The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Metabolic models comprising the entirety of reactions known to occur within a pathway and/or cell provide an increasingly popular and effective platform to study the internal states of a cell. Constraint based approaches are commonly employed to define a, usually near infinite, set of equally optimal feasible internal states the cell can operate in. Integration of experimental measurements of intracellular metabolite concentrations in genome scale models restricts the thermodynamically feasible flux space and reduces uncertainty regarding the net outcome of by-directional reactions. By combining Thermodynamics-based Flux Balance Analysis (TFBA), Marcov Chain sampling, Experimental Design and Global Sensitivity Analysis we present an efficient algorithm to quantify the effect of intracellular metabolites on the thermodynamic flexibility of cellular metabolism. Metabolites are ranked based on their ability to constrain the range of possible solutions to a limited, thermodynamically consistent set of internal states. The proposed methodology effectively defines the amount of experimental information required to reduce uncertainty in defining the state of cellular metabolism (i.e the flux distribution and displacement from thermodynamic equilibrium) by providing a ranked list of targets for metabolomics. The proposed approach is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network.