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A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast

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  • Joachim Almquist
  • Loubna Bendrioua
  • Caroline Beck Adiels
  • Mattias Goksör
  • Stefan Hohmann
  • Mats Jirstrand

Abstract

The last decade has seen a rapid development of experimental techniques that allow data collection from individual cells. These techniques have enabled the discovery and characterization of variability within a population of genetically identical cells. Nonlinear mixed effects (NLME) modeling is an established framework for studying variability between individuals in a population, frequently used in pharmacokinetics and pharmacodynamics, but its potential for studies of cell-to-cell variability in molecular cell biology is yet to be exploited. Here we take advantage of this novel application of NLME modeling to study cell-to-cell variability in the dynamic behavior of the yeast transcription repressor Mig1. In particular, we investigate a recently discovered phenomenon where Mig1 during a short and transient period exits the nucleus when cells experience a shift from high to intermediate levels of extracellular glucose. A phenomenological model based on ordinary differential equations describing the transient dynamics of nuclear Mig1 is introduced, and according to the NLME methodology the parameters of this model are in turn modeled by a multivariate probability distribution. Using time-lapse microscopy data from nearly 200 cells, we estimate this parameter distribution according to the approach of maximizing the population likelihood. Based on the estimated distribution, parameter values for individual cells are furthermore characterized and the resulting Mig1 dynamics are compared to the single cell times-series data. The proposed NLME framework is also compared to the intuitive but limited standard two-stage (STS) approach. We demonstrate that the latter may overestimate variabilities by up to almost five fold. Finally, Monte Carlo simulations of the inferred population model are used to predict the distribution of key characteristics of the Mig1 transient response. We find that with decreasing levels of post-shift glucose, the transient response of Mig1 tend to be faster, more extended, and displays an increased cell-to-cell variability.

Suggested Citation

  • Joachim Almquist & Loubna Bendrioua & Caroline Beck Adiels & Mattias Goksör & Stefan Hohmann & Mats Jirstrand, 2015. "A Nonlinear Mixed Effects Approach for Modeling the Cell-To-Cell Variability of Mig1 Dynamics in Yeast," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-32, April.
  • Handle: RePEc:plo:pone00:0124050
    DOI: 10.1371/journal.pone.0124050
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    References listed on IDEAS

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    1. Long Cai & Chiraj K. Dalal & Michael B. Elowitz, 2008. "Frequency-modulated nuclear localization bursts coordinate gene regulation," Nature, Nature, vol. 455(7212), pages 485-490, September.
    2. Eugene Losev & Catherine A. Reinke & Jennifer Jellen & Daniel E. Strongin & Brooke J. Bevis & Benjamin S. Glick, 2006. "Golgi maturation visualized in living yeast," Nature, Nature, vol. 441(7096), pages 1002-1006, June.
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    Cited by:

    1. 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.

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