mRNA diffusion explains protein gradients in Drosophila early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of _Drosophila_. In this model, we consider that _bicoid_ mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments.We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11 to 14 of the developing embryo of _Drosophila_. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of _bicoid_ mRNA is in the range 4.6 x 10^-12^ - 1.5 x10^-11^ m^2^s^-1^, in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of _bicoid_ mRNA in _Drosophila_ [Spirov _et al._ (2009) _Development_ 136:605-614]

The Dynamics of Knotted Strings Attached to D-Branes

We extend the general solution to the Cauchy problem for the relativistic closed string (Phys. Lett. B404 (1997) 57-65, hep-th/9704084) to the case of open strings attached to Dp-branes, including the cases where the initial data has a knotlike topology. We use this extended solution to derive intrinsic dynamical properties of open and closed relativistic strings attached to Dp-branes. We also study the singularity structure and the oscillating periods of this extended solution.Comment: 9 pages, 4 figures, Plain Te