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

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  • Jan Hasenauer
  • Christine Hasenauer
  • Tim Hucho
  • Fabian J Theis

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.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.

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  • Jan Hasenauer & Christine Hasenauer & Tim Hucho & Fabian J Theis, 2014. "ODE Constrained Mixture Modelling: A Method for Unraveling Subpopulation Structures and Dynamics," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-17, July.
  • Handle: RePEc:plo:pcbi00:1003686
    DOI: 10.1371/journal.pcbi.1003686
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    References listed on IDEAS

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    1. Fabian Fröhlich & Philipp Thomas & Atefeh Kazeroonian & Fabian J Theis & Ramon Grima & Jan Hasenauer, 2016. "Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion," PLOS Computational Biology, Public Library of Science, vol. 12(7), pages 1-28, July.
    2. Artémis Llamosi & Andres M Gonzalez-Vargas & Cristian Versari & Eugenio Cinquemani & Giancarlo Ferrari-Trecate & Pascal Hersen & Gregory Batt, 2016. "What Population Reveals about Individual Cell Identity: Single-Cell Parameter Estimation of Models of Gene Expression in Yeast," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-18, February.
    3. Wenlong He & Peng Xia & Xinan Zhang & Tianhai Tian, 2022. "Bayesian Inference Algorithm for Estimating Heterogeneity of Regulatory Mechanisms Based on Single-Cell Data," Mathematics, MDPI, vol. 10(24), pages 1-15, December.

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