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Supporting Information Supporting Information Saranathan et al. 10.1073/pnas.0909616107 SI Text coated and studied on an ISI-SS40 SEM and a Philips XL 30 We use the following formula to convert between chitin filling environmental SEM, at a range of tilt angles from −10° to 45°. f n fraction, c, and average refractive index, avg: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fibre optic spectrophotometry. Normal-incidence reflectance spec- n ¼ f n2 þð1 − f Þn2 ; [S1] avg c c c air tra of the structurally colored butterfly wings were measured with an Ocean Optics S2000 fiber optic spectrophotometer and an n n Ocean Optics deuterium-halogen light source on a Macintosh where c is the refractive index of chitin (1) (1.56), and air is that of air. computer, using standard procedure (3). The S2000 provides 2,048 data points between 178 and 879 nm. Reflectance was measured using normal incident light at a distance of 6 mm from SI Materials and Methods. Specimens. We analyzed the nanostruc- 3 2 ture and structural color production in five butterfly species from a mm patch of the integument with a 500 ms integration time two different lepidopteran families (Table S1): The green dorsal and calibrated using an Ocean Optics Spectralon matte white wing scales of the papilionids, Parides sesostris and Teinopalpus standard. imperialis; and the green ventral wing scales of the lycaenids, Cal- lophrys dumetorum, Callophrys (formerly Mitoura) gryneus,and Level set triply periodic minimal surface (TPMS) modeling. The center Cyanophrys herodotus (a close congener of Cyanophrys remus). of the invaginating lipid-bilayer plasma membrane during the de- Small (<1 cm2) samples of structurally colored butterfly wings velopment of the butterfly scale nanostructures is an example of a were taken from specimens obtained from the Snow Entomology TPMS that divides a volume into two bicontinuous, nonintersect- ’ G Collection of the University of Kansas Museum of Natural ing networks, namely Schoen s (space group Ia3d) surface (4). History and Yale Peabody Museum of Natural History. The interface of the two phases can also be described as constant mean curvature (CMC) surfaces because they possess net zero curvature throughout their volume, or as constant thickness Indexing small angle X-ray scattering (SAXS) data. We consulted the (CT) surfaces. These CMC and CT surfaces can be conveniently International Union of Crystallography (IUCr) International modeled in silico by their level set approximations (Eq. 2 from the Tables for Crystallography (2) to index the SAXS peaks and main text) (5, 6). assign crystallographic space group symmetries to the butterfly Three-dimensional level set approximations (6) of gyroid nanostructures. structures were volume rendered using MATLAB. Artificial sections of appropriate thicknesses, simulating SEM and TEM Optical microscopy. Light micrographs of the specimens were sections, were made from the 3D volumes visualized using the obtained on a Zeiss AxioCam stereo light microscope using a University of California, San Francisco Chimera package 0.63× objective at various magnifications. (http://www.cgl.ucsf.edu/chimera). The volume fractions of chi- tin, obtained from published sources (3, 5) and our own TEM Electron microscopy. We followed standard embedding procedures images, as well as from SAXS data (Tables S1 and S2) were used for TEM (3). For SEM, freeze-fractured samples were gold to make the simulated sections biologically relevant. 1. Vukusic P, Sambles JR, Lawrence CR, Wootton RJ (1999) Quantified interference and 7. Kertész K, et al. (2006) Gleaming and dull surface textures from photonic-crystal-type diffraction in single Morpho butterfly scales. P Roy Soc Lond B Bio 266(1427): nanostructures in the butterfly Cyanophrys remus. Phys Rev E 74(2, Pt 1):021922, 1403–1411. http://pre.aps.org/abstract/PRE/v74/i2/e021922. 2. Hahn T (2006) The 230 space groups. IUCr International Tables for Crystallography 8. Almsherqi ZA, Kohlwein SD, Deng Y (2006) Cubic membranes: A legend beyond the – Space-group symmetry, (Springer, New York), Vol A, Ch 7.1, pp 112 717. Flatland* of cell membrane organization. J Cell Biol 173(6):839–844. 3. Prum RO, Quinn T, Torres RH (2006) Anatomically diverse butterfly scales all produce 9. Hajduk DA, et al. (1995) A reevaluation of bicontinuous cubic phases in starblock structural colours by coherent scattering. J Exp Biol 209:748–765. copolymers. Macromolecules 28:2570–2573. 4. Schoen AH (1970) Infinite periodic minimal surfaces without self-intersections. (NASA Research Center, Cambridge, MA), NASA Technical Note C-98. 10. Hajduk DA, et al. (1994) The gyroid: A new equilibrium morphology in weakly – 5. Michielsen K, Stavenga DG (2008) Gyroid cuticular structures in butterfly wing scales: segregated diblock copolymers. Macromolecules 27:4063 4075. Biological photonic crystals. J R Soc Interface 5(18):85–94. 11. Argyros A, Large MCJ, McKenzie DR, Cox GC, Dwarte DM (2002) Electron tomography 6. Wohlgemuth M, Yufa N, Hoffman J, Thomas EL (2001) Triply periodic bicontinuous and computer visualization of a three-dimensional ‘photonic’ crystal in a butterfly cubic microdomain morphologies by symmetries. Macromolecules 34(17):6083–6089. wing-scale. Micron 33:483–487. Saranathan et al. www.pnas.org/cgi/doi/10.1073/pnas.0909616107 1of6 Fig. S1. Anatomy of the structural color producing nanostructure in papilionid and lycaenid butterflies. (A) Light micrograph of the dorsal wing cover scales of Teinopalpus imperialis (Papilionidae). (Scale bar: 150 μm.) (B) SEM image of the lateral surface of the wing scale nanostructure of T. imperialis showing fused polycrystalline domains beneath columnar windows created by a network of ridges and spaced cross-ribs. The fractured face features a square lattice of air holes in chitin. (Scale bar: 2 μm.) (Inset) Simulated SEM (100) projection from a thick slab of a level set single gyroid nanostructure. (C) TEM image of the T. imperialis nanostructure showing a distinctive trifoliate motif, uniquely characteristic of the (332) plane of the gyroid morphology. (Scale bar: 1 μm.) (Inset) A matching simulated (332) TEM section of a level set single gyroid model. (D) Light micrograph of the ventral wing cover scales of Callophrys dumetorum (Lycaenidae). The opalescent highlights are produced by randomly oriented crystallite domains. (Scale bar: 100 μm.) (E) SEM image of the lateral surface of the wing scale nanostructure of C. dumetorum. The fractured face features a triangular lattice of air holes in chitin. (Scale bar: 500 nm.) (Inset) Simulated SEM (111) projection of a thick slab of a level set single gyroid nanostructure. (F) TEM image of the C. dumetorum nanostructure showing a distinctive motif, uniquely characteristic of the (211) plane of the gyroid morphology. (Scale bar: 200 nm.) (Inset) A matching simulated (211) TEM section of a level set single gyroid model. (G) Light micrograph of the ventral wing cover scales of Cyanophrys herodotus (Lycaenidae). The opalescent highlights are produced by randomly oriented crystallite domains. (Scale bar: 100 μm.) (H) SEM image of the ventral surface of a C. herodotus scale showing disjoint crystallites. (Scale bar: 2 μm.) (Inset) Simulated SEM (111) section from a thick slab of a level set single gyroid nanostructure. (I) TEM image of the C. herodotus ventral wing scale nanostructure (from ref. 7) showing distinctive motifs, uniquely characteristic of the (211) and (110) planes of the gyroid morphology. (Scale bar: 2 μm.) (Inset) A matching simulated (110) TEM section of a level set single gyroid model corresponding to the motif within the red box. c, chitin; a, air void. (Reprinted figure with permission from ref. 7. Copyright 2006 by the American Physical Society). 0.103 0.069 0.035 0.000 0.035 0.069 0.103 0.103 0.103 c 332 420 50 100 a 422 0.069 400 0.069 45 b 90 321 40 80 35 70 0.035 220 0.035 ) 30 60 -1 211 25 50 0.000 110 0.000 20 40 q (nm 15 30 0.035 0.035 10 20 5 10 0.069 0.069 0 0 300 400 500 600 700 SAXS % Predicted Reflectance (black) λ (nm) % Measured Optical Reflectance (blue) 0.103 0.103 0.103 0.069 0.035 0.000 0.035 0.069 0.103 q (nm -1) Fig. S2. (A) Representative 2D SAXS pattern (original image 1340 × 1300 pixels), and (B) a comparison of predicted reflectance (black line) from an azimuthal average of the SAXS pattern against measured optical reflectance (blue line), for Callophrys dumetorum. The false color scale in A corresponds to the logarithm q of the X-ray scattering intensity. The radii of the concentric circles are given by the peak scattering wave vector ( max) times the moduli of the assigned hkl indices, where h, k, and l are integers allowed by the single gyroid (I4132) symmetry space group (IUCr International Tables for Crystallography, ref. 2). See main text for other details. Saranathan et al. www.pnas.org/cgi/doi/10.1073/pnas.0909616107 2of6 3 8 1112 16 19 24 27 323536 43 48 Fd3m 1 2 3 4 5 6 8910 11 12 13 14 16 Pm3m 2 6 8 10 14 16 18 12 20 22 24 26 30 32 I4 1 32 1.000 0.100 max Teinopalpus imperialis Parides sesostris Callophrys gryneus 0.010 Callophrys dumetorum Cyanophrys herodotus Calculated Structure Factors 0.001 Normalized Intensity, I/I 0.000 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 Normalized q, q/qmax I∕I q∕q Fig. S3. Normalized azimuthally averaged X-ray scattering profiles (intensity max vs. scattering wave vector max) calculated from the respective 2D SAXS patterns for Teinopalpus imperialis, Parides sesostris, Callophrys (Mitoura) gryneus, Callophrys dumetorum, and Cyanophrys herodotus. The sets of color-coded vertical lines correspond to the expected Bragg peak positional ratios for the single gyroid (I4132; black), single diamond (Fd3m; cyan), and simple primitive (Pm3m; mauve) cubic crystallographic space groups, presented together for direct comparison and positive exclusion of all but one of these plausible alternative cubic symmetries.
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