Parametric Global sensitivity analysis in metabolic networks,

JIMENA DI MAGGIO; JUAN C. DIAZ RICCI; M. SOLEDAD DIAZ

Puerto Vallarta, Mexico

Congreso; Metabolic Engineering VII Health and Sustainability Conference; 2008

Dynamic models for metabolic networks 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. In this work, we have performed a global sensitivity analysis through variance-based techniques to identify most influential parameters 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 system representing a dynamic model for the Embden-Meyerhof-Parnas pathway, the phosphotransferase system and the pentose phosphate pathway of Escherichia coli (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 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. 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. Calculated sensitivity indices show, for example, that all parameters affect the concentration of ribu5p, but the most influential one is Nptsg6p, which is involved in the kinetic expression for phophotransferase system. Pgp concentration is sensitive to only four parameters, Kpglumueq, Kgapdhgap, Kgapdhpgp y Rgapdhmax which are involved in the kinetic expressions for glyceraldehyde 3-phosphate dehydrogenase and phosphoglycerate mutase REFERENCES Chassagnole, C., Noisommit-Rizzi, N., Schimd, J.W., Mauch, K., Reuss, M.. Dynamic modeling of the Central Carbon Metabolism of Escherichia coli, Biotechnology and Bioengineering 79, 2002, 53-72. Di Maggio, J., J.C. Diaz Ricci, M.S. Diaz, Global Sensitivity analysis: Estimation of Sensitivity Indexes In Metabolic Network Dynamic Models, accepted for presentation at AIChE annual meeting 2008, November 16-21, 2008, Philadelphia, USA. Process Systems Enterprise, gPROMS Introductory User guide, Process Systems Enterprise Ltd., London, 2007. Sobol’, I.M.. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Mathematics and Computers in Simulation 55, 2001, 271-280.