The Osr1 and Osr2 genes act in the pronephric anlage downstream of retinoic acid signaling and upstream of Wnt2b to maintain pectoral fin development.

Vertebrate odd-skipped related genes (Osr) have an essential function during the formation of the intermediate mesoderm (IM) and the kidney structures derived from it. Here, we show that these genes are also crucial for limb bud formation in the adjacent lateral plate mesoderm (LPM). Reduction of zebrafish Osr function impairs fin development by the failure of tbx5a maintenance in the developing pectoral fin bud. Osr morphant embryos show reduced wnt2b expression, and increasing Wnt signaling in Osr morphant embryos partially rescues tbx5a expression. Thus, Osr genes control limb bud development in a non-cell-autonomous manner, probably through the activation of Wnt2b. Finally, we demonstrate that Osr genes are downstream targets of retinoic acid (RA) signaling. Therefore, Osr genes act as a relay within the genetic cascade of fin bud formation: by controlling the expression of the signaling molecule Wnt2ba in the IM they play an essential function transmitting the RA signaling originated in the somites to the LPM.

Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.

Characterising the three-dimensional ozone distribution of a tidally locked Earth-like planet

We simulate the 3D ozone distribution of a tidally locked Earth-like exoplanet using the high-resolution, 3D chemistry climate model CESM1(WACCM) and study how the ozone layer of a tidally locked Earth (TLE) (ΩTLE = 1/365 days) differs from that of our present-day Earth (PDE) (ΩPDE = 1/1 day). The middle atmosphere reaches a steady state a symptotically within the first 80 days of the simulation. An upwelling, centred on the subsolar point, is present on the day side while a downwelling, centred on the antisolar point, is present on the night side. In the mesosphere, we find similar global ozone distributions for the TLE and the PDE, with decreased ozone on the day side and enhanced ozone on the night side. In the lower mesosphere, a jet stream transitions into a large-scale vortex around a low-pressure system, located at low latitudes of the TLE night side. In the middle stratosphere, the concentration of odd oxygen is approximately equal to that of the ozone [(Ox) ≈ (O3)]. At these altitudes, the lifetime of odd oxygen is ~16 h and the transport processes significantly contribute to the global distribution of stratospheric ozone. Compared to the PDE, where the strong Coriolis force acts as a mixing barrier between low and high latitudes, the transport processes of the TLE are governed by jet streams variable in the zonal and meridional directions. In the middle stratosphere of the TLE, we find high ozone values on the day side, due to the increased production of atomic oxygen on the day side, where it immediately recombines with molecular oxygen to form ozone. In contrast, the ozone is depleted on the night side, due to changes in the solar radiation distribution and the presence of a downwelling. As a result of the reduced Coriolis force, the tropical and extratropical air masses are well mixed and the global temperature distribution of the TLE stratosphere has smaller horizontal gradients than the PDE. Compared to the PDE, the total ozone column global mean is reduced by ~19.3 %. The day side and the night side total ozone column means are reduced by 23.21 and 15.52 %, respectively. Finally, we present the total ozone column (TOC) maps as viewed by a remote observer for four phases of the TLE during its revolution around the star. The mean TOC values of the four phases of the TLE vary by up to 23 %.