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Statistical Applications in Genetics and Molecular Biology

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Volume 13, Issue 3


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Efficient parametric inference for stochastic biological systems with measured variability

Iain G. Johnston
Published Online: 2014-05-10 | DOI: https://doi.org/10.1515/sagmb-2013-0061


Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system’s behavior. It is often desirable to infer properties of the parameters governing such systems given experimental observations of the mean and variance of observed quantities. In some circumstances, analytic forms for the likelihood of these observations allow very efficient inference: we present these forms and demonstrate their usage. When likelihood functions are unavailable or difficult to calculate, we show that an implementation of approximate Bayesian computation (ABC) is a powerful tool for parametric inference in these systems. However, the calculations required to apply ABC to these systems can also be computationally expensive, relying on repeated stochastic simulations. We propose an ABC approach that cheaply eliminates unimportant regions of parameter space, by addressing computationally simple mean behavior before explicitly simulating the more computationally demanding variance behavior. We show that this approach leads to a substantial increase in speed when applied to synthetic and experimental datasets.

Keywords: cellular noise; parametric inference; approximate Bayesian computation


  • Bailey, N. T. J. (1964): The elements of stochastic processes with applications to the natural sciences, Wiley: New York.Google Scholar

  • Beaumont, M. A., W. Zhang and D. J. Balding (2002): “Approximate bayesian computation in population genetics,” Genetics, 162, 2025–2035.Google Scholar

  • Blake, W. J., M. Kærn, C. R. Cantor and J. J. Collins (2003): “Noise in eukaryotic gene expression,” Nature, 422, 633–637.Google Scholar

  • Brock, A., H. Chang and S. Huang (2009): “Non-genetic heterogeneity – a mutation-independent driving force for the somatic evolution of tumours,” Nat. Rev. Genet., 10, 336–342.Web of ScienceGoogle Scholar

  • Chang, H. H., M. Hemberg, M. Barahona, D. E. Ingber and S. Huang (2008): “Transcriptome-wide noise controls lineage choice in mammalian progenitor cells,” Nature, 453, 544–547.Web of ScienceGoogle Scholar

  • das Neves, R. P., N. S. Jones, L. Andreu, R. Gupta, T. Enver and F. J. Iborra (2010): “Connecting variability in global transcription rate to mitochondrial variability,” PLoS Biol., 8, 451–464.Web of ScienceGoogle Scholar

  • Ding, H., G. Trajcevski, P. Scheuermann, X. Wang and E. Keogh (2008): “Querying and mining of time series data: experimental comparison of representations and distance measures,” Proceedings of the VLDB Endowment, 1, 1542–1552.Google Scholar

  • Elowitz, M. B., A. J. Levine, E. D. Siggia and P. S. Swain (2002): “Stochastic gene expression in a single cell,” Science, 297, 1183–1186.Google Scholar

  • Enver, T., M. Pera, C. Peterson and P. W. Andrews (2009): “Stem cell states, fates, and the rules of attraction,” Cell Stem Cell, 4, 387–397.Web of ScienceGoogle Scholar

  • Gillespie, D. T. (1977) “Exact stochastic simulation of coupled chemical reactions,” J. Phys. Chem., 81, 2340–2361.Google Scholar

  • Golding, I., J. Paulsson, S. M. Zawilski and E. C. Cox (2005): “Real-time kinetics of gene activity in individual bacteria,” Cell, 123, 1025–1036.Google Scholar

  • Graf, T. and M. Stadtfeld (2008): “Heterogeneity of embryonic and adult stem cells,” Cell Stem Cell, 3, 480–483.Google Scholar

  • Johnston, I. G., B. Gaal, R. P. das Neves, T. Enver, F. J. Iborra and N. S. Jones (2012): “Mitochondrial variability as a source of extrinsic cellular noise,” PLoS Comput. Biol., 8, e1002416.Web of ScienceGoogle Scholar

  • Kærn, M., T. C. Elston, W. J. Blake and J. J. Collins (2005): “Stochasticity in gene expression: from theories to phenotypes,” Nat. Rev. Genet., 6, 451–464.Google Scholar

  • Knight, K. (2000): Mathematical statistics. Chapman & Hall: New York, NY, USA.Google Scholar

  • Kussell, E., R. Kishony, N. Q. Balaban and S. Leibler (2005): “Bacterial persistence: a model of survival in changing environments,” Genetics, 169, 1807.Google Scholar

  • Marin, J.-M., P. Pudlo, C. P. Robert and R. J. Ryder (2012): “Approximate bayesian computational methods,” Stat. Comput., 22, 1167–1180.Web of ScienceGoogle Scholar

  • Marjoram, P., J. Molitor, V. Plagnol and S. Tavaré (2003): “Markov chain monte carlo without likelihoods,” Proc. Natl. Acad. Sci., 100, 15324–15328.Google Scholar

  • Paulsson, J. (2005): “Models of stochastic gene expression,” Phys. Life Rev., 2, 157–175.Google Scholar

  • Raser, J. M. and E. K. O’Shea (2004): “Control of stochasticity in eukaryotic gene expression,” Science, 304, 1811–1814.Google Scholar

  • Rausenberger, J. and M. Kollmann (2008): “Quantifying origins of cell-to-cell variations in gene expression,” Biophys. J., 95, 4523–4528.Web of ScienceGoogle Scholar

  • Sisson, S. A., Y. Fan and M. M. Tanaka (2007): “Sequential monte carlo without likelihoods,” Proc. Natl. Acad. Sci., 104, 1760–1765.Google Scholar

  • Spencer, S. L., S. Gaudet, J. G. Albeck, J. M. Burke and P. K. Sorger (2009): “Non-genetic origins of cell-to-cell variability in TRAIL-induced apoptosis,” Nature, 459, 428–432.Web of ScienceGoogle Scholar

  • Sunnåker, Mikael, Alberto Giovanni Busetto, Elina Numminen, Jukka Corander, Matthieu Foll and Christophe Dessimoz (2013): “Approximate bayesian computation,” PLoS Comput. Biol., 9, e1002803.Google Scholar

  • Toni, T., D. Welch, N. Strelkowa, A. Ipsen and M. P. H. Stumpf (2009): “Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems,” J. Roy. Soc. Interface, 6, 187–202.Web of ScienceGoogle Scholar

  • Wilkinson, D. J. (2012): Stochastic modelling for systems biology. CRC press: Boca Raton, FL, USA.Google Scholar

About the article

Corresponding author: Iain G. Johnston, Department of Mathematics, Imperial College London, London SW7 2AZ, UK, e-mail:

Published Online: 2014-05-10

Published in Print: 2014-06-01

Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 13, Issue 3, Pages 379–390, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.1515/sagmb-2013-0061.

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