Robust Analysis of Metabolic Pathways

Flux balance analysis (FBA) is a standard optimization model that is used to study the metabolisms of cells that are in a steady state of optimal growth. The model optimizes a biologically defined objective while assuming (1) equilibria of a linear system of ordinary differential equations, and (2) deterministic data. However, the steady state assumption is imperfect from a biological point of view, and several of the coefficients are experimentally inferred from situations of inherent variation. Here, we propose a robust extension of FBA that removes the firm imposition of reaching steady state, instead capturing the innate variability of a cell culture probabilistically. Our mathematical study of the stochastic problem provides three key insights: 1) metabolic states are (Lipschitz) continuous with regards to the probabilistic modeling parameters, 2) convergent states of the stochastic model are solutions to the deterministic FBA paradigm as the stochastic elements dissipate, and 3) the stochastic model can help identify biological diversity of metabolic networks in an optimized culture. We benchmark our robust counterpart against traditional FBA on two genome-scale metabolic reconstructed models of E. coli, and the results show that the stochastic adaptation achieves results comparable to FBA.