Thermodynamically consistent estimation of Gibbs free energy from data: data reconciliation approach

Motivation: Thermodynamic analysis of biological reaction networks requires the availability of accurate and consistent values of Gibbs free energies of reaction and formation. These Gibbs energies can be measured directly via the careful design of experiments or can be computed from the curated Gibbs free energy databases. However, the computed Gibbs free energies of reactions and formations do not satisfy the thermodynamic constraints due to the compounding effect of measurement errors in the experimental data. The propagation of these errors can lead to a false prediction of pathway feasibility and uncertainty in the estimation of thermodynamic parameters. Results: This work proposes a data reconciliation framework for thermodynamically consistent estimation of Gibbs free energies of reaction, formation and group contributions from experimental data. In this framework, we formulate constrained optimization problems that reduce measurement errors and their effects on the estimation of Gibbs energies such that the thermodynamic constraints are satisfied. When a subset of Gibbs free energies of formations is unavailable, it is shown that the accuracy of their resulting estimates is better than that of existing empirical prediction methods. Moreover, we also show that the estimation of group contributions can be improved using this approach. Further, we provide guidelines based on this approach for performing systematic experiments to estimate unknown Gibbs formation energies.