Global Sensitivity Analysis: Estimation of Sensitivity Indexes in Metabolic Network Dynamic Models

Jimena A. Di Maggio, Chemical Engineering, Planta Piloto de Ingenieria Quimica (PLAPIQUI), Universidad Nacional del Sur, Camino La carrindanga Km 7, Bahia Blanca, 8000, Argentina, Juan C. Diaz Ricci, Instituto Superior de Investigaciones Biológicas (INSIBIO), Universidad Nacional de Tucuman, Chacabuco 461, Tucuman, 4000, and Maria Soledad Diaz, Chemical Engineering, Planta Piloto de Ingenieria Quimica (PLAPIQUI), Universidad Nacional del Sur - CONICET, Camino La Carrindanga Km 7, Bahia Blanca, 8000, Argentina.

Dynamic models for metabolic pathways that can predict the microbial behavior constitute important tools in metabolic engineering. During the past few years, there has been a great increase in the availability of high-throughput data that characterize the status of cells at the genomic, proteomic, metabolic and physiological levels. It is now possible to use the same methods to record the status of cells over time, which gives a large amount of information on the dynamics of functioning cells. Dynamic models comprise a nonlinear differential algebraic system of equations, which arise from mass balances for metabolites and have a large number of kinetic parameters that require tuning for an specific growth condition. The first step in the solution of the inverse problem is the sensitivity analysis. Global sensitivity approaches estimate the effect on the output of a factor when all the others are varying, enabling the identification of interactions in nonlinear and/or nonadditive models. Generally, global approaches allow the use of model-independent methods as they do not require assumptions of additivity or linearity. Model responses are then analyzed statistically to yield the empirical distribution function/probability distribution of the model outputs.

In this work, a global sensistivity analysis has been performed through variance-based techniques to identify which parameters have the largest impact on the model output and which of them account for most of the uncertainty in that output. Sensitivity indexes have been calculated for each parameter, based on Sobol's method (1993); in which the first-order sensitivity index for each parameters is calculated as the ratio between the variance of the expected valued of the mean of the output (Vi) for the corresponding parameter and the total variance (V).

The global sensitivity analysis has been performed on a dynamic model for the Embden-Meyerhof-Parnas pathway, the phosphotransferase system and the pentose phosphate pathway of Escherichia coli K-12 strain W3110 (Chassagnole et al., 2002). The model comprises nineteen dynamic mass balance equations for extracellular glucose and intracellular metabolites, twenty nine kinetic rate expressions and seven additional algebraic equations to represent the concentration of co-metabolites. The model involves around one hundred parameters. Each parameter has been considered to have a normal probability distribution centered on its nominal value and sample sizes of one thousand scenarios have been considered. The preceding analysis has allowed identification of less than thirty parameters as the most influential ones on the complex metabolic network under study.


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