title: ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.
abstract: Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.
authors.affiliation: Institute of Computational Biology, Helmholtz Center Munich, Munich, Germany; Division of Mathematical Modeling of Biological Systems, Department of Mathematics, University of Technology Munich, Munich, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Hasenauer
authors.affiliation: Max Planck Institute for Molecular Genetics, Berlin, Germany.
authors.forename: Christine
authors.initials: C
authors.lastname: Hasenauer
authors.affiliation: Max Planck Institute for Molecular Genetics, Berlin, Germany; Division of Experimental Anesthesiology and Pain Research, Department of Anesthesiology and Intensive Care Medicine, University Hospital Cologne, Cologne, Germany.
authors.forename: Tim
authors.initials: T
authors.lastname: Hucho
authors.affiliation: Institute of Computational Biology, Helmholtz Center Munich, Munich, Germany; Division of Mathematical Modeling of Biological Systems, Department of Mathematics, University of Technology Munich, Munich, Germany.
authors.forename: Fabian J
authors.initials: FJ
authors.lastname: Theis
mesh_terms: D000818:Animals; D048049:Extracellular Signal-Regulated MAP Kinases / Q000378:metabolism; D020935:MAP Kinase Signaling System / Q000502:physiology*; D008297:Male; D008959:Models, Neurological; D020932:Nerve Growth Factor / Q000378:metabolism; D051381:Rats; D017207:Rats, Sprague-Dawley; D011984:Sensory Receptor Cells / Q000502:physiology*
chemical_list: D020932:Nerve Growth Factor; D048049:Extracellular Signal-Regulated MAP Kinases