Fluorescence polarization of green fluorescence protein

We report here the striking anisotropy of fluorescence exhibited by crystals of native green fluorescence protein (GFP). The crystals were generated by water dialysis of highly purified GFP obtained from the jellyfish Aequorea. We find that the fluorescence becomes six times brighter when the excitation, or emission, beam is polarized parallel (compared with perpendicular) to the crystal long axis. Thus, the major dipoles of the fluorophores must be oriented very nearly parallel to the crystal long axis. Observed in a polarizing microscope between parallel polars instead of either a polarizer or analyzer alone, the fluorescence polarization ratio rises to an unexpectedly high value of about 30:1, nearly the product of the fluorescence excitation and emission ratios, suggesting a sensitive method for measuring fluorophore orientations, even of a single fluorophore molecule. We have derived equations that accurately describe the relative fluorescence intensities of crystals oriented in various directions, with the polarizer and analyzer arranged in different configurations. The equations yield relative absorption and fluorescence coefficients for the four transition dipoles involved. Finally, we propose a model in which the elongated crystal is made of GFP molecules that are tilted 60 degrees to align the fluorophores parallel to the crystal long axis. The unit layer in the model may well correspond to the arrangement of functional GFP molecules, to which resonant energy is efficiently transmitted from Ca2+-activated aequorin, in the jellyfish photophores.     

Structural basis of AdoMet-dependent aminocarboxypropyl transfer reaction catalyzed by tRNA-wybutosine synthesizing enzyme,TYW2

S-adenosylmethionine (AdoMet) is a methyl donor used by a wide variety of methyltransferases, and it is also used as the source of an α-amino-α-carboxypropyl (“acp”) group by several enzymes. tRNA-yW synthesizing enzyme-2 (TYW2) is involved in the biogenesis of a hypermodified nucleotide, wybutosine (yW), and it catalyzes the transfer of the “acp” group from AdoMet to the C7 position of the imG-14 base, a yW precursor. This modified nucleoside yW is exclusively located at position 37 of eukaryotic tRNA^Phe, and it ensures the anticodon-codon pairing on the ribosomal decoding site. Although this “acp” group has a significant role in preventing decoding frame shifts, the mechanism of the “acp” group transfer by TYW2 remains unresolved. Here we report the crystal structures and functional analyses of two archaeal homologs of TYW2 from Pyrococcus horikoshii and Methanococcus jannaschii. The in vitro mass spectrometric and radioisotope-labeling analyses confirmed that these archaeal TYW2 homologues have the same activity as yeast TYW2. The crystal structures verified that the archaeal TYW2 contains a canonical class-I methyltransferase (MTase) fold. However, their AdoMet-bound structures revealed distinctive AdoMet-binding modes, in which the “acp” group, instead of the methyl group, of AdoMet is directed to the substrate binding pocket. Our findings, which were confirmed by extensive mutagenesis studies, explain why TYW2 transfers the “acp” group, and not the methyl group, from AdoMet to the nucleobase.     

Molecular organization of Gram-negative peptidoglycan

The stress-bearing component of the bacterial cell wall—a multi-gigadalton bag-like molecule called the sacculus—is synthesized from peptidoglycan. Whereas the chemical composition and the 3-dimensional structure of the peptidoglycan subunit (in at least one conformation) are known, the architecture of the assembled sacculus is not. Four decades' worth of biochemical and electron microscopy experiments have resulted in two leading 3-D peptidoglycan models: “Layered” and “Scaffold”, in which the glycan strands are parallel and perpendicular to the cell surface, respectively. Here we resolved the basic architecture of purified, frozen-hydrated sacculi through electron cryotomography. In the Gram-negative sacculus, a single layer of glycans lie parallel to the cell surface, roughly perpendicular to the long axis of the cell, encircling the cell in a disorganized hoop-like fashion.     

Electrochemical and homogeneous electron transfers to the Alzheimer amyloid-β copper complex follow a preorganization mechanism

Deciphering the electron transfer reactivity characteristics of amyloid β-peptide copper complexes is an important task in connection with the role they are assumed to play in Alzheimer’s disease. A systematic analysis of this question with the example of the amyloid β-peptide copper complex by means of its electrochemical current–potential responses and of its homogenous reactions with electrogenerated fast electron exchanging osmium complexes revealed a quite peculiar mechanism: The reaction proceeds through a small fraction of the complex molecules in which the peptide complex is “preorganized” so as the distances and angles in the coordination sphere to vary minimally upon electron transfer, thus involving a remarkably small reorganization energy (0.3 eV). This preorganization mechanism and its consequences on the reactivity should be taken into account for reactions involving dioxygen and hydrogen peroxide that are considered to be important in Alzheimer’s disease through the production of harmful reactive oxygen species.     

Lipidic cubic phases: A novel concept for the crystallization of membrane proteins

Understanding the mechanisms of action of membrane proteins requires the elucidation of their structures to high resolution. The critical step in accomplishing this by x-ray crystallography is the routine availability of well-ordered three-dimensional crystals. We have devised a novel, rational approach to meet this goal using quasisolid lipidic cubic phases. This membrane system, consisting of lipid, water, and protein in appropriate proportions, forms a structured, transparent, and complex three-dimensional lipidic array, which is pervaded by an intercommunicating aqueous channel system. Such matrices provide nucleation sites (“seeding”) and support growth by lateral diffusion of protein molecules in the membrane (“feeding”). Bacteriorhodopsin crystals were obtained from bicontinuous cubic phases, but not from micellar systems, implying a critical role of the continuity of the diffusion space (the bilayer) on crystal growth. Hexagonal bacteriorhodopsin crystals diffracted to 3.7 Å resolution, with a space group P6₃, and unit cell dimensions of a = b = 62 Å, c = 108 Å; α = β = 90° and γ = 120°.     

Assembly and organization processes in DNA-directed colloidal crystallization

We present an analysis of the key steps involved in the DNA-directed assembly of nanoparticles into crystallites and polycrystalline aggregates. Additionally, the rate of crystal growth as a function of increased DNA linker length, solution temperature, and self-complementary versus non-self-complementary DNA linker strands (1- versus 2-component systems) has been studied. The data show that the crystals grow via a 3-step process: an initial “random binding” phase resulting in disordered DNA-AuNP aggregates, followed by localized reorganization and subsequent growth of crystalline domain size, where the resulting crystals are well-ordered at all subsequent stages of growth.     

The intrinsic conformational propensities of the 20 naturally occurring amino acids and reflection of these propensities in proteins

Here, we compare the distributions of main chain (Φ,Ψ) angles (i.e., Ramachandran maps) of the 20 naturally occurring amino acids in three contexts: (i) molecular dynamics (MD) simulations of Gly-Gly-X-Gly-Gly pentapeptides in water at 298 K with exhaustive sampling, where X = the amino acid in question; (ii) 188 independent protein simulations in water at 298 K from our Dynameomics Project; and (iii) static crystal and NMR structures from the Protein Data Bank. The GGXGG peptide series is often used as a model of the unstructured denatured state of proteins. The sampling in the peptide MD simulations is neither random nor uniform. Instead, individual amino acids show preferences for particular conformations, but the peptide is dynamic, and interconversion between conformers is facile. For a given amino acid, the (Φ,Ψ) distributions in the protein simulations and the Protein Data Bank are very similar and often distinct from those in the peptide simulations. Comparison between the peptide and protein simulations shows that packing constraints, solvation, and the tendency for particular amino acids to be used for specific structural motifs can overwhelm the “intrinsic propensities” of amino acids for particular (Φ,Ψ) conformations. We also compare our helical propensities with experimental consensus values using the host–guest method, which appear to be determined largely by context and not necessarily the intrinsic conformational propensities of the guest residues. These simulations represent an improved coil library free from contextual effects to better model intrinsic conformational propensities and provide a detailed view of conformations making up the “random coil” state.     

Neural and behavioral bases of age differences in perceptions of trust

Older adults are disproportionately vulnerable to fraud, and federal agencies have speculated that excessive trust explains their greater vulnerability. Two studies, one behavioral and one using neuroimaging methodology, identified age differences in trust and their neural underpinnings. Older and younger adults rated faces high in trust cues similarly, but older adults perceived faces with cues to untrustworthiness to be significantly more trustworthy and approachable than younger adults. This age-related pattern was mirrored in neural activation to cues of trustworthiness. Whereas younger adults showed greater anterior insula activation to untrustworthy versus trustworthy faces, older adults showed muted activation of the anterior insula to untrustworthy faces. The insula has been shown to support interoceptive awareness that forms the basis of “gut feelings,” which represent expected risk and predict risk-avoidant behavior. Thus, a diminished “gut” response to cues of untrustworthiness may partially underlie older adults’ vulnerability to fraud.     

The "fire stick farming" hypothesis: Australian Aboriginal foraging strategies, biodiversity, and anthropogenic fire mosaics

Aboriginal burning in Australia has long been assumed to be a “resource management” strategy, but no quantitative tests of this hypothesis have ever been conducted. We combine ethnographic observations of contemporary Aboriginal hunting and burning with satellite image analysis of anthropogenic and natural landscape structure to demonstrate the processes through which Aboriginal burning shapes arid-zone vegetational diversity. Anthropogenic landscapes contain a greater diversity of successional stages than landscapes under a lightning fire regime, and differences are of scale, not of kind. Landscape scale is directly linked to foraging for small, burrowed prey (monitor lizards), which is a specialty of Aboriginal women. The maintenance of small-scale habitat mosaics increases small-animal hunting productivity. These results have implications for understanding the unique biodiversity of the Australian continent, through time and space. In particular, anthropogenic influences on the habitat structure of paleolandscapes are likely to be spatially localized and linked to less mobile, “broad-spectrum” foraging economies.     

Emergent gene order in a model of modular polyketide synthases

Polyketides are a class of biologically active heteropolymers produced by assembly line-like multiprotein complexes of modular polyketide synthases (PKS). The polyketide product is encoded in the order of the PKS proteins in the assembly line, suggesting that polyketide diversity derives from combinatorial rearrangement of these PKS complexes. Remarkably, the order of PKS genes on the chromosome follows the order of PKS proteins in the assembly line: This fact is commonly referred to as “collinearity”. Here we propose an evolutionary origin for collinearity and demonstrate the mechanism by using a computational model of PKS evolution in a population. Assuming continuous evolutionary pressure for novel polyketides, and that new polyketide pathways are formed by horizontal transfer/recombination of PKS-encoding DNA, we demonstrate the existence of a broad range of parameters for which collinearity emerges spontaneously. Collinearity confers no fitness advantage in our model; it is established and maintained through a “secondary selection” mechanism, as a trait which increases the probability of forming long, novel PKS complexes through recombination. Consequently, collinearity hitchhikes on the successful genotypes which periodically sweep through the evolving population. In addition to computer simulation of a simplified model of PKS evolution, we provide a mathematical framework describing the secondary selection mechanism, which generalizes beyond the context of the present model.     

From the Cover: Goniometer-based femtosecond crystallography with X-ray free electron lasers

The emerging method of femtosecond crystallography (FX) may extend the diffraction resolution accessible from small radiation-sensitive crystals and provides a means to determine catalytically accurate structures of acutely radiation-sensitive metalloenzymes. Automated goniometer-based instrumentation developed for use at the Linac Coherent Light Source enabled efficient and flexible FX experiments to be performed on a variety of sample types. In the case of rod-shaped Cpl hydrogenase crystals, only five crystals and about 30 min of beam time were used to obtain the 125 still diffraction patterns used to produce a 1.6-Å resolution electron density map. For smaller crystals, high-density grids were used to increase sample throughput; 930 myoglobin crystals mounted at random orientation inside 32 grids were exposed, demonstrating the utility of this approach. Screening results from cryocooled crystals of β₂-adrenoreceptor and an RNA polymerase II complex indicate the potential to extend the diffraction resolution obtainable from very radiation-sensitive samples beyond that possible with undulator-based synchrotron sources.Using extremely bright, short-timescale X-ray pulses produced by X-ray free-electron lasers (XFELs), femtosecond crystallography (FX) is an emerging method that expands the structural information accessible from very small or very radiation-sensitive macromolecular crystals. Central to this method is the “diffraction before destruction” (1) process in which a still diffraction image is produced by a single X-ray pulse before significant radiation-induced electronic and atomic rearrangements occur within the crystal (1–3). At the Linac Coherent Light Source (LCLS) at SLAC, a single ∼50-fs–long X-ray pulse can expose a crystal to as many X-ray photons as a typical synchrotron beam line produces in about a second. Exposing small crystals to these intense ultrashort pulses circumvents the dose limitations of conventional X-ray diffraction experiments (4) and may produce useful data to resolutions beyond what is achievable at synchrotrons (5). This innovation provides a pathway to obtain atomic information from proteins that only form micrometer- to nanometer-sized crystals, such as many membrane proteins and large multiprotein complexes. Moreover, XFELs enable “diffraction before reduction” data collection to address another major challenge in structural enzymology by providing a means to determine catalytically accurate structures of acutely radiation-sensitive metalloenzyme active sites (6), such as high-valency reaction intermediates that may be significantly photoreduced during a single X-ray exposure at a synchrotron, even at very small doses (7–11). Furthermore, the use of short (tens of femtoseconds) X-ray pulses further complements the structural characterization of biochemical reaction processes by providing access to a time domain two to three orders of magnitude faster (12, 13) than currently accessible using synchrotrons.A single X-ray pulse from the LCLS damages the illuminated sample volume and also some of the sample in the immediate vicinity, requiring the combination of measurements from discrete volumes or units of crystalline material to obtain a complete dataset (14). The first FX experiments were carried out in vacuum at the LCLS using a gas dynamic virtual nozzle (GDVN) liquid injector (15), which delivered crystals of submicron to a few microns in size, suspended in carrier solution to a series of X-ray pulses produced at up to a 120-Hz repetition rate. These pioneering experiments demonstrated the utility of serial femtosecond crystallography (SFX) and the use of crystals of less than 5 μm in size, often termed “nanocrystals” (NCs), for macromolecular structure determination to high resolution (16, 17). As NCs may be a ubiquitous but generally overlooked outcome of commercial crystallization screens that fail to produce larger crystals (18), FX may open up many systems to crystallographic analysis. However, to develop FX into a generally applicable method, a number of challenges in the areas of sample preparation, data collection, and data processing must be overcome.Obtaining a sufficient supply of crystals in an appropriate carrier solution is a first hurdle to conducting a SFX experiment. In addition to the GDVN (2, 3, 14, 16, 17, 19, 20), other injectors such as a nanoflow electrospinning injector (21) and a lipidic cubic phase (LCP) injector (22), have been developed that have a reduced flow rate and lower sample consumption. However, because injectors deliver a continuous stream of solution containing a random distribution of crystals, and the X-ray pulses are extremely short, often only a small percentage of pulses hit a crystal and produce a useful diffraction pattern. Carrying out these experiments at room temperature avoids the difficulties associated with cryoprotection, and datasets obtained at ambient temperatures can provide insight on the functional motions of protein molecules (23). However, there are different and often more complex optimization steps associated with specific injector technologies. Solutions containing a mixture of crystal sizes may require filtering to avoid clogging in the injector nozzle, and delicate crystals may be damaged from the pressures and shear forces of the delivery process itself (24). For experiments conducted in vacuo, stream formation may be disrupted by solution bubbling, drying, or freezing as it exits the injector and enters the vacuum chamber. Drop-on-demand methods that deliver single drops containing crystals to individual X-ray pulses have the potential to significantly reduce sample consumption are in development, such as acoustic and micropiezo activated technologies, but implementation has been complicated by a variety of factors, including difficulties imposed by viscous solutions and unpredictable trajectories of drops that contain crystals of varied shapes and sizes.Here, we describe an alternative strategy for FX experiments that leverages the well-established benefits of the highly automated goniometer-based setups used at state-of-the-art microfocus synchrotron beam lines, and expands these technologies to take full advantage of the unique capabilities of XFEL sources. Key to this approach is the coupling of highly automated instrumentation with specialized sample containers and customized software for efficient data collection with minimal sample consumption. High-density sample containers, such as microfluidic chips or microcrystal traps (25) for room temperature studies or grids for experiments at cryogenic temperatures, hold samples in known locations. These sample holders enable very rapid and precise positioning of crystals into the X-ray interaction region for consistent production of diffraction patterns. To optimize data completeness and resolution, data may be collected using a range of crystal sizes with a variety of X-ray beam sizes, and different regions of larger crystals may be exposed in different orientations. When small crystals align with the sample holder in a preferred orientation, exposing each crystal at varied angles to the holder surface may take advantage of this effect to enhance completeness. When the X-ray pulse mean diameter is greater than about 8 μm or is highly attenuated, the protein crystal may remain intact after exposure to the X-ray pulse and still diffract, but usually to a lower resolution as a result of radiation damage. In these cases, it is possible to rotate the crystal and collect additional diffraction patterns to use as an aid in indexing and scaling the partially recorded reflections of the initial still diffraction pattern.     

Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal

Nacre is an exquisitely structured biocomposite of the calcium carbonate mineral aragonite with small amounts of proteins and the polysaccharide chitin. For many years, it has been the subject of research, not just because of its beauty, but also to discover how nature can produce such a superior product with excellent mechanical properties from such relatively weak raw materials. Four decades ago, Wada [Wada K (1966) Spiral growth of nacre. Nature 211:1427] proposed that the spiral patterns in nacre could be explained by using the theory Frank [Frank F (1949) The influence of dislocations on crystal growth. Discuss Faraday Soc 5:48–54] had put forward of the growth of crystals by means of screw dislocations. Frank''s mechanism of crystal growth has been amply confirmed by experimental observations of screw dislocations in crystals, but it is a growth mechanism for a single crystal, with growth fronts of molecules. However, the growth fronts composed of many tablets of crystalline aragonite visible in micrographs of nacre are not a molecular-scale but a mesoscale phenomenon, so it has not been evident how the Frank mechanism might be of relevance. Here, we demonstrate that nacre growth is organized around a liquid-crystal core of chitin crystallites, a skeleton that the other components of nacre subsequently flesh out in a process of hierarchical self-assembly. We establish that spiral and target patterns can arise in a liquid crystal formed layer by layer through the Burton–Cabrera–Frank [Burton W, Cabrera N, Frank F (1951) The growth of crystals and the equilibrium structure of their surfaces. Philos Trans R Soc London Ser A 243:299–358] dynamics, and furthermore that this layer growth mechanism is an instance of an important class of physical systems termed excitable media. Artificial liquid crystals grown in this way may have many technological applications.     

Liquid- and Gas-Phase Diffusion of Ferrocene in Thin Films of Metal-Organic Frameworks

The mass transfer of the guest molecules in nanoporous host materials, in particular in metal-organic frameworks (MOFs), is among the crucial features of their applications. By using thin surface-mounted MOF films in combination with a quartz crystal microbalance (QCM), the diffusion of ferrocene vapor and of ethanolic and hexanic ferrocene solution in HKUST-1 was investigated. For the first time, liquid- and gas-phase diffusion in MOFs was compared directly in the identical sample. The diffusion coefficients are in the same order of magnitude (~10⁻¹⁶ m²·s⁻¹), whereas the diffusion coefficient of ferrocene in the empty framework is roughly 3-times smaller than in the MOF which is filled with ethanol or n-hexane.     

Prior knowledge of illumination for 3D perception in the human brain

In perceiving 3D shape from ambiguous shading patterns, humans use the prior knowledge that the light is located above their head and slightly to the left. Although this observation has fascinated scientists and artists for a long time, the neural basis of this “light from above left” preference for the interpretation of 3D shape remains largely unexplored. Combining behavioral and functional MRI measurements coupled with multivoxel pattern analysis, we show that activations in early visual areas predict best the light source direction irrespective of the perceived shape, but activations in higher occipitotemporal and parietal areas predict better the perceived 3D shape irrespective of the light direction. These findings demonstrate that illumination is processed earlier than the representation of 3D shape in the visual system. In contrast to previous suggestions, we propose that prior knowledge about illumination is processed in a bottom-up manner and influences the interpretation of 3D structure at higher stages of processing.     

Universal collapse of stress and wrinkle-to-scar transition in spherically confined crystalline sheets

Imposing curvature on crystalline sheets, such as 2D packings of colloids or proteins, or covalently bonded graphene leads to distinct types of structural instabilities. The first type involves the proliferation of localized defects that disrupt the crystalline order without affecting the imposed shape, whereas the second type consists of elastic modes, such as wrinkles and crumples, which deform the shape and also are common in amorphous polymer sheets. Here, we propose a profound link between these types of patterns, encapsulated in a universal, compression-free stress field, which is determined solely by the macroscale confining conditions. This “stress universality” principle and a few of its immediate consequences are borne out by studying a circular crystalline patch bound to a deformable spherical substrate, in which the two distinct patterns become, respectively, radial chains of dislocations (called “scars”) and radial wrinkles. The simplicity of this set-up allows us to characterize the morphologies and evaluate the energies of both patterns, from which we construct a phase diagram that predicts a wrinkle–scar transition in confined crystalline sheets at a critical value of the substrate stiffness. The construction of a unified theoretical framework that bridges inelastic crystalline defects and elastic deformations opens unique research directions. Beyond the potential use of this concept for finding energy-optimizing packings in curved topographies, the possibility of transforming defects into shape deformations that retain the crystalline structure may be valuable for a broad range of material applications, such as manipulations of graphene’s electronic structure.     

Structure and function of broadly reactive antibody PG16 reveal an H3 subdomain that mediates potent neutralization of HIV-1

Development of an effective vaccine against HIV-1 will likely require elicitation of broad and potent neutralizing antibodies against the trimeric surface envelope glycoprotein (Env). Monoclonal antibodies (mAbs) PG9 and PG16 neutralize ~80% of HIV-1 isolates across all clades with extraordinary potency and target novel epitopes preferentially expressed on Env trimers. As these neutralization properties are ideal for a vaccine-elicited antibody response to HIV-1, their structural basis was investigated. The crystal structure of the antigen-binding fragment (Fab) of PG16 at 2.5 Å resolution revealed its unusually long, 28-residue, complementarity determining region (CDR) H3 forms a unique, stable subdomain that towers above the antibody surface. A 7-residue “specificity loop” on the “hammerhead” subdomain was identified that, when transplanted from PG16 to PG9 and vice versa, accounted for differences in the fine specificity and neutralization of these two mAbs. The PG16 electron density maps also revealed that a CDR H3 tyrosine was sulfated, which was confirmed for both PG9 (doubly) and PG16 (singly) by mass spectral analysis. We further showed that tyrosine sulfation plays a role in binding and neutralization. An N-linked glycan modification is observed in the variable light chain, but not required for antigen recognition. Further, the crystal structure of the PG9 light chain at 3.0 Å facilitated homology modeling to support the presence of these unusual features in PG9. Thus, PG9 and PG16 use unique structural features to mediate potent neutralization of HIV-1 that may be of utility in antibody engineering and for high-affinity recognition of a variety of therapeutic targets.     

Dune formation under bimodal winds

The study of dune morphology represents a valuable tool in the investigation of planetary wind systems—the primary factor controlling the dune shape is the wind directionality. However, our understanding of dune formation is still limited to the simplest situation of unidirectional winds: There is no model that solves the equations of sand transport under the most common situation of seasonally varying wind directions. Here we present the calculation of sand transport under bimodal winds using a dune model that is extended to account for more than one wind direction. Our calculations show that dunes align longitudinally to the resultant wind trend if the angle θ_w between the wind directions is larger than 90°. Under high sand availability, linear seif dunes are obtained, the intriguing meandering shape of which is found to be controlled by the dune height and by the time the wind lasts at each one of the two wind directions. Unusual dune shapes including the “wedge dunes” observed on Mars appear within a wide spectrum of bimodal dune morphologies under low sand availability.     

Monkey visual behavior falls into the uncanny valley

Very realistic human-looking robots or computer avatars tend to elicit negative feelings in human observers. This phenomenon is known as the “uncanny valley” response. It is hypothesized that this uncanny feeling is because the realistic synthetic characters elicit the concept of “human,” but fail to live up to it. That is, this failure generates feelings of unease due to character traits falling outside the expected spectrum of everyday social experience. These unsettling emotions are thought to have an evolutionary origin, but tests of this hypothesis have not been forthcoming. To bridge this gap, we presented monkeys with unrealistic and realistic synthetic monkey faces, as well as real monkey faces, and measured whether they preferred looking at one type versus the others (using looking time as a measure of preference). To our surprise, monkey visual behavior fell into the uncanny valley: They looked longer at real faces and unrealistic synthetic faces than at realistic synthetic faces.     

Diamond-Structured Photonic Crystals with Graded Air Spheres Radii

A diamond-structured photonic crystal (PC) with graded air spheres radii was fabricated successfully by stereolithography (SL) and gel-casting process. The graded radii in photonic crystal were formed by uniting different radii in photonic crystals with a uniform radius together along the Г-Х <100> direction. The stop band was observed between 26.1 GHz and 34.3 GHz by reflection and transmission measurements in the direction. The result agreed well with the simulation attained by the Finite Integration Technique (FIT). The stop band width was 8.2 GHz and the resulting gap/midgap ratio was 27.2%, which became respectively 141.4% and 161.9% of the perfect PC. The results indicate that the stop band width of the diamond-structured PC can be expanded by graded air spheres radii along the Г-Х <100> direction, which is beneficial to develop a multi bandpass filter.     

"...the tyranny of the lattice...".

A systematic comparison of crystal structures of nine different B-DNA dodecamers, in three different space groups, with and without A-tracts, shows that crystal packing or lattice forces are of secondary importance for helix axis bending, minor-groove width, and propeller twist. While other local helix parameters may be influenced or even established by crystal packing, the properties just enumerated are determined primarily by base sequence. One and the same crystal packing scheme can accommodate a bend in one of two different directions, or no bend at all. A-tract regions of B-DNA are inherently straight and unbent, with base-pair inclination no different from that of general-sequence B-DNA. Where bends are observed at junctions between G.C and A.T regions, they always involve a roll about base-pair long axes in a direction that compresses the wide major groove and, hence, are 90 degrees away from that necessary for the correctness of the junction model of A-tract bending. The G.C/A.T junction appears to be a flexible hinge, capable of adopting either a straight or a bent conformation under the local influence of weak crystal packing forces. Such forces therefore are a source of information about DNA deformability and not a curse to be deplored. But as an indication of the weakness of crystal packing forces, introduction of a single bromine atom in the major groove is sufficient to eliminate a bend, although brominated and unbrominated crystals are isomorphous.