Accelerating flux balance calculations in genome-scale metabolic models by localizing the application of loopless constraints

Background: Genome-scale metabolic network models and constraint-based modeling techniques have become important tools for analyzing cellular metabolism. Thermodynamically infeasible cy-cles (TICs) causing unbounded metabolic flux ranges are often encountered. TICs satisfy the mass balance and directionality constraints but violate the second law of thermodynamics. Current prac-tices involve implementing additional constraints to ensure not only optimal but also loopless flux distributions. However, the mixed integer linear programming problems required to solve become computationally intractable for genome-scale metabolic models. Results: We aimed to identify the fewest needed constraints sufficient for optimality under the loop-less requirement. We found that loopless constraints are required only for the reactions that share elementary flux modes representing TICs with reactions that are part of the objective function. We put forth the concept of localized loopless constraints (LLCs) to enforce this minimal required set of loopless constraints. By combining with a novel procedure for minimal null-space calculation, the computational time for loopless flux variability analysis is reduced by a factor of 10-150 compared to the original loopless constraints and by 4-20 times compared to the currently fastest method Fast-SNP with the percent improvement increasing with model size. Importantly, LLCs offer a scalable strategy for loopless flux calculations for multi-compartment/multi-organism models of very large sizes (e.g. >104 reactions) not feasible before. Matlab functions are available at https://github.com/maranasgroup/lll-FVA.