Metabolic potentials method for adding loopless constraints in steady-state metabolic flux modeling using mixed-integer linear programming

In modeling of steady-state metabolic fluxes in metabolic networks, Flux Balance Analysis (FBA) is widely used. However, the standard FBA formulation can admit biochemically infeasible solutions due to thermodynamically infeasible (futile) cycles. Enforcing thermodynamic feasibility with loopless constraints yields an NP-hard problem, which motivates the development of efficient Mixed-Integer Linear Programming (MILP) formulations of loopless FBA. In this work, we propose a new efficient metabolic potentials method for FBA with loopless constraints. This method is based on a novel MILP formulation of loopless constraints. Our analysis of the prior Fast-SNP method, which achieved an order-of-magnitude speedup, allowed us to identify and quantify the contributions of two key optimization ideas: using sparse constraints and reducing the number of integer variables. The proposed metabolic potentials method adopts these ideas and introduces an equivalent MILP formulation of loopless constraints. We compare the performance of the metabolic potentials method using metabolic models from the BiGG database. The proposed method shows performance comparable to Fast-SNP on small and medium scale metabolic models and achieves an approximately 30 % reduction in runtime on a large genome-scale human cell metabolic model RECON1. We also demonstrate that reducing the number of integer variables is the dominant factor in the overall speedup. The proposed metabolic potentials method retains the benefits of the optimization ideas introduced in Fast-SNP and achieves the same or better efficiency. Therefore, it can be used as a drop-in replacement for Fast-SNP and other standard methods for FBA with loopless constraints.