Theory and applications of unstructured growth models: Kinetic and energetic aspects

Microbial kinetics and energetics are discussed in connection with the formulation of unstructured growth models. The development of microbial energetics and the use of macroscopic methods in the study of microbial growth are briefly evaluated. The general approach to the modelling of microbial growth has been critically discussed and a strategy for the formulation of unstructured models is presented. A simple unstructured model based on Monod kinetics and the linear relation for substrate consumption is evaluated with reference to extensive experimental and simulation data obtained in batch, fed‐batch, and continuous cultivation modes. Choice for a kinetic expression is discussed and has been shown not to be critical in most situations. It is shown that during growth in batch mode, the behavior of the system is rigidly fixed by the kinetic parameter: the maximum specific growth rate. The energetic parameters have minimal influence. In continuous cultivation the behavior is fixed by the energetic parameters: the maximum yield and the coefficient of maintenance. Implications of these observations have also been discussed. The linear relation for substrate consumption is tested with continuous culture data. It is shown that significant deviations at low growth rates cannot be fully accounted by the loss of viability. The situations where unstructured models will be adequate or not for system description, are evaluated and checked experimentally. Influence of an environmental factor, the temperature, on the unstructured model parameters is also quantitatively described. It is concluded that the art of unstructured model building has already reached its maturity and that now much effort should be channelled into the development and verification of structured models.

[1]  N. W. F. Kossen,et al.  Fed‐batch culture: Modeling and application in the study of microbiol energetics , 1981 .

[2]  N. Kossen,et al.  Carbon dioxide hold‐up as a source of error in batch‐culture calculations , 1980 .

[3]  Willy Verstraete,et al.  Comparison of maximum cell yield and maintenance coefficients in axenic cultures and activated sludge communities , 1978 .

[4]  David Mautner Himmelblau,et al.  Process analysis by statistical methods , 1970 .

[5]  J. A. Roels,et al.  Simple model for the energetics of growth on substrates with different degrees of reduction , 1980 .

[6]  James E. Bailey,et al.  Measurement of structured microbial population dynamics by flow microfluorometry , 1978 .

[7]  N. W. F. Kossen,et al.  On the statistical analysis of batch data , 1981 .

[8]  S Nagai,et al.  Fed batch culture of Saccharomyces cerevisiae: A perspective of computer control to enhance the productivity in baker's yeast cultivation , 1976, Biotechnology and bioengineering.

[9]  F. Incropera,et al.  The effect of temperature control on biological wastewater treatment processes , 1978 .

[10]  S. Pirt,et al.  The theory of fed batch culture with reference to the penicillin fermentation , 1974 .

[11]  I. Minkevich,et al.  Time scale in the dynamics of continuous cultivation of microorganisms , 1979 .

[12]  A A Esener,et al.  Modeling of bacterial growth; Formulation and evaluation of a structured model , 1982, Biotechnology and bioengineering.

[13]  N. Kossen,et al.  Volume changes during fermentation processes due to gas exchange. , 1982, Biotechnology and bioengineering.

[14]  Allen G. Marr,et al.  THE MAINTENANCE REQUIREMENT OF ESCHERICHIA COLI , 1963 .

[15]  C. W. Jones,et al.  The effect of temperature on the molar growth yield and maintenance requirement of Escherichia coli W during aerobic growth in continuous culture , 1976, FEBS letters.

[16]  Tsuneo Yamane,et al.  Fed‐batch hydrocarbon fermentation with colloidal emulsion feed , 1973 .

[17]  I. Watanabe,et al.  EFFECTS OF TEMPERATURE ON GROWTH RATE OF CULTURED MAMMALIAN CELLS (L5178Y) , 1967, The Journal of cell biology.

[18]  Shigeki Hirano,et al.  Semi-batch Culture of Microorganisms with Constant Feed of Substrate : A Methematical Simulation : Kinetic Studies on Fed-batch Cultures(III) , 1977 .

[19]  A. H. Stouthamer,et al.  Utilization of energy for growth and maintenance in continuous and batch cultures of microorganisms. A reevaluation of the method for the determination of ATP production by measuring molar growth yields. , 1973, Biochimica et biophysica acta.

[20]  J A Roels,et al.  A quantitative description of the growth of Saccharomyces cerevisiae CBS 426 on a mixed substrate of glucose and ethanol , 1980, Biotechnology and bioengineering.

[21]  N. Kossen,et al.  The influence of temperature on the energetics of Klebsiella pneumoniae. , 1983, Biotechnology and bioengineering.

[22]  J. E. Bailey,et al.  Bacterial population dynamics in batch and continuous-flow microbial reactors , 1981 .

[23]  N. W. F. Kossen,et al.  The influence of temperature on the maximum specific growth rate of Klebsiella pneumoniae , 1981 .

[24]  A. F. Gaudy,et al.  Response of biological waste treatment systems to changes in salt concentrations , 1968 .

[25]  C. G. Sinclair,et al.  Temperature relationship in continuous culture , 1971 .

[26]  F. F. Blackman.  Optima and Limiting Factors , 1905 .

[27]  S. Pirt.  The maintenance energy of bacteria in growing cultures , 1965, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[28]  J. A. Roels,et al.  Method for the statistical treatment of elemental and energy balances with application to steady‐state continuous‐culture growth of saccharomyces cerevisiae CBS 426 in the respiratory region , 1980 .

[29]  Tsuneo Yamane,et al.  Start‐up of chemostat: Application of fed‐batch culture , 1979 .

[30]  Michael L. Shuler,et al.  Generalized differential specific rate equation for microbial growth , 1979 .

[31]  J. Monod,et al.  Genetic regulatory mechanisms in the synthesis of proteins. , 1961, Journal of molecular biology.

[32]  E. Schrödinger.  What Is Life , 1946 .

[33]  E. Gaudy,et al.  Sequential substrate removal by activated sludge after a change in salt concentration , 1966 .

[34]  Michael A. Savageau,et al.  Growth equations: A general equation and a survey of special cases , 1980 .

[35]  W. Payne,et al.  Energy yields and growth of heterotrophs. , 1970, Annual review of microbiology.

[36]  H. M. Tsuchiya,et al.  Mathematical Models for Fermentation Processes , 1970 .

[37]  Anthony F. Gaudy,et al.  Microbiology for environmental scientists and engineers , 1981 .

[38]  J. Changeux,et al.  ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. , 1965, Journal of molecular biology.

[39]  R. Keller,et al.  Computer simulation of the biomass production rate of cyclic fed batch continuous culture , 1978 .

[40]  L. Erickson.  Energetic efficiency of biomass and product formation , 1979 .

[41]  W. Hempfling,et al.  Effects of growth temperature on yield and maintenance during glucose-limited continuous culture of Escherichia coli , 1976, Journal of bacteriology.

[42]  N. Kossen,et al.  Dependence of the element composition of K. pneumoniae on the steady-state specific growth rate. , 1982, Biotechnology and bioengineering.

[43]  A. L. Koch,et al.  Overall controls on the biosynthesis of ribosomes in growing bacteria. , 1970, Journal of theoretical biology.

[44]  D. Koshland,et al.  Comparison of experimental binding data and theoretical models in proteins containing subunits. , 1966, Biochemistry.

[45]  J J Heijnen,et al.  Application of balancing methods in modeling the penicillin fermentation , 1979, Biotechnology and bioengineering.

[46]  H. E. Umbarger,et al.  Evidence for a negative-feedback mechanism in the biosynthesis of isoleucine. , 1956, Science.

[47]  H C Lim,et al.  An analysis of extended and exponentially‐fed‐batch cultures , 1977, Biotechnology and bioengineering.

[48]  Tsuneo Yamane,et al.  A Simple Optimization Technique for Fed-batch Culture : Kinetic Studies on Fed-batch Cultures (VI) , 1977 .

[49]  J. J. Heijnen,et al.  A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes , 1981 .

[50]  Shigeki Hirano,et al.  Semi-batch Culture of Microorganisms with Constant Feed of Substrate : An Experimental Study : Kinetic Studies on Fed-batch Cultures (V) , 1977 .

[51]  J. Senez.  Some considerations on the energetics of bacterial growth. , 1962, Bacteriological reviews.

[52]  S. John Pirt.  FED‐BATCH CULTURE OF MICROBES , 1979 .

[53]  Irving J. Dunn,et al.  ANALYSIS OF FED‐BATCH MICROBIAL CULTURE , 1979 .

[54]  T. G. Watson,et al.  Effects of sodium chloride on steady-state growth and metabolism of Saccharomyces cerevisiae. , 1970, Journal of general microbiology.

[55]  I. Pastan,et al.  Cyclic Adenosine Monophosphate in Bacteria , 1970, Science.