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.

cut11+: A Gene Required for Cell Cycle-dependent Spindle Pole Body Anchoring in the Nuclear Envelope and Bipolar Spindle Formation in Schizosaccharomyces pombe

The “cut” mutants of Schizosaccharomyces pombe are defective in spindle formation and/or chromosome segregation, but they proceed through the cell cycle, resulting in lethality. Analysis of temperature-sensitive alleles of cut11+ suggests that this gene is required for the formation of a functional bipolar spindle. Defective spindle structure was revealed with fluorescent probes for tubulin and DNA. Three-dimensional reconstruction of mutant spindles by serial sectioning and electron microscopy showed that the spindle pole bodies (SPBs) either failed to complete normal duplication or were free floating in the nucleoplasm. Localization of Cut11p tagged with the green fluorescent protein showed punctate nuclear envelope staining throughout the cell cycle and SPBs staining from early prophase to mid anaphase. This SPB localization correlates with the time in the cell cycle when SPBs are inserted into the nuclear envelope. Immunoelectron microscopy confirmed the localization of Cut11p to mitotic SPBs and nuclear pore complexes. Cloning and sequencing showed that cut11+ encodes a novel protein with seven putative membrane-spanning domains and homology to the Saccharomyces cerevisiae gene NDC1. These data suggest that Cut11p associates with nuclear pore complexes and mitotic SPBs as an anchor in the nuclear envelope; this role is essential for mitosis.

A Mutational Analysis Identifies Three Functional Regions of the Spindle Pole Component Spc110p in Saccharomyces cerevisiae

The central coiled coil of the essential spindle pole component Spc110p spans the distance between the central and inner plaques of the Saccharomyces cerevisiae spindle pole body (SPB). The carboxy terminus of Spc110p, which binds calmodulin, resides at the central plaque, and the amino terminus resides at the inner plaque from which nuclear microtubules originate. To dissect the functions of Spc110p, we created temperature-sensitive mutations in the amino and carboxy termini. Analysis of the temperature-sensitive spc110 mutations and intragenic complementation analysis of the spc110 alleles defined three functional regions of Spc110p. Region I is located at the amino terminus. Region II is located at the carboxy-terminal end of the coiled coil, and region III is the previously defined calmodulin-binding site. Overexpression of SPC98 suppresses the temperature sensitivity conferred by mutations in region I but not the phenotypes conferred by mutations in the other two regions, suggesting that the amino terminus of Spc110p is involved in an interaction with the γ-tubulin complex composed of Spc97p, Spc98p, and Tub4p. Mutations in region II lead to loss of SPB integrity during mitosis, suggesting that this region is required for the stable attachment of Spc110p to the central plaque. Our results strongly argue that Spc110p links the γ-tubulin complex to the central plaque of the SPB.

Invariant scaling relationships for interspecific plant biomass production rates and body size

The allometric relationships for plant annualized biomass production (“growth”) rates, different measures of body size (dry weight and length), and photosynthetic biomass (or pigment concentration) per plant (or cell) are reported for multicellular and unicellular plants representing three algal phyla; aquatic ferns; aquatic and terrestrial herbaceous dicots; and arborescent monocots, dicots, and conifers. Annualized rates of growth G scale as the 3/4-power of body mass M over 20 orders of magnitude of M (i.e., G ∝ M3/4); plant body length L (i.e., cell length or plant height) scales, on average, as the 1/4-power of M over 22 orders of magnitude of M (i.e., L ∝ M1/4); and photosynthetic biomass Mp scales as the 3/4-power of nonphotosynthetic biomass Mn (i.e., Mp ∝ Mn3/4). Because these scaling relationships are indifferent to phylogenetic affiliation and habitat, they have far-reaching ecological and evolutionary implications (e.g., net primary productivity is predicted to be largely insensitive to community species composition or geological age).

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.

Hypothalamic integration of body fluid regulation.

The progression of animal life from the paleozoic ocean to rivers and diverse econiches on the planet's surface, as well as the subsequent reinvasion of the ocean, involved many different stresses on ionic pattern, osmotic pressure, and volume of the extracellular fluid bathing body cells. The relatively constant ionic pattern of vertebrates reflects a genetic "set" of many regulatory mechanisms--particularly renal regulation. Renal regulation of ionic pattern when loss of fluid from the body is disproportionate relative to the extracellular fluid composition (e.g., gastric juice with vomiting and pancreatic secretion with diarrhea) makes manifest that a mechanism to produce a biologically relatively inactive extracellular anion HCO3- exists, whereas no comparable mechanism to produce a biologically inactive cation has evolved. Life in the ocean, which has three times the sodium concentration of extracellular fluid, involves quite different osmoregulatory stress to that in freshwater. Terrestrial life involves risk of desiccation and, in large areas of the planet, salt deficiency. Mechanisms integrated in the hypothalamus (the evolutionary ancient midbrain) control water retention and facilitate excretion of sodium, and also control the secretion of renin by the kidney. Over and above the multifactorial processes of excretion, hypothalamic sensors reacting to sodium concentration, as well as circumventricular organs sensors reacting to osmotic pressure and angiotensin II, subserve genesis of sodium hunger and thirst. These behaviors spectacularly augment the adaptive capacities of animals. Instinct (genotypic memory) and learning (phenotypic memory) are melded to give specific behavior apt to the metabolic status of the animal. The sensations, compelling emotions, and intentions generated by these vegetative systems focus the issue of the phylogenetic emergence of consciousness and whether primal awareness initially came from the interoreceptors and vegetative systems rather than the distance receptors.

Whole-body protochordate regeneration from totipotent blood cells.

Cell differentiation, tissue formation, and organogenesis are fundamental patterns during the development of multicellular animals from the dividing cells of fertilized eggs. Hence, the complete morphogenesis of any developing organism of the animal kingdom is based on a complex series of interactions that is always associated with the development of a blastula, a one-layered hollow sphere. Here we document an alternative pathway of differentiation, organogenesis, and morphogenesis occurring in an adult protochordate colonial organism. In this system, any minute fragment of peripheral blood vessel containing a limited number of blood cells isolated from Botrylloides, a colonial sea squirt, has the potential to give rise to a fully functional organism possessing all three embryonic layers. Regeneration probably results from a small number of totipotent stem cells circulating in the blood system. The developmental process starts from disorganized, chaotic masses of blood cells. At first an opaque cell mass is formed. Through intensive cell divisions, a hollow, blastula-like structure results, which may produce a whole organism within a short period of a week. This regenerative power of the protochordates may be compared with some of the characteristics associated with the formation of mammalian embryonal carcinomous bodies. It may also serve as an in vivo model system for studying morphogenesis and differentiation by shedding more light on the controversy of the "stem cell" vs. the "dedifferentiation" theories of regeneration and pattern formation.