Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper bound is found by minimising the quadratic form for the operator over a test space consisting of separable functions. These bounds can be used to show that the negative part of the groundstate is small.Comment: 27 pages, 4 diagrams, 2 table

The Hardy-Rellich Inequality for Polyharmonic Operators

The Hardy-Rellich inequality given here generalizes a Hardy inequality of Davies (1984), from the case of the Dirichlet Laplacian of a region $\Omega\subseteq\real^N$ to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.Comment: 19 pages, 2 diagram

A Riemannian Off-Diagonal Heat Kernel Bound for Uniformly Elliptic Operators

We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions $\Omega\subseteq\real^N$, where the order $2m$ of the operator satisfies $N<2m$. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on $\Omega$. Work of Barbatis is applied to find the best constant in this expression.Comment: 29 pages, 6 diagram

Urine metabolomic analysis to detect metabolites associated with the development of contrast induced nephropathy.

ObjectiveContrast induced nephropathy (CIN) is a result of injury to the proximal tubules. The incidence of CIN is around 11% for imaging done in the acute care setting. We aim to analyze the metabolic patterns in the urine, before and after dosing with intravenous contrast for computed tomography (CT) imaging of the chest, to determine if metabolomic changes exist in patients who develop CIN.MethodsA convenience sample of high risk patients undergoing a chest CT with intravenous contrast were eligible for enrollment. Urine samples were collected prior to imaging and 4 to 6 hours post imaging. Samples underwent gas chromatography/mass spectrometry profiling. Peak metabolite values were measured and data was log transformed. Significance analysis of microarrays and partial least squares was used to determine the most significant metabolites prior to CT imaging and within subject. Analysis of variance was used to rank metabolites associated with temporal change and CIN. CIN was defined as an increase in serum creatinine level of ≥ 0.5 mg/dL or ≥ 25% above baseline within 48 hours after contrast administration.ResultsWe sampled paired urine samples from 63 subjects. The incidence of CIN was 6/63 (9.5%). Patients without CIN had elevated urinary citric acid and taurine concentrations in the pre-CT urine. Xylulose increased in the post CT sample in patients who developed CIN.ConclusionDifferences in metabolomics patterns in patients who do and do not develop CIN exist. Metabolites may be potential early identifiers of CIN and identify patients at high-risk for developing this condition prior to imaging

Insights into membrane protein–lipid interactions from free energy calculations

Integral membrane proteins are regulated by specific interactions with lipids from the surrounding bilayer. The structures of protein–lipid complexes can be determined through a combination of experimental and computational approaches, but the energetic basis of these interactions is difficult to resolve. Molecular dynamics simulations provide the primary computational technique to estimate the free energies of these interactions. We demonstrate that the energetics of protein–lipid interactions may be reliably and reproducibly calculated using three simulation-based approaches: potential of mean force calculations, alchemical free energy perturbation, and well-tempered metadynamics. We employ these techniques within the framework of a coarse-grained force field and apply them to both bacterial and mammalian membrane protein–lipid systems. We demonstrate good agreement between the different techniques, providing a robust framework for their automated implementation within a pipeline for annotation of newly determined membrane protein structures

Human prostate sphere-forming cells represent a subset of basal epithelial cells capable of glandular regeneration in vivo.

BackgroundProstate stem/progenitor cells function in glandular development and maintenance. They may be targets for tumor initiation, so characterization of these cells may have therapeutic implications. Cells from dissociated tissues that form spheres in vitro often represent stem/progenitor cells. A subset of human prostate cells that form prostaspheres were evaluated for self-renewal and tissue regeneration capability in the present study.MethodsProstaspheres were generated from 59 prostatectomy specimens. Lineage marker expression and TMPRSS-ERG status was determined via immunohistochemistry and fluorescence in situ hybridization (FISH). Subpopulations of prostate epithelial cells were isolated by cell sorting and interrogated for sphere-forming activity. Tissue regeneration potential was assessed by combining sphere-forming cells with rat urogenital sinus mesenchyme (rUGSM) subcutaneously in immunocompromised mice.ResultsProstate tissue specimens were heterogeneous, containing both benign and malignant (Gleason 3-5) glands. TMPRSS-ERG fusion was found in approximately 70% of cancers examined. Prostaspheres developed from single cells at a variable rate (0.5-4%) and could be serially passaged. A basal phenotype (CD44+CD49f+CK5+p63+CK8-AR-PSA-) was observed among sphere-forming cells. Subpopulations of prostate cells expressing tumor-associated calcium signal transducer 2 (Trop2), CD44, and CD49f preferentially formed spheres. In vivo implantation of sphere-forming cells and rUGSM regenerated tubular structures containing discreet basal and luminal layers. The TMPRSS-ERG fusion was absent in prostaspheres derived from fusion-positive tumor tissue, suggesting a survival/growth advantage of benign prostate epithelial cells.ConclusionHuman prostate sphere-forming cells self-renew, have tissue regeneration capability, and represent a subpopulation of basal cells

Establishment of a positive-readout reporter system for siRNAs

The use of small interfering RNA molecules for therapeutic applications requires development of improved delivery systems, a process that would be facilitated by a non-invasive positive-readout mouse model for studying siRNA pharmacodynamics. Positive readout would yield better signal/noise ratios than existing negative-readout systems. We have engineered a positive-readout luciferase reporter system, activated by successful delivery of siRNA targeting the lac repressor. Co-transfection of a plasmid expressing lac repressor and a plasmid expressing firefly luciferase under the control of an RSV promoter, containing two lac operator sites, resulted in 5.7-fold lower luciferase activity than luciferase-encoding plasmid alone. Inhibition was reversed following addition of synthetic inducer, IPTG, which elevated luciferase expression to normal levels and confirmed functionality of the lac operon. Delivery of 1nM siRNA targeting lac repressor to repressor/reporter co-transfected cells was sufficient to fully restore luciferase expression to levels observed in the absence of repressor. Maximum expression was observed after 48hr, with a rapid decrease thereafter due to the short half life of luciferase. The luciferase positive-readout reporter system is therefore a dynamic indicator of successful RNAi delivery in vitro and could be adapted to generate a transgenic mouse capable of reporting RNAi activity non-invasively in vivo

A Kidney Biopsy Simulation Training Program for Renal Fellows: Two Years of Results

Renal interventions could re-foster interest in Nephrology and attract more medical graduates. Percutaneous kidney biopsy (PKB) is an important diagnostic tool and should be taught through simulation. We initiated a PKB simulation training program and designed a 2-year study to examine its effect on the confidence level, the procedural competence and the satisfaction with this training of Nephrology fellows compared to historical controls. All fellows were consented and trained at UNM’s simulation center (BATCAVE) with a simulation training model (CAE Healthcare Blue PhantomTM). Trainees’ demographics and previous PKB experience were collected. We utilized pre-assigned readings, online videos and hands-on simulation practice. Performance of each trainee during each session was graded with a procedural competence evaluation form. Drs. JO and MER were present in all sessions and completed these forms. Each session lasted 1 to 1-1 1/2 h. Pre-and post-simulation surveys evaluated the participants’ confidence level quantitatively on a 5-point Likert scale. All participants completed the satisfaction with PKB simulation experience scale (PKB-SSE). All three 1st and 2nd year renal fellows completed the simulation training in 2018 and two first year fellows completed the training in 2019. Independent of their previous experience on PKBs all renal fellows expressed a high level of satisfaction from their participation (4 to 5) and increased their confidence level. This year’s trainees increased their performance level from 2 to 5 and from 1 to 5, respectively. PKB simulation may improve trainees’ confidence level and their satisfaction with the training. The procedural competence of the trainees on PKBs will be evaluated during the 2nd year of their fellowship and will be compared to the procedural competence of historical controls. We expect that the simulation training will reduce the discomfort and minimize the adverse PKB outcomes in patients undergoing PKB in UNMH