  Current mathematical frameworks for predicting the flux state and
macromolecular composition of the cell do not rely on thermodynamic constraints
to determine the spontaneous direction of reactions. These predictions may be
biologically infeasible as a result. Imposing thermodynamic constraints
requires accurate estimations of intracellular metabolite concentrations. These
concentrations are constrained within physiologically possible ranges to enable
an organism to grow in extreme conditions and adapt to its environment. Here,
we introduce tractable computational techniques to characterize intracellular
metabolite concentrations within a constraint-based modeling framework. This
model provides a feasible concentration set, which can generally be nonconvex
and disconnected. We examine three approaches based on polynomial optimization,
random sampling, and global optimization. We leverage the sparsity and
algebraic structure of the underlying biophysical models to enhance the
computational efficiency of these techniques. We then compare their performance
in two case studies, showing that the global-optimization formulation exhibits
more desirable scaling properties than the random-sampling and
polynomial-optimization formulation, and, thus, is a promising candidate for
handling large-scale metabolic networks.
