Interrogating Progenitor Fate Processes in the Developing Zebrafish Pronephros Using Mathematical Models

Background: A core component of developmental and regenerative nephrology is aimed at determining critical relationships between renal progenitors, cells with stem-like qualities, and their progeny. Zebrafish, a vertebrate model well suited for studies involving nephrogenesis and neonephrogenesis, presents with a unique progenitor-rich environment that allows us to characterize and hypothesize qualities and relationships that these precursors hold. Previously, much of the work using this model has been aimed at better understanding conserved genetic regulators of renal development. While this work has been foundational to our understanding of pronephros development, there is still much to be uncovered with respect to the cellular relationships present in early nephrogenesis. Using mathematical models, we are able to hypothesize and interrogate these properties and relationships that precursor populations hold during zebrafish pronephros development. Methods: To parameterize our model, we have utilized techniques such as whole-mount and fluorescent in situ hybridization as well as immunohistochemistry. For our mathematical modeling, we have used both ordinary differential equations as well as statistical models to characterize multiple cellular populations present in the zebrafish pronephros. For our algorithmic approaches to model parameterization, we have utilized the Nelder-Mead method. Results: Using the aforementioned methods, we have constructed models that contain different forms of fate processes during nephrogenesis including asymmetric differentiation as well as division independent differentiation. From these models, we can speculate how and when precursors differentiate during pronephros development in the zebrafish model. Using ordinary differential equations that represent multiple cell populations through time and by using multiple goodness of fit indicators to compare model outcomes to biological data, we can arrive at properties of progenitor populations. Conclusion: Using this model for pronephric development, we test hypotheses on the necessity for division dependent/ asymmetric fate processes, characterize progenitor activity in the earliest stages of renal development, and demonstrate the need for independent qualities among progenitor populations that exist in nephrogenesis.