Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures.

Growth of Saccharomyces cerevisiae on glucose in aerobic batch culture follows the well-documented diauxic pattern of completely fermenting glucose to ethanol during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming ethanol. In continuous cultures over a range of intermediate dilution rates, the yeast bioreactor exhibits sustained oscillations in all the measured concentrations, such as cell mass, glucose, ethanol, and dissolved oxygen, the amounts of intracellular storage carbohydrates, such as glycogen and trehalose, the fraction of budded cells as well as the culture pH. We present here a structured, unsegregated model for the yeast growth dynamics developed from the 'cybernetic' modeling framework, to simulate the dynamic competition between all the available metabolic pathways. This cybernetic model accurately predicts all the key experimentally observed aspects: (i) in batch cultures, duration of the intermediate lag phase, sequential production and consumption of ethanol, and the dynamics of the gaseous exchange rates of oxygen and carbon dioxide; and (ii) in continuous cultures, the spontaneous generation of oscillations as well as the variations in period and amplitude of oscillations when the dilution rate or agitatin rate are changed.     

Recombinant protein synthesis and plasmid instability in continuous cultures of Escherichia coli JM103 harboring a high copy number plasmid

Escherichia coli JM103[pUC8] was employed as a model to investigate the behavior of a recombinant microbial system harboring a plasmid at high copy numbers. Experiments with batch and continuous cultures of recombinant and plasmid-free cells were conducted in a well-controlled bio-reactor. In batch experiments, plasmid copy number varied typically from an average of 500 during the exponential growth phase to as high as 1250 during the stationary phase. While the segregational plasmid instability was negligible in batch experiments, severe segregational instability occurred in continuous experiments conducted over a range of dilution rates, resulting in complete loss of plasmid-bearing cells from the continuous cultures within few residence times after transition to continuous operation. The profound differences in the specific growth rates and mass yields of the plasmid-free and plasmid-bearing cells resulting from the extra metabolic burden on the plasmid-bearing cells mainly due to excessive plasmid DNA content was the major cause for the plasmid instability. Plasmid multirnerization was detected in batch and continuous cultures and was found to have significant influence on the effective copy number and was partially responsible for the severe segregational instability in continuous cultures. A quasi-steady state representative of plasmid-bearing cells was established in the initial portion of each continuous culture experiment. Due to the profound growth rate differential between the two types of cells, transients of considerable duration were observed in each continuous culture experiment (initiated with a pure culture of plasmid bearing cells) following the slow accumulation of plasmid-free cells near the end of the quasi-steady state. Significant variations in various culture parameters (including a rapid decline in the plasmid-bearing fraction of the total cell population) occurred during this period, leading ultimately to a steady state for a culture dominated entirely by plasmid-free cells. In continuous cultures, plasmid copy number during the quasi-steady states increased with decreasing dilution rate from 50 (at 0.409 h(-1)) to 941 (at 0.233 h(-1)). Production of the plasmid-encoded protein (beta-lactamase) in these experiments was maximized at an intermediate dilution rate, corresponding to an optimum copy number of about 450. A similar optimum copy number was observed in batch cultures. Significant excretion of beta-lactamase was observed at both low and high dilution rates.     

Modeling of typical microbial cell growth in batch culture

A mathematical model was developed, based on the time dependent changes of the specific growth rate, for prediction of the typical microbial cell growth in batch cultures. This model could predict both the lag growth phase and the stationary growth phase of batch cultures, and it was tested with the batch growth ofTrichoderma reesei andLactobacillus delbrucckii.     

Continuous cultures limited by a gaseous substrate: Development of a simple, unstructured mathematical model and experimental verification with Methanobacterium thermoautotrophicum

This article presents a simple, unstructured mathematical model describing microbial growth in continuous culture limited by a gaseous substrate. The model predicts constant gas conversion rates and a decreasing biomass concentration with increasing dilution rate. It has been found that the parameters influencing growth are primarily the gas transfer rate and the dilution rate. Furthermore, it is shown that, for correct simulation of growth, the influence of gaseous substrate consumption on the effective gas flow through the system has to be taken into account.Continuous cultures of Methanobacterium thermoautotrophicum were performed at three different gassing rates. In addition to the measurement of the rates of biomass production, product formation, and substrate consumption, microbial heat dissipation was assessed using a reaction calorimeter. For the on-line measurement of the concentration of the growth-limiting substrate, H(2), a specially developed probe has been used. Experimental data from continuous cultures were in good agreement with the model simulations. An increase in gassing rate enhanced gaseous substrate consumption and methane production rates. However, the biomass yield as well as the specific conversion rates remained constant, irrespective of the gassing rate. It was found that growth performance in continuous culture limited by a gaseous substrate is substantially different from "classic" continuous culture in which the limiting substrate is provided by the liquid feed. In this report, the differences between both continuous culture systems are discussed.     

Comparison of specific rates of hybridoma growth and metabolism in batch and continuous cultures

For the mouse hybridoma cell line VO 208, kinetics of growth, consumption of glucose and glutamine, and production of lactate, ammonia and antibodies were compared in batch and continuous cultures. At a given specific growth rate, different metabolic activities were observed: a 40% lower glucose and glutamine consumption rate, but a 70% higher antibody production rate in continuous than in batch culture. Much higher metabolic rates were also measured during the initial lag phase of the batch culture. When representing the variation of the specific antibody production rate as a function of the specific growth rate, there was a positive association between growth and antibody production in the batch culture, but a negative association during the transient phase of the continuous culture. The kinetic differences between cellular metabolism in batch and continuous cultures may be result of modifications in the physiology and metabolism of cells which, in continuous cultures, were extensively exposed to glucose limitations.Institut National Polytechnique de Lorraine, ENSAIA BP 172, 2 avenue de la forêt de Haye, 54505, Vandoeuvre Cedex France     

An alternate method for estimation of cell growth kinetics from batch cultures

An alternative to estimation of cell growth kinetics via continuous culture experiments is proposed in this article. The method employed is based on batch culture experiments with very small inocula (initial cell concentrations being typically less than 5000 cells/mL). Such low initial cell concentrations result in extended exponential cell growth phase during which culture conditions remain unchanged, thereby permitting precise estimation of specific cell growth rates from batch experiments especially for fast-growing microorganisms such as Bacillus species. The effectiveness and utility of this approach are demonstrated via several experiments conducted with a wild-type strain (Bacillus subtilis TN106) and a recombinant strain (B. subtilis TN106[pAT5]). True establishment of exponential growth phase requires insignificant variance of most of the culture conditions during the initial growth phase. Satisfaction of this requirement is demonstrated for microbial systems investigated here. This approach is especially well suited for recombinant microorganisms containing segregationally unstable plasmids, since estimation of growth kinetics of these from continuous cultures is very difficult and highly unreliable due to continual reversion of recombinant ceils to plasmid-free host cells unless some selection pressure is applied at levels sufficient to keep the presence of plasmid-free cells minimal.     

The relationship between kinetics of substrate-limited transitions and steady-state growth in continuous cultures ofAquaspirillum autotrophicum limited by pyruvate

Heterotrophic growth at steady state and during transient states caused by the sudden change of the concentration of the limiting factor in the feed medium was investigated experimentally for continuous cultures ofAquaspirillum autotrophicum limited by pyruvate. A model for describing the growth at steady state was selected from three unstructured models after statistical tests of the data. This model postulates that the growth yield increases linearly with the growth rate. Growth during transitions where the substrate remained limiting at all times was fitted with first-order kinetics. Theoretical predictions of these kinetics were derived from the unstructured models used to describe steady state. The predicted rate coefficients of the transients were compared to the experimental coefficients. It appeared that the model which best described steady-state growth also provided the best predictions for growth during the transient state. It is a widespread opinion that unstructured models are adequate to describe growth under steady-state conditions but not to predict transitions in continuous culture. However, for the particular case studied here, no higher degree of complexity was required to describe transitions, provided the growth of the culture was always limited by the substrate.     

Mathematical modeling for mixed culture growth of two bacterial populations with opposite substrate preferences

An unstructured mathematical model is proposed for mixed culture growth of two different bacterial species that exhibit "opposite" substrate preferences in response to the "same" environmental conditions. The model incorporates enzymatic control mechanisms such as induction, repression, and inhibition in the microorganisms as manifested in their preferential utilization of substrates and microbial interactions such as amensalism and competition. The model predicts cell mass, substrate concentrations, dissolved oxygen tension, as well as key enzyme levels. The predictions of the model are compared with experimental data for pure culture growth and for mixed culture growth on two substrates, glucose and citrate, in a batch reactor.     

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.     

Timing is everything: optimizing crop yield for <Emphasis Type="Italic">Thalassiosira pseudonana</Emphasis> (Bacillariophyceae) with semi-continuous culture

There is relatively little choice in cultivation methods for growing algae outdoors, either in open pond systems or closed photobioreactors—as batch, continuous, or semi-continuous culture. Algal batch culture grown in a nutrient replete environment with adequate sunlight will become self-shaded with sufficient cell density and enter a stage in the growth dynamic known as the “phase of linear growth.” It is during this phase of linear growth that primary production is at maximum and that the highest biomass is harvested. The inherent problem with batch culture is that the exponential (and possibly lag) phases necessary to achieve densities required prior to the phase of linear growth consume time and waste surface area, and thereby make this an inefficient method to grow algae. Semi-continuous culture can be forced into shade-limiting conditions by reducing growth rate from maximum through dilution, whereby phases of lag and exponential growth are skipped, and culture growth is put into a state similar to a perpetual phase of linear growth with an appropriate culture harvest/dilution cycle. Importantly, semi-continuous culture can increase net growth efficiency over batch culture when compared by shade-limited growth rate. However, scientific study and theory covering shade-limited algal growth under semi-continuous culture conditions are nearly non-existent, which currently makes its application to phycological technologies impractical through “hit and miss” strategies. This laboratory study compares shade-limited growth dynamics for batch and semi-continuous cultures of Thalassiosira pseudonana (small-sized, marine diatom). Theory for optimizing production of mass algal culture with semi-continuous culture technique through cycle period and harvest volume is developed, and guidelines to practical industrial applications are provided.     

Bioactivity of immobilized microalgal cells: application potential of vegetable sponge in microbial biotechnology

Bioactivity of immobilized cells, as evidenced by the production of intracellular phycoerythrin and extracellular polysaccharides by Porphyridium cruentum , in batch and repeated batch culture, respectively, is reported. Cells of P. cruentum immobilized within the vegetable sponge of Luffa cylindrica were grown in batch culture for 24 d and maintained at the stationary phase of growth in repeated batch cultures in a growth-limiting medium for 50 d. The study indicates the application potential of this recently reported biostructure as an immobilization matrix in microbial biotechnology.     

The renaissance of continuous culture in the post-genomics age

The development of continuous culture techniques 60 years ago and the subsequent formulation of theory and the diversification of experimental systems revolutionised microbiology and heralded a unique period of innovative research. Then, progressively, molecular biology and thence genomics and related high-information-density omics technologies took centre stage and microbial growth physiology in general faded from educational programmes and research funding priorities alike. However, there has been a gathering appreciation over the past decade that if the claims of systems biology are going to be realised, they will have to be based on rigorously controlled and reproducible microbial and cell growth platforms. This revival of continuous culture will be long lasting because its recognition as the growth system of choice is firmly established. The purpose of this review, therefore, is to remind microbiologists, particularly those new to continuous culture approaches, of the legacy of what I call the first age of continuous culture, and to explore a selection of researches that are using these techniques in this post-genomics age. The review looks at the impact of continuous culture across a comprehensive range of microbiological research and development. The ability to establish (quasi-) steady state conditions is a frequently stated advantage of continuous cultures thereby allowing environmental parameters to be manipulated without causing concomitant changes in the specific growth rate. However, the use of continuous cultures also enables the critical study of specified transition states and chemical, physical or biological perturbations. Such dynamic analyses enhance our understanding of microbial ecology and microbial pathology for example, and offer a wider scope for innovative drug discovery; they also can inform the optimization of batch and fed-batch operations that are characterized by sequential transitions states.     

The ferrous iron oxidation kinetics of Thiobacillus ferrooxidans in batch cultures

The ferrous iron oxidation kinetics of Thiobacillus ferrooxidans in batch cultures was examined, using on-line off-gas analyses to measure the oxygen and carbon dioxide consumption rates continuously. A cell suspension from continuous cultures at steady state was used as the inoculum. It was observed that a dynamic phase occurred in the initial phase of the experiment. In this phase the bacterial ferrous iron oxidation and growth were uncoupled. After about 16 h the bacteria were adapted and achieved a pseudo-steady state, in which the specific growth rate and oxygen consumption rate were coupled and their relationship was described by the Pirt equation. In pseudo-steady state, the growth and oxidation kinetics were accurately described by the rate equation for competitive product inhibition. Bacterial substrate consumption is regarded as the primary process, which is described by the equation for competitive product inhibition. Subsequently the kinetic equation for the specific growth rate, μ, is derived by applying the Pirt equation for bacterial substrate consumption and growth. The maximum specific growth rate, μ _max, measured in the batch culture agrees with the dilution rate at which washout occurs in continuous cultures. The maximum oxygen consumption rate, q _O2,max, of the cell suspension in the batch culture was determined by respiration measurements in a biological oxygen monitor at excess ferrous iron, and showed changes of up to 20% during the course of the experiment. The kinetic constants determined in the batch culture slightly differ from those in continuous cultures, such that, at equal ferric to ferrous iron concentration ratios, biomass-specific rates are up to 1.3 times higher in continuous cultures. Received: 8 February 1999 / Accepted: 17 February 1999     

A structured model for simulation of cultures of the cyanobacterium Spirulina platensis in photobioreactors: II. Identification of kinetic parameters under light and mineral limitations

A structured model for the culture of cyanobacteria in photobioreactors is developed on the basis of Schuster's approximations for radiative light transfer. This model is therefore limited to monodimensional geometries and kinetic aspects.Light-harvesting pigments play a crucial role in defining the profile of radiative transfer inside the culture medium and in controlling the metabolism, particularly the metabolic deviations induced by mineral limitations. Modeling therefore requires the biomass to be divided into several compartments, among which the light-harvesting compartment allows a working illuminated volume to be defined within the photobioreactor. This volume may change during batch cultures, largely decreasing as pigment concentration increases during growth but increasing as pigments are consumed during mineral limitation. This approach enables, in photobioreactors of simple parallelepipedic, geometries, kinetic parameters to be determined with high accuracy; this may then be extended to vessels of more complex geometries, such as cylindrical photobioreactors.The model is applied to controlled batch cultures of the cyanobacterium Spirulina platensis in parallelepipedic photobioreactors to assess its ability to predict the behavior of these microorganisms in conditions of light and mineral limitations. Results allowed the study of optimal operating condition for continuous cultures to be approached (c) 1992 John Wiley & Sons, Inc.     

Fermentation kinetics of Zymomonas mobilis at high ethanol concentrations: Oscillations in continuous cultures

Substrate-limited continuous culture results at 47 g/L ethanol show that the maintenance factor and the yield factor of an unstructured maintenance model are lower compared to the values at 23 g/L ethanol. Computing the results according to a structured two-compartment model predicts an enhanced turnover rate of the K-compartment (RNA fraction) by ethanol, resulting in a lower steady-state amount of K-compartment. This is in agreement with experimentally determined RNA fractions. The parameters of both models respond qualitatively in the same way to elevation of the ethanol concentration as to elevation of the temperature. In product-inhibited continuous cultures, at ethanol concentrations above 55 g/L, nearly sustained oscillations in biomass, substrate, and products were observed. The maximum ethanol concentration achieved in these continuous cultures was 70 g/L. The oscillations could be described by a structured mathematical model, in which ethanol inhibits the maximum specific growth rate indirectly by inhibiting the synthesis of an internal growth-rate-determining compound.     

The influence of cultivation methods on Shewanella oneidensis physiology and proteome expression

High-throughput analyses that are central to microbial systems biology and ecophysiology research benefit from highly homogeneous and physiologically well-defined cell cultures. While attention has focused on the technical variation associated with high-throughput technologies, biological variation introduced as a function of cell cultivation methods has been largely overlooked. This study evaluated the impact of cultivation methods, controlled batch or continuous culture in bioreactors versus shake flasks, on the reproducibility of global proteome measurements in Shewanella oneidensis MR-1. Variability in dissolved oxygen concentration and consumption rate, metabolite profiles, and proteome was greater in shake flask than controlled batch or chemostat cultures. Proteins indicative of suboxic and anaerobic growth (e.g., fumarate reductase and decaheme c-type cytochromes) were more abundant in cells from shake flasks compared to bioreactor cultures, a finding consistent with data demonstrating that “aerobic” flask cultures were O₂ deficient due to poor mass transfer kinetics. The work described herein establishes the necessity of controlled cultivation for ensuring highly reproducible and homogenous microbial cultures. By decreasing cell to cell variability, higher quality samples will allow for the interpretive accuracy necessary for drawing conclusions relevant to microbial systems biology research.     

Application of a competition model to the growth of Streptococcus mutans and Streptococcus sanguis in binary continuous culture.

Streptococcus mutans 6715-15 and Streptococcus sanguis 10558 were grown together in continuous culture with glucose as the limiting carbon source. The relationship of growth rate to substrate concentration was determined for pure cultures of each organism in continuous and batch cultures. A model based on competition for a growth-limiting substrate (glucose) was used to predict the proportions of each organism when grown in binary cultures. The results indicate that interactions other than competition for glucose carbon exist between S. mutans and S. sanguis grown under these conditions.     

Application of a competition model to the growth of Streptococcus mutans and Streptococcus sanguis in binary continuous culture

Streptococcus mutans 6715-15 and Streptococcus sanguis 10558 were grown together in continuous culture with glucose as the limiting carbon source. The relationship of growth rate to substrate concentration was determined for pure cultures of each organism in continuous and batch cultures. A model based on competition for a growth-limiting substrate (glucose) was used to predict the proportions of each organism when grown in binary cultures. The results indicate that interactions other than competition for glucose carbon exist between S. mutans and S. sanguis grown under these conditions.