Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Silver-based crystalline nanoparticles, microbially fabricated

One mechanism of silver resistance in microorganisms is accumulation of the metal ions in the cell. Here, we report on the phenomenon of biosynthesis of silver-based single crystals with well-defined compositions and shapes, such as equilateral triangles and hexagons, in Pseudomonas stutzeri AG259. The crystals were up to 200 nm in size and were often located at the cell poles. Transmission electron microscopy, quantitative energy-dispersive x-ray analysis, and electron diffraction established that the crystals comprise at least three different types, found both in whole cells and thin sections. These Ag-containing crystals are embedded in the organic matrix of the bacteria. Their possible potential as organic-metal composites in thin film and surface coating technology is discussed.

Wheat grain hardness results from highly conserved mutations in the friabilin components puroindoline a and b

“Soft” and “hard” are the two main market classes of wheat (Triticum aestivum L.) and are distinguished by expression of the Hardness gene. Friabilin, a marker protein for grain softness (Ha), consists of two proteins, puroindoline a and b (pinA and pinB, respectively). We previously demonstrated that a glycine to serine mutation in pinB is linked inseparably to grain hardness. Here, we report that the pinB serine mutation is present in 9 of 13 additional randomly selected hard wheats and in none of 10 soft wheats. The four exceptional hard wheats not containing the serine mutation in pinB express no pinA, the remaining component of the marker protein friabilin. The absence of pinA protein was linked inseparably to grain hardness among 44 near-isogenic lines created between the soft variety Heron and the hard variety Falcon. Both pinA and pinB apparently are required for the expression of grain softness. The absence of pinA protein and transcript and a glycine-to-serine mutation in pinB are two highly conserved mutations associated with grain hardness, and these friabilin genes are the suggested tightly linked components of the Hardness gene. A previously described grain hardness related gene termed “GSP-1” (grain softness protein) is not controlled by chromosome 5D and is apparently not involved in grain hardness. The association of grain hardness with mutations in both pinA or pinB indicates that these two proteins alone may function together to effect grain softness. Elucidation of the molecular basis for grain hardness opens the way to understanding and eventually manipulating this wheat endosperm property.

The pre-S domain of the large viral envelope protein determines host range in avian hepatitis B viruses.

In addition to their well-recognized hepatotropism, all hepatitis B viruses (HBVs) display marked species specificity, growing poorly or not at all in species other than those closely related to their natural hosts. We have examined the molecular basis for this narrow host range, using duck HBV (DHBV) and heron HBV (HHBV) as a model system. HHBV virions will not infect ducks in vivo and infect cultured duck hepatocytes extremely inefficiently in vitro. Mutant HHBV genomes lacking all viral envelope proteins (HHBV env-) can be complemented in trans with DHBV envelope proteins; the resulting pseudotyped virions can efficiently infect duck hepatocytes. Further complementation analysis reveals that of the two viral surface proteins (L and S), it is the L protein that determines host range. Pseudotyping of HHBV env- with DHBV/HHBV chimeric envelope proteins reveals that replacement of as few as 69 amino acids of the pre-S domain of the HHBV L protein by their DHBV counterparts is sufficient to permit infection of duck hepatocytes. These studies indicate that the species-specificity of hepadnaviral infection is determined at the level of virus entry and is governed by the pre-S domain of the viral L protein.