QUANTITATIVE ASSESSMENT OF UNCERTAINTY IN THE OPTIMIZATION OF METABOLIC PATHWAYS

The S-System formalism provides a popular, versatile and mathematicall y tractable representation of metabolic pathways. At steady-state, aft er a logarithmic transformation, the S-System representation reduces i nto a system of linear equations. Thus, the maximization of a particul ar metabolite concentration or a flux subject to physiological constra ints can be expressed as a linear programming (LP) problem which can b e 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 t he first time, the systematic quantitative description of modeling/exp erimental uncertainty is attempted by utilizing probability density di stributions to model the uncertainty in assigning a unique value to sy stem 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 existin g optimization algorithms. The proposed framework is applied to two me tabolic pathways characterized with experimental and modeling uncertai nty in the kinetic orders. The computational results indicate the trac tability of the method and the significant role that modeling and expe rimental uncertainty may play in the optimization of networks of metab olic reactions. While optimization results ignoring uncertainty someti mes violate physiological constraints and may fail to correctly assess objective targets, the proposed framework provides quantitative answe rs to questions regarding how likely it is to achieve a particular met abolic objective without exceeding a prespecified probability of viola ting 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 syste matic way to guide enzyme activity alterations to meet an objective in the face of modeling and experimental uncertainty. (C) 1997 John Wile y & Sons, Inc.