Bayesian inference for kinetic models of biotransformation using a generalized rate equation.

Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.

[1]  Hilary I. Inyang,et al.  The Elovich equation as a predictor of lead and cadmium sorption rates on contaminant barrier minerals , 2016 .

[2]  K. R. Reddy.  Nitrogen cycling in a flooded-soil ecosystem planted to rice (Oryza sativa L.) , 1982, Plant and Soil.

[3]  A. Mosier,et al.  Gas chromatographic system for precise, rapid analysis of nitrous oxide. , 1980 .

[4]  Youssef M. Marzouk,et al.  Bayesian inference of chemical kinetic models from proposed reactions , 2015 .

[5]  Heinz Singer,et al.  A tiered procedure for assessing the formation of biotransformation products of pharmaceuticals and biocides during activated sludge treatment. , 2010, Journal of environmental monitoring : JEM.

[6]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[7]  P. Green,et al.  Reversible jump MCMC , 2009 .

[8]  Mary F. Mahon,et al.  Magnesium-catalysed hydroboration of pyridines:kinetic analysis and poly-pyridine dearomatisation , 2016 .

[9]  M. Alexander,et al.  Kinetics of mineralization of organic compounds at low concentrations in soil , 1986, Applied and environmental microbiology.

[10]  Chris J. Oates,et al.  Network inference using steady-state data and Goldbeter-Koshland kinetics , 2012, Bioinform..

[11]  Jens Kattge,et al.  Estimation of parameters in complex 15N tracing models by Monte Carlo sampling , 2007 .

[12]  K. Mengersen,et al.  A flexible Bayesian model for describing temporal variability of N₂O emissions from an Australian pasture. , 2013, The Science of the total environment.

[13]  Peng Wang,et al.  A Bayesian method for multi-pollution source water quality model and seasonal water quality management in river segments , 2014, Environ. Model. Softw..

[14]  F X Casey,et al.  Inverse analyses of transport of chlorinated hydrocarbons subject to sequential transformation reactions. , 2001, Journal of environmental quality.

[15]  Kim Pilegaard,et al.  Processes regulating nitric oxide emissions from soils , 2013, Philosophical Transactions of the Royal Society B: Biological Sciences.

[16]  R. J. Stevens,et al.  A 15N tracing model to analyse N transformations in old grassland soil , 2004 .

[17]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[18]  Willi Jäger,et al.  Modelling of Chemical Reaction Systems , 1981 .

[19]  E. Baggs.  Soil microbial sources of nitrous oxide: recent advances in knowledge, emerging challenges and future direction , 2011 .

[20]  Jasper A. Vrugt,et al.  UvA-DARE ( Digital Academic Repository ) DREAM ( D ) : An adaptive Markov chain Monte Carlo simulation algorithm to solve discrete , noncontinuous , and combinatorial posterior parameter estimation problems , 2011 .

[21]  Ming Ye,et al.  Effects of error covariance structure on estimation of model averaging weights and predictive performance , 2013 .

[22]  R. F. Howe,et al.  The effect of gold loading and particle size on photocatalytic hydrogen production from ethanol over Au/TiO₂ nanoparticles. , 2011, Nature chemistry.

[23]  D. Sedlak,et al.  Biotransformation of trace organic contaminants in open-water unit process treatment wetlands. , 2014, Environmental science & technology.

[24]  Rolf Nieder,et al.  Processes leading to N2O and NO emissions from two different Chinese soils under different soil moisture contents , 2013, Plant and Soil.

[25]  B. C. Young,et al.  Nitrous oxide emissions , 1992 .

[26]  A. Xu,et al.  The preparation, characterization, and their photocatalytic activities of rare-earth-doped TiO2 nanoparticles , 2002 .

[27]  K. A. Smith,et al.  Nitrous oxide emissions from fertilised grassland: A 2-year study of the effects of N fertiliser form and environmental conditions , 1997, Biology and Fertility of Soils.

[28]  B. Bekins,et al.  A Comparison of Zero‐Order, First‐Order, and Monod Biotransformation Models , 1998 .

[29]  Willi Jäger,et al.  Modelling of chemical reaction systems : proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, September 1-5, 1980 , 1981 .

[30]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[31]  A. Shimada,et al.  Evidence for recent invasion of the medaka fish genome by the Tol2 transposable element. , 2000, Genetics.

[32]  Anònim Anònim.  Keys to Soil Taxonomy , 2010 .

[33]  Ming Ye,et al.  Assessment of parametric uncertainty for groundwater reactive transport modeling , 2014 .

[34]  Donald L. Sparks,et al.  KINETICS OF SOIL CHEMICAL REACTIONS : RELATIONSHIPS BETWEEN EMPIRICAL EQUATIONS AND DIFFUSION MODELS , 1991 .

[35]  Ming Ye,et al.  Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff , 2003 .

[36]  David Welch,et al.  Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems , 2009, Journal of The Royal Society Interface.

[37]  N. Wrage,et al.  Nitrifier denitrification as a distinct and significant source of nitrous oxide from soil , 2011 .

[38]  K. R. Reddy,et al.  Denitrification losses in flooded rice fields , 1986 .

[39]  Christoph Müller,et al.  Quantification of N2O emission pathways via a 15N tracing model , 2014 .

[40]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[41]  Jürgen Augustin,et al.  A modeling study on mitigation of N2O emissions and NO3 leaching at different agricultural sites across Europe using LandscapeDNDC. , 2016, The Science of the total environment.

[42]  Donald L. Sparks,et al.  Kinetics of Soil Chemical Processes , 2013 .

[43]  L. Aquilina,et al.  Reaction chain modeling of denitrification reactions during a push-pull test. , 2013, Journal of contaminant hydrology.

[44]  Jasper A. Vrugt,et al.  Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation , 2016, Environ. Model. Softw..

[45]  Yanyun Li,et al.  Substantivity of Ag–Ca–Si mesoporous nanoparticles on dentin and its ability to inhibit Enterococcus faecalis , 2015, Journal of Materials Science: Materials in Medicine.

[46]  Steven D. Allison,et al.  The Michaelis–Menten kinetics of soil extracellular enzymes in response to temperature: a cross‐latitudinal study , 2012 .

[47]  Masaaki Hosomi,et al.  Assessing nitrification and denitrification in a paddy soil with different water dynamics and applied liquid cattle waste using the ¹⁵N isotopic technique. , 2012, The Science of the total environment.

[48]  Hamid Moradkhani,et al.  Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging , 2014 .

[49]  D. Tarsitano,et al.  Simulation of nitrous oxide emissions at field scale using the SPACSYS model , 2015, The Science of the total environment.

[50]  Wasserman,et al.  Bayesian Model Selection and Model Averaging. , 2000, Journal of mathematical psychology.

[51]  Yong Wang,et al.  Mitigation of soil N2O emission by inoculation with a mixed culture of indigenous Bradyrhizobium diazoefficiens , 2016, Scientific Reports.

[52]  K. R. Reddy,et al.  Nitrogen transformations and loss in flooded soils and sediments , 1984 .

[53]  R. Meffe,et al.  The role of sorption and biodegradation in the removal of acetaminophen, carbamazepine, caffeine, naproxen and sulfamethoxazole during soil contact: A kinetics study. , 2016, The Science of the total environment.

[54]  Miguel A. Sánchez-Monedero,et al.  Biochar increases soil N2O emissions produced by nitrification-mediated pathways , 2014, Front. Environ. Sci..