Identifiability of population models via a measure theoretical approach

Heterogeneity in cell populations is a major factor in the dynamics of cellular systems in living tissue or microbial colonies. This heterogeneity needs to be taken into account for the interpretation of experimental observations as well as in the construction of predictive models for cellular systems. A common modelling framework for heterogeneous cell population is by an infinite ensemble of single cell models. The state of a cell population is in this framework modelled by the distribution of the single cell states. In this paper we study under which conditions the population model is identifiable, i.e., we can determine the initial distribution of cell states and parameters from a dynamic output distribution. We derive a necessary condition on the single cell model based on the classical observability results from linear and nonlinear control theory. Our results are illustrated via examples.