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Overview of some theoretical approaches for derivation of the Monod equation

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Abstract

The Monod equation has been widely applied to describe microbial growth, but it has no mechanistic basis and is purely empirical. Extensive efforts have been dedicated to develop theoretical approaches for derivation of the Monod equation, which can be classified into three major groups, i.e., kinetic, thermodynamic, and substance transport approaches. In this review, four representative approaches are thus discussed. Due to the fact that different assumptions are made in each approach, no universal physical meaning of the Monod constant (K s) can be revealed. However, it seems that the Monod constant would be free energy-dependent and have nonequilibrium thermodynamic characteristics.

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References

  • Alexander M (1999) Biodegradation and bioremediation, 2nd edn. Academic, New York

    Google Scholar 

  • Bailey JE, Ollis DF (1986) Biochemical engineering fundamentals. McGraw-Hill, Singapore

    Google Scholar 

  • Bekins BA, Warren AE, Godsy EM (1998) A comparison of aero-order, first-order and Monod biotransformation models. Ground Water 36:261–268

    Article  CAS  Google Scholar 

  • Bitton G (1999) Wastewater microbiology. Wiley-Liss, New York

    Google Scholar 

  • Blok J (2001) A single model for mass transfer and growth for biodegradation rates in activated sludge. Ecotoxicol Environ Saf 48:148–160

    Article  CAS  Google Scholar 

  • Boudart M (1976) Consistency between kinetics and thermodynamics. J Phys Chem 80:2869–2870

    Article  CAS  Google Scholar 

  • Brady JE, Russell JW, Holum JR (2000) Chemistry: matter and its changes. Wiley, Singapore

    Google Scholar 

  • Button DK (1998) Nutrient uptake by microorganisms according to kinetic parameters from theory as related to cytoarchitecture. Microbiol Mol Biol Rev 62:636–645

    Article  CAS  Google Scholar 

  • Ferenci T (1999) Growth of bacterial cultures’ 50 years on: towards an uncertainty principle instead of constants in bacterial growth kinetics. Res Microbiol 150:431–438

    Article  CAS  Google Scholar 

  • Flickinger MC, Drew SW (1999) Encyclopedia of bioprocess technology: fermentation, biocatalysis and bioseparation. Wiley, New York

    Google Scholar 

  • Gaudy AF, Gaudy ET (1980) Microbiology for environmental scientists and engineers. McGraw-Hill, New York

    Google Scholar 

  • Grady CPL, Daigger GT, Lim HC (1999) Biological wastewater treatment. Marcel Dekker, New York

    Google Scholar 

  • Heijnen JJ, Romein B (1995) Derivation of kinetic equation for growth on single substrates based on general properties of a simple metabolic network. Biotechnol Prog 11:712–716

    Article  CAS  Google Scholar 

  • Jin Q, Bethke CM (2002) Kinetics of electron transfer through the respiratory chain. Biophys J 83:1797–1808

    Article  CAS  Google Scholar 

  • Jin Q, Bethke CM (2003) A new rate law describing microbial respiration. Appl Environ Microbiol 69:2340–2348

    Article  CAS  Google Scholar 

  • Kovarova-Kovar K, Egli T (1998) Growth kinetics of suspended microbial cells: from single-substrate-controlled growth to mixed-substrate kinetics. Microbiol Mol Biol Rev 62:646–666

    Article  CAS  Google Scholar 

  • Merchuk JC, Asenjo JA (1995) The Monod equation and mass transfer. Biotechnol Bioeng 45:91–94

    Article  CAS  Google Scholar 

  • Monod J (1949) The growth of bacterial cultures. Annu Rev Microbiol 3:371–394

    Article  CAS  Google Scholar 

  • Rittmann B, McCarty P (2001) Environmental biotechnology: principles and applications. McGraw Hill, New York

    Google Scholar 

  • Roels JA (1983) Energetics and kinetics in biotechnology. Elsevier, New York

    Google Scholar 

  • Russell JB (1993) Effect of amino acids on the heat production and growth efficiency of Streptococcus bovis: balance of anabolic and catabolic rates. Appl Environ Microbiol 59:1747–1751

    Article  CAS  Google Scholar 

  • Shulter ML, Kargi F (2002) Bioprocess engineering: basic concepts. Prentice Hall PTR, Englewood Cliffs

    Google Scholar 

  • Tan Y, Wang ZX, Schneider RP, Marshall KC (1994) Modelxling microbial growth: a statistical thermodynamic approach. J Biotechnol 32:97–106

    Article  Google Scholar 

  • Westerhoff HV, Lolkema JS, Otto R, Hellingwerf KJ (1982) Thermodynamics of growth. Non-equilibrium thermodynamics of bacterial growth. The phenomenological and the mosaic approach. Biochim Biophys Acta 683:181–220

    Article  CAS  Google Scholar 

Download references

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  1. Division of Environmental and Water Resource Engineering, School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Yu Liu

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  1. Yu Liu
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Correspondence to Yu Liu.

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Liu, Y. Overview of some theoretical approaches for derivation of the Monod equation. Appl Microbiol Biotechnol 73, 1241–1250 (2007). https://doi.org/10.1007/s00253-006-0717-7

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  • DOI: https://doi.org/10.1007/s00253-006-0717-7

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