ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics

Jan Hasenauer, Christine Hasenauer, Tim Hucho, Fabian J. Theis

Abstract: Author Summary In this manuscript, we introduce ODE constrained mixture models for the analysis of population snapshot data of kinetics and dose responses. Population snapshot data can for instance be derived from flow cytometry or single-cell microscopy and provide information about the population structure and the dynamics of subpopulations. Currently available methods enable, however, only the extraction of this information if the subpopulations are very different. By combining pathway-specific ODE and mixture models, a more sensitive method is obtained, which can simultaneously analyse a variety of experimental conditions. ODE constrained mixture models facilitate the reconstruction of subpopulation sizes and dynamics, even in situations where the subpopulations are hardly distinguishable. This is shown for a simulation example as well as for the process of NGF-induced Erk1/2 phosphorylation in primary sensory neurones. We find that the proposed method allows for a simple but pervasive analysis of heterogeneous cell systems and more profound, mechanistic insights.