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Front. Bioeng. Biotechnol. | doi: 10.3389/fbioe.2019.00234

Global Sensitivity Analysis of Metabolic Models for Phosphorus Accumulating Organisms in Enhanced Biological Phosphorus Removal

Minh Q. Nguyen1, 2, Tim Rogers3, 4, Jan Hofman1, 2 and  Ana B. Lanham1, 2*
  • 1Water Innovation and Research Centre, University of Bath, United Kingdom
  • 2Department of Chemical Engineering, Faculty of Engineering and Design, University of Bath, United Kingdom
  • 3Centre for Networks and Collective Behaviour, Faculty of Science, University of Bath, United Kingdom
  • 4Department of Mathematical Sciences, Faculty of Science, University of Bath, United Kingdom

The aim of this study was to identify, quantify and prioritise for the first time the sources of uncertainty in a mechanistic model describing the anaerobic-aerobic metabolism of phosphorus accumulating organisms (PAO) in enhanced biological phosphorus removal (EBPR) systems. These wastewater treatment systems play an important role in preventing eutrophication and metabolic models provide an advanced tool for improving their stability via system design, monitoring and prediction.
To this end, a global sensitivity analysis was conducted using standard regression coefficients and Sobol sensitivity indices, taking into account the effect of 39 input parameters on 10 output variables.
Input uncertainty was characterised with data in the literature and propagated to the output using the Monte Carlo method.
The low degree of linearity between input parameters and model outputs showed that model simplification by linearisation can be pursued only in very well defined circumstances. Differences between first and total-order sensitivity indices showed that variance in model predictions was due to interactions between combinations of inputs, as opposed to the direct effect of individual inputs.
The major sources of uncertainty affecting the prediction of liquid phase concentrations, as well as intra-cellular glycogen and poly-phosphate was due to 64\% of the input parameters. In contrast, the contribution to variance in intra-cellular PHA constituents was uniformly distributed among all inputs.
In addition to the intra-cellular biomass constituents, notably PHB, \ce{PH2MV} and glycogen, uncertainty with respect to input parameters directly related to anaerobic propionate uptake, aerobic poly-phosphate formation, glycogen formation and temperature contributed most to the variance of all model outputs. Based on the distribution of total-order sensitivities, characterisation of the influent stream and intra-cellular fractions of PHA can be expected to significantly improve model reliability.
The variance of EBPR metabolic model predictions was quantified. The means to account for this variance, with respect to each quantity of interest, given knowledge of the corresponding input uncertainties, was prescribed.
On this basis, possible avenues and pre-requisite requirements to simplify EBPR metabolic models for PAO, both structurally via linearisation, as well as by reduction of the number of non-influential variables were outlined.

Keywords: Enhanced Biological Phosphorus Removal (EBPR), Global sensitivity analysis (GSA), Metabolic model, Phosphorus accumulating organism (PAO), Standard regression coefficient, Sobol sensitivity analysis, Monte Carlo (MC)

Received: 20 Dec 2018; Accepted: 09 Sep 2019.

Copyright: © 2019 Nguyen, Rogers, Hofman and Lanham. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Ana B. Lanham, Water Innovation and Research Centre, University of Bath, Bath, United Kingdom, a.lanham@bath.ac.uk