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.

A repressible female-specific lethal genetic system for making transgenic insect strains suitable for a sterile-release program

We have developed a tetracycline-repressible female-specific lethal genetic system in the vinegar fly Drosophila melanogaster. One component of the system is the tetracycline-controlled transactivator gene under the control of the fat body and female-specific transcription enhancer from the yolk protein 1 gene. The other component consists of the proapoptotic gene hid under the control of a tetracycline-responsive element. Males and females of a strain carrying both components are viable on medium supplemented with tetracycline, but only males survive on normal medium. A strain with such properties would be ideal for a sterile-insect release program, which is most effective when only males are released in the field.

The Arabidopsis Information Resource (TAIR): a comprehensive database and web-based information retrieval, analysis, and visualization system for a model plant

Arabidopsis thaliana, a small annual plant belonging to the mustard family, is the subject of study by an estimated 7000 researchers around the world. In addition to the large body of genetic, physiological and biochemical data gathered for this plant, it will be the first higher plant genome to be completely sequenced, with completion expected at the end of the year 2000. The sequencing effort has been coordinated by an international collaboration, the Arabidopsis Genome Initiative (AGI). The rationale for intensive investigation of Arabidopsis is that it is an excellent model for higher plants. In order to maximize use of the knowledge gained about this plant, there is a need for a comprehensive database and information retrieval and analysis system that will provide user-friendly access to Arabidopsis information. This paper describes the initial steps we have taken toward realizing these goals in a project called The Arabidopsis Information Resource (TAIR) (www.arabidopsis.org).

A total system approach to sustainable pest management

A fundamental shift to a total system approach for crop protection is urgently needed to resolve escalating economic and environmental consequences of combating agricultural pests. Pest management strategies have long been dominated by quests for “silver bullet” products to control pest outbreaks. However, managing undesired variables in ecosystems is similar to that for other systems, including the human body and social orders. Experience in these fields substantiates the fact that therapeutic interventions into any system are effective only for short term relief because these externalities are soon “neutralized” by countermoves within the system. Long term resolutions can be achieved only by restructuring and managing these systems in ways that maximize the array of “built-in” preventive strengths, with therapeutic tactics serving strictly as backups to these natural regulators. To date, we have failed to incorporate this basic principle into the mainstream of pest management science and continue to regress into a foot race with nature. In this report, we establish why a total system approach is essential as the guiding premise of pest management and provide arguments as to how earlier attempts for change and current mainstream initiatives generally fail to follow this principle. We then draw on emerging knowledge about multitrophic level interactions and other specific findings about management of ecosystems to propose a pivotal redirection of pest management strategies that would honor this principle and, thus, be sustainable. Finally, we discuss the potential immense benefits of such a central shift in pest management philosophy.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.

A novel nonneuronal catecholaminergic system: exocrine pancreas synthesizes and releases dopamine.

Cells of the exocrine pancreas produce digestive enzymes potentially harmful to the intestinal mucosa. Dopamine has been reported to protect against mucosal injury. In looking for the source of dopamine in the small intestine, we found that the duodenal juice contains high levels of dopamine and that the pancreas itself has a high dopamine [and dihydroxyphenylalanine (dopa)] content that does not change significantly after chemical sympathectomy. Furthermore, we were able to demonstrate tyrosine hydroxylase (TH) activity in control pancreas as well as in pancreas from rats after chemical sympathectomy. Immunostaining and in situ hybridization histochemistry confirmed both the presence of TH, dopamine, and the dopamine transporter, and the mRNAs encoding TH and dopamine transporter, and the presence of both types of vesicular monoamine transporters in the exocrine cells of the pancreas. Since there are no catecholaminergic enteric ganglia in the pancreas, the above results indicate that pancreatic cells have all the characteristics of dopamine-producing cells. We suggest that the pancreas is an important source of nonneuronal dopamine in the body, and that this dopamine has a role in protecting the intestinal mucosa and suggests that dopamine D1b receptor agonists might be used to help mucosal healing in the gastrointestinal tract.

GABAergic feedforward projections from the inferior colliculus to the medial geniculate body.

A novel and robust projection from gamma-aminobutyric acid-containing (GABAergic) inferior colliculus neurons to the media] geniculate body (MGB) was discovered in the cat using axoplasmic transport methods combined with immunocytochemistry. This input travels with the classical inferior colliculus projection to the MGB, and it is a direct ascending GABAergic pathway to the sensory thalamus that may be inhibitory. This bilateral projection constitutes 10-30% of the neurons in the auditory tectothalamic system. Studies by others have shown that comparable input to the corresponding thalamic visual or somesthetic nuclei is absent. This suggests that monosynaptic inhibition or disinhibition is a prominent feature in the MGB and that differences in neural circuitry distinguish it from its thalamic visual and somesthetic counterparts.

Evolution of GABAergic circuitry in the mammalian medial geniculate body.

Many features in the mammalian sensory thalamus, such as the types of neurons, their connections, or their neurotransmitters, are conserved in evolution. We found a wide range in the proportion of gamma-aminobutyric acidergic (GABAergic) neurons in the medial geniculate body, from <1% (bat and rat) to 25% or more (cat and monkey). In the bat, some medial geniculate body subdivisions have no GABAergic cells. Species-specific variation also occurs in the somesthetic ventrobasal complex. In contrast, the lateral geniculate body of the visual system has about the same proportion of GABAergic cells in many species. In the central auditory pathway, only the medial geniculate body shows this arrangement; the relative number of GABAergic cells in the inferior colliculus and auditory cortex is similar in each species. The range in the proportion of GABAergic neurons suggests that there are comparative differences in the neural circuitry for thalamic inhibition. We conclude that the number of GABAergic neurons in thalamic sensory nuclei may have evolved independently or divergently in phylogeny. Perhaps these adaptations reflect neurobehavioral requirements for more complex, less stereotyped processing, as in speech-like communication.

Neural correlates of mental transformations of the body-in-space.

Regional cerebral blood flow was measured with positron emission tomography in human subjects during the performance of a task requiring mental rotation of their hand and a perceptually equivalent control task that did not require such a process. Comparison of the distribution of cerebral activity between these conditions demonstrated significant blood flow increases in the superior parietal cortex, the intraparietal sulcus, and the adjacent rostralmost part of the inferior parietal lobule. These findings demonstrated that, in the human brain, there is a specific system of parietal areas that are involved in mental transformations of the body-in-space.

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.

Bioenergetic scaling: metabolic design and body-size constraints in mammals.

The cytosolic phosphorylation ratio ([ATP]/[ADP][P(i)]) in the mammalian heart was found to be inversely related to body mass with an exponent of -0.30 (r = 0.999). This exponent is similar to -0.25 calculated for the mass-specific O2 consumption. The inverse of cytosolic free [ADP], the Gibbs energy of ATP hydrolysis (delta G'ATP), and the efficiency of ATP production (energy captured in forming 3 mol of ATP per cycle along the mitochondrial respiratory chain from NADH to 1/2 O2) were all found to scale with body mass with a negative exponent. On the basis of scaling of the phosphorylation ratio and free cytosolic [ADP], we propose that the myocardium and other tissues of small mammals represent a metabolic system with a higher driving potential (a higher delta G'ATP from the higher [ATP]/[ADP][P(i)]) and a higher kinetic gain [(delta V/Vmax)/delta [ADP]] where small changes in free [ADP] produce large changes in steady-state rates of O2 consumption. From the inverse relationship between mitochondrial efficiency and body size we calculate that tissues of small mammals are more efficient than those of large mammals in converting energy from the oxidation of foodstuffs to the bond energy of ATP. A higher efficiency also indicates that mitochondrial electron transport is not the major site for higher heat production in small mammals. We further propose that the lower limit of about 2 g for adult endotherm body size (bumblebee-bat, Estrucan shrew, and hummingbird) may be set by the thermodynamics of the electron transport chain. The upper limit for body size (100,000-kg adult blue whale) may relate to a minimum delta G'ATP of approximately 55 kJ/mol for a cytoplasmic phosphorylation ratio of 12,000 M-1.