Stoichiometric models and flux balance analysis, or FBA, have become workhorses of modern metabolism research. These models describe the full network of biochemical reactions inside an organism, from bacteria to yeast to plant cells, and allow researchers to compute how fluxes of matter flow through metabolism. They have been used to identify essential genes, discover metabolic engineering targets, and probe the fundamental logic of growth. But FBA has a well-known weakness: its predictions are only as good as the constraints fed into it. Without thermodynamic grounding, the method can permit reaction directions that are physically impossible, generating flux distributions that no real cell could ever sustain.

Thermodynamic constraints solve this problem in principle, by demanding that every reaction proceed only in the direction of negative Gibbs energy, in accordance with the second law of thermodynamics. Implementing them, however, has historically demanded painstaking manual curation: balancing protons and charges, estimating Gibbs formation energies, and defining the exact species of each metabolite transported across membranes. Existing tools such as pyTFA, multiTFA, probabilistic thermodynamic analysis, ThermOptCobra, and ETGEM addressed parts of this challenge, but none offered a fully systematic workflow that handles charge balancing, transporter thermodynamics, and uncertain Gibbs energy estimates together. Thermo-Flux was designed to close that gap.

The package operates through a seven-step workflow. First, users define the physical and biochemical parameters of each subcellular compartment, including pH, magnesium concentration, ionic strength, temperature, and membrane potential differences. Second, every metabolite in the model is linked to its chemical structure through the eQuilibrator database, using annotations ranging from InChI notations to KEGG or BiGG identifiers. From acid dissociation constants calculated with ChemAxon, the software determines how each metabolite distributes among its protonation species. Crucially, Thermo-Flux merges these species into a single reactant with average protonation and charge states, which can be non-integer values. At pH 7, for example, inorganic phosphate behaves as a reactant carrying an average of 1.2 protons and a charge of minus 1.8, a subtlety that conventional models routinely overlook.

Next, the package calculates standard Gibbs formation energies for all metabolites using the component contribution method, which decomposes compounds into chemical groups with known energetics. Because cells do not live at standard conditions, Thermo-Flux applies a Legendre transformation to correct for constant pH and the extended Debye-Hückel equation to correct for ionic strength, yielding transformed formation energies together with their uncertainties. These uncertainties are carried through the entire model as correlated, multivariate confidence intervals, ensuring that errors in one reaction’s energetics remain statistically consistent with those of its neighbors rather than being treated as independent numbers.

Transport reactions receive particularly careful treatment. Transporter proteins are often specific to a single protonation species of a metabolite, and the Gibbs energy of moving that species across a membrane depends on pH gradients, membrane potentials, and the number of charges translocated. When experimental information is lacking, Thermo-Flux assumes the most abundant species in the inner compartment is the one transported, then computes the protons bound or released as species equilibrate on each side of the membrane. The package also generates transporter variants, including charge-neutral forms that couple metabolite movement to proton symport, preventing the model from being over-constrained. A pseudo-metabolite representing electrical charge is introduced into the stoichiometric matrix so that net charge movement across every membrane must balance out, satisfying the steady-state assumption that membrane potentials remain constant.

With Gibbs reaction energies in hand, the final step imposes the second law directly into the optimization problem: only reactions with negative Gibbs energy may carry flux in the forward direction. Because both fluxes and Gibbs energies are variables, this constraint is bilinear and renders the solution space non-convex, increasing computational cost, but it rigorously eliminates thermodynamically infeasible cycles. The framework also supports an upper limit on the total cellular Gibbs energy dissipation rate, a constraint that previous work by the same group linked to overflow metabolism, the phenomenon in which cells excrete valuable carbon such as ethanol even when oxygen is plentiful.

To demonstrate scalability, the researchers ran all 107 stoichiometric models from the BiGG database through the pipeline. Thermo-Flux automatically converted 87 of them, or 77 percent, spanning organisms from bacteria to eukaryotes, with minimal manual intervention. Most failures traced back to defects in the original models themselves: missing biomass equations, incomplete annotations, reactions spanning more than three compartments, or transport reactions coupled to chemical transformations, such as those mediated by the bacterial phosphotransferase system. Of the converted models, 82 still supported biomass production under thermodynamic constraints, showing that adding physical realism does not break metabolic functionality.

The predictive payoff was striking. When the team converted an Escherichia coli model with 623 reactions and confronted it with physiological and metabolome data, flux variability analysis revealed that several predefined reaction directions in the original reconstruction were incorrect, and incorporating metabolite concentration data narrowed feasible flux ranges for roughly eight percent of reactions. For the yeast Saccharomyces cerevisiae, a fully parameterized thermodynamic-stoichiometric version of the genome-scale model iMM904, equipped with the Gibbs dissipation limit of 3700 joules per gram dry weight per hour, accurately reproduced experimental extracellular fluxes across a range of glucose uptake rates, including the onset of overflow metabolism, a phenotype fundamentally out of reach for standard FBA.

The authors anticipate that Thermo-Flux will serve both fundamental and applied research. By linking flux predictions explicitly to pH, ionic strength, temperature, and membrane potential, the tool opens the door to systematic sensitivity analyses of proton- and charge-coupled pathways, genome-scale tests of thermodynamic principles such as yield-growth trade-offs and maximum-minimum driving force analysis, and refined estimation of Gibbs energies by regression against experimental data. On the applied side, biotechnologists could use the framework to expose thermodynamic bottlenecks in engineered pathways before a single experiment is run. Limitations remain, notably the reliance of Gibbs energy estimates on aqueous-phase data that poorly captures membrane-bound compounds or extremophile conditions, but the authors argue that incorporating newer molecular thermodynamic models will progressively extend the tool’s reach. For a field that has long treated the second law of thermodynamics as an inconvenient complication, Thermo-Flux makes it what it should have been all along: a foundation.

Subject of Research: Semi-automated generation and analysis of thermodynamic-stoichiometric metabolic network models

Article Title: Thermo-flux: generation and analysis of thermodynamic-stoichiometric metabolic network models

Article References: Smith, E. N., Fargier, N., Losa, J., & Heinemann, M. (2026). Thermo-flux: generation and analysis of thermodynamic-stoichiometric metabolic network models. Molecular Systems Biology. https://doi.org/10.1038/s44320-026-00227-4

Image Credits: AI Generated

DOI: 10.1038/s44320-026-00227-4

Keywords: Thermo-Flux, metabolic modeling, flux balance analysis, thermodynamics, Gibbs energy, stoichiometric models, genome-scale models, transporter thermodynamics, overflow metabolism, systems biology, Saccharomyces cerevisiae, Escherichia coli