Fig. 1.

Integration of thermodynamics in CBMs. (A) Group contribution methods provide estimates of standard reaction energies. The uncertainties of multiple estimates may be correlated and lie in a lower dimensional subspace. (B) Probability distributions of metabolite concentrations can be constructed from measured or assumed data. (C) The space of reaction energies and metabolite concentrations defined by TMFA, with regions that are not feasible at steady-state removed (red). The space is defined by independent bounds on each variable of $\ln \mathbf{c}$ and ${\Delta }_{\mathbf{r}}\mathbf{G}\prime °$, leading to an overapproximation of the uncertainty. (D) PTA models the complete uncertainty information probabilistically, leading to a joint probability distribution over the reaction energies of the entire network. Steady-state flux constraints restrict it to feasible orthants