X‐ray diffraction imaging (XDI) is utilized for visualizing the structures of non‐crystalline particles in material sciences and biology. In the structural analysis, phase‐retrieval (PR) algorithms ...are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X‐rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small‐angle regions and Poisson noise in X‐ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non‐crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity‐score‐selected maps is discussed.
The similarity score is a useful metric for screening electron density maps from phase‐retrieval calculations in X‐ray diffraction imaging. The characteristics of the score have been studied in reciprocal space and are described here.
•We develop a model of departure time and parking location choices by heterogeneous commuters.•We examine the distributional effects of imposing a congestion toll and/or a parking fee.•The expansion ...of parking capacity does not necessarily lead to a Pareto improvement when a parking fee is not imposed.•The self-financing principle holds separately for bottleneck capacity and parking capacity.
This study examines the effects of a time-varying congestion toll and a location-dependent parking fee on the behavior of heterogeneous commuters and their commuting costs. To this end, we develop a model of departure time and parking location choices by heterogeneous commuters and characterize its equilibrium. By comparing the equilibrium with and without pricing policies, we obtain the following results: (1) imposing a parking fee and expanding parking capacity may concentrate the temporal distribution of traffic demand, thereby exacerbating traffic congestion; (2) the expansion of parking capacity does not necessarily lead to a Pareto improvement when a parking fee is not imposed; (3) the social optimum is achieved by combining a parking fee with a congestion toll; and (4) the revenue obtained from pricing of roads and parking exactly equals the costs for optimal bottleneck and parking capacities, respectively; that is, the self-financing principle holds separately for bottleneck capacity and parking capacity.
In X‐ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase‐retrieval (PR) algorithms. However, ...the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero‐scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study Sekiguchi et al. (2017), J. Synchrotron Rad.24, 1024–1038. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron‐density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non‐crystalline particles using synchrotron X‐rays and X‐ray free‐electron laser pulses.
A protocol to steer phase‐retrieval calculations to realistic density maps is proposed.
•We develop a model of work start time choice with bottleneck congestion.•By utilizing the properties of a potential game, we characterize equilibrium and optimal distributions of work start ...times.•We show that Pigouvian tax/subsidy policies can be ineffective for achieving an optimum.
Since the seminal work of Henderson (Henderson, J.V., 1981. The economics of staggered work hours. Journal of Urban Economics 9 (3), 349–364), a number of studies have examined the effect of staggered work hours by analyzing models of work start time choice that consider the trade-off between negative congestion externalities and positive production externalities. However, these studies employed flow congestion models to describe traffic congestion. This study develops a model of work start time choice with bottleneck congestion and discloses the intrinsic properties of the model. To this end, this study extends Henderson’s model to incorporate bottleneck congestion. By utilizing the properties of a potential game, we characterize equilibrium and optimal distributions of work start times. We also show that Pigouvian tax/subsidy policies generally yield multiple equilibria and that the first-best optimum must be a stable equilibrium under Pigouvian policies, whereas the second-best optimum in which policymakers cannot eliminate queuing congestion can be unstable.
A novel type of zone plate (ZP), termed an inverse‐phase composite ZP, is proposed to gain a deeper focus than the standard diffraction‐limited depth of focus, with little reduction in spatial ...resolution. The structure is a combination of an inner ZP functioning as a conventional phase ZP and an outer ZP functioning with third‐order diffraction with opposite phase to the inner ZP. Two‐dimensional complex amplitude distributions neighboring the focal point were calculated using a wave‐optical approach of diffraction integration with a monochromatic plane‐wave illumination, where one dimension is the radial direction and the other dimension is the optical‐axis direction. The depth of focus and the spatial resolution were examined as the main focusing properties. Two characteristic promising cases regarding the depth of focus were found: a pit‐intensity focus with the deepest depth of focus, and a flat‐intensity focus with deeper depth of focus than usual ZPs. It was found that twice the depth of focus could be expected with little reduction in the spatial resolution for 10 keV X‐ray energy, tantalum zone material, 84 nm minimum fabrication zone width, and zone thickness of 2.645 µm. It was also found that the depth of focus and the spatial resolution were almost unchanged in the photon energy range from 8 to 12 keV. The inverse‐phase composite ZP has high potential for use in analysis of practical thick samples in X‐ray microbeam applications.
A novel type of zone plate, i.e. an inverse‐phase composite zone plate, is proposed and examined with the aim of achieving deeper focus with little reduction in spatial resolution.
Visualization of intracellular structures and their spatial organization inside cells without any modification is essential to understand the mechanisms underlying the biological functions of cells. ...Here, we investigated the intracellular structure of cyanobacteria Prochlorococcus in the interphase by X-ray diffraction imaging using X-ray free-electron laser. A number of diffraction patterns from single cells smaller than 1 µm in size were collected with high signal-to-noise ratio with a resolution of up to 30 nm. From diffraction patterns, a set of electron density maps projected along the direction of the incident X-ray were retrieved with high reliability. The most characteristic structure found to be common among the cells was a C-shaped arrangement of 100-nm sized high-density spots, which surrounded a low-density area of 100 nm. Furthermore, a three-dimensional map reconstructed from the projection maps of individual cells was non-uniform, indicating the presence of common structures among cyanobacteria cells in the interphase. By referring to the fluorescent images for distributions of thylakoid membranes, nucleoids, and carboxysomes, we inferred and represented their spatial arrangements in the three-dimensional map. The arrangement allowed us to discuss the relevance of the intracellular organization to the biological functions of cyanobacteria.
Egr-1 is an inducible transcription factor that recognizes 9-bp target DNA sites via three zinc finger domains and activates genes in response to cellular stimuli such as synaptic signals and ...vascular stresses. Using spectroscopic and computational approaches, we have studied structural, dynamic, and kinetic aspects of the DNA-scanning process in which Egr-1 is nonspecifically bound to DNA and perpetually changes its location on DNA. Our NMR data indicate that Egr-1 undergoes highly dynamic domain motions when scanning DNA. In particular, the zinc finger 1 (ZF1) of Egr-1 in the nonspecific complex is mainly dissociated from DNA and undergoes collective motions on a nanosecond timescale, whereas zinc fingers 2 and 3 (ZF2 and ZF3, respectively) are bound to DNA. This was totally unexpected because the previous crystallographic studies of the specific complex indicated that all of Egr-1’s three zinc fingers are equally involved in binding to a target DNA site. Mutations that are expected to enhance ZF1’s interactions with DNA and with ZF2 were found to reduce ZF1’s domain motions in the nonspecific complex suggesting that these interactions dictate the dynamic behavior of ZF1. By experiment and computation, we have also investigated kinetics of Egr-1’s translocation between two nonspecific DNA duplexes. Our data on the wild type and mutant proteins suggest that the domain dynamics facilitate Egr-1’s intersegment transfer that involves transient bridging of two DNA sites. These results shed light on asymmetrical roles of the zinc finger domains for Egr-1 to scan DNA efficiently in the nucleus.
Genome compaction and activity in the nucleus depend on spatiotemporal changes in the organization of chromatins in chromosomes. However, the direct imaging of the chromosome structures in the nuclei ...has been difficult and challenging. Herein, we directly visualized the structure of chromosomes in frozen-hydrated nuclei of budding yeast in the interphase using X-ray laser diffraction. The reconstructed projection electron density maps revealed inhomogeneous distributions of chromosomes, such as a 300 nm assembly and fibrous substructures in the elliptic-circular shaped nuclei of approximately 800 nm. In addition, from the diffraction patterns, we confirmed the absence of regular arrangements of chromosomes and chromatins with 400-20 nm spacing, and demonstrated that chromosomes were composed of self-similarly assembled substructural domains with an average radius of gyration of 58 nm and smooth surfaces. Based on these analyses, we constructed putative models to discuss the organization of 16 chromosomes, carrying DNA of 4.1 mm in 800 nm ellipsoid of the nucleus at the interphase. We anticipate the structural parameters on the fractal property of chromosomes and the experimental images to be a starting point for constructing more sophisticated 3D structural models of the nucleus.
ABSTRACT
Harris and Wilson (1978)'s retail location model is a pioneering work that utilizes the combination of the “fast” and “slow” dynamics to describe the space economy. This paper elucidates the ...model's previously unknown comparative static (bifurcation) properties in a many‐location setting beyond two. We show that the spatial structure's evolutionary path in line with decreasing transport costs exhibits a remarkable property, namely, a “spatial period‐doubling cascade.” Furthermore, we reveal strong linkages between the model and “new economic geography” models in terms of their model structures and bifurcation properties, offering a new theoretical perspective for understanding agglomeration behaviors in multilocation settings.
Phototropin2 (phot2) is a blue-light (BL) receptor protein that regulates the BL-dependent activities of plants for efficient photosynthesis. Phot2 is composed of two light-oxygen-voltage sensing ...domains (LOV1 and LOV2) to absorb BL, and a kinase domain. Photo-activated LOV domains, especially LOV2, play a major role in photo-dependent increase in the phosphorylation activity of the kinase domain. The atomic details of the overall structure of phot2 and the intramolecular mechanism to convert BL energy to a phosphorylation signal remain unknown. We performed structural studies on the LOV fragments LOV1, LOV2, LOV2-linker, and LOV2-kinase, and full-length phot2, using small-angle X-ray scattering (SAXS). The aim of the study was to understand structural changes under BL irradiation and discuss the molecular mechanism that enhance the phosphorylation activity under BL. SAXS is a suitable technique for visualizing molecular structures of proteins in solution at low resolution and is advantageous for monitoring their structural changes in the presence of external physical and/or chemical stimuli. Structural parameters and molecular models of the recombinant specimens were obtained from SAXS profiles in the dark, under BL irradiation, and after dark reversion. LOV1, LOV2, and LOV2-linker fragments displayed minimal structural changes. However, BL-induced rearrangements of functional domains were noted for LOV2-kinase and full-length phot2. Based on the molecular model together with the absorption measurements and biochemical assays, we discuss the intramolecular interactions and domain motions necessary for BL-enhanced phosphorylation activity of phot2.
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