Mathematical Modeling Reveals Cell Differentiation Processes and Progenitor Kinetics Necessary for Proper Nephrogenesis

Matthew R Hawkins^*Stuart JonesHannah M. WesselmanCecilia CesaJoshua MoellerRebecca Ann Wingert^*

• University of Notre Dame, Notre Dame, United States

The developing zebrafish nephron contains a diverse repertoire of cell populations with intrinsically dynamic roles and interactions. Previous work to characterize these populations has been performed through genetic studies with powerful molecular methods such as in situ hybridization, immunohistochemistry, and both live and fixed imaging. Using these approaches, in conjunction with regression techniques, parameter optimization, and the use of foundational work provided by so many, here we created an ordinary differential equation based model that describes the population and cellular dynamics of tubule, multiciliated, and progenitor populations that are existent in the developing zebrafish pronephros, and how some of these populations interact to form the functional early kidney. In generating this model, and through various sensitivity analyses, model structure experiments utilizing varied forms of fate processes, and interrogating optimized parameter sets, we demonstrate that 1) differentiated cell populations may be responsible for growth in the developing zebrafish nephron and 2) varied form of cell fate processes, including division independent differentiation may be necessary for proper nephrogenesis in the zebrafish model. With these models, we hope to provide a platform to formulate new hypotheses for progenitor kinetics with respect to forms and timing of nephrogenesis fate processes, as well as timing of proliferation across renal progenitors and differentiated cell populations.