Modelling in vitro lung branching morphogenesis during development.
It has been shown experimentally that lung epithelial explants have an ability to undergo branching morphogenesis without mesenchyme. However, the mechanisms of this phenomenon remain to be elucidated. In the present study, we construct a mathematical model that can reproduce the dynamics of in vitro branching morphogenesis. We show that the system is essentially governed by three variables--c(0) which is the initial fibroblast growth factor (FGF) concentration, D which is the diffusion coefficient of FGF, and beta which describes the mechanical strength of the cytoskeleton. It is confirmed by numerical simulations that this model can reproduce the experimentally obtained patterns qualitatively. Finally, we experimentally verify two predictions from the model: effects of very high FGF concentration and effects of small mechanical contributions of the cytoskeleton. The theoretical predictions match well with the experimental results.
Hartmann
Dirk
D
Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany. Dirk.Hartmann@iwr.uni-heidelberg.de <Dirk.Hartmann@iwr.uni-heidelberg.de>
Miura
Takashi
T
D000818:Animals; D019521:Body Patterning; D003094:Collagen; D003470:Culture Media; D004058:Diffusion; D004305:Dose-Response Relationship, Drug; D004338:Drug Combinations; D005346:Fibroblast Growth Factors / Q000494:pharmacology; D007797:Laminin; D008168:Lung / Q000187:drug effects / Q000196:embryology*; D051379:Mice; D008954:Models, Biological; D009024:Morphogenesis / Q000187:drug effects; D011509:Proteoglycans; D020545:Respiratory Mucosa / Q000196:embryology; D046509:Tissue Culture Techniques
D003470:Culture Media; D004338:Drug Combinations; D007797:Laminin; D011509:Proteoglycans; C059485:matrigel; D005346:Fibroblast Growth Factors; D003094:Collagen