Detection of translational noncrystallographic symmetry in Patterson functions

Detection of translational noncrystallographic symmetry (TNCS) can be critical for success in crystallographic phasing, particularly when molecular-replacement models are poor or anomalous phasing information is weak. If the correct TNCS is detected then expected intensity factors for each reflection can be refined, so that the maximum-likelihood functions underlying molecular replacement and single-wavelength anomalous dispersion use appropriate structure-factor normalization and variance terms. Here, an analysis of a curated database of protein structures from the Protein Data Bank to investigate how TNCS manifests in the Patterson function is described. These studies informed an algorithm for the detection of TNCS, which includes a method for detecting the number of vectors involved in any commensurate modulation (the TNCS order). The algorithm generates a ranked list of possible TNCS associations in the asymmetric unit for exploration during structure solution.

Method for Recovering Lost Ultrasonic Information Using the Echo-intensity Mean

The axial resolution of a B-mode (or intensity) image is limited by the bandwidth of the pulse envelope. In this report, we investigate the source of this limitation by examining the transfer of high-resolution information from the tissue impedance variance throughout the imaging process. For that purpose, we express the mean and variance of the echo-intensity signal as a linear system to track the flow of object information along the image-formation chain. The results reveal how demodulation influences the available information by discarding high spatial-frequency information. This analysis further points to a simple way to recover lost information with only a minor addition to signal processing. Software phantoms are used to show that under ideal conditions, information from small-scale high-contrast reflectors, such as microcalcifications, can be significantly enhanced with this simple change to echo processing.

Intensity statistics in the presence of translational noncrystallographic symmetry

In the case of translational noncrystallographic symmetry (tNCS), two or more copies of a component in the asymmetric unit of the crystal are present in a similar orientation. This causes systematic modulations of the reflection intensities in the diffraction pattern, leading to problems with structure determination and refinement methods that assume, either implicitly or explicitly, that the distribution of intensities is a function only of resolution. To characterize the statistical effects of tNCS accurately, it is necessary to determine the translation relating the copies, any small rotational differences in their orientations, and the size of random coordinate differences caused by conformational differences. An algorithm to estimate these parameters and refine their values against a likelihood function is presented, and it is shown that by accounting for the statistical effects of tNCS it is possible to unmask the competing statistical effects of twinning and tNCS and to more robustly assess the crystal for the presence of twinning.

Detection and analysis of unusual features in the structural model and structure-factor data of a birch pollen allergen

Physically improbable features in the model of the birch pollen structure Bet v 1d (PDB entry 3k78) are faithfully reproduced in electron density generated with the deposited structure factors, but these structure factors themselves exhibit properties that are characteristic of data calculated from a simple model and are inconsistent with the data and error model obtained through experimental measurements. The refinement of the 3k78 model against these structure factors leads to an isomorphous structure different from the deposited model with an implausibly small R value (0.019). The abnormal refinement is compared with normal refinement of an isomorphous variant structure of Bet v 1l (PDB entry 1fm4). A variety of analytical tools, including the application of Diederichs plots, Rσ plots and bulk-solvent analysis are discussed as promising aids in validation. The examination of the Bet v 1d structure also cautions against the practice of indicating poorly defined protein chain residues through zero occupancies. The recommendation to preserve diffraction images is amplified.