Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

A Molecular Signature of Proteinuria in Glomerulonephritis

Proteinuria is the most important predictor of outcome in glomerulonephritis and experimental data suggest that the tubular cell response to proteinuria is an important determinant of progressive fibrosis in the kidney. However, it is unclear whether proteinuria is a marker of disease severity or has a direct effect on tubular cells in the kidneys of patients with glomerulonephritis. Accordingly we studied an in vitro model of proteinuria, and identified 231 “albumin-regulated genes” differentially expressed by primary human kidney tubular epithelial cells exposed to albumin. We translated these findings to human disease by studying mRNA levels of these genes in the tubulo-interstitial compartment of kidney biopsies from patients with IgA nephropathy using microarrays. Biopsies from patients with IgAN (n = 25) could be distinguished from those of control subjects (n = 6) based solely upon the expression of these 231 “albumin-regulated genes.” The expression of an 11-transcript subset related to the degree of proteinuria, and this 11-mRNA subset was also sufficient to distinguish biopsies of subjects with IgAN from control biopsies. We tested if these findings could be extrapolated to other proteinuric diseases beyond IgAN and found that all forms of primary glomerulonephritis (n = 33) can be distinguished from controls (n = 21) based solely on the expression levels of these 11 genes derived from our in vitro proteinuria model. Pathway analysis suggests common regulatory elements shared by these 11 transcripts. In conclusion, we have identified an albumin-regulated 11-gene signature shared between all forms of primary glomerulonephritis. Our findings support the hypothesis that albuminuria may directly promote injury in the tubulo-interstitial compartment of the kidney in patients with glomerulonephritis

Dissecting the Shared Genetic Architecture of Suicide Attempt, Psychiatric Disorders, and Known Risk Factors

Background Suicide is a leading cause of death worldwide, and nonfatal suicide attempts, which occur far more frequently, are a major source of disability and social and economic burden. Both have substantial genetic etiology, which is partially shared and partially distinct from that of related psychiatric disorders. Methods We conducted a genome-wide association study (GWAS) of 29,782 suicide attempt (SA) cases and 519,961 controls in the International Suicide Genetics Consortium (ISGC). The GWAS of SA was conditioned on psychiatric disorders using GWAS summary statistics via multitrait-based conditional and joint analysis, to remove genetic effects on SA mediated by psychiatric disorders. We investigated the shared and divergent genetic architectures of SA, psychiatric disorders, and other known risk factors. Results Two loci reached genome-wide significance for SA: the major histocompatibility complex and an intergenic locus on chromosome 7, the latter of which remained associated with SA after conditioning on psychiatric disorders and replicated in an independent cohort from the Million Veteran Program. This locus has been implicated in risk-taking behavior, smoking, and insomnia. SA showed strong genetic correlation with psychiatric disorders, particularly major depression, and also with smoking, pain, risk-taking behavior, sleep disturbances, lower educational attainment, reproductive traits, lower socioeconomic status, and poorer general health. After conditioning on psychiatric disorders, the genetic correlations between SA and psychiatric disorders decreased, whereas those with nonpsychiatric traits remained largely unchanged. Conclusions Our results identify a risk locus that contributes more strongly to SA than other phenotypes and suggest a shared underlying biology between SA and known risk factors that is not mediated by psychiatric disorders.Peer reviewe

Interaction between Poly(9,9-bis(6′-N,N,N-trimethylammonium)hexyl)fluorene phenylene) Bromide and DNA as Seen by Spectroscopy, Viscosity, and Conductivity: Effect of Molecular Weights and DNA Secondary Structure

The interaction between three poly(9,9-bis(6-N,N,N-trimethylammonium)hexyl)fluorene phenylene) bromide (HTMA-PFP) samples of different molecular weights (Mn = 14.5, 30.1 and 61.3 kg/mol) and both dsDNA and ssDNA secondary structures has been studied using UV−visible absorption and fluorescence spectroscopies (including steady-state, time-resolved, and anisotropy measurements for the latter), viscosity, and electrical conductivity in 4% (v/v) DMSO−water mixtures. At low nucleic acid concentrations, formation of a 1:1 complex in terms of HTMA-PFP repeat units and DNA bases occurs. This interaction results in quenching of polymer emission. For higher molar ratios of DNA to HTMA-PFP, corresponding to charge neutralization, a second process is observed that is attributed to aggregate formation. From the changes in the absorption spectra, the polymer aggregation constant and the aggregate absorption spectra were calculated by applying an iterative method. Polymer aggregation dramatically quenches HTMA-PFP fluorescence in the region of the electroneutrality point. Under these conditions, the ratio of the emission intensity at 412 nm (maximum) to that at 434 nm (I412/I434) reaches a minimum, the electrical conductivity decreases, and the viscosity of the solution remains constant, showing that the DNA concentration can be determined through various HTMA-PFP physicochemical properties. With respect to the photophysical parameters (emission quantum yield, shape and shift of emission spectra), no significant differences were observed between dsDNA and ssDNA or with conjugated polymer or DNA molecular weight. The two short-lived components in the fluorescence decays are attributed to the presence of aggregates. Aggregates are also suggested to be responsible for the decrease in the fluorescence anisotropy through interchain exciton migration

Alternating Binaphthyl−Thiophene Copolymers: Synthesis, Spectroscopy, and Photophysics and Their Relevance to the Question of Energy Migration versus Conformational Relaxation

The synthesis and a comprehensive spectroscopic and photophysical study are presented of four alternating binaphthyl−oligothiophene copolymers (DP: 10−15 repeat units) in solution at room and low temperature and in the solid state (thin films). Detailed results are presented on absorption, emission, and triplet−triplet absorption spectra together with all relevant quantum yields (fluorescence, intersystem crossing, internal conversion, and singlet oxygen formation), excited-state lifetimes, and singlet and triplet energies. From these, several conclusions can be drawn. First, the main deactivation channels for the molecules in solution are the radiationless processes (S1 → S0 internal conversion and S1 → T1 intersystem crossing). Second, in the solid state the fluorescence quantum yields are smaller than those in solution. From time-resolved fluorescence decays in the picosecond time domain, three decay components are seen: a fast decay (40−60 ps) at short wavelengths, which becomes a rising component at longer wavelengths, an intermediate decay component (330−477 ps) associated with an ensemble of isolated segment-like units, which is dominant at the initial part of the emissive spectra and progressively decreases for longer emissions, and a third exponential related to the emission of the fully relaxed polymer. Together with steady-state anisotropy studies, this is discussed in terms of the possibilities of energy migration/transfer along the polymer chain and of the conformational (torsional) relaxation of the systems studied