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

Abstract

The aim of this study was to identify, quantify and prioritize 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 characterized 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 linearization 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, 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, characterization 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 linearization, as well as by reduction of the number of non-influential variables were outlined.

Analysis of Hepatic Lipid Metabolism Model: Simulation and Non-Stationary Global Sensitivity Analysis

“…This study examined the influence of input parameter uncertainty on the variance of metabolic model predictions. The majority of the propagated uncertainty is due to the interactions of numerous factors rather than being linear from one parameter to one result as previously presented by Quang et al [ 51 ].…”

“…Mathematical models make it possible to integrate information collected from different sources using common mathematical methods. By increasing the availability of information about the metabolic activity of an organism through the application of advanced molecular techniques, the complexity of the proposed mathematical models also increases [ 51 ]. Mathematical models of biological systems are most often derived in the form of differential equations that describe the changes in a single variable over time [ 52 ].…”

The limitations of phenotype prediction in metabolism

“…We use the method first proposed by Sobol for its easy implementation and interpretation [46,47]. Note that this differs from previous fluxbased applications [48,49]. Briefly, we focus on two indices for the ith gene, the first order index S i 0 and the total effect index S i T .…”

The limitations of phenotype prediction in metabolism

“…We used the method first proposed by Sobol for its easy implementation and interpretation (Sobol 1993;Saltelli et al 2008). Note that this differs from previous flux-based applications (Nguyen Quang et al 2019;Nobile et al 2021). Briefly, we focus on two indices for the i-eth gene, the first order index S i 0 and the total effect index S i T .…”