Ranking of most influential kinetic parameters in metabolic networks through Global Sensitivity Analysis

JIMENA ANDREA DI MAGGIO; JUAN CARLOS DIAZ RICCI; MARÍA SOLEDAD DÍAZ

Puerto Vallarta

Congreso; Metabolic Engineering VII: Health and Sustainability; 2008

Engineering Conference International (ECI)

Dynamic models for metabolic networks that can predict the microbial behavior constitute important tools in metabolic engineering. Nowadays it is possible to obtain data characterizing the status of microorganisms over time at genomic, proteomic, metabolomic and physiological levels. It means that intracellular and extracellular metabolites concentrations, measurements of protein levels and activity are available for the building of dynamic models for metabolic networks. 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 a specific growth condition. However, uncertainty in input parameters has different effect on model outputs. Thus the first step to solve the inverse problem is to carry out a sensitivity analysis, which provides knowledge about the parameters that have the largest impact on model outputs. There are local and global sensitivity analysis methodologies. The first ones study the effect of small changes of parameters on model outputs assuming linearity of variables around the nominal trajectory. On the other hand global approaches are based on exploring the whole range of variation of model parameters and on performing repeated simulations to obtain the output distributions, allowing the evaluation of the effect on the output of a factor when all the others are varying, enabling the identification of interactions in nonlinear and/or non-additive models. Therefore, computational cost is much higher in global sensitivity than in local sensitivity methods. In this work, we have performed a global sensitivity analysis through variance-based techniques to identify which parameters have the largest impact on model output and which of them account for most of the uncertainty in that output. Sensitivity indices have been calculated for each parameter, based on Sobol’s approach (2001), which makes use of Monte Carlo methods for the calculation of times profiles for main effect variances in input parameters for main state variables. The global sensitivity analysis has been carried out on a large-scale differential algebraic (DAE) system representing 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 eighteen dynamic mass balance equations for extracellular glucose and intracellular metabolites, thirty kinetic rate expressions and seven additional algebraic equations to represent the concentration of co-metabolites. The model involves around one hundred parameters (Di Maggio et al., 2008). We have implemented the large-scale metabolic network model in g-PROMS (PSE Enterprise, 2007), in which the differential algebraic system of equations is solved with DASSL (Brenan et al., 1996). In this environment, two different sets of random parameters have been generated for k=20 parameters, which were selected with a preliminary screening. Sample size of N=2500 scenarios have been considered. Normal distribution has been assumed for each parameter, with mean equal to nominal values from the literature and 10% standard deviation. We have performed the N(2k+1) Monte Carlo simulations in g-Proms and output temporal profiles for state and algebraic variables have been exported for subsequent variance and sensitivity indices calculation within a Fortran 90 environment. Global sensitivity analysis has been performed on a large-scale metabolic network model, allowing a ranking of the most influential input parameters to pave the way to formulation and solution to the dynamic parameter estimation problem for the main parameters.