A hierarchical Bayesian model for understanding the spatiotemporal dynamics of the intestinal epithelium

Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions—uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales.Author summary: The intestinal epithelium is an important model system for studying the dynamics and regulation of multicellular populations. It is characterised by rapid rates of self-renewal and repair; dysregulation of these processes is thought to explain, in part, why many tumours form in the intestinal and similar epithelial tissues. These features have led to a large amount of work on estimating cell kinetic parameters in the intestine. There remain, however, large gaps between the raw data collected, the interpretation of these experimental data, and mechanistic models that describe the underlying processes. Hierarchical statistical modelling provides a natural method with which to bridge these gaps, but has, to date, been underutilised in the study of intestinal tissue self-renewal. As we illustrate, this approach makes essential use of the distinction between ‘measurement’, ‘process’ and ‘parameter’ models, giving an explicit framework for combining experimental data and mechanistic modelling in the presence of multiple sources of uncertainty. We apply this approach to analyse experiments on healthy, damaged and recovering intestinal tissue, finding that observed data can be explained by a model in which cell movement is driven primarily by proliferation.