Reducing Uncertainty in Metabolic Networks through Thermodynamics Based Flux Analysis

Almost every process or action that occurs within a cell involves a metabolic reaction. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. 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 within a pathway and/or cell provide an increasingly popular and effective platform to study the internal states of a cell. However unless all intracellular fluxes are known, constraint-based models, by design, lead to underdetermined problem formulations. This results in the existence of numerous alternate internal flux distributions that satisfy the mass balance constraints and can achieve the same optimum. Experimental information, when available, allows for some of these solutions to be discarded. Reaction fluxes that are not measured experimentally are allowed to vary between physiologically relevant bounds often derived from literature. The size of the resulting solution space, comprising the gamut of alternate optimal flux distributions, can be viewed as a representation of the uncertainty in predicting an exact intracellular state relevant to the studied physiology. The space of steady state flux solutions under uncertainty has attracted significant scientific interest in a number of studies that either attempted to correlate biological significance with characteristics of the solution space or attempted to achieve more accurate flux distributions by incorporating additional physicochemical information such as thermodynamic and molecular crowding constraints.  However the problem of identifying network components with a significant contribution towards the observed uncertainty remains far from trivial.

In the present work we combine thermodynamics based constraint based modeling, Monte Carlo sampling, Design of Experiments (DoE) and global sensitivity analysis (GSA) in order to rank metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. The proposed approach is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.