Metabolic flux estimation--a self-adaptive evolutionary algorithm with singular value decomposition

Metabolic flux analysis is important for metabolic system regulation and intracellular pathway identification. A popular approach for intracellular flux estimation involves using ¹³C tracer experiments to label states that can be measured by nuclear magnetic resonance spectrometry or gas chromatography mass spectrometry. However, the bilinear balance equations derived from ¹³C tracer experiments and the noisy measurements require a nonlinear optimization approach to obtain the optimal solution. In this paper, the flux quantification problem is formulated as an error-minimization problem with equality and inequality constraints through the ¹³C balance and stoichiometric equations. The stoichiometric constraints are transformed to a null space by singular value decomposition. Self-adaptive evolutionary algorithms are then introduced for flux quantification. The performance of the evolutionary algorithm is compared with ordinary least squares estimation by the simulation of the central pentose phosphate pathway. The proposed algorithm is also applied to the central metabolism of Corynebacterium glutamicum under lysine-producing conditions. A comparison between the results from the proposed algorithm and data from the literature is given. The complexity of a metabolic system with bidirectional reactions is also investigated by analyzing the fluctuations in the flux estimates when available measurements are varied.