A chemo-mechanical model of endoderm movements driving elongation of the amniote hindgut.

While mechanical and biochemical descriptions of development are each essential, integration of upstream morphogenic cues with downstream tissue mechanics remains understudied during vertebrate morphogenesis. Here, we developed a two-dimensional chemo-mechanical model to investigate how mechanical properties of the endoderm and transport properties of FGF coordinately regulate avian hindgut morphogenesis. Posterior endoderm cells convert a gradient of FGF ligands into a contractile force gradient, leadingto a force imbalance that drives collective cell movements that elongate the forming hindgut tube. We formulated a 2-D reaction-diffusion-advection model describing the formation of an FGF protein gradient due to posterior displacement of cells transcribing unstable Fgf8 mRNA during axis elongation, coupled with translation, diffusion, and degradation of FGF protein. The endoderm was modeled as an active viscous fluid that generates contractile stresses in proportion to FGF concentration. With parameter values constrained by experimental data, the model replicates key aspects of hindgut morphogenesis, suggests that graded isotropic contraction is sufficient to generate large anisotropic cell movements, and provides new insight into how chemo-mechanical coupling across the mesoderm and endoderm coordinates hindgut elongation with axis elongation.