Computational Modeling of FGF10 Mediated Buckling Morphogenesis Within the Embryonic Airway Epithelium

Abstract

The embryonic lung is an excellent model system to study mechanisms of branching morphogenesis, since the embryonic airways undergo a series of recursive branching events to build the bronchial tree. This process involves reciprocal signaling interactions between the branching airway epithelium and a surrounding layer of pulmonary mesenchyme. Focal regions of fibroblast growth factor (FGF10) expression within the pulmonary mesenchyme are thought to provide a biochemical template for the overall airway branching pattern. Recent work, however, has shown that mechanical forces can also impact this process, and it remains unclear how patterns of FGF10 expression interact with biophysical cues in the developing lung to sculpt incipient branches. This is, in part, owing a lack of computational models that incorporate both growth-factor diffusion and the mechanics of growth and remodeling. Several previous studies have used computational modeling to suggest how specific spatial patterns of FGF10 expression might arise spontaneously within the pulmonary mesenchyme, while others have used continuum mechanics to identify the forces involved in bud initiation, but no computational framework has been developed which unite these different approaches. Here, we developed a finite-element model in COMSOL Multiphysics, which couples growth-factor diffusion to the mechanics of epithelial morphogenesis. We first consider the axial growth of a constrained bar, in which the components of the growth tensor depend on the local concentration of a diffusible molecule. This framework is then extended to determine how growth factor diffusion from a focal source within the pulmonary mesenchyme elicits patterns of epithelial growth and budding morphogenesis along the embryonic airway epithelium. This work highlights the importance of both mechanical forces and growth factor diffusion during airway branching morphogenesis.