  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.
