On the theory of drainage area for regular and non-regular points.

The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res.47, W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology219, 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

Is the kinetic equation for turbulent gas-particle flows ill posed?

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Differential effect of alpha-syntrophin knockout on aquaporin-4 and Kir4.1 expression in retinal macroglial cells in mice.

Aquaporin-4 water channels and the inwardly rectifying potassium channels Kir4.1 are coexpressed in a highly polarized manner at the perivascular and subvitreal endfeet of retinal Müller cells and astrocytes. The present study was aimed at resolving the anchoring mechanisms responsible for the coexpression of these molecules. Both aquaporin-4 and Kir4.1 contain PDZ-domain binding motifs at their C-termini and it was recently shown that mice with targeted disruption of the dystrophin gene display altered distribution of aquaporin-4 and Kir4.1 in the retina. To test our hypothesis that alpha-syntrophin (a PDZ-domain containing protein of the dystrophin associated protein complex) is involved in aquaporin-4 and Kir4.1 anchoring in retinal cells, we studied the expression pattern of these molecules in alpha-syntrophin null mice. Judged by quantitative immunogold cytochemistry, deletion of the alpha-syntrophin gene causes a partial loss (by 70%) of aquaporin-4 labeling at astrocyte and Müller cell endfeet but no decrease in Kir4.1 labeling at these sites. These findings suggest that alpha-syntrophin is not involved in the anchoring of Kir4.1 and only partly responsible for the anchoring of aquaporin-4 in retinal endfeet membranes. Furthermore we show that wild type and alpha-syntrophin null mice exhibit strong beta1 syntrophin labeling at perivascular and subvitreal Müller cell endfeet, raising the possibility that beta1 syntrophin might be involved in the anchoring of Kir4.1 and the alpha-syntrophin independent pool of aquaporin-4.

Signaling to the epithelium is not sufficient to mediate all of the effects of transforming growth factor beta and bone morphogenetic protein 4 on murine embryonic lung development.

Many studies have suggested that transforming growth factor beta (TGF-beta) and bone morphogenetic protein 4 (Bmp4) regulate early development of the lung. In this study, administration of growth factors directly into the lumen of lungs grown in organ culture was used to limit their activity to the epithelium and test the hypothesis that signaling to the epithelium is sufficient to mediate the known effects of TGF-beta and BMP-4 on early lung development. Addition of TGF-beta1, beta2, or beta3 to the medium surrounding lungs grown in organ culture resulted in decreased branching, reduced cell proliferation, accumulation of alpha-smooth muscle actin protein (alpha-SMA) in the mesenchyme, and decreased expression of a marker for respiratory epithelium, surfactant protein-C (Sp-C). When TGF-beta1 was restricted to the epithelium, accumulation of alpha-SMA and inhibition of Sp-C expression were not observed but branching and proliferation were inhibited. In contrast, branching was not inhibited in lungs where TGF-beta2 or TGF-beta3 were restricted to the epithelium suggesting differences in the mechanism of signaling by TGF-beta1, TGF-beta2 or TGF -beta3 in lung. Addition of Bmp4 to the medium surrounding lungs grown in organ culture stimulated cell proliferation and branching morphogenesis; however, direct injection of Bmp4 into the lung lumen had no effect on proliferation or branching. Based on these data and data from mesenchyme-free cultures, we propose that the mesenchyme influences growth factor signaling in the lung.