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An upper limit on Gibbs energy dissipation governs cellular metabolism


The principles governing cellular metabolic operation are poorly understood. Because diverse organisms show similar metabolic flux patterns, we hypothesized that a fundamental thermodynamic constraint might shape cellular metabolism. Here, we develop a constraint-based model for Saccharomyces cerevisiae with a comprehensive description of biochemical thermodynamics including a Gibbs energy balance. Non-linear regression analyses of quantitative metabolome and physiology data reveal the existence of an upper rate limit for cellular Gibbs energy dissipation. By applying this limit in flux balance analyses with growth maximization as the objective function, our model correctly predicts the physiology and intracellular metabolic fluxes for different glucose uptake rates as well as the maximal growth rate. We find that cells arrange their intracellular metabolic fluxes in such a way that, with increasing glucose uptake rates, they can accomplish optimal growth rates but stay below the critical rate limit on Gibbs energy dissipation. Once all possibilities for intracellular flux redistribution are exhausted, cells reach their maximal growth rate. This principle also holds for Escherichia coli and different carbon sources. Our work proposes that metabolic reaction stoichiometry, a limit on the cellular Gibbs energy dissipation rate, and the objective of growth maximization shape metabolism across organisms and conditions.

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Fig. 1: Overview of workflow and model.
Fig. 2: Rate of cellular Gibbs energy dissipation does not exceed an upper limit.
Fig. 3: Accurate predictions of cellular physiology with flux balance analysis using the combined thermodynamic and stoichiometric model constrained by gdisslim.
Fig. 4: Accurate predictions of intracellular fluxes with flux balance analysis using the model constrained by gdisslim.
Fig. 5: Predictive capabilities of flux balance analysis using the genome-scale combined thermodynamic and stoichiometric model of E. coli constrained by gdisslim.
Fig. 6: Cells redistribute flux to avoid critical Gibbs energy dissipation rates.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. The code is available from the corresponding author upon request and the code to perform the flux balance analyses is deposited on GitHub (


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This work was funded by the Netherlands Organisation for Scientific Research (NWO) through the Systems Biology Centre for Metabolism and Ageing (Groningen), and by the BE-Basic R&D Program, which was granted as FES subsidy from the Dutch Ministry of Economic Affairs, Agriculture and Innovation (EL&I). We thank A. Canelas for sharing raw data, E. Noor for help with the component contribution method, E. Wit for statistics advice, G. Zampar for helpful discussions and B. Bakker, A. Bardow, D. Huberts, A. Ortega, U. Sauer, S. Stratmann and J. Radzikowski for helpful comments on the manuscript.

Author information




B.N., S.L. and M.H. designed the study. B.N. and M.H. developed the concept. B.N. developed and implemented the model for S. cerevisiae. S.L. developed and implemented the model for E. coli. B.N. and S.L. carried out the simulations, analysed the data, and made the figures. B.N., S.L. and M.H. wrote the manuscript.

Corresponding author

Correspondence to Matthias Heinemann.

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The authors declare no competing interests.

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Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–18, Supplementary Methods 1–3 and Supplementary Notes 1 and 2

Reporting Summary

Supplementary Data 1

Model for S. cerevisiae

Supplementary Data 2

Model for E. coli

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Niebel, B., Leupold, S. & Heinemann, M. An upper limit on Gibbs energy dissipation governs cellular metabolism. Nat Metab 1, 125–132 (2019).

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  • Gibbs Energy Dissipation
  • Glucose Uptake Rate (GURs)
  • Flux Balance Analysis (FBA)
  • Quantitative Metabolomics
  • Stoichiometric Network Model

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