title: The metabolic network of Clostridium acetobutylicum: Comparison of the approximate Bayesian computation via sequential Monte Carlo (ABC-SMC) and profile likelihood estimation (PLE) methods for determinability analysis.
abstract: The Gram-positive bacterium Clostridium acetobutylicum is an anaerobic endospore-forming species which produces acetone, butanol and ethanol via the acetone-butanol (AB) fermentation process, leading to biofuels including butanol. In previous work we looked to estimate the parameters in an ordinary differential equation model of the glucose metabolism network using data from pH-controlled continuous culture experiments. Here we combine two approaches, namely the approximate Bayesian computation via an existing sequential Monte Carlo (ABC-SMC) method (to compute credible intervals for the parameters), and the profile likelihood estimation (PLE) (to improve the calculation of confidence intervals for the same parameters), the parameters in both cases being derived from experimental data from forward shift experiments. We also apply the ABC-SMC method to investigate which of the models introduced previously (one non-sporulation and four sporulation models) have the greatest strength of evidence. We find that the joint approximate posterior distribution of the parameters determines the same parameters as previously, including all of the basal and increased enzyme production rates and enzyme reaction activity parameters, as well as the Michaelis-Menten kinetic parameters for glucose ingestion, while other parameters are not as well-determined, particularly those connected with the internal metabolites acetyl-CoA, acetoacetyl-CoA and butyryl-CoA. We also find that the approximate posterior is strongly non-Gaussian, indicating that our previous assumption of elliptical contours of the distribution is not valid, which has the effect of reducing the numbers of pairs of parameters that are (linearly) correlated with each other. Calculations of confidence intervals using the PLE method back this up. Finally, we find that all five of our models are equally likely, given the data available at present.
authors.affiliation: School of Pharmacy, East Drive, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Electronic address: graeme.thorn@nottingham.ac.uk.
authors.forename: Graeme J
authors.initials: GJ
authors.lastname: Thorn
authors.affiliation: School of Mathematical Sciences, Mathematical Sciences Building, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Electronic address: john.king@nottingham.ac.uk.
authors.forename: John R
authors.initials: JR
authors.lastname: King
mesh_terms: D001499:Bayes Theorem; D046969:Clostridium acetobutylicum / Q000378:metabolism*; D016013:Likelihood Functions; D053858:Metabolic Networks and Pathways; D008962:Models, Theoretical; D009010:Monte Carlo Method
keywords: AB fermentation; Bayesian parameter estimation; Clostridium acetobutylicum; ODE modeling; Profile likelihood estimation; Systems biology