A Simplex Approach to Solving Robust Metabolic Models with Low-Dimensional Uncertainty

We address the problem of solving difficult metabolic models that arise in the study of flux balance analysis (FBA). FBA problems are regularly linear due to simplifying assumptions although quadratic, combinatorial, and robust extensions are pragmatic variations. All such extensions inherit an underlying computational difficulty from the linear model, although in many instances this concern can be avoided by selecting an appropriate solution algorithm. Robust extensions unfortunately lack a trustworthy computational standard and are thus difficult to solve and problematic to employ. We show that a robust model’s optimal value can be calculated by coupling standard nonlinear schemes with a technique of successive linear approximation, and we further indicate how the computational outcome might differ from the intent of the original robust model. We test our algorithm on two simple, motivating examples and on a standard FBA problem.