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An upper limit on Gibbs energy dissipation governs cellular metabolism

Nature Metabolism volume 1, pages 125–132 (2019)Cite this article

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Abstract

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.

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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 (https://doi.org/10.5281/zenodo.1401220).

References

  1. Molenaar, D., Van Berlo, R., De Ridder, D. & Teusink, B. Shifts in growth strategies reflect tradeoffs in cellular economics. Mol. Syst. Biol. 5, 323 (2009).

  2. Basan, M. et al. Overflow metabolism in Escherichia coli results from efficient proteome allocation. Nature 528, 99–104 (2015).

    Article  CAS  Google Scholar 

  3. Rozpędowska, E. et al. Parallel evolution of the make–accumulate–consume strategy in Saccharomyces and Dekkera yeasts. Nat. Commun. 2, 302 (2011).

  4. Beg, Q. K. et al. Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity. Proc. Natl Acad. Sci. USA 104, 12663–12668 (2007).

    Article  CAS  Google Scholar 

  5. Zhuang, K., Vemuri, G. N. & Mahadevan, R. Economics of membrane occupancy and respiro-fermentation. Mol. Syst. Biol. 7, 500–500 (2014).

    Article  Google Scholar 

  6. Koppenol, W. H., Bounds, P. L. & Dang, C. V. Otto Warburg’s contributions to current concepts of cancer metabolism. Nat. Rev. Cancer 11, 325–337 (2011).

    Article  CAS  Google Scholar 

  7. Vander Heiden, M. G., Cantley, L. C. & Thompson, C. B. Understanding the Warburg effect: the metabolic requirements of cell proliferation. Science 324, 1029–1033 (2009).

    Article  Google Scholar 

  8. Mori, M., Hwa, T., Martin, O. C., De Martino, A. & Marinari, E. Constrained allocation flux balance analysis. PLoS Comput. Biol. 12, e1004913 (2016).

    Article  Google Scholar 

  9. Sánchez, B. J. et al. Improving the phenotype predictions of a yeast genome-scale metabolic model by incorporating enzymatic constraints. Mol. Syst. Biol. 13, 935 (2017).

    Article  Google Scholar 

  10. Zabalza, A. et al. Regulation of respiration and fermentation to control the plant internal oxygen concentration. Plant Physiol. 149, 1087–1098 (2009).

    Article  CAS  Google Scholar 

  11. Huberts, D. H. E. W., Niebel, B. & Heinemann, M. A flux-sensing mechanism could regulate the switch between respiration and fermentation. FEMS Yeast. Res. 12, 118–128 (2012).

    Article  CAS  Google Scholar 

  12. von Bertalanffy, L. The theory of open systems in physics and biology. Science 111, 23–29 (1950).

    Article  Google Scholar 

  13. von Stockar, U. Biothermodynamics of live cells: a tool for biotechnology and biochemical engineering. J. Non-equilib. Thermodyn. 35, 415–475 (2010).

    Google Scholar 

  14. Lewis, N. E., Nagarajan, H. & Palsson, B. O. Constraining the metabolic genotype–phenotype relationship using a phylogeny of in silico methods. Nat. Rev. Microbiol. 10, 291–305 (2012).

    Article  CAS  Google Scholar 

  15. Jol, S. J., Kümmel, A., Hatzimanikatis, V., Beard, D. A. & Heinemann, M. Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks. Biophys. J. 99, 3139–3144 (2010).

    Article  CAS  Google Scholar 

  16. Alberty, R. A. et al. Recommendations for terminology and databases for biochemical thermodynamics. Biophys. Chem. 155, 89–103 (2011).

    Article  CAS  Google Scholar 

  17. Canelas, A. B., Ras, C., ten Pierick, A., van Gulik, W. M. & Heijnen, J. J. An in vivo data-driven framework for classification and quantification of enzyme kinetics and determination of apparent thermodynamic data. Metab. Eng. 13, 294–306 (2011).

    Article  CAS  Google Scholar 

  18. Noor, E., Haraldsdóttir, H. S., Milo, R. & Fleming, R. M. T. Consistent estimation of Gibbs energy using component contributions. PLoS Comput. Biol. 9, e1003098 (2013).

    Article  CAS  Google Scholar 

  19. Beard, Da, Liang, S. & Qian, H. Energy balance for analysis of complex metabolic networks. Biophys. J. 83, 79–86 (2002).

    Article  CAS  Google Scholar 

  20. Price, N. D., Famili, I., Beard, D. A. & Palsson, B. Ø. Extreme pathways and Kirchhoff’s second law. Biophys. J. 83, 2879–2882 (2002).

    Article  CAS  Google Scholar 

  21. Misener, R. & Floudas, C. A. ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations. J. Glob. Optim. 59, 503–526 (2014).

    Article  Google Scholar 

  22. Schuetz, R., Kuepfer, L. & Sauer, U. Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol. Syst. Biol. 3, 119 (2007).

    Article  Google Scholar 

  23. Reed, J. L., Vo, T. D., Schilling, C. H. & Palsson, B. O. An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR). Genome. Biol. 4, R54 (2003).

    Article  Google Scholar 

  24. Vemuri, G. N., Altman, E., Sangurdekar, D. P., Khodursky, A. B. & Eiteman, M. A. Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio. Appl. Environ. Microbiol. 72, 3653–3661 (2006).

    Article  CAS  Google Scholar 

  25. You, C. et al. Coordination of bacterial proteome with metabolism by cyclic AMP signalling. Nature 500, 301–306 (2013).

    Article  CAS  Google Scholar 

  26. Schuetz, R., Zamboni, N., Zampieri, M., Heinemann, M. & Sauer, U. Multidimensional Optimality of Microbial Metabolism. Science 336, 601–604 (2012).

    Article  CAS  Google Scholar 

  27. Kümmel, A., Panke, S. & Heinemann, M. Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data. Mol. Syst. Biol. 2, 2006.0034 (2006).

    Article  Google Scholar 

  28. Henry, C. S., Broadbelt, L. J. & Hatzimanikatis, V. Thermodynamics-based metabolic flux analysis. Biophys. J. 92, 1792–1805 (2007).

    Article  CAS  Google Scholar 

  29. Fleming, R. M. T., Thiele, I. & Nasheuer, H. P. Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli. Biophys. Chem. 145, 47–56 (2009).

    Article  CAS  Google Scholar 

  30. Bennett, B. D. et al. Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat. Chem. Biol. 5, 593–599 (2009).

    Article  CAS  Google Scholar 

  31. Bordel, S. & Nielsen, J. Identification of flux control in metabolic networks using non-equilibrium thermodynamics. Metab. Eng. 12, 369–377 (2010).

    Article  CAS  Google Scholar 

  32. Noor, E. et al. Pathway thermodynamics highlights kinetic obstacles in central metabolism. PLoS Comput. Biol. 10, e1003483 (2014).

    Article  Google Scholar 

  33. Schrödinger, E. What Is Life? The Physical Aspect of the Living Cell (Cambridge Univ. Press, 1944).

  34. Okabe, K. et al. Intracellular temperature mapping with a fluorescent polymeric thermometer and fluorescence lifetime imaging microscopy. Nat. Commun. 3, 705 (2012).

    Article  Google Scholar 

  35. Lane, N. Hot mitochondria? PLoS Biol. 16, e2005113 (2018).

    Article  Google Scholar 

  36. Baffou, G., Rigneault, H., Marguet, D. & Jullien, L. A critique of methods for temperature imaging in single cells. Nat. Methods 11, 899–901 (2014).

    Article  CAS  Google Scholar 

  37. Weber, J. K., Shukla, D. & Pande, V. S. Heat dissipation guides activation in signaling proteins. Proc. Natl. Acad. Sci. USA 112, 10377–10382 (2015).

    Article  CAS  Google Scholar 

  38. Slochower, D. R. & Gilson, M. K. Motor-like properties of nonmotor enzymes. Biophys J. 114, 2174–2179 (2018).

    Article  CAS  Google Scholar 

  39. Riedel, C. et al. The heat released during catalytic turnover enhances the diffusion of an enzyme. Nature 517, 227–230 (2014).

    Article  Google Scholar 

  40. Golestanian, R. Anomalous diffusion of symmetric and asymmetric active colloids. Phys. Rev. Lett. 102, 188305 (2009).

    Article  Google Scholar 

  41. Gallet, F., Arcizet, D., Bohec, P. & Richert, A. Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence. Soft Matter 5, 2947 (2009).

    Article  CAS  Google Scholar 

  42. Milstein, J. N., Chu, M., Raghunathan, K. & Meiners, J. C. Two-color DNA nanoprobe of intracellular dynamics. Nano. Lett. 12, 2515–2519 (2012).

    Article  CAS  Google Scholar 

  43. Weber, S. C., Spakowitz, A. J. & Theriot, J. A. Nonthermal ATP-dependent fluctuations contribute to the in vivo motion of chromosomal loci. Proc. Natl Acad. Sci. USA 109, 7338–7343 (2012).

    Article  CAS  Google Scholar 

  44. Chen, Y.-F., Milstein, J. N. & Meiners, J.-C. Protein-mediated DNA loop formation and breakdown in a fluctuating environment. Phys. Rev. Lett. 104, 258103 (2010).

    Article  Google Scholar 

  45. Milstein, J. N. & Meiners, J.-C. On the role of DNA biomechanics in the regulation of gene expression. J. R. Soc. Interface 8, 1673–1681 (2011).

    Article  CAS  Google Scholar 

  46. Kochanowski, K. et al. Functioning of a metabolic flux sensor in Escherichia coli. Proc. Natl Acad. Sci. USA 110, 1130–1135 (2013).

    Article  CAS  Google Scholar 

  47. Nilsson, A., Nielsen, J. & Palsson, B. O. Metabolic models of protein allocation call for the kinetome. Cell Syst. 5, 538–541 (2017).

    Article  CAS  Google Scholar 

  48. Burgard, A. P., Nikolaev, E. V., Schilling, C. H. & Maranas, C. D. Flux coupling analysis of genome-scale metabolic network reconstructions. Genome Res. 14, 301–312 (2004).

    Article  CAS  Google Scholar 

  49. Drud, A. S. CONOPT—A large-scale GRG code. ORSA J. Comput. 6, 207–216 (1994).

    Article  Google Scholar 

  50. Hastie, T. J., Tibshirani, R. & Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer-Verlag New York, 2011).

  51. Schellenberger, J., Lewis, N. E. & Palsson, B. Ø. Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys. J. 100, 544–553 (2011).

    Article  CAS  Google Scholar 

  52. van Hoek, P. et al. Effects of pyruvate decarboxylase overproduction on flux distribution at the pyruvate branch point in Saccharomyces cerevisiae. Appl. Environ. Microbiol. 64, 2133–2140 (1998).

    PubMed  PubMed Central  Google Scholar 

  53. Kümmel, A. et al. Differential glucose repression in common yeast strains in response to HXK2 deletion. FEMS Yeast. Res. 10, 322–332 (2010).

    Article  Google Scholar 

  54. van Winden, W. et al. Metabolic-flux analysis of CEN.PK113-7D based on mass isotopomer measurements of C-labeled primary metabolites. FEMS Yeast. Res. 5, 559–568 (2005).

    Article  Google Scholar 

  55. Fendt, S.-M. & Sauer, U. Transcriptional regulation of respiration in yeast metabolizing differently repressive carbon substrates. BMC Syst. Biol. 4, 12 (2010).

    Article  Google Scholar 

  56. Gombert, A. K., Moreira dos Santos, M., Christensen, B. & Nielsen, J. Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression. J. Bacteriol. 183, 1441–1451 (2001).

    Article  CAS  Google Scholar 

  57. Frick, O. & Wittmann, C. Characterization of the metabolic shift between oxidative and fermentative growth in Saccharomyces cerevisiae by comparative 13C flux analysis. Microb. Cell. Fact. 4, 30 (2005).

    Article  Google Scholar 

  58. Perrenoud, A. & Sauer, U. Impact of global transcriptional regulation by ArcA, ArcB, Cra, Crp, Cya, Fnr, and Mlc on glucose catabolism in Escherichia coli. J. Bacteriol. 187, 3171–3179 (2005).

    Article  CAS  Google Scholar 

  59. Valgepea, K. et al. Systems biology approach reveals that overflow metabolism of acetate in Escherichia coli is triggered by carbon catabolite repression of acetyl-CoA synthetase. BMC Syst. Biol. 4, 166 (2010).

    Article  CAS  Google Scholar 

  60. Nanchen, A., Schicker, A. & Sauer, U. Nonlinear dependency of intracellular fluxes on growth rate in miniaturized continuous cultures of Escherichia coli. Appl. Environ. Microbiol. 72, 1164–1172 (2006).

    Article  CAS  Google Scholar 

  61. Peebo, K. et al. Proteome reallocation in Escherichia coli with increasing specific growth rate. Mol. BioSyst. 11, 1184–1193 (1184).

    Article  Google Scholar 

  62. Gerosa, L. et al. Pseudo-transition analysis identifies the key regulators of dynamic metabolic adaptations from steady-state data. Cell Syst. 1, 270–282 (2015).

    Article  CAS  Google Scholar 

  63. Schmidt, A. et al. The quantitative and condition-dependent Escherichia coli proteome. Nat. Biotechnol. 34, 104–110 (2015).

    Article  Google Scholar 

  64. Scott, M. et al. Emergence of robust growth laws from optimal regulation of ribosome synthesis. Mol. Syst. Biol. 10, 747 (2014).

    Article  Google Scholar 

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Acknowledgements

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.

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  1. These authors contributed equally: B. Niebel, S. Leupold.

Authors and Affiliations

  1. Molecular Systems Biology, Groningen Biomolecular Sciences and Biotechnology Institute, University of Groningen, Groningen, The Netherlands

    Bastian Niebel, Simeon Leupold & Matthias Heinemann

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  1. Bastian Niebel
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Contributions

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.

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Correspondence to Matthias Heinemann.

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Supplementary Text and Figures

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

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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). https://doi.org/10.1038/s42255-018-0006-7

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