Model of branching development requirements in lung airways.
(A) Low cell concentration scenario. The local morphogen concentration is insufficient to promote branching structure development. (B) High cell concentration, but low gradient scenario. Neighboring cells increase localized morphogen production, but long-range inhibitors from other cells prevent branching development. (C) High cell concentration gradient scenario. Cells in neighbors increase morphogen productions and the inhibitors produced by other cells do not interrupt branching morphogenesis. (D) Model and the reaction-diffusion simulation result under conditions in which cell concentration is low and an external factor is applied to stimulate morphogen productions. The initial cell concentration in the simulation was 0.8% over the calculated space and 2000 calculation iterations were performed. The results indicate that the branching structure will be produced even in homogeneously distributed cell cultures when cellular production rate of morphogen is increased by external stimulation such as co-culturing with heterotypic cells. Parameters: c = 0.04 ± 5%, μ = 0.12, ν = 0.04, ρA = 0.03, ρH = 0.0003, c0 = 0.02, γ = 0.02, ε = 0.2, d = 0.0013, e = 0.1, f = 10, DA = 0.015, DH = 0.18, DS = 0.06.