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.

Ciliary neurotrophic factor activates leptin-like pathways and reduces body fat, without cachexia or rebound weight gain, even in leptin-resistant obesity

Ciliary Neurotrophic Factor (CNTF) was first characterized as a trophic factor for motor neurons in the ciliary ganglion and spinal cord, leading to its evaluation in humans suffering from motor neuron disease. In these trials, CNTF caused unexpected and substantial weight loss, raising concerns that it might produce cachectic-like effects. Countering this possibility was the suggestion that CNTF was working via a leptin-like mechanism to cause weight loss, based on the findings that CNTF acts via receptors that are not only related to leptin receptors, but also similarly distributed within hypothalamic nuclei involved in feeding. However, although CNTF mimics the ability of leptin to cause fat loss in mice that are obese because of genetic deficiency of leptin (ob/ob mice), CNTF is also effective in diet-induced obesity models that are more representative of human obesity, and which are resistant to leptin. This discordance again raised the possibility that CNTF might be acting via nonleptin pathways, perhaps more analogous to those activated by cachectic cytokines. Arguing strongly against this possibility, we now show that CNTF can activate hypothalamic leptin-like pathways in diet-induced obesity models unresponsive to leptin, that CNTF improves prediabetic parameters in these models, and that CNTF acts very differently than the prototypical cachectic cytokine, IL-1. Further analyses of hypothalamic signaling reveals that CNTF can suppress food intake without triggering hunger signals or associated stress responses that are otherwise associated with food deprivation; thus, unlike forced dieting, cessation of CNTF treatment does not result in binge overeating and immediate rebound weight gain.

Multiple DNA and protein sequence alignment based on segment-to-segment comparison.

In this paper, a new way to think about, and to construct, pairwise as well as multiple alignments of DNA and protein sequences is proposed. Rather than forcing alignments to either align single residues or to introduce gaps by defining an alignment as a path running right from the source up to the sink in the associated dot-matrix diagram, we propose to consider alignments as consistent equivalence relations defined on the set of all positions occurring in all sequences under consideration. We also propose constructing alignments from whole segments exhibiting highly significant overall similarity rather than by aligning individual residues. Consequently, we present an alignment algorithm that (i) is based on segment-to-segment comparison instead of the commonly used residue-to-residue comparison and which (ii) avoids the well-known difficulties concerning the choice of appropriate gap penalties: gaps are not treated explicity, but remain as those parts of the sequences that do not belong to any of the aligned segments. Finally, we discuss the application of our algorithm to two test examples and compare it with commonly used alignment methods. As a first example, we aligned a set of 11 DNA sequences coding for functional helix-loop-helix proteins. Though the sequences show only low overall similarity, our program correctly aligned all of the 11 functional sites, which was a unique result among the methods tested. As a by-product, the reading frames of the sequences were identified. Next, we aligned a set of ribonuclease H proteins and compared our results with alignments produced by other programs as reported by McClure et al. [McClure, M. A., Vasi, T. K. & Fitch, W. M. (1994) Mol. Biol. Evol. 11, 571-592]. Our program was one of the best scoring programs. However, in contrast to other methods, our protein alignments are independent of user-defined parameters.