Cellular Automaton for Kidney Branching Morphogenesis

Abstract

Epithelium is a complex component in the mammalian kidney that has a highly branched duct system. Branching morphogenesis has a hierarchy structure in the ureteric bud and produces the collecting duct tree through repetitive processes. Epithelial and mesenchymal cells surround the tips of growing branches, and their cellular reactions adjust the ureteric bud branching. Mesenchymal cells produce a small protein called glial cellline derived neurotrophic factor (GDNF) that connects to te Rearranged in Transfection (RET) receptors on the surface of epithelial cells. The identified reactions are a necessity for the normal branching growth and their roles exist for using biological features in the proposed model. This paper presents an agent-based model based on cellular automaton for kidney branching in ex-vivo using the features that are expressed as artificial patterns in algorithms. This model extending the groundbreaking approach of Lambert et al. is flexible in features and high compatibility with experimental data. Mesenchymal cells and RET receptors are also expressed as mathematical patterns in the algorithms. The growth mechanism is determined by the growth factor, which indicates the epithelial cell branch when its cell division depends on the local concentration growth factor. Cell division occurs when the level of stimulus growth factor exceeds the threshold. Comparison shows that the model mimics experimental data with high consistency and reveals the dependence between growth factor parameters and features. Results indicate the superiority of compatibility with nature when compared with the model mentioned above.