Mathematical modelling of cell fate dynamics in homeostasis

Abstract

Many biological tissues are not static but continuously renewed through cycles of cell production and cell loss which must be perfectly balanced to maintain the tissue’s healthy state, also called homeostasis. The underlying dynamics of cell fate choices in homeostasis are complex and often not well understood. Although an experimental approach is of utmost importance to understand the mechanism regulating cell fate, mathematical modelling of the cell fate dynamics is essential to interpret experimental data. This project develops a framework for studying cell fate dynamics in homeostasis that combines theoretical modelling and numerical simulations given lineage-tracing experimental data. A correct and reliable definition of a cell fate model is a complex task due to the number of unknowns, the scarcity of the data and their uncertainty. Therefore, our approach is to simplify the problem of identifying the lineage hierarchy and the cell proliferation, differentiation and death rates by restricting the search to models compatible with homeostasis and presenting specific tissue-related features. For doing so, we use graph theory, deterministic approximation, stochastic models and Bayesian inference. Based on purely theoretical considerations, this research proves that any homeostatic cell fate model must follow strict rules, requiring self-renewing cells at the apex of the lineage hierarchy and only there. Importantly, self-renewal does not need to be an intrinsic property of a cell type since any cell type located at the apex of a lineage hierarchy may acquire it by interacting with the cell environment. Besides, we showed how stem cells and their self-renewing strategy could be determined based on qualitative features of lineage-tracing experimental data, such as the shape of the clonal size distribution and discrepancies in cell cluster sizes from tissue assays. The developed framework is validated using synthetic data for a study case, the mouse mammary gland, paving the way for future studies where experimental data might be available.

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ORCID for Philip Greulich: orcid.org/0000-0001-5247-6738

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