Contributions to the Theory of the Continuous Bacterial Growth Apparatus

Moser, H.

doi:10.1073/pnas.43.2.222

Cited by 16 publications

(4 citation statements)

References 2 publications

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“…where the symbols are as defined previously. Equation 5 is analogous to e(uation 2 and the system of equations 1, 3, and 5 may be solved by the method Moser (1957) employed for solving the system of equations 1, 2, and 3. This solution, which will not be detailed here for the sake of brevity, proves that a stable equilibrium condition exists for this type of culture.…”

Section: Pipesmentioning

confidence: 99%

“…where a is a constant (AMonod, 1949). 281 Moser (1957) solved the system of simultaneous equations 1, 2, and 3 and showed that at equilibrium N = Q(a-c) (4) For this solution it was assumed that Q is independent of c. If c is small enough that it may be neglected in comparison with a, then N is approximately equal to Qa and thus independent of dilution rate. In general, the nutrient limiting growth in a continuous culture does not have to be supplied in the feed medium but may be supplied at a rate which is independent of the medium feed rate.…”

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confidence: 99%

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Carbon Dioxide-Limited Growth of Chlorella in Continuous Culture1

Pipes¹

1962

Applied Microbiology

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P)IPES, W. 0. (Northwestern Technological Institute, Evanston, Ill.). Carbon dioxide-limited growth of Chlorella in continuous culture. 1962.-The original mathematical model of microbial growth in the Chemostat is modified to describe continuous cultures in which the limiting nutrient is supplied at a rate independent of the dilution rate. The application of this model to continuous Chlorella cultures in which CO2 is the factor limiting growth is discussed. The conclusions from the model are: (i) at a constant rate of CO2 supply, the equilibrium population density is directly proportional to the retention time; and (ii) the production rate is directly proportional to the rate of CO2 supply. Experimental data are presented to verify the theoretical conclusions. on July 11, 2020 by guest http://aem.asm.org/ Downloaded from 1962] 287i on July 11, 2020 by guest http://aem.asm.org/ Downloaded from

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Section: Pipesmentioning

confidence: 99%

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confidence: 99%

Carbon Dioxide-Limited Growth of Chlorella in Continuous Culture1

Pipes¹

1962

Applied Microbiology

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“…Specific applications of the theory to continuous chemical reactions and continuous culture have also been published by Denbigh (1944Denbigh ( , 1947, Monod (1950) ~ Novick & Szilard (1950), Danckwerts (1954), Denbigh & Page (1954), Spicer (1955), Herbert, Elsworth & Telling (1956), Perret (1956Perret ( , 1957) and Moser (1957). The initial section of this paper starts with a non-mathematical description of the properties of simple open systems, based on the publications cited above (particularly those of Burton, 1939 andDenbigh et al 1948).…”

Section: Open Systemsmentioning

confidence: 99%

A New Kinetic Model of a Growing Bacterial Population

Perret

1960

Journal of General Microbiology

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SUMMARY:A chemical open system of fixed volume in a constant environment tends towards a steady s t a t e in which its mass remains unchanged. Such a system is not a satisfactory kinetic model of a growing bacterial population, which increases its mass and volume, or grows, logarithmically, in a constant environment. However, when the material limiting the volume of an open system is itself one of the dynamic components the system can then grow logarithmically of its own accord. If the surface-area-to-volume ratio of such an 'expanding system' remains unchanged logarithmic growth can continue indefinitely, and in a constant environment the system enters a time-dependent 'exponential state '. Autocatalysis is not involved in the Iogarithmic growth of an expanding system ; but when an autocatalytic stage is included the growth curve can exhibit a typical log-phase during which growth rate is virtually independent of concentrations of source material above a threshold level. The properties of expanding systems are deduced from those of open systems by non-mathematical arguments, and some of the implications of the expanding system concept in practical and theoretical microbiology are discussed. It is suggested that the spontaneous occurrence of expanding systems in a non-living environment might be the first step towards the evolution of living organisms. Throughout the paper all reactions are treated as reversible, since there seems to be no justification for the concept of an irreversible chemical change. The reactions are also assumed to be homogeneous, unimolecular, and of the first order, except where otherwise stated. Those assumptions are made in order to keep the examples in the text as simple as possible; but the * Present address :

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“…It seems to be the best starting point of many models possible (e .g . Teissier, 1936 ;Moser, 1957 ;Contois, 1959) to describe the growth of microorganisms . The Monod-model was tested in chemostats of bacteria (e .g.…”

Section: Introductionmentioning

confidence: 99%

Model simulations of continuous rotifer cultures

Walz¹

1993

Hydrobiologia

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Derived from the Monod-model and regulating principles a regulation model of the rotifer development in chemostats was developed . The model was validated in continuous cultures of Brachionus angularis both in steady-states, when undisturbed, and in transient-states after perturbations by step changes of dilution rate or input substrate concentration . Simulations of the simple model monotonically approached steady-states, but cultures show overshoots and damped oscillations before reaching this state . After introducing time-lags into the model it depends on the size of the time lag if model rotifer densities reach stable steady-state values (at low time lags) or stable limit cycles with periodic oscillations (at high time lags). At even higher time lags chaotic conditions occur in the model with final extinction of the rotifers .

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Contributions to the Theory of the Continuous Bacterial Growth Apparatus

Cited by 16 publications

References 2 publications

Carbon Dioxide-Limited Growth of Chlorella in Continuous Culture1

Carbon Dioxide-Limited Growth of Chlorella in Continuous Culture1

A New Kinetic Model of a Growing Bacterial Population

Model simulations of continuous rotifer cultures

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