Incorporation of flexible objectives and time-linked simulation with flux balance analysis

We present two modifications of the flux balance analysis (FBA) metabolic modeling framework which relax implicit assumptions of the biomass reaction. Our flexible flux balance analysis (flexFBA) objective removes the fixed proportion between reactants, and can therefore produce a subset of biomass reactants. Our time-linked flux balance analysis (tFBA) simulation removes the fixed proportion between reactants and byproducts, and can therefore describe transitions between metabolic steady states. Used together, flexFBA and tFBA model a time scale shorter than the regulatory and growth steady state encoded by the biomass reaction. This combined short-time FBA method is intended for integrated modeling applications to enable detailed and dynamic depictions of microbial physiology such as whole-cell modeling. For example, when modeling Escherichia coli, it avoids artifacts caused by low-copy-number enzymes in single-cell models with kinetic bounds. Even outside integrated modeling contexts, the detailed predictions of flexFBA and tFBA complement existing FBA techniques. We show detailed metabolite production of in silico knockouts used to identify when correct essentiality predictions are made for the wrong reason.