ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics

PLoS Comput Biol. 2014 Jul 3;10(7):e1003686. doi: 10.1371/journal.pcbi.1003686. eCollection 2014 Jul.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Extracellular Signal-Regulated MAP Kinases / metabolism
  • MAP Kinase Signaling System / physiology*
  • Male
  • Models, Neurological*
  • Nerve Growth Factor / metabolism
  • Rats
  • Rats, Sprague-Dawley
  • Sensory Receptor Cells / physiology*

Substances

  • Nerve Growth Factor
  • Extracellular Signal-Regulated MAP Kinases

Grants and funding

The authors would like to acknowledge financial support from the German Federal Ministry of Education and Research (BMBF) within the Virtual Liver project (Grant No. 0315766), LungSys II (Grant No. 0316042G), MoPS (Grant No. 0315449D) and NoPain (Grant No. 0316177A), and the European Union within the ERC grant “LatentCauses.” The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.