Robust Prediction of Minimal Medium Composition Using Sparse Optimization

In cellular metabolism, extracellular transport reactions transfer metabolites between the extracellular space and the cytosol. Determining which transport reactions are active is an important part of setting the boundary conditions for a constraint-based model. Assuming that cells aim to minimise the set of active extracellular transport reactions, subject to viability of a condition-specific model results requires the minimisation of a zero norm of a vector over a convex polyhedral set. This results in a Non-deterministic Polynomial-time hard optimisation problem. In some instances, this problem be approximated by minimising the absolute-value norm. In other instances, the mathematical conditions for exact recovery of a minimal zero norm solution, by a absolute-value norm, are not met. We explore the utility of alternate relaxations of the absolute-value norm, where conditions for exact recovery are well suited to metabolic network modelling. We apply this algorithm to predict the minimal set of extracellular transport reactions in a human in vitro dopaminergic neuronal cell model and compare the results with extracellular metabolomic data.