S. G. J. Mochrie

Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales

Complex three-dimensional biophotonic nanostructures produce the vivid structural colors of many butterfly wing scales, but their exact nanoscale organization is uncertain. We used small angle X-ray scattering (SAXS) on single scales to characterize the 3D photonic nanostructures of five butterfly species from two families (Papilionidae, Lycaenidae). We identify these chitin and air nanostructures as single network gyroid (I4132) photonic crystals. We describe their optical function from SAXS data and photonic band-gap modeling. Butterflies apparently grow these gyroid nanostructures by exploiting the self-organizing physical dynamics of biological lipid-bilayer membranes. These butterfly photonic nanostructures initially develop within scale cells as a core-shell double gyroid (Ia3d), as seen in block-copolymer systems, with a pentacontinuous volume comprised of extracellular space, cell plasma membrane, cellular cytoplasm, smooth endoplasmic reticulum (SER) membrane, and intra-SER lumen. This double gyroid nanostructure is subsequently transformed into a single gyroid network through the deposition of chitin in the extracellular space and the degeneration of the rest of the cell. The butterflies develop the thermodynamically favored double gyroid precursors as a route to the optically more efficient single gyroid nanostructures. Current approaches to photonic crystal engineering also aim to produce single gyroid motifs. The biologically derived photonic nanostructures characterized here may offer a convenient template for producing optical devices based on biomimicry or direct dielectric infiltration.

Rapid compaction during RNA folding

We have used small angle x-ray scattering and computer simulations with a coarse-grained model to provide a time-resolved picture of the global folding process of the Tetrahymena group I RNA over a time window of more than five orders of magnitude. A substantial phase of compaction is observed on the low millisecond timescale, and the overall compaction and global shape changes are largely complete within one second, earlier than any known tertiary contacts are formed. This finding indicates that the RNA forms a nonspecifically collapsed intermediate and then searches for its tertiary contacts within a highly restricted subset of conformational space. The collapsed intermediate early in folding of this RNA is grossly akin to molten globule intermediates in protein folding.

Evolution of particle-scale dynamics in an aging clay suspension.

Multispeckle x-ray photon correlation spectroscopy was employed to characterize the slow dynamics of a suspension of highly charged, nanometer-sized disks. At wave vectors q corresponding to interparticle length scales, the dynamic structure factor follows a form f(q,t) approximately exp([-(t/tau)(beta)], where beta approximately 1.5. The relaxation time tau increases with the sample age t(a) approximately as tau approximately t(1.8)(a) and decreases with q as tau approximately q(-1). Such behavior is consistent with models that describe the dynamics in disordered elastic media in terms of strain from random, local structural rearrangements. The measured amplitude of f(q,t) varies with q in a manner that implies caged particle motion. The decrease in the range of this motion and an increase in suspension conductivity with increasing t(a) indicate a growth in interparticle repulsion as the mechanism for internal stress development implied by these models.

Biomimetic Isotropic Nanostructures for Structural Coloration

The self-assembly of films that mimic color-producing nanostructures in bird feathers is described. These structures are isotropic and have a characteristic length-scale comparable to the wavelength of visible light. Structural colors are produced when wavelength-independent scattering is suppressed by limiting the optical path length through geometry or absorption.

How Noniridescent Colors Are Generated by Quasi‐ordered Structures of Bird Feathers

We investigate the mechanism of structural coloration by quasi-ordered nanostructures in bird feather barbs. Small-angle X-ray scattering (SAXS) data reveal the structures are isotropic and have short-range order on length scales comparable to optical wavelengths. We perform angle-resolved reflection and scattering spectrometry to fully characterize the colors under directional and omni-directional illumination of white light. Under directional lighting, the colors change with the angle between the directions of illumination and observation. The angular dispersion of the primary peaks in the scattering/reflection spectra can be well explained by constructive interference of light that is scattered only once in the quasi-ordered structures. Using the Fourier power spectra of structure from the SAXS data we calculate optical scattering spectra and explain why the light scattering peak is the highest in the backscattering direction. Under omni-directional lighting, colors from the quasi-ordered structures are invariant with the viewing angle. The non-iridescent coloration results from the isotropic nature of structures instead of strong backscattering.

Self-assembly of amorphous biophotonic nanostructures by phase separation

Some of the most vivid colors in the animal kingdom are created not by pigments, but by wavelength-selective scattering of light from nanostructures. Here we investigate quasi-ordered nanostructures of avian feather barbs which produce vivid non-iridescent colors. These β-keratin and air nanostructures are found in two basic morphologies: tortuous channels and amorphous packings of spheres. Each class of nanostructure is isotropic and has a pronounced characteristic length scale of variation in composition. These local structural correlations lead to strong backscattering over a narrow range of optical frequencies and little variation with angle of incidence. Such optical properties play important roles in social and sexual communication. To be effective, birds need to precisely control the development of these nanoscale structures, yet little is known about how they grow. We hypothesize that multiple lineages of birds have convergently evolved to exploit phase separation and kinetic arrest to self-assemble spongy color-producing nanostructures in feather barbs. Observed avian nanostructures are strikingly similar to those self-assembled during the phase separation of fluid mixtures; the channel and sphere morphologies are characteristic of phase separation by spinodal decomposition and nucleation and growth, respectively. These unstable structures are locked-in by the kinetic arrest of the β-keratin matrix, likely through the entanglement or cross-linking of supermolecular β-keratin fibers. Using the power of self-assembly, birds can robustly realize a diverse range of nanoscopic morphologies with relatively small physical and chemical changes during feather development.

Area detector based photon correlation in the regime of short data batches: Data reduction for dynamic x-ray scattering

A method for reducing time sequences of raw scattering images to intensity time-autocorrelation functions is presented. The procedure is based on the use of a charge coupled device (CCD) area detector, and optimized for operating in the regime of short data batches. Its application to x-ray photon correlation spectroscopy (XPCS) measurements is described in detail. Using a slow-scan CCD, we explain how to achieve data acquisition on a 30 ms or faster time scale, while simultaneously acquiring data from many coherence areas in parallel. The statistical uncertainties of the acquired XPCS data are quantified experimentally, and compared to the theoretically expected noise levels of the correlation functions.

Structure and stability of designed TPR protein superhelices: unusual crystal packing and implications for natural TPR proteins.

The structure and stability of repeat proteins has been little studied in comparison to the properties of the more familiar globular proteins. Here, the structure and stability of designed tetratricopeptide-repeat (TPR) proteins is described. The TPR is a 34-amino-acid motif which adopts a helix-turn-helix structure and occurs as tandem repeats. The design of a consensus TPR motif (CTPR) has previously been described. Here, the crystal structures and stabilities of proteins that contain eight or 20 identical tandem repeats of the CTPR motif (CTPR8 and CTPR20) are presented. Both CTPR8 and CTPR20 adopt a superhelical overall structure. The structures of the different-length CTPR proteins are compared with each other and with the structures of natural TPR domains. Also, the unusual and perhaps unique crystal-packing interactions resulting in pseudo-infinite crystalline superhelices observed in the different crystal forms of CTPR8 and CTPR20 are discussed. Finally, it is shown that the thermodynamic behavior of CTPR8 and CTPR20 can be predicted from the behavior of other TPRs in this series using an Ising model-based analysis. The designed protein series CTPR2-CTPR20 covers the natural size repertoire of TPR domains and as such is an excellent model system for natural TPR proteins.

Small-angle X-ray scattering using coherent undulator radiation at the ESRF.

A simple approach for producing a high-coherent-flux X-ray beam for small-angle-scattering studies used at the Troika beamline of the European Synchrotron Radiation Facility is reported. For such small-angle studies it is permissible to reduce the longitudinal coherence .length of the beam, thus increasing the energy bandpass and intensity of the beam, because there is only a small optical path-length difference. By using mirrors and filters to cut unwanted energies from the undulator harmonic structure, a high-flux beam of >10(9) photons s(-1) through a 5 micron-diameter pinhole at 8.2 keV with a bandpass of 1.3% can be produced. The coherent properties of this beam have been measured by analyzing a static speckle pattern from an aerogel sample imaged by a directly illuminated CCD camera. The speckle size and contrast are compared with the expected values based on a statistical analysis of the intensity distribution of speckle patterns obtained using partially coherent conditions. The expected widths of the spatial autocorrelation are found, but there is an apparent incoherent fraction of the beam which reduces the measured contrast. The method presented is to be used as a tool to optimize conditions for diffraction experiments using coherent X-rays.

Measuring the nematic order of suspensions of colloidal fd virus by x-ray diffraction and optical birefringence

The orientational distribution function of the nematic phase of the semi-flexible rod-like virus fd is measured by x-ray diffraction as a function of concentration and ionic strength. The angular distribution of the scattered intensity from a single-domain nematic phase of fd arises from only the single particle orientational distribution function at high angle but it also includes spatial and orientational correlations at low angle. Experimental measurements of the orientational distribution function from both the interparticle and intraparticle scattering were made to test whether the correlations present in interparticle scatter influence the measurement of the single particle orientational distribution function. It was found that the two types of scatter yield consistent values for the nematic order parameter. It was also found that x-ray diffraction is insensitive to the orientational distribution functions precise form, and the measured angular intensity distribution is described equally well by both Onsagers trial function and a Gaussian. At high ionic strength the order parameter S of the nematic phase coexisting with the isotropic phase approaches theoretical predictions for long semi-flexible rods S=0.55, but deviations from theory increase with decreasing ionic strength. The concentration dependence of the nematic order parameter was also found to better agree with theoretical predictions at high ionic strength, indicating that electrostatic interactions have a measurable effect on the nematic order parameter. The measured x-ray order parameters are also shown to be proportional to the measured birefringence and the saturation birefringence of fd is measured, enabling a simple, inexpensive way to measure the order parameter.