Methods of Computational Analysis in Kidney Development.

This chapter reviews some currently available methodologies for constructing mathematical models in kidney development. Mammalian nephrogenesis is a complex biological process, which in its earliest stages involves migration, condensation, proliferation, and differentiation of metanephric mesenchymal (MM) cells interacting with the uroepithelial cells of the ureteric bud (UB). First, the mathematical modelling in biology is generally described. Secondly, some accounts to biological pattern formation in modelling are given in general, including models that transcend the Turing model. This is followed by a short assessment on the main branch of models in the kidney development, the evaluation of the branching morphogenesis of the kidney. Finally, two alternative models in the early kidney development processes are given as an example. They also elucidate the difficulties in the model building process. Firstly, a computational model building with the CompuCell3D program for the early nephron progenitor cell movements with the key extracellular signaling effectors is depicted. This collective migration leads to the first pretubular aggregate (PTA). The simulation parameters of the program imitate the program's cell sorting example with different adhesions and chemoattractants. The program utilizes Cellular Potts Model (CPM) to describe the development. Secondly, an example of PTA to renal vesicle (RV) transition modelling is described. In that case, the model is unique, where the model process is based on the chemoattractants from UB.