Constraint-based modeling has proven to be a useful tool in the analysis of biochemical networks. To date, most studies in this field have focused on the use of linear constraints, resulting from mass balance and capacity constraints, which lead to the definition of convex solution spaces. One additional constraint arising out of thermodynamics is known as the "loop law" for reaction fluxes, which states that the net flux around a closed biochemical loop must be zero because no net thermodynamic driving force exists. The imposition of the loop-law can lead to nonconvex solution spaces making the analysis of the consequences of its imposition challenging. A four-step approach is developed here to apply the loop-law to study metabolic network properties: 1), determine linear equality constraints that are necessary (but not necessarily sufficient) for thermodynamic feasibility; 2), tighten V max and Vmin constraints to enclose the remaining nonconvex space; 3), uniformly sample the convex space that encloses the nonconvex space using standard Monte Carlo techniques; and 4), eliminate from the resulting set all solutions that violate the loop-law, leaving a subset of steady-state solutions. This subset of solutions represents a uniform random sample of the space that is defined by the additional imposition of the loop-law. This approach is used to evaluate the effect of imposing the loop-law on predicted candidate states of the genome-scale metabolic network of Helicobacter pylori.
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