Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

Identification of a novel biomarker candidate, a 4.8-kDa peptide fragment from a neurosecretory protein VGF precursor, by proteomic analysis of cerebrospinal fluid from children with acute encephalopathy using SELDI-TOF-MS

<p>Abstract</p> <p>Background</p> <p>Acute encephalopathy includes rapid deterioration and has a poor prognosis. Early intervention is essential to prevent progression of the disease and subsequent neurologic complications. However, in the acute period, true encephalopathy cannot easily be differentiated from febrile seizures, especially febrile seizures of the complex type. Thus, an early diagnostic marker has been sought in order to enable early intervention. The purpose of this study was to identify a novel marker candidate protein differentially expressed in the cerebrospinal fluid (CSF) of children with encephalopathy using proteomic analysis.</p> <p>Methods</p> <p>For detection of biomarkers, CSF samples were obtained from 13 children with acute encephalopathy and 42 children with febrile seizure. Mass spectral data were generated by surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) technology, which is currently applied in many fields of biological and medical sciences. Diagnosis was made by at least two pediatric neurologists based on the clinical findings and routine examinations. All specimens were collected for diagnostic tests and the remaining portion of the specimens were used for the SELDI-TOF MS investigations.</p> <p>Results</p> <p>In experiment 1, CSF from patients with febrile seizures (n = 28), patients with encephalopathy (n = 8) (including influenza encephalopathy (n = 3), encephalopathy due to rotavirus (n = 1), human herpes virus 6 (n = 1)) were used for the SELDI analysis. In experiment 2, SELDI analysis was performed on CSF from a second set of febrile seizure patients (n = 14) and encephalopathy patients (n = 5). We found that the peak with an m/z of 4810 contributed the most to the separation of the two groups. After purification and identification of the 4.8-kDa protein, a 4.8-kDa proteolytic peptide fragment from the neurosecretory protein VGF precursor (VGF4.8) was identified as a novel biomarker for encephalopathy.</p> <p>Conclusions</p> <p>Expression of VGF4.8 has been reported to be decreased in pathologically degenerative changes such as Alzheimer's disease, amyotrophic lateral sclerosis (ALS), frontotemporal dementia, and encephalopathy. Thus, the VGF4.8 peptide might be a novel marker for degenerative brain conditions.</p

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

Functional Genomics Complements Quantitative Genetics in Identifying Disease-Gene Associations

An ultimate goal of genetic research is to understand the connection between genotype and phenotype in order to improve the diagnosis and treatment of diseases. The quantitative genetics field has developed a suite of statistical methods to associate genetic loci with diseases and phenotypes, including quantitative trait loci (QTL) linkage mapping and genome-wide association studies (GWAS). However, each of these approaches have technical and biological shortcomings. For example, the amount of heritable variation explained by GWAS is often surprisingly small and the resolution of many QTL linkage mapping studies is poor. The predictive power and interpretation of QTL and GWAS results are consequently limited. In this study, we propose a complementary approach to quantitative genetics by interrogating the vast amount of high-throughput genomic data in model organisms to functionally associate genes with phenotypes and diseases. Our algorithm combines the genome-wide functional relationship network for the laboratory mouse and a state-of-the-art machine learning method. We demonstrate the superior accuracy of this algorithm through predicting genes associated with each of 1157 diverse phenotype ontology terms. Comparison between our prediction results and a meta-analysis of quantitative genetic studies reveals both overlapping candidates and distinct, accurate predictions uniquely identified by our approach. Focusing on bone mineral density (BMD), a phenotype related to osteoporotic fracture, we experimentally validated two of our novel predictions (not observed in any previous GWAS/QTL studies) and found significant bone density defects for both Timp2 and Abcg8 deficient mice. Our results suggest that the integration of functional genomics data into networks, which itself is informative of protein function and interactions, can successfully be utilized as a complementary approach to quantitative genetics to predict disease risks. All supplementary material is available at http://cbfg.jax.org/phenotype

Calcium and copper transport ATPases: analogies and diversities in transduction and signaling mechanisms

The calcium transport ATPase and the copper transport ATPase are members of the P-ATPase family and retain an analogous catalytic mechanism for ATP utilization, including intermediate phosphoryl transfer to a conserved aspartyl residue, vectorial displacement of bound cation, and final hydrolytic cleavage of Pi. Both ATPases undergo protein conformational changes concomitant with catalytic events. Yet, the two ATPases are prototypes of different features with regard to transduction and signaling mechanisms. The calcium ATPase resides stably on membranes delimiting cellular compartments, acquires free Ca2+ with high affinity on one side of the membrane, and releases the bound Ca2+ on the other side of the membrane to yield a high free Ca2+ gradient. These features are a basic requirement for cellular Ca2+ signaling mechanisms. On the other hand, the copper ATPase acquires copper through exchange with donor proteins, and undergoes intracellular trafficking to deliver copper to acceptor proteins. In addition to the cation transport site and the conserved aspartate undergoing catalytic phosphorylation, the copper ATPase has copper binding regulatory sites on a unique N-terminal protein extension, and has also serine residues undergoing kinase assisted phosphorylation. These additional features are involved in the mechanism of copper ATPase intracellular trafficking which is required to deliver copper to plasma membranes for extrusion, and to the trans-Golgi network for incorporation into metalloproteins. Isoform specific glyocosylation contributes to stabilization of ATP7A copper ATPase in plasma membranes

Beyond R0 : demographic models for variability of lifetime reproductive output

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS One 6 (2011): e20809, doi:10.1371/journal.pone.0020809.The net reproductive rate measures the expected lifetime reproductive output of an individual, and plays an important role in demography, ecology, evolution, and epidemiology. Well-established methods exist to calculate it from age- or stage-classified demographic data. As an expectation, provides no information on variability; empirical measurements of lifetime reproduction universally show high levels of variability, and often positive skewness among individuals. This is often interpreted as evidence of heterogeneity, and thus of an opportunity for natural selection. However, variability provides evidence of heterogeneity only if it exceeds the level of variability to be expected in a cohort of identical individuals all experiencing the same vital rates. Such comparisons require a way to calculate the statistics of lifetime reproduction from demographic data. Here, a new approach is presented, using the theory of Markov chains with rewards, obtaining all the moments of the distribution of lifetime reproduction. The approach applies to age- or stage-classified models, to constant, periodic, or stochastic environments, and to any kind of reproductive schedule. As examples, I analyze data from six empirical studies, of a variety of animal and plant taxa (nematodes, polychaetes, humans, and several species of perennial plants).Supported by National Science Foundation Grant DEB-0816514 and by a Research Award from the Alexander von Humboldt Foundation