cell lattice constant of the butterfly scale photonic nanostructures was estimated as a > 300nm which is consistent with EM-estimated lattice parameters assuming a single gyroid space group, rather than a simple primitive or a single diamond symmetry. Higher-order reflections in T. imperialis, C. gryneus, and C. herodotus (Figs. 2 and 3) proves a high degree of order within the nanostructure. Computer models of the single gyroid, simple primitive, and single diamond nanostructures were also performed, which produced simulated TEM and SEM projections of appropriate thicknesses and chitin volume fractions, along various lattice directions/cleavage planes, including (110), (111), and (211). SEM and TEM images of all five butterfly show characteristics of the single gyroid space group (Fig. 1 B and E, and Fig. S1 B, E, and H).
For each species, the optical and X-ray scattering peaks agree reasonably well (< ∼ 15 nm) with a value of 1.16 for nav, which corresponds to a chitin volume fraction of 0.25 (Fig. 4).
The breadth of the predicted reflectance peaks (Fig. 4 and Fig. S2) are a result of single scattering from multiple randomly oriented crystallite domains, which is captured by the azimuthal averages of the SAXS data
Our estimates of nav are also comparable to previous estimates based on electron micrographs (8, 18). Bandgap calculations predict three relatively closely spaced pseudogaps or partial photonic bandgaps along Γ-N (110), Γ-P (111), and Γ-H (200) directions for the butterfly photonic nanostructures
Bragg attenuation lengths of the butterfly nanostructures to be between 3.9–4.4 a (Table S1). Except for C. dumetorum, the average size of the crystallite domains is several times larger than the Bragg length of the corresponding nanostructure (Table S1). Along with the congruence of our photonic bandgap analyses to optical measurements (Fig. S7), this result suggests that most or all of the incident light is essentially reflected when the Bragg condition is satisfied, and that the broader reflectance spectra observed for the optical reflectance as compared to the SAXS single-scattering reflectance predictions is due to multiple scattering.
Here we present a model for the development of the 3D photonic nanostructure in the wing scale cells of lepidopteran pupae. Based on published TEM images of the nanostructure in developing pupae of C. gryneus (11, 21) (Fig. 5A), we hypothesize that the cell plasma membrane and the SER membrane interact to form a pair of parallel lipid-bilayer membranes, separated by the cellular cytoplasm. The two parallel lipid-bilayer membranes of the developing scale cell form a pentacontinuous structure with a core-shell double gyroid morphology, similar to those seen in ABC triblock copolymer melts (40, 41) (Fig. 5 A and B). Exploiting the inherent biological differentiation between the intracellular and extracellular volumes of a cell, the lipid-bilayer membranes of developing butterfly photonic scale cells define the unique pentacontinuous volumes of a core-shell double gyroid (Ia3d) structure of the form ABCB′A′, in which A is the extracellular space, B is the plasma membrane, C is the cell’s cytoplasmic volume, B′ is the SER membrane, and A′ is the intra-SER space (Fig. 5A and Insets). As in a triblock copolymer system, the proposed ABCB′A′ core-shell double gyroid system in the butterfly scale has the lipid-bilayer membranes (B and B′) together with the intervening cytoplasmic space (C) forming the matrix phase (BCB′) of the system. The complexity of this biological double gyroid with distinctly differentiated core-shells can be appreciated more fully through a movie of serial sections from various angles
chitin is deposited and polymerized in the extracellular space (A) that is now within the peripheral outline of the scale cell. This extracellular space forms the core of one of the gyroid networks (Fig. 5C, red), which is enclosed by the plasma membrane (Fig. 5C, black). As the cell dies, the cellular cytoplasm and the membranes (BCB0A0 blocks of the core-shell double gyroid) are replaced with air, leaving behind a single gyroid network of chitin (A) in air (Fig. 5C). We present a visualization of this transformation and the associated changes in structure factors of the developing nanostructure in Movie S2. Published TEM images by H. Ghiradella (11, 16, 21) of a developing butterfly wing scale exhibit the diagnostic double gyroid motif of two concentric thick black rings arranged in a triangular lattice found in triblock-copolymers (Fig. 5 A and B). Sections through the (110) plane of a core-shell double gyroid model structure reproduces such a pattern (Fig. 5A and Insets, and Movie S1). Furthermore, the TEM section in Fig. 5A (from 11) strikingly shows two different regions through the (110) plane, confirming our model. To the right (Fig. 5A, red square), initial chitin deposition is visible as dark lines in the spaces surrounding the double rings, whereas on the left (Fig. 5A, yellow square), chitin rods are visible as dark spots in the center of the double rings. The chirality of the resulting single gyroid nanostructure is not straightforward to ascertain from TEM or SAXS data (42). However, visual inspection of SEM images reveals clear examples of single gyroid networks with both left- and right-handed chiralities (Fig. S8). Although the original EM images were not all obtained in an unbiased manner, i.e., from multiple independent domains, it appears that both chiralities occur at similar frequencies, but further EM observations are necessary to confirm this. However, this implies that the initiation of gyroid chirality during development is random across the domains within a single scale cell, as hypothesized for symmetric amphiphilic systems (42). Our developmental model proposes that the butterfly scale cells exploit the energetics of cubic membrane folding commonly seen in lipid-bilayer membranes of cellular organelles (34–36) to develop a single gyroid photonic nanostructures that are used in social
By initially developing the thermodynamically favored double gyroid nanostructure (29, 37–39), and then transforming it into the optically more efficient single gyroid photonic crystal (43, 44), these butterflies have evolved to use biological and physical mechanisms that anticipate contemporary approaches to the engineering and manufacture of photonic materials
Thus, it is likely that the perforated lamellar morphology shares the same general membrane folding developmental mechanism that produces the gyroid morphology seen in these closely related species.