Mathematical Modeling of Branching Morphogenesis in Organ Development

In the branched organ development, a simple epithelial tube makes well-arranged branching patterns in the mesenchymal tissue through repeated use of elongation and branching. To understand how to make the spatial pattern I focus on some regulation of branching inducers that can trigger cell division and cell migration of epithelia. In the talk I will be presenting three topics that would each correspond to basic step of branching morphogenesis. First, I talk about mechanisms of how to form localized branching inducer's expression as observed in in vivo experiments of early lung development. To explain the spatial pattern of branching inducer's expression, I developed a mathematical model based on its gene interaction with geometrical conditions including shapes of the lung buds and the lung border. I found that different localization patterns of the expression can be explained by the geometrical conditions. The second topic is about a tube growth modeling, illustrating early kidney development. In the study, I examined how the branching morphology depends on different physical or chemical properties affected by branching inducers. I concluded that a proper balance between growth speed of epithelial sheet due to cell division and cell migration due to chemotaxis is necessary to realize the development of normal Y-shaped pattern. Lastly, we go on to see a mathematical modeling for retroactive signal properties, emerged on MAPK pathway located in the downstream of branching inducers. I propose a mass-action kinetic model of MAPK cycle with a substrate, and demonstrate that the substrate can modulate the ERK activity by directly interacting with ERK.