Modeling morphogen gradient formation from arbitrary realistically shaped sources

Much of the analytical modeling of morphogen profiles is based on simplistic scenarios, where the source is abstracted to be point-like and fixed in time, and where only the steady state solution of the morphogen gradient in one dimension is considered. Here we develop a general formalism allowing to model diffusive gradient formation from an arbitrary source. This mathematical framework, based on the Green's function method, applies to various diffusion problems. In this paper, we illustrate our theory with the explicit example of the Bicoid gradient establishment in Drosophila embryos. The gradient formation arises by protein translation from a mRNA distribution followed by morphogen diffusion with linear degradation. We investigate quantitatively the influence of spatial extension and time evolution of the source on the morphogen profile. For different biologically meaningful cases, we obtain explicit analytical expressions for both the steady state and time-dependent 1D problems. We show that extended sources, whether of finite size or normally distributed, give rise to more realistic gradients compared to a single point-source at the origin. Furthermore, the steady state solutions are fully compatible with a decreasing exponential behavior of the profile. We also consider the case of a dynamic source (e.g. bicoid mRNA diffusion) for which a protein profile similar to the ones obtained from static sources can be achieved.

[Avian influenza: wildbird monitoring in Switzerland between 2003-2006]

During various surveillance programs more than 3500 cloacal swabs and organ samples from songbirds, waterbirds and poultry have been tested for avian influenza using real time RT-PCR. Switzerland carried out the first wildbird monitoring between autumn 2003 and spring 2005. 1053 samples, mostly from songbirds, were tested. LPAI-strains were found in two cases. A second intensified surveillance program started in October 2005 along with the first ban on free range poultry farming. Until the end of April 2006 2455 cloacal swabs from dead wildbirds have been analysed. By the end of february H5N1 was for the first time detected in Switzerland and by the end of march 32 waterbirds have been found positive for H5N1. 146 poultry flocks with a special permission for free range management proved to be AI negative.