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Consistent microbial dynamics and functional community patterns derived from first principles

The ISME Journal (2018) | Download Citation


Microbial communities are key engines that drive earth’s biogeochemical cycles. However, existing ecosystem models have only limited ability to predict microbial dynamics and require the calibration of multiple population-specific empirical equations. In contrast, we build on a new kinetic “Microbial Transition State” (MTS) theory of growth derived from first principles. We show how the theory coupled to simple mass and energy balance calculations provides a framework with intrinsically important qualitative properties to model microbial community dynamics. We first show how the theory can simultaneously account for the influence of all the resources needed for growth (electron donor, acceptor, and nutrients) while still producing consistent dynamics that fulfill the Liebig rule of a single limiting substrate. We also show consistent patterns of energy-dependent microbial successions in mixed culture without the need for calibration of population-specific parameters. We then show how this approach can be used to model a simplified activated sludge community. To this end, we compare MTS-derived dynamics with those of a widely used activated sludge model and show that similar growth yields and overall dynamics can be obtained using two parameters instead of twelve. This new kinetic theory of growth grounded by a set of generic physical principles parsimoniously gives rise to consistent microbial population and community dynamics, thereby paving the way for the development of a new class of more predictive microbial ecosystem models.

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  1. 1.

    Whitman WB, Coleman DC, Wiebe WJ. Prokaryotes: the unseen majority. Proc Natl Acad Sci USA. 1998;95:6578–83.

  2. 2.

    Falkowski PG, Fenchel T, Delong EF. The microbial engines that drive Earth’s biogeochemical cycles. Science. 2008;320:1034–9.

  3. 3.

    Rodríguez J, Lema JM, Kleerebezem R. Energy-based models for environmental biotechnology. Trends Biotechnol. 2008;26:366–74.

  4. 4.

    Verstraete W. Microbial ecology and environmental biotechnology. ISME J. 2007;1:4–8.

  5. 5.

    Widder S, Allen RJ, Pfeiffer T, Curtis TP, Wiuf C, Sloan WT et al. Challenges in microbial ecology: building predictive understanding of community function and dynamics. ISME J. 2016;10: 2557–68.

  6. 6.

    Monod J. The growth of bacterial cultures. Annu Rev Microbiol. 1949;3:371–94.

  7. 7.

    Contois. D. E. Kinetics of Bacterial Growth: Relationship between Population Density and Specific Growth Rate of Continuous Cultures. Journal of General Microbiology, 1959;21:40–50.

  8. 8.

    Andrews. J.F. A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates. Biotechnol Bioeng. 1968;10:707–23.

  9. 9.

    Louca S, Jacques SMS, Pires APF, Leal JS, Srivastava DS, Parfrey LW, et al. High taxonomic variability despite stable functional structure across microbial communities. Nat Ecol Evol. 2016;1:15.

  10. 10.

    Louca S, Parfrey LW, Doebeli M. Decoupling function and taxonomy in the global ocean microbiome. Science. 2016;353:1272–7.

  11. 11.

    Raes J, Letunic I, Yamada T, Jensen LJ, Bork P. Toward molecular trait-based ecology through integration of biogeochemical, geographical and metagenomic data. Mol Syst Biol. 2011;7:473–3.

  12. 12.

    Kaiser K, Wemheuer B, Korolkow V, Wemheuer F, Nacke H, Schöning I, et al. Driving forces of soil bacterial community structure, diversity, and function in temperate grasslands and forests. Sci Rep. 2016;6:33696–6.

  13. 13.

    Nelson MB, Martiny AC, Martiny JBH. Global biogeography of microbial nitrogen-cycling traits in soil. Proc Natl Acad Sci USA. 2016;113:8033–40.

  14. 14.

    Ju F, Guo F, Ye L, Xia Y, Zhang T. Metagenomic analysis on seasonal microbial variations of activated sludge from a full-scale wastewater treatment plant over 4 years. Environ Microbiol Rep. 2014;6:80–9.

  15. 15.

    De Filippis F, Genovese A, Ferranti P, Gilbert JA, Ercolini D. Metatranscriptomics reveals temperature-driven functional changes in microbiome impacting cheese maturation rate. Sci Rep. 2016;6:1–2.

  16. 16.

    Huttenhower C, Gevers D, Knight R, Abubucker S, Badger JH, Chinwalla AT, et al. Structure, function and diversity of the healthy human microbiome. Nature. 2012;486:207–14.

  17. 17.

    Hansson L. Why ecology fails at application: should we consider variability more than regularity? OIKOS. 2003;100:624–7.

  18. 18.

    Lawton JH. Are there general laws in ecology? OIKOS. 1999;84:177–92.

  19. 19.

    McGill BJ, Enquist BJ, Weiher E, Westoby M. Rebuilding community ecology from functional traits. Trends Ecol Evol. 2006;21:178–85.

  20. 20.

    Simberloff D. Community ecology: is it time to move on? (An American Society of Naturalists Presidential Address). Am Nat. 2004;163:787–99.

  21. 21.

    Odum E. P. The strategy of ecosystem development. Science, New series, 1969;164:262--70.

  22. 22.

    McCarty PL. Thermodynamics of biological synthesis and growth. Air Water Pollut. 1965;9:621–39.

  23. 23.

    Heijnen JJ, Dijken JPV. In search of a thermodynamic description of biomass yields for the chemotrophic growth of microorganisms. Biotechnol Bioeng. 1991;39:833–58.

  24. 24.

    Heijnen JJ, Kleerebezem R. Bioenergetics of microbial growth. In: Flickinger MC, editors. Encyclopedia of industrial biotechnology: bioprocess, bioseparation and cell technology. John Wiley & Sons, Inc; 2010. pp. 1–24.

  25. 25.

    McCarty PL. Thermodynamic electron equivalents model for bacterial yield prediction: modifications and comparative evaluations. Biotechnol Bioeng. 2007;97:377–88.

  26. 26.

    Roels JA. Application of macroscopic principles to microbial metabolism. Biotechnol Bioeng. 1980;103:2–59. discussion 51

  27. 27.

    von Stockar U, Liu J. Does microbial life always feed on negative entropy? Thermodynamic analysis of microbial growth. Biochim Biophys Acta. 1999;1412:191–211.

  28. 28.

    Kleerebezem R, Van Loosdrecht MCM. A generalized method for thermodynamic state analysis of environmental systems. Crit Rev Environ Sci Technol. 2010;40:1–54.

  29. 29.

    von Stockar U, Vojinović V, Maskow T, Liu J. Can microbial growth yield be estimated using simple thermodynamic analogies to technical processes? Chem Eng Process: Process Intensif. 2008;47:980–90.

  30. 30.

    Gonzalez-Cabaleiro R, Ofiteru ID, Lema JM, Rodriguez J. Microbial catabolic activities are naturally selected by metabolic energy harvest rate. ISME J. 2015;9:2630–41.

  31. 31.

    González-Cabaleiro R, Lema JM, Rodríguez J, Kleerebezem R. Linking thermodynamics and kinetics to assess pathway reversibility in anaerobic bioprocesses. Energy Environ Sci. 2013;6:3780–80.

  32. 32.

    González-Cabaleiro R, Lema JM, Rodríguez J. Metabolic energy-based modelling explains product yielding in anaerobic mixed culture fermentations. PLoS ONE. 2015;10:1–17.

  33. 33.

    Jin Q, Bethke CM. A new rate law describing microbial. Respiration. 2003;69:2340–8.

  34. 34.

    Noguera DR, Brusseau GA, Rittmann BE, Stahl DA. A unified model describing the role of hydrogen in the growth of desulfovibrio vulgaris under different environmental conditions. Biotechnol Bioeng. 1998;59: 732–746.

  35. 35.

    Hoh CY, Cord-Ruwisch R. A practical kinetic model that considers endproduct inhibition in anaerobic digestion processes by including the equilibrium constant. Biotechnol Bioeng. 1996;51:597–604.

  36. 36.

    Button DK. Nutrient uptake by microorganisms according to kinetic parameters from theory as related to cytoarchitecture. Microbiol Mol Biol Rev. 1998;62:636–45.

  37. 37.

    Liu Y. A simple thermodynamic approach for derivation of a general Monod equation for microbial growth. Biochem Eng J. 2006;31:102–5.

  38. 38.

    Desmond-Le Quéméner E, Bouchez T. A thermodynamic theory of microbial growth. ISME J. 2014;8:1747–1751.

  39. 39.

    Battley E. The development of direct and indirect methods for the study of the thermodynamics of microbial growth 1. Thermochim Acta. 1998;309:17–37.

  40. 40.

    Milo R, Phillips R. Cell biology by the number. Garland Science 2015:358.

  41. 41.

    Eyring H. The activated complex in chemical reactions. J Chem Phys. 1935;3:107–15.

  42. 42.

    Hiatt WC, Grady CPL. An updated process model for carbon oxidation, nitrification, and denitrification. Water Environ Res. 2008;80:2145–56.

  43. 43.

    Müller B, Bryant LD, Matzinger A, Wüest A. Hypolimnetic oxygen depletion in eutrophic lakes. Environ Sci Technol. 2012;46:9964–71.

  44. 44.

    Hutchinson GE. A treatise on limnology: geography, physics, and chemistry. pt. 1. Geography and physics of lakes. John Wiley & Sons Inc; 1957. p. 1016.

  45. 45.

    Boehrer B, Schultze M. Stratification lakes. Rev Geophys. 2008;46:1–27.

  46. 46.

    Hauduc H, Gillot S, Rieger L, Ohtsuki T, Shaw a, Takàcs I, et al. Activated sludge modelling in practice: an international survey. Water Sci Technol. 2009;60:1943–51.

  47. 47.

    Henze M, Grady CPL, Gujer W, Marais GVR, Matuso T. Activated sludge model no. 1. IAWQ Scientific and Technical Report No. 1; 1987.

  48. 48.

    Rössle WH, Pretorius Wa. A review of characterisation requirements for in-line prefermenters paper 2: process characterisation. Water SA. 2001;27:413–22.

  49. 49.

    Rajagopal R, Rousseau P, Bernet N, Beline F. Combined anaerobic and activated sludge anoxic/oxic treatment for piggery wastewater. Bioresour Technol. 2011;102:2185–92.

  50. 50.

    Westerhoff HV, Hellingwerf KJ, Van Dam K. Thermodynamic efficiency of microbial growth is low but optimal for maximal growth rate. Proc Natl Acad Sci USA. 1983;80:305–9.

  51. 51.

    Kovarova-Kovar K, Egli T. Growth kinetics of suspended microbial cells: from single-substrate-controlled growth to mixed-substrate kinetics. Microbiol Mol Biol Rev. 1998;62:646–66.

  52. 52.

    Droop MR. The nutrient status of algal cells in continuous culture. J Mar Biol Assoc UK. 1974;54:825.

  53. 53.

    Bajpai-Dikshit J, Suresh AK, Venkatesh KV. An optimal model for representing the kinetics of growth and product formation by Lactobacillus rhamnosus on multiple substrates. J Biosci Bioeng. 2003;96:481–86.

  54. 54.

    Bapat PM, Bhartiya S, Venkatesh KV, Wangikar PP. Structured kinetic model to represent the utilization of multiple substrates in complex media during rifamycin B fermentation. Biotechnol Bioeng. 2006;93:779–90.

  55. 55.

    Nikolajsen K, Nielsen J, Villadsen J. Structured modeling of a microbial system: III. Growth on mixed substrates. Biotechnol Bioeng. 1991;38:24–29.

  56. 56.

    Bethke CM, Sanford Ra, Kirk MF, Jin Q, Flynn TM. The thermodynamic ladder in geomicrobiology. Am J Sci. 2011;311:183–10.

  57. 57.

    González-Cabaleiro R, Ofiţeru ID, Lema JM, Rodríguez J. Microbial catabolic activities are naturally selected by metabolic energy harvest rate. ISME J. 2015;9:2630–41.

  58. 58.

    Gujer W, Morgens I, Mino T, Van Loosdrecht MCM. Activated sludge models asm1, asm2, asm2d and asm3. London: IWA Publishing; 2000.

  59. 59.

    Shammas N. Interactions of temperature, pH, and biomass on the nitrification process. Water Pollut Control Fed. 1986;58:52–59.

  60. 60.

    Meister M, Winkler D, Rezavand M, Rauch W. Integrating hydrodynamics and biokinetics in wastewater treatment modelling by using smoothed particle hydrodynamics. Comput Chem Eng. 2017;99:1–2.

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The authors thank D. Bart Haegeman for the very useful comments he made on a preliminary version of this manuscript. The authors are also grateful to Région Ile de France for funding Hadrien Delattre’s PhD in the framework of the DIM R2DS project. The authors thank the French “Agence Nationale de la Recherche” for its financial support through the “THERMOMIC” project ANR-16-CE04-0003-01.

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  1. Irstea, UR HBAN, F-92761, Antony, France

    • Hadrien Delattre
    • , Elie Desmond-Le Quéméner
    • , Christian Duquennoi
    • , Ahlem Filali
    •  & Théodore Bouchez
  2. LBE, University of Montpellier, INRA, Narbonne, France

    • Elie Desmond-Le Quéméner


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Correspondence to Théodore Bouchez.

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