Thermodynamic Metabolic Flux Analysis with Consistent Handling of Errors in the Estimates from the Component Contribution Method

Thermodynamic metabolic flux balance analysis (TMFA) is used extensively in genome scale metabolic modeling to obtain thermodynamically consistent flux and metabolic concentration profiles. TMFA involves the use of thermodynamic constraints to avoid thermodynamically infeasible solutions and provides information about free energy change of reactions as well as the range of metabolite activity. The current best method for estimating standard Gibbs energy of reaction (Δ_rG⁰) uses the component contribution method combining reactant and group contribution methods. The estimates of Δ_rG⁰ are associated with an error, which is calculated from errors on the individual reactant and group contributions.

Recent implementations of TMFA allow for the error in the estimates by allowing each individual Δ_rG⁰ to vary independently within its estimated confidence. However, this is not the correct treatment as the individual Δ_rG⁰ are not independent; they share reactant and group contributions. Allowing them to vary independently will inevitably result thermodynamic inconsistencies, where closed loops have non-zero ΔG. This problem was resolved by returning to the original TMFA formulation, where the error was allowed in the individual groups and then identically propagated to all Δ_rG⁰. Using the component method, this approach is here expanded by allowing for errors in both reaction and group contributions (each is allowed with their respective confidence ellipsoid) and then propagating the adjusted estimates correctly to all Δ_rG⁰. The method is made available as an OpenCobra function.