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In 2008, we established the Integrated Graduate Program in Physical and Engineering Biology (IGPPEB) at Yale University. Our goal was to create a comprehensive graduate program to train a new generation of scientists who possess a sophisticated understanding of biology and who are capable of applying physical and quantitative methodologies to solve biological problems. Here we describe the framework of the training program, report on its effectiveness, and also share the insights we gained during its development and implementation. The program features co-teaching by faculty with complementary specializations, student peer learning, and novel hands-on courses that facilitate the seamless blending of interdisciplinary research and teaching. It also incorporates enrichment activities to improve communication skills, engage students in science outreach, and foster a cohesive program cohort, all of which promote the development of transferable skills applicable in a variety of careers. The curriculum of the graduate program is integrated with the curricular requirements of several Ph.D.-granting home programs in the physical, engineering, and biological sciences. Moreover, the wide-ranging recruiting activities of the IGPPEB serve to enhance the quality and diversity of students entering graduate school at Yale. We also discuss some of the challenges we encountered in establishing and optimizing the program, and describe the institution-level changes that were catalyzed by the introduction of the new graduate program. The goal of this article is to serve as both an inspiration and as a practical "how to" manual for those who seek to establish similar programs at their own institutions. © 2016 by The International Union of Biochemistry and Molecular Biology, 44(6):537-549, 2016., (© 2016 The Authors Biochemistry and Molecular Biology Education published by Wiley Periodicals, Inc. on behalf of International Union of Biochemistry and Molecular Biology.)

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, an accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum-likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean-square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions that give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.

Fluorescence imaging is a powerful tool to study protein function in living cells. Here, we introduce a novel imaging strategy that is fully genetically encodable, does not require the use of exogenous substrates, and adds a minimally disruptive tag to the protein of interest (POI). Our method was based on a set of designed tetratricopeptide repeat affinity proteins (TRAPs) that specifically and reversibly interact with a short, extended peptide tag. We co-expressed the TRAPs fused to fluorescent proteins (FPs) and the peptide tags fused to the POIs. We illustrated the method using the Escherichia coli protein FtsZ and showed that our system could track distinct FtsZ structures under both low and high expression conditions in live cells. We anticipate that our imaging strategy will be a useful tool for imaging the subcellular localization of many proteins, especially those recalcitrant to imaging by direct tagging with FPs., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Many aspects of chromatin biology are influenced by the nuclear compartment in which a locus resides, from transcriptional regulation to DNA repair. Further, the dynamic and variable localization of a particular locus across cell populations and over time makes analysis of a large number of cells critical. As a consequence, robust and automatable methods to measure the position of individual loci within the nuclear volume in populations of cells are necessary to support quantitative analysis of nuclear position. Here, we describe a three-dimensional membrane reconstruction approach that uses fluorescently tagged nuclear envelope or endoplasmic reticulum membrane marker proteins to precisely map the nuclear volume. This approach is robust to a variety of nuclear shapes, providing greater biological accuracy than alternative methods that enforce nuclear circularity, while also describing nuclear position in all three dimensions. By combining this method with established approaches to reconstruct the position of diffraction-limited chromatin markers-in this case, lac Operator arrays bound by lacI-GFP-the distribution of loci positions within the nuclear volume with respect to the nuclear periphery can be quantitatively obtained. This stand-alone image analysis pipeline should be of broad practical utility for individuals interested in various aspects of chromatin biology, while also providing, to our knowledge, a new conceptual framework for investigators who study organelle shape., (Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Many organisms in nature have evolved sophisticated cellular mechanisms to produce photonic nanostructures and, in recent years, diverse crystalline symmetries have been identified and related to macroscopic optical properties. However, because we know little about the distributions of domain sizes, the orientations of photonic crystals, and the nature of defects in these structures, we are unable to make the connection between the nanostructure and its development and functionality. We report on nondestructive studies of the morphology of chitinous photonic crystals in butterfly wing scales. Using spatially and angularly resolved x-ray diffraction, we find that the domains are highly oriented with respect to the whole scale, indicating growth from scale boundaries. X-ray coherent diffractive imaging reveals two types of crystalline domain interfaces: abrupt changes between domains emerging from distinct nucleation sites and smooth transitions with edge dislocations presumably resulting from internal stresses during nanostructure development. Our study of the scale structure reveals new aspects of photonic crystal growth in butterfly wings and shows their similarity to block copolymer materials. It opens new avenues to exploration of fundamental processes underlying the growth of biological photonic nanostructures in a variety of species.

Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and demonstrate that pEM is capable of uncovering the proper number of underlying diffusive states with an accurate characterization of their diffusion properties. We then apply pEM to experimental protein trajectories of Rho GTPases, an integral regulator of cytoskeletal dynamics and cellular homeostasis, in vivo via single particle tracking photo-activated localization microscopy. Remarkably, pEM uncovers 6 distinct diffusive states conserved across various Rho GTPase family members. The variability across family members in the propensities for each diffusive state reveals non-redundant roles in the activation states of RhoA and RhoC. In a resting cell, our results support a model where RhoA is constantly cycling between activation states, with an imbalance of rates favoring an inactive state. RhoC, on the other hand, remains predominantly inactive.

The diverse morphologies of animal tissues are underlain by different configurations of adherent cells and extracellular matrix (ECM). Here, we elucidate a cross-scale mechanism for tissue assembly and ECM remodeling involving Cadherin 2, the ECM protein Fibronectin, and its receptor Integrin α5. Fluorescence cross-correlation spectroscopy within the zebrafish paraxial mesoderm mesenchyme reveals a physical association between Integrin α5 on adjacent cell membranes. This Integrin-Integrin complex correlates with conformationally inactive Integrin. Cadherin 2 stabilizes both the Integrin association and inactive Integrin conformation. Thus, Integrin repression within the adherent mesenchymal interior of the tissue biases Fibronectin fibrillogenesis to the tissue surface lacking cell-cell adhesions. Along nascent somite boundaries, Cadherin 2 levels decrease, becoming anti-correlated with levels of Integrin α5. Simultaneously, Integrin α5 clusters and adopts the active conformation and then commences ECM assembly. This cross-scale regulation of Integrin activation organizes a stereotypic pattern of ECM necessary for vertebrate body elongation and segmentation., (Copyright © 2015 Elsevier Inc. All rights reserved.)

The nuclear lamina is thought to be the primary mechanical defence of the nucleus. However, the lamina is integrated within a network of lipids, proteins and chromatin; the interdependence of this network poses a challenge to defining the individual mechanical contributions of these components. Here, we isolate the role of chromatin in nuclear mechanics by using a system lacking lamins. Using novel imaging analyses, we observe that untethering chromatin from the inner nuclear membrane results in highly deformable nuclei in vivo, particularly in response to cytoskeletal forces. Using optical tweezers, we find that isolated nuclei lacking inner nuclear membrane tethers are less stiff than wild-type nuclei and exhibit increased chromatin flow, particularly in frequency ranges that recapitulate the kinetics of cytoskeletal dynamics. We suggest that modulating chromatin flow can define both transient and long-lived changes in nuclear shape that are biologically important and may be altered in disease.

Many organisms, especially arthropods, produce vivid interference colors using diverse mesoscopic (100-350 nm) integumentary biophotonic nanostructures that are increasingly being investigated for technological applications. Despite a century of interest, precise structural knowledge of many biophotonic nanostructures and the mechanisms controlling their development remain tentative, when such knowledge can open novel biomimetic routes to facilely self-assemble tunable, multifunctional materials. Here, we use synchrotron small-angle X-ray scattering and electron microscopy to characterize the photonic nanostructure of 140 integumentary scales and setae from ∼127 species of terrestrial arthropods in 85 genera from 5 orders. We report a rich nanostructural diversity, including triply periodic bicontinuous networks, close-packed spheres, inverse columnar, perforated lamellar, and disordered spongelike morphologies, commonly observed as stable phases of amphiphilic surfactants, block copolymer, and lyotropic lipid-water systems. Diverse arthropod lineages appear to have independently evolved to utilize the self-assembly of infolding lipid-bilayer membranes to develop biophotonic nanostructures that span the phase-space of amphiphilic morphologies, but at optical length scales.

DNA is known to condense with multivalent cations and positively charged proteins. However, the properties and energetics of DNA superstructures, such as chromatin, are poorly understood. As a model system, we investigate histone H1 condensation of DNA with tethered particle motion and force-extension measurements. We show that after the addition of H1 to DNA, a concentration dependent lag time is followed by the DNA spontaneously condensing. The trigger for this condensation phase transition can be modeled as sufficient H1s having bound to the DNA, providing insight into the 30 nm fiber condensation upon H1 binding. Furthermore, optical tweezers force-extension measurements of histone H1 condensed DNA reveals a sequence of state transitions corresponding to the unwinding of superhelical turns. We determine the complete, experimental, multi-state free energy landscape for the complex using Crooks fluctuation theorem. The measured force-versus-extension and free energy landscape are compared to predictions from a simple, theoretical model. This work encourages the theoretical description of DNA/protein structure and energetics and their role in chromatin and other, more complex, systems.

By monitoring stage drift via the normalized cross-correlation of an image of a stuck bead, obtained in real-time, with an out-of-focus "template" image of a similar immobile bead, stored in memory, we implement a simple approach to actively stabilize drift in all three dimensions for existing video microscopy setups. We demonstrate stability to 0.0062 nm along the Z-axis and 0.0031 nm along the X- and Y-axes for long (100 s) timescales.

By monitoring multiple molecular transitions, force-clamp, and trap-position-clamp methods have led to precise determinations of the free energies and free energy landscapes for molecular states populated in equilibrium at the same or similar forces. Here, we present a powerful new elaboration of the force-clamp and force-jump methods, applicable to transitions far from equilibrium. Specifically, we have implemented a live jump detection and force-clamp algorithm that intelligently adjusts and maintains the force on a single molecule in response to the measured state of that molecule. We are able to collect hundreds of individual molecular transitions at different forces, many times faster than previously, permitting us to accurately determine force-dependent lifetime distributions and reaction rates. Application of our method to unwinding and rewinding the nucleosome inner turn, using optical tweezers reveals experimental lifetime distributions that comprise a statistically meaningful number of transitions, and that are accurately single exponential. These measurements significantly reduce the error in the previously measured rates, and demonstrate the existence of a single, dominant free energy barrier at each force studied. A key benefit of the molecular yo-yo method for nucleosomes is that it reduces as far as possible the time spent in the tangentially bound state, which minimizes the loss of nucleosomes by dissociation.

A simple model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn is constructed and quantitatively compared to the results of recent measurements [A. H. Mack et al., J. Mol. Biol. 423, 687 (2012)]. First, a coarse-grained model for the histone-DNA free-energy landscape that incorporates both an elastic free-energy barrier and specific histone-DNA bonds is developed. Next, a theoretical expression for the rate of transitions across a piecewise linear free-energy landscape with multiple minima and maxima is presented. Then, the model free-energy landscape, approximated as a piecewise linear function, and the theoretical expression for the transition rates are combined to construct a model for the force-dependent unwinding and rewinding rates of the nucleosome inner turn. Least-mean-squares fitting of the model rates to the rates observed in recent experiments rates demonstrates that this model is able to well describe the force-dependent unwinding and rewinding rates of the nucleosome inner turn, observed in the recent experiments, except at the highest forces studied, where an additional ad hoc term is required to describe the data, which may be interpreted as an indication of an alternate high-force nucleosome disassembly pathway, that bypasses simple unwinding. The good agreement between the measurements and the model at lower forces demonstrates that both specific histone-DNA contacts and an elastic free-energy barrier play essential roles for nucleosome winding and unwinding, and quantifies their relative contributions.

Chromatin "remodeling" is widely accepted as the mechanism that permits access to DNA by the transcription machinery. To date, however, there has been no experimental measurement of the changes in the kinetics and thermodynamics of the DNA-histone octamer association that are required to remodel chromatin so that transcription may occur. Here, we present the results of optical tweezer measurements that compare the kinetic and thermodynamic properties of nucleosomes composed of unmodified histones with those of nucleosomes that contain a mutant histone H4 (H4-R45H), which has been shown to allow SWI/SNF remodeling factor-independent transcription from the yeast HO promoter in vivo. Our measurements, carried out in a force-clamp mode, determine the force-dependent unwinding and rewinding rates of the nucleosome inner turn. At each force studied, nucleosomes containing H4-R45H unwind more rapidly and rewind more slowly than nucleosomes containing unmodified H4, indicating that the latter are the more stable. Extrapolation to forces at which the winding and unwinding rates are equal determines the absolute free energy of the nucleosome inner turn to be -32k(B)T for nucleosomes containing unmodified H4 and -27k(B)T for nucleosomes containing H4-R45H. Thus, the "loosening" or "remodeling" caused by this point mutation, which is demonstrated to be sufficient to allow transcriptional machinery access to the HO promoter (in the absence of other remodeling factors), is 5k(B)T. The correlation between the free energy of the nucleosome inner turn and the sin (SWI/SNF-independent) transcription suggests that, beyond partial unwinding, complete histone unwinding may play a role in transcriptional activation., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Non-iridescent structural colours of feathers are a diverse and an important part of the phenotype of many birds. These colours are generally produced by three-dimensional, amorphous (or quasi-ordered) spongy β-keratin and air nanostructures found in the medullary cells of feather barbs. Two main classes of three-dimensional barb nanostructures are known, characterized by a tortuous network of air channels or a close packing of spheroidal air cavities. Using synchrotron small angle X-ray scattering (SAXS) and optical spectrophotometry, we characterized the nanostructure and optical function of 297 distinctly coloured feathers from 230 species belonging to 163 genera in 51 avian families. The SAXS data provided quantitative diagnoses of the channel- and sphere-type nanostructures, and confirmed the presence of a predominant, isotropic length scale of variation in refractive index that produces strong reinforcement of a narrow band of scattered wavelengths. The SAXS structural data identified a new class of rudimentary or weakly nanostructured feathers responsible for slate-grey, and blue-grey structural colours. SAXS structural data provided good predictions of the single-scattering peak of the optical reflectance of the feathers. The SAXS structural measurements of channel- and sphere-type nanostructures are also similar to experimental scattering data from synthetic soft matter systems that self-assemble by phase separation. These results further support the hypothesis that colour-producing protein and air nanostructures in feather barbs are probably self-assembled by arrested phase separation of polymerizing β-keratin from the cytoplasm of medullary cells. Such avian amorphous photonic nanostructures with isotropic optical properties may provide biomimetic inspiration for photonic technology.

We describe a new method for calibrating optical trapping measurements in which tension is applied in the direction of the laser beam to a molecule tethered between a surface and an optically trapped bead. Specifically, we present a generally-applicable procedure for converting from the measured scattering intensity and the measured stage displacement to applied tension and bead-coverslip separation, using measurements of the light intensity scattered from an untethered, trapped bead. Our calibration accounts for a number of effects, including aberrations and the interference of forward-reflected bead-scattered light with the trapping beam. To demonstrate the accuracy of our method, we show measurements of the DNA force-versus-extension relation using a range of laser intensities, and show that these measurements match the expected extensible wormlike-chain (WLC) behavior. Finally, we also demonstrate a force-clamp, in which the tension in a tether is held fixed while the extension varies as a result of molecular events.

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration., (© 2011 American Institute of Physics)

The newly introduced coherence-based technique of X-ray near-field speckle (XNFS) has been implemented at 8-ID-I at the Advanced Photon Source. In the near-field regime of high-brilliance synchrotron X-rays scattered from a sample of interest, it turns out that, when the scattered radiation and the main beam both impinge upon an X-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. A micrometer-resolution XNFS detector with a high numerical aperture microscope objective has been built and its capability for studying static structures and dynamics at longer length scales than traditional far-field X-ray scattering techniques is demonstrated. Specifically, the dynamics of dilute silica and polystyrene colloidal samples are characterized. This study reveals certain limitations of the XNFS technique, especially in the characterization of static structures, which is discussed.

Repeat proteins are tandem arrays of a small structural motif, in which tertiary structure is stabilized by interactions within a repeat and between neighboring repeats. Several studies have shown that this modular structure is manifest in modular thermodynamic properties. Specifically, the global stability of a repeat protein can be described by simple linear models, considering only two parameters: the stability of the individual repeated units (H) and the coupling interaction between the units (J). If the repeat units are identical, single values of H and J, together with the number of repeated units, is sufficient to completely describe the thermodynamic behavior of any protein within a series. In this work, we demonstrate how the global stability of a repeat protein can be changed, in a predictable fashion, by modifying only the H parameter. Taking a previously characterized series of consensus tetratricopeptide repeats (TPR) (CTPRa) proteins, we introduced mutations into the basic repeating unit, such that the stability of the individual repeat unit was increased, but its interaction with neighboring units was unchanged. In other words, we increased H but kept J constant. We demonstrated that the denaturation curves for a series of such repeat proteins can be fit and additional curves can be predicted by the one-dimensional Ising model in which only H has changed from the original fit for the CTPRa series. Our results show that we can significantly increase the stability of a repeat protein by rationally increasing the stability of the units (H), whereas the interaction between repeats (J) remains unchanged., (Copyright © 2011 The Protein Society.)

Attachments between DNA and a surface or bead are often necessary for single-molecule studies of DNA and DNA-protein interactions. In single-molecule mechanical studies using optical or magnetic tweezers, such attachments must be able to withstand the applied forces. Here we present a new method for covalently attaching DNA to a glass surface, which uses N-hydroxysuccinimide (NHS) modified PEG that is suitable for high-force single-molecule mechanical studies. A glass surface is coated with silane-PEG-NHS and DNA is covalently linked through a reaction between the NHS group and an amine modified nucleotide that has been incorporated into the DNA. After DNA attachment, non-reacted NHS groups are hydrolyzed leaving a PEG-covered surface which has the added benefit of reducing non-specific surface interactions. This method permits specific binding of the DNA to the surface through a covalent bond. At the DNA end not attached to the surface, we attach a streptavidin-coated polystyrene bead and measure force-versus-extension using an optical trap. We show that our method allows a tethered DNA molecule to be pulled through its overstretching transition (> 60pN) multiple times. We anticipate this simple yet powerful method will be useful for many researchers., (2010 Elsevier B.V. All rights reserved.)

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has concentrated mostly on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small-angle x-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high-density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by standard interparticle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium densification processes.

A transfer matrix method is described for the conformational spread (CS) model of allosteric cooperativity within a one-dimensional arrangement of four-state binding sites. Each such binding site can realize one of two possible conformational states. Each of these states can either bind ligand or not bind ligand. Thus, analytical expressions that are exact within the context of the CS model are derived for the grand partition function, for the mean fraction of binding sites occupied by ligand versus ligand concentration, and for the mean fraction of binding sites in a given allosteric state versus ligand concentration. The utility of our analytical results is demonstrated by least-mean-square fitting of prior experimental results obtained on the bacterial flagellar motor for the fraction of FliM/FliG/FliN complexes with CheY-P bound [V. Sourjik and H. C. Berg, Proc. Natl. Acad. Sci. U.S.A. 99, 12669 (2002)] and for the cw bias [P. Cluzel, Science 287, 1652 (2000)], which plausibly may be identified as the fraction of protomers realizing state 2. Finally, the relationships between our analytical results and the classical Monod-Wyman-Changeaux, Koshland-Nemethy-Filmer, and McGhee-Von Hippel treatments of allosteric cooperativity are elucidated, as is the connection to an earlier approximate analytical treatment of the CS model.

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.

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 (I4(1)32) 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.

We investigate the physical mechanism for color production by isotropic nanostructures with short-range order in bird feather barbs. While the primary peak in optical scattering spectra results from constructive interference of singly-scattered light, many species exhibit secondary peaks with distinct characteristic. Our experimental and numerical studies show that these secondary peaks result from double scattering of light by the correlated structures. Without an analog in periodic or random structures, such a phenomenon is unique for short-range ordered structures, and has been widely used by nature for non-iridescent structural coloration.

We measured the polarization- and angle-resolved optical scattering and reflection spectra of the quasiordered nanostructures in the bird feather barbs. In addition to the primary peak that originates from single scattering, we observed a secondary peak which exhibits depolarization and distinct angular dispersion. We explained the secondary peak in terms of double scattering, i.e., light is scattered successively twice by the structure. The two sequential single-scattering events are considered uncorrelated. Using the Fourier power spectra of the nanostructures obtained from the small-angle x-ray scattering experiment, we calculated the double scattering of light in various directions. The double-scattering spectrum is broader than the single-scattering spectrum, and it splits into two subpeaks at larger scattering angle. The good agreement between the simulation results and the experimental data confirms that double scattering of light makes a significant contribution to the structural color.

We describe a simple-to-construct programmable direct-digital-synthesis-based controller for use with acousto-optic deflectors. Our controller corrects for nonlinear diffraction efficiency versus diffraction angle, provides superior stability, functionality, and configurability, and costs a fraction of commercially available systems. Using this instrument, we move a 1 mum diameter bead by 1-nm-sized steps and resolve these steps.

Repeat proteins contain tandem arrays of a simple structural motif. In contrast to globular proteins, repeat proteins are stabilized only by interactions between residues that are relatively close together in the sequence, with no "long-range" interactions. Our work focuses on the tetratricopeptide repeat (TPR), a 34 amino acid helix-turn-helix motif found in tandem arrays in many natural proteins. Earlier, we reported the design and characterization of a series of consensus TPR (CTPR) proteins, which are built as arrays of multiple tandem copies of a 34 amino acid consensus sequence. Here, we present the results of extensive hydrogen exchange (HX) studies of the folding-unfolding behavior of two CTPR proteins (CTPR2 and CTPR3). We used HX to detect and characterize partially folded species that are populated at low frequency in the nominally folded state. We show that for both proteins the equilibrium folding-unfolding transition is non-two-state, but sequential, with the outermost helices showing a significantly higher probability than inner helices of being unfolded. We show that the experimentally observed unfolding behavior is consistent with the predictions of a simple Ising model, in which individual helices are treated as "spin-equivalents". The results that we present have general implications for our understanding of the thermodynamic properties of repeat proteins.

The onset of structural arrest and glass formation in a concentrated suspension of silica nanoparticles in a water-lutidine binary mixture near its consolute point is studied by exploiting the near-critical fluid degrees of freedom to control the strength of an attraction between particles and multispeckle x-ray photon correlation spectroscopy to determine the particles' collective dynamics. This model system undergoes a glass transition both on cooling and on heating, and the intermediate liquid realizes unusual logarithmic relaxations. How vitrification occurs for the two different glass transitions is characterized in detail and comparisons are drawn to recent theoretical predictions for glass formation in systems with attractive interactions.

Small-angle x-ray scattering (SAXS) was used to measure the microstructure of isotopic mixtures of 3He and 4He adsorbed into silica aerogels as a function of temperature and 3He concentration. The SAXS measurements could be well described by the formation of a nearly pure film of 4He which separates from the bulk mixture onto the aerogel strands and which thickens with decreasing temperature. Previous observations of a superfluid 3He -rich phase are consistent with superfluidity existing within this film phase. Observed differences between different density aerogels are explained in terms of the depletion of 4He from the bulk mixture due to film formation.

X-ray photon correlation spectroscopy was used to characterize the wave vector- and temperature-dependent dynamics of spontaneous thermal fluctuations in a sponge (L3) phase that occurs in a blend of a symmetric poly(styrene-ethylene/butylene-styrene) triblock copolymer with a polystyrene homopolymer. Measurements of the intermediate scattering function reveal a crossover from stretched- to compressed-exponential relaxations as the temperature is lowered from 180 to 120 degrees C.

The theory for surface dynamics of the thermally excited fluctuations on a homogenous single-layer film of arbitrary depth is generalized to describe surface and interfacial dynamics of polymeric liquid bilayer films in terms of susceptibilities, power spectra, and characteristic relaxation time constants. The effects on surface dynamics originating from viscosity inhomogeneities close to the surface and interfacial regions are investigated by the bilayer theory and compared with the surface dynamics of homogeneous single-layer films under nonslip and slip boundary conditions. Our bilayer theory can also be extended to study interfacial dynamics of more generalized multilayer systems. The effects of viscoelasticity and van der Waals interactions on surface and interfacial dynamics are also briefly discussed.

The relationship between structural relaxation on molecular length scales and macroscopic stress relaxation was explored in a disordered block-copolymer melt. Experiments show that the structural relaxation time, measured by x-ray photon correlation spectroscopy is larger than the terminal stress relaxation time, measured by rheology, by factors as large as 100. We demonstrate that the structural relaxation data are dominated by the diffusion of intact micelles while the stress relaxation data are dominated by contributions due to disordered concentration fluctuations.

An analysis is presented of how to optimize the experimental beamline configuration for achieving the best possible signal-to-noise ratio (SNR) in X-ray photon correlation spectroscopy experiments using area detectors. It is shown that there exists an optimum detector distance; namely, the highest SNR is achieved by matching the angular pixel size with the angular source size. Binning several pixels together can increase the SNR by permitting to match the shape of a detector pixel to the shape of the source. It is also shown that collimating slits several times wider than the effective transverse coherence length are optimal; further, it is demonstrated that the energy dependence of the SNR is dictated by the energy dependence of detector efficiency and source brilliance. Ultimately the effects of focusing and low longitudinal coherence are discussed.

Repeat proteins are ubiquitous and are involved in a myriad of essential processes. They are typically non-globular structures that act as diverse scaffolds for the mediation of protein-protein interactions. These excitingly different structures, which arise from tandem arrays of a repeated structural motif, have generated significant interest with respect to protein engineering and design. Recent advances have been made in the design and characterisation of repeat proteins. The highlights include re-engineering of binding specificity, quantitative models of repeat protein stability and kinetic studies of repeat protein folding.

The folding/unfolding transitions of a series of designed consensus tetratricopeptide repeat proteins are quantitatively described by the classical one-dimensional Ising model, which thus represents a new folding paradigm for repeat proteins. Moreover, for the first time for any protein, a theoretical model predicts the folding/unfolding transition midpoint and the width of the transition.

X-ray photon correlation spectroscopy was used to characterize the wave-vector- and temperature-dependent dynamics of spontaneous thermal fluctuations in a vesicle (L4) phase that occurs in a blend of a symmetric poly(styrene-ethylene/butylene-styrene) triblock copolymer with a polystyrene homopolymer. Measurements of the intermediate scattering function reveal stretched-exponential behavior versus time, with a stretching exponent slightly larger than 2/3. The corresponding relaxation rates show an approximate q(3) dependence versus wave vector. Overall, the experimental measurements are well described by theories that treat the dynamics of independent membrane plaquettes.

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.

In blends of a symmetric poly(styrene-ethylene/butylene-styrene) tri-block-copolymer with a polystyrene homopolymer, small-angle x-ray scattering and cryotransmission electron microscopy measurements reveal a microstructure consisting of a disordered arrangement of poly(ethylene/butylene) membranes suspended in polystyrene. For triblock volume fractions less than 0.22, the membranes form an asymmetric sponge or L4 phase, consisting predominantly of equilibrium vesicles. For volume fractions greater than 0.22, they form a symmetric sponge-phase (L3 phase), separated from the L4 phase by a first-order transition.

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.

The orientational distribution function of the nematic phase of suspensions of the semiflexible rodlike virus fd is measured by x-ray diffraction as a function of concentration and ionic strength. X-ray diffraction from a single-domain nematic phase of fd is influenced by interparticle correlations at low angle, while only intraparticle scatter contributes at high angle. Consequently, the angular distribution of the scattered intensity 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 (structure factor) and intraparticle (form factor) 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 function's precise form, and the measured angular intensity distribution is described equally well by both Onsager's 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 semiflexible rods S=0.55, but deviations from theory increase with decreasing ionic strength. The concentration dependence of the nematic order parameter also better agrees with theoretical predictions at high ionic strength indicating that electrostatic interactions have a measurable effect on the nematic order parameter. The x-ray order parameters are shown to be proportional to the measured birefringence, and the saturation birefringence of fd is determined enabling a simple, inexpensive way to measure the order parameter. Additionally, the spatial ordering of nematic fd was probed. Measurements of the nematic structure factor revealed a single large peak in contrast to nematics of rigid rods.

The dynamics of supported polymer films were studied by probing the surface height fluctuations as a function of lateral length scale using x-ray photon correlation spectroscopy. Measurements were performed on polystyrene (PS) films of thicknesses varying from 84 to 333 nm at temperatures above the PS glass transition temperature. Within a range of wave vectors spanning 10(-3) to 10(-2) nm(-1), good agreement is found between the measured surface dynamics and the theory of overdamped thermal capillary waves on thin films. Quantitatively, the data can be accounted for using the viscosity of bulk PS.

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.

High-intensity, "pink" beam from an undulator was used in conjunction with microfabricated rapid-fluid mixing devices to monitor the early events in protein folding with time resolved small angle x-ray scattering. This Letter describes recent work on the protein bovine beta-lactoglobulin where collapse from an expanded to a compact set of states was directly observed on the millisecond time scale. The role of chain collapse, one of the initial stages of protein folding, is not currently understood. The characterization of transient, compact states is vital in assessing the validity of theories and models of the folding process.

The dynamics of compositional fluctuations in a miscible, entangled homopolymer blend of poly(ethylene oxide) and poly(methyl methacrylate) were studied on length scales smaller than the polymer radii of gyration, and for times comparable to the polymers' disentanglement time. The measured relaxation rates are consistent with predictions of the reptation model, as expressed via the dynamic random-phase approximation. Moreover, the observed mode amplitudes allow for an estimate of the entanglement length in the blend.

X-ray photon correlation spectroscopy and small-angle x-ray scattering measurements are applied to characterize the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions between 2.7% and 52%. The static structures of the suspensions show essentially hard-sphere behavior. The short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient, which are based on a hard-sphere model [C. W. J. Beenakker and P. Mazur, Physica A 126, 349 (1984)]. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension [P. N. Segre and P. N. Pusey, Phys. Rev. Lett. 77, 771 (1996)]. Our measurements are parametrized in terms of a viscoelastic model for the intermediate scattering function [W. Hess and R. Klein, Adv. Phys. 32, 173 (1983)]. Within this framework, two relaxation modes are predicted to contribute to the decay of the dynamic structure factor, with mode amplitudes depending on both wave vector and volume fraction. Our measurements indicate that, for particle volume fractions smaller than about 0.30, the intermediate scattering function is well described in terms of single-exponential decays, whereas a double-mode structure becomes apparent for more concentrated systems.

X-ray photon correlation spectroscopy and small-angle scattering measurements are presented of the dynamics and structure of concentrated suspensions of charge-stabilized polystyrene latex spheres dispersed in glycerol, for volume fractions from 3% to 52%. The static structures of the suspensions show essentially hard-sphere behavior, and the short-time dynamics shows good agreement with predictions for the wave-vector-dependent collective diffusion coefficient. However, the intermediate scattering function is found to violate a scaling behavior found previously for a sterically stabilized hard-sphere suspension.