Quantitative assessment of uncertainty in the optimization of metabolic pathways

The S-System formalism provides a popular, versatile and mathematically tractable representation of metabolic pathways. At steady-state, after a logarithmic transformation, the S-System representation reduces into a system of linear equations. Thus, the maximization of a particular metabolite concentration or a flux subject to physiological constraints can be expressed as a linear programming (LP) problem which can be solved explicitly and exactly for the optimum enzyme activities. So far, the quantitative effect of parametric/experimental uncertainty on the S-model predictions has been largely ignored. In this work, for the first time, the systematic quantitative description of modeling/experimental uncertainty is attempted by utilizing probability density distributions to model the uncertainty in assigning a unique value to system parameters. This probabilistic description of uncertainty renders both objective and physiological constraints stochastic, demanding a probabilistic description for the optimization of metabolic pathways. Based on notions from chance-constrained programming and statistics, a novel approach is introduced for transforming the original stochastic formulation into a deterministic one which can be solved with existing optimization algorithms. The proposed framework is applied to two metabolic pathways characterized with experimental and modeling uncertainty in the kinetic orders. The computational results indicate the tractability of the method and the significant role that modeling and experimental uncertainty may play in the optimization of networks of metabolic reactions. While optimization results ignoring uncertainty sometimes violate physiological constraints and may fail to correctly assess objective targets, the proposed framework provides quantitative answers to questions regarding how likely it is to achieve a particular metabolic objective without exceeding a prespecified probability of violating the physiological constraints. Trade-off curves between metabolic objectives, probabilities of meeting these objectives, and chances of satisfying the physiological constraints, provide a concise and systematic way to guide enzyme activity alterations to meet an objective in the face of modeling and experimental uncertainty. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 145-161, 1997.