Gyroid networks in butterflies

Triply periodic minimal surfaces are excellent examples of the importance of geometrical principles in understanding materials at nano-sized length scales. These can be most notably observed in the biophotonic structures of weevil and butterfly wing scales.

An uncommon occurrence of these complex structured solids is found in the hierarchical structure of the single gyroid chitin nanostructure in the butterfly species Thecla opisena (Figure 1),^{Reference Saba, Thiel, Turner, Hyde, Gu, Grosse-Brauckmann, Neshev, Mecke and Schröder-Turk23} where each “crystallite” of a wing scale is in fact a single crystal of a single network gyroid structure.^{Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20} In general, butterfly wing scales are hollow “casings” with dimensions of ∼200 × 60 × 5 µm^{Reference Srinivasarao3} with the upper, outward-facing side forming a porous cross-hatched lattice of “ribs” and “cross-ribs.” Gyroid photonic structures, when present, are found inside the casing, which is called lumen, and are normally observed in a space-filling, multidomain nature.^{Reference Saranathan, Seago, Sandy, Narayanan, Mochrie, Dufresne, Cao, Osuji and Prum19,Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20,Reference Wilts, Michielsen, De Raedt and Stavenga24}

Figure 1.

(a–d) Hierarchical nanostructural organization of gyroid crystallites in the Neotropical Green Hairstreak butterfly, Thecla opisena.^{Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20} (e) Model of a single gyroid network with a demonstration of two of the high-symmetry orientations.^{Reference Saba, Thiel, Turner, Hyde, Gu, Grosse-Brauckmann, Neshev, Mecke and Schröder-Turk23}

In contrast to other gyroid-forming butterfly species (e.g., the Emerald-patched Cattlehear, Parides sesostris; the Green Hairstreak, Callophrys rubi; or the Kaiser-i-Hind, Teinopalpus imperialis),^{Reference Wilts, Michielsen, De Raedt and Stavenga24–Reference Schröder-Turk, Wickham, Averdunk, Brink, Fitz Gerald, Poladian, Large and Hyde28} in T. opisena the gyroid nanostructure forms disconnected micron-sized crystallites of a single orientation and handedness—without internal defects. This structure is particularly exciting as it allows a glimpse into the development of these structures, as inferences from multidomain structures are strenuous and inconclusive.

Disordered networks in birds

The amazing variety of structural color in nature is not restricted to ordered photonic structures such as the gyroid, but can also result from quasi-ordered materials.^{Reference John29,Reference Yablonovitch30} A prominent example is the feathers of the kingfisher and parrot, where bright structural color arises from the interference of light with disordered network-like morphologies created from keratin.^{Reference Saranathan, Forster, Noh, Liew, Mochrie, Cao, Dufresne and Prum31–Reference Stavenga, Tinbergen, Leertouwer and Wilts36} An isotropic bandgap can be exhibited from quasi-ordered nanostructures, resulting in angle-independent colors (Figure 2a–d).

Figure 2.

Disordered photonics of a scarlet macaw feather. (a) Scarlet macaw, Ara macao. (b, c) The photonic structure is present in the outermost cells of the barbs, covered by a transparent envelope. (d) Scanning electron microscope image showing a disordered network. (e) The underlying growth process is assumed to be spinodal decomposition. Shown here is a schematic phase diagram of a polymer solution as a function of polymer volume fraction, ϕ, temperature, T, and interaction parameter, χ. The black line indicates the phase boundary that separates the single-phase system (above) from a solution that separates into two distinct phases either via spinodal decomposition or nucleation and growth. (b–d) Adapted with permission from Reference Reference Yin, Dong, Liu, Zhan, Shi, Zi and Yablonovitch38. © 2012 National Academy of Sciences. (e) Adapted with permission from References Reference Dufresne, Noh, Saranathan, Mochrie, Cao and Prum52 and Reference Prum, Dufresne, Quinn and Waters54. © 2009 Royal Society of Chemistry and The Royal Society, respectively. Note: k _B, Boltzmann constant.

At first glance, these network morphologies look random, but at closer inspection, a dominant length scale of ∼180–250 nm can be found in the networks.^{Reference Saranathan, Forster, Noh, Liew, Mochrie, Cao, Dufresne and Prum31,Reference Prum, Torres, Williamson and Dyck34,Reference Stavenga, Tinbergen, Leertouwer and Wilts36} This length scale, together with the mean refractive index of keratin of ∼1.55,^{Reference Leertouwer, Wilts and Stavenga37} results in the blue and green colors observed in many bird barbs. Yin and colleagues^{Reference Yin, Dong, Liu, Zhan, Shi, Zi and Yablonovitch38} described these structures as “amorphous” diamond. Whether the growth and assembly of these disordered structures is identical to the growth of the ordered structures will be discussed next.

Biological bicontinuous structures’ unique properties

Biological optical nanostructures are remarkable for a number of reasons: (1) Large structural length scales—the length scale is often an order of magnitude or more above what can be achieved in synthetic self-assembled systems.^{Reference Dolan, Wilts, Vignolini, Baumberg, Steiner and Wilkinson8,Reference Angelov, Angelova, Drechsler, Garamus, Mutafchieva and Lesieur39} (2) Solid form—complex nanostructures in animals appear in a solid form, made from simple biomaterials, such as keratin or chitin, that have been synthesized at ambient conditions. (3) Single-network structures—bicontinuous nanostructures occur in their “single form” (i.e., consisting of a single solid component and a single void component). In synthetic systems,^{Reference Cao, Xu, Yao, Han, Terasaki and Che40} single systems are largely unknown. (4) Chirality—the chiral single gyroid structure in the Green Hairstreak butterfly reveals a bias for one of the two enantiomers.^{Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20,Reference Winter, Butz, Dieker, Schröder-Turk, Mecke and Spiecker26} All of these properties make them excellent candidates for bioinspired applications.

Growth of ordered structures

Conceptual models for the growth and development of butterfly cubic nanostructures have been proposed by Ghiradella^{Reference Ghiradella41,Reference Ghiradella42} and others.^{Reference Saranathan, Osuji, Mochrie, Noh, Narayanan, Sandy, Dufresne and Prum43} Ghiradella associated this class of complex nanomorphologies with self-assembly of lipid membranes almost 30 years ago,^{Reference Ghiradella44,Reference Ghiradella and Locke45} based on detailed studies of the growth of wing scales within butterfly pupae (Figure 3). Figure 3a shows a cross-sectional scheme of a developing wing scale, derived from the transmission electron microscope (TEM) cross section shown in the inset. The resulting single gyroid structures (Figure 3b–c) can have a complex, single crystalline shape.

Figure 3.

(a) Ghiradella’s model for the formation of wing scale nanostructures, as based on postmortem transmission electron micrographs of the developing wing scale. (b) Scanning electron microscope image of a faceted gyroid allows us to draw conclusions about the growth mechanism (c).^{Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20} (a) Adapted with permission from Reference Reference Ghiradella44. © 1989 Wiley.

In fact, each wing scale of an adult butterfly corresponds to a single developing cell, which adopts (through F-actin^{Reference Dinwiddie, Null, Pizzano, Chuong, Krup, Tan and Patel46}) a highly anisotropic shape during development (Figure 4). During cell growth, the cell membrane (magenta) envelops the interior, while an internal network of F-actin (yellow) shapes the organization inside the cell resulting in three-dimensional forms. The internal nanostructure resulting in the complex structured networks has been suggested to form by a process where the intracellular endoplasmic reticulum membrane adopts an achiral double gyroid shape (similar to those reported in other intracellular membranes).^{Reference Almsherqi, Landh, Kohlwein and Deng18} Ghiradella’s model, a model that is now commonly used,^{Reference Saranathan, Seago, Sandy, Narayanan, Mochrie, Dufresne, Cao, Osuji and Prum19,Reference Saranathan, Osuji, Mochrie, Noh, Narayanan, Sandy, Dufresne and Prum47} states that the topologically complex chitin matrix seen in mature wing scales is formed by gradual polymerization of chitin oligomers within a water matrix defined by the bounding lipid membrane, where the lipid membrane spontaneously forms the gyroid structure. Chitin is then extruded into the network-like domain connected to the extracellular space, and solidifies as the cell dies off—leaving the observed single-network gyroid structures behind.

Figure 4.

(a, b) Confocal laser scanning microscope allows 3D imaging of wing scale development of wing scale cells of Junonia coenia at 32% of pupal development, stained for the cell membrane (magenta) and F-actin (yellow). The wing scales are already elongated, anisotropic in shape and the lumen becomes discernible. A field of scales is viewed from the apical surface in (a), while a cross section of two scales is shown in (b). This level of detail can only be imaged postmortem with the appropriate fluorescent markers.^{Reference Dinwiddie, Null, Pizzano, Chuong, Krup, Tan and Patel46}

This model is based on inferences from the postmortem study of butterfly pupae using two-dimensional TEM cross sections—and not on dynamic time-dependent studies. Performing such measurements is difficult, and little development has followed up on Ghiradella’s seminal studies. Recently, the study of the Neotropical Hairstreak butterfly T. opisena, with its isolated single-crystalline gyroid domains, has allowed the postmortem elucidation of details of this time-dependent process. By analyzing the pigment composition, the handedness of the single gyroids and the crystalline nature, Wilts et al. inferred that the gyroid is grown in a multistep process, by which an initially liquid water-lipid system is infiltrated by chitin and subsequently polymerized.^{Reference Wilts, Zubiri, Klatt, Butz, Fischer, Kelly, Spiecker, Steiner and Schröder-Turk20} Whether or not the membrane organelle takes the complex gyroid shapes upon membrane presence of the chitin or whether it is prefolded within the cell is still a debated topic.

The current model for the formation of ordered structures is inferred from scanning electron microscope images, and is ultimately somewhat speculative. To date, there has been no systematic experimental work confirming this mechanism due to difficulties in imaging folding tissue in vivo, due to the difficulty in imaging processes on this length scale deep within the optically thick tissue of a butterfly chrysalis over an extended period of time. Recent advances in the labeling of wing scale substructure during development (though primarily applied postmortem)^{Reference Dinwiddie, Null, Pizzano, Chuong, Krup, Tan and Patel46} and the isolated growth of individual wings within cell cultures^{Reference Parker and Townley48} might lead to further insight into the nonequilibrium development processes in the near future.

There has been substantial recent progress in imaging techniques for biological tissues, with specific areas of application. Super-resolution microscopy allows imaging with a routine resolution of ∼40 nm, but relies on the availability of substructure-specific dyes and—usually—postmortem fixed samples.^{Reference Dinwiddie, Null, Pizzano, Chuong, Krup, Tan and Patel46,Reference Guo, Li, Zhang, Yang, Liu, Wang, Liu, Milkie, Moore, Tulu, Kiehart, Hu, Lippincott-Schwartz, Betzig and Li49} The imaging of developing tissue in vivo would require transgenic butterfly lines that express fluorescent proteins specific to the structure that one wishes to image in a nonlethal way. Environmental electron microscopy allows imaging of wet samples at reduced pressure, but is significantly limited to thin samples or surface observations.^{Reference Wagner, Cavalca, Damsgaard, Duchstein and Hansen50}

For the butterfly system discussed here, it is now possible to grow butterfly species in a lab environment (with the pupae suitably dissected so that the developing wing scales can be observed using light microscopy from the outside. What is missing for this butterfly system and for many other membrane-structured systems with length scales in the range of 10–100 nm, including plant chloroplasts^{Reference Pribil, Labs and Leister51}) is an imaging system that allows imaging the cellular dynamics in vivo.

Growth or self-assembly of disordered structures?

While the previously discussed growth model holds true for periodic micromorphologies, quasi-ordered systems could also be produced in this fashion. This could be achieved either by incorporating elements (e.g., membrane proteins) that disturb the periodic assembly of the lipid membrane, or by “freezing-in” the (then disordered) structure far from its thermodynamic equilibrium.

However, the growth model most commonly assumed to lead to the quasi-ordered network morphologies within a feather barb is spinodal decomposition^{Reference Dufresne, Noh, Saranathan, Mochrie, Cao and Prum52} (i.e., the process driving the spontaneous demixing of two immiscible components).^{Reference Saranathan, Forster, Noh, Liew, Mochrie, Cao, Dufresne and Prum31,Reference Dufresne, Noh, Saranathan, Mochrie, Cao and Prum52,Reference Dong, Zhan, Liu, Jiang, Liu, Hu and Zi53} Phase separation usually occurs through either spinodal decomposition or nucleation and growth, depending on the position in phase space and the kinetics of the system. Spinodally demixed structures are usually channel-like, can be described as self-similar, can be found from the cosmic scale down to the nanoscale and are most readily observed in phase-separating mixtures. Energetically, spinodal decomposition arises in mixtures with little (or no) energetic barrier for the nucleation of a phase, quite in contrast to nucleation and growth processes where the nucleation is subject to a large energetic penalty.

Prum and colleagues showed that the color-producing channel-type nanostructures develop intracellularly in the absence of any biological prepattern created by a cell membrane in a TEM study of developing feather barbs of the blue-and-yellow macaw (Ara ararauna) that were arrested in growth.^{Reference Prum, Dufresne, Quinn and Waters54} The authors argue that the color-producing, intracellular, quasi-ordered nanostructures develop their characteristic sizes and shapes by phase separation, via spinodal decomposition of keratin in the cellular watery matrix (Figure 2e). The shape and size of these self-assembled, intracellular nanostructures are determined by phase separation of keratin proteins from the cytoplasm of the cell rather than a membrane-supported growth process as in the ordered structures.