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.

New Alleles of the Yeast MPS1 Gene Reveal Multiple Requirements in Spindle Pole Body Duplication

In Saccharomyces cerevisiae, the Mps1p protein kinase is critical for both spindle pole body (SPB) duplication and the mitotic spindle assembly checkpoint. The mps1–1 mutation causes failure early in SPB duplication, and because the spindle assembly checkpoint is also compromised, mps1–1 cells proceed with a monopolar mitosis and rapidly lose viability. Here we report the genetic and molecular characterization of mps1–1 and five new temperature-sensitive alleles of MPS1. Each of the six alleles contains a single point mutation in the region of the gene encoding the protein kinase domain. The mutations affect several residues conserved among protein kinases, most notably the invariant glutamate in subdomain III. In vivo and in vitro kinase activity of the six epitope-tagged mutant proteins varies widely. Only two display appreciable in vitro activity, and interestingly, this activity is not thermolabile under the assay conditions used. While five of the six alleles cause SPB duplication to fail early, yielding cells with a single SPB, mps1–737 cells proceed into SPB duplication and assemble a second SPB that is structurally defective. This phenotype, together with the observation of intragenic complementation between this unique allele and two others, suggests that Mps1p is required for multiple events in SPB duplication.

A conserved mode of head segmentation in arthropods revealed by the expression pattern of Hox genes in a spider

Chelicerates constitute a basic arthropod group with fossil representatives from as early as the Cambrian period. Embryonic development and the subdivision of the segmented body region into a prosoma and an opisthosoma are very similar in all extant chelicerates. The mode of head segmentation, however, has long been controversial. Although all other arthropod groups show a subdivision of the head region into six segments, the chelicerates are thought to have the first antennal segment missing. To examine this problem on a molecular level, we have compared the expression pattern of Hox genes in the spider Cupiennius salei with the pattern known from insects. Surprisingly, we find that the anterior expression borders of the Hox genes are in the same register and the same relative segmental position as in Drosophila. This contradicts the view that the homologue of the first antennal segment is absent in the spider. Instead, our data suggest that the cheliceral segment is homologous to the first antennal segment and the pedipalpal segment is homologous to the second antennal (or intercalary) segment in arthropods. Our finding implies that chelicerates, myriapods, crustaceans, and insects share a single mode of head segmentation, reinforcing the argument for a monophyletic origin of the arthropods.

Whole body nitric oxide synthesis in healthy men determined from [15N] arginine-to-[15N]citrulline labeling.

The rates of whole body nitric oxide (NO) synthesis, plasma arginine flux, and de novo arginine synthesis and their relationships to urea production, were examined in a total of seven healthy adults receiving an L-amino acid diet for 6 days. NO synthesis was estimated by the rate of conversion of the [15N] guanidino nitrogen of arginine to plasma [15N] ureido citrulline and compared with that based on urinary nitrite (NO2-)/nitrate (NO3-) excretion. Six subjects received on dietary day 7, a 24-hr (12-hr fed/12-hr fasted) primed, constant, intravenous infusion of L-[guanidino-15N2]arginine and [13C]urea. A similar investigation was repeated with three of these subjects, plus an additional subject, in which they received L-[ureido-13C]citrulline, to determine plasma citrulline fluxes. The estimated rates (mean +/- SD) of NO synthesis over a period of 24 hr averaged 0.96 +/- 0.1 mumol .kg-1.hr-1 and 0.95 +/- 0.1 mumol.kg-1.hr-1, for the [15N]citrulline and the nitrite/nitrate methods, respectively. About 15% of the plasma arginine turnover was associated with urea formation and 1.2% with NO formation. De novo arginine synthesis averaged 9.2 +/- 1.4 mumol. kg-1.hr-1, indicating that approximately 11% of the plasma arginine flux originates via conversion of plasma citrulline to arginine. Thus, the fraction of the plasma arginine flux associated with NO and also urea synthesis in healthy humans is small, although the plasma arginine compartment serves as a significant precursor pool (54%) for whole body NO formation. This tracer model should be useful for exploring these metabolic relationships in vivo, under specific pathophysiologic states where the L-arginine-NO pathway might be altered.