An algebraic method to solve the radial Schrödinger equation

AbstractWe propose a method of numerical integration of differential equations of the type x2y″+f(x)y=0 by approximating its solution with solutions of equations of the type x2y″+(ax2+bx+c)y=0. This approximation is performed by segmentary approximation on an interval. We apply the method to obtain approximate solutions of the radial Schrödinger equation on a given interval and test it for two different potentials. We conclude that our method gives a similar accuracy than the Taylor method of higher order

Variational dynamics in open spacetimes

We study the effect of non-vanishing surface terms at spatial infinity on the dynamics of a scalar field in an open FLRW spacetime. Starting from the path-integral formulation of quantum field theory we argue that classical physics is described by field configurations which extremize the action functional in the space of field configurations for which the variation of the action is well defined. Since these field configurations are not required to vanish outside a bounded domain, there is generally a non-vanishing contribution of a surface term to the variation of the action. We then investigate whether this surface term has an effect on the dynamics of the action-extremizing field configurations. This question appears to be surprisingly nontrivial in the case of the open FLRW geometry, since surface terms tend to grow as fast as volume terms in the infinite volume limit. We find that surface terms can be important for the dynamics of the field at a classical and at a quantum level, when there are supercurvature perturbations.Comment: 21 pages, Latex, no figure

Why Do Species Co-Occur? A Test of Alternative Hypotheses Describing Abiotic Differences in Sympatry versus Allopatry Using Spadefoot Toads

Areas of co-occurrence between two species (sympatry) are often thought to arise in regions where abiotic conditions are conducive to both species and are therefore intermediate between regions where either species occurs alone (allopatry). Depending on historical factors or interactions between species, however, sympatry might not differ from allopatry, or, alternatively, sympatry might actually be more extreme in abiotic conditions relative to allopatry. Here, we evaluate these three hypothesized patterns for how sympatry compares to allopatry in abiotic conditions. We use two species of congeneric spadefoot toads, Spea multiplicata and S. bombifrons, as our study system. To test these hypotheses, we created ecological niche models (specifically using Maxent) for both species to create a map of the joint probability of occurrence of both species. Using the results of these models, we identified three types of locations: two where either species was predicted to occur alone (i.e., allopatry for S. multiplicata and allopatry for S. bombifrons) and one where both species were predicted to co-occur (i.e., sympatry). We then compared the abiotic environment between these three location types and found that sympatry was significantly hotter and drier than the allopatric regions. Thus, sympatry was not intermediate between the alternative allopatric sites. Instead, sympatry occurred at one extreme of the conditions occupied by both species. We hypothesize that biotic interactions in these extreme environments facilitate co-occurrence. Specifically, hybridization between S. bombifrons females and S. multiplicata males may facilitate co-occurrence by decreasing development time of tadpoles. Additionally, the presence of alternative food resources in more extreme conditions may preclude competitive exclusion of one species by the other. This work has implications for predicting how interacting species will respond to climate change, because species interactions may facilitate survival in extreme habitats

Differential Impact of Tetratricopeptide Repeat Proteins on the Steroid Hormone Receptors

Tetratricopeptide repeat (TPR) motif containing co-chaperones of the chaperone Hsp90 are considered control modules that govern activity and specificity of this central folding platform. Steroid receptors are paradigm clients of Hsp90. The influence of some TPR proteins on selected receptors has been described, but a comprehensive analysis of the effects of TPR proteins on all steroid receptors has not been accomplished yet.We compared the influence of the TPR proteins FK506 binding proteins 51 and 52, protein phosphatase-5, C-terminus of Hsp70 interacting protein, cyclophillin 40, hepatitis-virus-B X-associated protein-2, and tetratricopeptide repeat protein-2 on all six steroid hormone receptors in a homogeneous mammalian cell system. To be able to assess each cofactor's effect on the transcriptional activity of on each steroid receptor we employed transient transfection in a reporter gene assay. In addition, we evaluated the interactions of the TPR proteins with the receptors and components of the Hsp90 chaperone heterocomplex by coimmunoprecipitation. In the functional assays, corticosteroid and progesterone receptors displayed the most sensitive and distinct reaction to the TPR proteins. Androgen receptor's activity was moderately impaired by most cofactors, whereas the Estrogen receptors' activity was impaired by most cofactors only to a minor degree. Second, interaction studies revealed that the strongly receptor-interacting co-chaperones were all among the inhibitory proteins. Intriguingly, the TPR-proteins also differentially co-precipitated the heterochaperone complex components Hsp90, Hsp70, and p23, pointing to differences in their modes of action.The results of this comprehensive study provide important insight into chaperoning of diverse client proteins via the combinatorial action of (co)-chaperones. The differential effects of the TPR proteins on steroid receptors bear on all physiological processes related to steroid hormone activity

The Unified Multiple System Atrophy Rating Scale: Status, Critique, and Recommendations

: The Unified Multiple System Atrophy (MSA) Rating Scale was developed to provide a surrogate marker of disease severity and clinical progression in patients with MSA. It is comprised of four subscales: UMSARS-I (12 items) rates patient-reported functional disability; UMSARS-II (14 items) assesses motor impairment based on a clinical examination; UMSARS-III records blood pressure and heart rate in the supine and standing positions; and UMSARS-IV (1 item) rates chore-based disability. Strengths of the UMSARS include its wide acceptance in the field, the comprehensive coverage of motor symptoms and its clinimetric properties (including reliability and validity). However, with its increasing use, potential areas of improvement in the UMSARS have become apparent. To address these limitations, a task force, involving clinicians, researchers, patient groups, and industry representatives, has recently been endorsed by the International Parkinson’s Disease and Movement Disorders Society. The present viewpoint summarizes strengths and weaknesses of the UMSARS and suggests a roadmap to develop an improved MSA clinical outcome assessment

Validating visual evoked potentials as a preclinical, quantitative biomarker for remyelination efficacy.

Many biomarkers in clinical neuroscience lack pathological certification. This issue is potentially a significant contributor to the limited success of neuroprotective and neurorestorative therapies for human neurological disease-and is evident even in areas with therapeutic promise such as myelin repair. Despite the identification of promising remyelinating candidates, biologically validated methods to demonstrate therapeutic efficacy or provide robust preclinical evidence of remyelination in the CNS are lacking. Therapies with potential to remyelinate the CNS constitute one of the most promising and highly anticipated therapeutic developments in the pipeline to treat multiple sclerosis and other demyelinating diseases. The optic nerve has been proposed as an informative pathway to monitor remyelination in animals and human subjects. Recent clinical trials using visual evoked potential have had promising results, but without unequivocal evidence about the cellular and molecular basis for signal changes on visual evoked potential, the interpretation of these trials is constrained. The visual evoked potential was originally developed and used in the clinic as a diagnostic tool but its use as a quantitative method for assessing therapeutic response requires certification of its biological specificity. Here, using the tools of experimental pathology we demonstrate that quantitative measurements of myelination using both histopathological measures of nodal structure and ultrastructural assessments correspond to visual evoked potential latency in both inflammatory and chemical models of demyelination. Visual evoked potential latency improves after treatment with a tool remyelinating compound (clemastine), mirroring both quantitative and qualitative myelin assessment. Furthermore, clemastine does not improve visual evoked potential latency following demyelinating injury when administered to a transgenic animal incapable of forming new myelin. Therefore, using the capacity for therapeutic enhancement and biological loss of function we demonstrate conclusively that visual evoked potential measures myelin status and is thereby a validated tool for preclinical verification of remyelination

A Selective Novel Peroxisome Proliferator-Activated Receptor ( PPAR)-alpha Antagonist Induces Apoptosis and Inhibits Proliferation of CLL Cells In Vitro and In Vivo

Tumor-specific metabolic changes can reveal new therapeutic targets. Our findings implicate a supporting role for fatty acid metabolism in chronic lymphocytic leukemia (CLL) cell survival. Peroxisome proliferator-activated receptor (PPAR)-alpha, a major transcriptional regulator of fatty acid oxidation, was recently shown to be upregulated in CLL. To evaluate PPAR alpha as a potential therapeutic target, we developed a highly selective, potent small molecule antagonist of PPAR alpha, NXT629. NXT629 inhibited agonist-induced transcription of PPAR alpha-regulated genes, demonstrating target engagement in CLL cells. Furthermore, NXT629 induced apoptosis of CLL cells even in the presence of a protective microenvironment. To mimic the proliferative lymphoid compartment of CLL, we examined the activity of NXT629 on CLL cells that were stimulated to proliferate in vitro. NXT629 reduced the number of leukemia cells undergoing cell division. In addition, in two xenograft mouse models of CLL (one a model for nondividing and one for dividing CLL), NXT629 reduced the number of viable CLL cells in vivo. Overall, these results suggest that fatty acid metabolism promotes survival and proliferation of primary CLL cells and that inhibiting PPAR alpha gene regulation could be a new therapeutic approach to treating CLL