Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in Sec. 3 are correcte

Choriocapillaris and Choroidal Microvasculature Imaging with Ultrahigh Speed OCT Angiography

We demonstrate in vivo choriocapillaris and choroidal microvasculature imaging in normal human subjects using optical coherence tomography (OCT). An ultrahigh speed swept source OCT prototype at 1060 nm wavelengths with a 400 kHz A-scan rate is developed for three-dimensional ultrahigh speed imaging of the posterior eye. OCT angiography is used to image three-dimensional vascular structure without the need for exogenous fluorophores by detecting erythrocyte motion contrast between OCT intensity cross-sectional images acquired rapidly and repeatedly from the same location on the retina. En face OCT angiograms of the choriocapillaris and choroidal vasculature are visualized by acquiring cross-sectional OCT angiograms volumetrically via raster scanning and segmenting the three-dimensional angiographic data at multiple depths below the retinal pigment epithelium (RPE). Fine microvasculature of the choriocapillaris, as well as tightly packed networks of feeding arterioles and draining venules, can be visualized at different en face depths. Panoramic ultra-wide field stitched OCT angiograms of the choriocapillaris spanning ~32 mm on the retina show distinct vascular structures at different fundus locations. Isolated smaller fields at the central fovea and ~6 mm nasal to the fovea at the depths of the choriocapillaris and Sattler's layer show vasculature structures consistent with established architectural morphology from histological and electron micrograph corrosion casting studies. Choriocapillaris imaging was performed in eight healthy volunteers with OCT angiograms successfully acquired from all subjects. These results demonstrate the feasibility of ultrahigh speed OCT for in vivo dye-free choriocapillaris and choroidal vasculature imaging, in addition to conventional structural imaging.National Institutes of Health (U.S.) (NIH R01-EY011289-27)National Institutes of Health (U.S.) (NIH R01-EY013178-12)National Institutes of Health (U.S.) (NIH R44-EY022864-01)National Institutes of Health (U.S.) (NIH R01-CA075289-16)United States. Air Force Office of Scientific Research (AFOSR FA9550-10-1-0551)United States. Air Force Office of Scientific Research (AFOSR FA9550-12-1-0499

Development of a lung slice preparation for recording ion channel activity in alveolar epithelial type I cells

BACKGROUND: Lung fluid balance in the healthy lung is dependent upon finely regulated vectorial transport of ions across the alveolar epithelium. Classically, the cellular locus of the major ion transport processes has been widely accepted to be the alveolar type II cell. Although evidence is now emerging to suggest that the alveolar type I cell might significantly contribute to the overall ion and fluid homeostasis of the lung, direct assessment of functional ion channels in type I cells has remained elusive. METHODS: Here we describe a development of a lung slice preparation that has allowed positive identification of alveolar type I cells within an intact and viable alveolar epithelium using living cell immunohistochemistry. RESULTS: This technique has allowed, for the first time, single ion channels of identified alveolar type I cells to be recorded using the cell-attached configuration of the patch-clamp technique. CONCLUSION: This exciting new development should facilitate the ascription of function to alveolar type I cells and allow us to integrate this cell type into the general model of alveolar ion and fluid balance in health and disease

Predominant constitutive CFTR conductance in small airways

BACKGROUND: The pathological hallmarks of chronic obstructive pulmonary disease (COPD) are inflammation of the small airways (bronchiolitis) and destruction of lung parenchyma (emphysema). These forms of disease arise from chronic prolonged infections, which are usually never present in the normal lung. Despite the fact that primary hygiene and defense of the airways presumably requires a well controlled fluid environment on the surface of the bronchiolar airway, very little is known of the fluid and electrolyte transport properties of airways of less than a few mm diameter. METHODS: We introduce a novel approach to examine some of these properties in a preparation of minimally traumatized porcine bronchioles of about 1 mm diameter by microperfusing the intact bronchiole. RESULTS: In bilateral isotonic NaCl Ringer solutions, the spontaneous transepithelial potential (TEP; lumen to bath) of the bronchiole was small (mean ± sem: -3 ± 1 mV; n = 25), but when gluconate replaced luminal Cl(-), the bionic Cl(- )diffusion potentials (-58 ± 3 mV; n = 25) were as large as -90 mV. TEP diffusion potentials from 2:1 NaCl dilution showed that epithelial Cl(- )permeability was at least 5 times greater than Na(+ )permeability. The anion selectivity sequence was similar to that of CFTR. The bionic TEP became more electronegative with stimulation by luminal forskolin (5 μM)+IBMX (100 μM), ATP (100 μM), or adenosine (100 μM), but not by ionomycin. The TEP was partially inhibited by NPPB (100 μM), GlyH-101* (5–50 μM), and CFTR(Inh)-172* (5 μM). RT-PCR gave identifying products for CFTR, α-, β-, and γ-ENaC and NKCC1. Antibodies to CFTR localized specifically to the epithelial cells lining the lumen of the small airways. CONCLUSION: These results indicate that the small airway of the pig is characterized by a constitutively active Cl(- )conductance that is most likely due to CFTR

Genome-Wide Analyses of Nkx2-1 Binding to Transcriptional Target Genes Uncover Novel Regulatory Patterns Conserved in Lung Development and Tumors

The homeodomain transcription factor Nkx2-1 is essential for normal lung development and homeostasis. In lung tumors, it is considered a lineage survival oncogene and prognostic factor depending on its expression levels. The target genes directly bound by Nkx2-1, that could be the primary effectors of its functions in the different cellular contexts where it is expressed, are mostly unknown. In embryonic day 11.5 (E11.5) mouse lung, epithelial cells expressing Nkx2-1 are predominantly expanding, and in E19.5 prenatal lungs, Nkx2-1-expressing cells are predominantly differentiating in preparation for birth. To evaluate Nkx2-1 regulated networks in these two cell contexts, we analyzed genome-wide binding of Nkx2-1 to DNA regulatory regions by chromatin immunoprecipitation followed by tiling array analysis, and intersected these data to expression data sets. We further determined expression patterns of Nkx2-1 developmental target genes in human lung tumors and correlated their expression levels to that of endogenous NKX2-1. In these studies we uncovered differential Nkx2-1 regulated networks in early and late lung development, and a direct function of Nkx2-1 in regulation of the cell cycle by controlling the expression of proliferation-related genes. New targets, validated in Nkx2-1 shRNA transduced cell lines, include E2f3, Cyclin B1, Cyclin B2, and c-Met. Expression levels of Nkx2-1 direct target genes identified in mouse development significantly correlate or anti-correlate to the levels of endogenous NKX2-1 in a dosage-dependent manner in multiple human lung tumor expression data sets, supporting alternative roles for Nkx2-1 as a transcriptional activator or repressor, and direct regulator of cell cycle progression in development and tumors

Movement Timing and Invariance Arise from Several Geometries

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations