Morphogen gradients are regulated by porous media characteristics of the developing tissue

Long-range morphogen gradients have been proposed to form by morphogen diffusion from a localized source to distributed sinks in the target tissue. The role of complex embryo geometries in this process is less well understood and ignored by most mathematical models. We address this by numerically reconstructing pore-scale 3D geometries of zebrafish embryos during epiboly from light-sheet microscopy images. In these high-resolution 3D geometries, we simulate Fgf8a gradient formation. The simulations show that when realistic embryo geometries are considered, a source-diffusion-degradation mechanism with additional binding to polymers of the extracellular matrix (HSPG) is sufficient to explain self-organized emergence and robust maintenance of Fgf8a gradients. The predicted normalized gradient is robust against changes in source and sink rates but sensitive to changes in the pore connectivity of the extracellular space, demonstrating the importance of considering realistic geometries when studying morphogen gradients.