Loop law constraints on metabolic networks. (a) Metabolic network reconstructions frequently have sets of reactions that cycle all metabolites internally. The fluxes of these reactions are therefore unconstrained. (b) Metabolic network solutions are found within a convex space, which is enclosed by known constraints on metabolite inputs, outputs, and known fluxes. Loops result in unconstrained dimensions in the solution space (blue). By implementing loopless-COBRA constraints, all loop-containing solutions are removed, leaving only solutions that do not contain loops (orange).