Constraints-based models: regulation of gene expression reduces the steady-state solution space.

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.