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.
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, 544–547.10.1038/nature06965)| false
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.
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.
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, 1542–1552.10.14778/1454159.1454226)| false
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.
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, 428–432.10.1038/nature08012)| false
Sunnåker, Mikael, Alberto Giovanni Busetto, Elina Numminen, Jukka Corander, Matthieu Foll and Christophe Dessimoz (2013): “Approximate bayesian computation,” PLoS Comput. Biol., 9, e1002803.
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.
Wilkinson, D. J. (2012): Stochastic modelling for systems biology. CRC press: Boca Raton, FL, USA.
SAGMB publishes significant research on the application of statistical ideas to problems arising from computational biology. The range of topics includes linkage mapping, association studies, gene finding and sequence alignment, protein structure prediction, design and analysis of microarrary data, molecular evolution and phylogenetic trees, DNA topology, and data base search strategies.