Model of dissolved organic carbon distribution for substrate-sufficient continuous culture.

The growth yields (Yobs) are greater under substrate-limited conditions than those under substrate-sufficient conditions in continuous cultures. This indicates that the excess substrate should cause uncoupling between anabolism and catabolism. It appears that the excess substrate could determine metabolic pathways of microorganisms, which further control dissolved organic carbon (DOC) distribution under substrate-sufficient conditions. However, how to quantitatively describe the DOC distribution remains unclear in substrate-sufficient continuous culture. Based on a balanced DOC reaction, a DOC distribution model was developed in relation to residual substrate concentration for substrate-sufficient continuous cultures. Results showed that a considerable portion of the DOC consumed was directly oxidized to carbon dioxide through energy spilling under substrate-sufficient conditions. The proposed model for the first time quantified the DOC distribution between nongrowth-associated and growth-associated metabolisms of cells. The proposed model was verified with literature data very well.     

A kinetic model for energy spilling-associated product formation in substrate-sufficient continuous culture

It has been demonstrated that excess substrate can cause uncoupling between anabolism and catabolism, which leads to energy spilling. However, the Luedeking-Piret equation for product formation does not account for the energy spilling-associated product formation due to substrate excess. Based on the growth yield and energy uncoupling models proposed earlier, a kinetic model describing energy spilling-associated product formation in relation to residual substrate concentration was developed for substrate-sufficient continuous culture and was further verified with literature data. The parameters in the proposed model are well defined and have their own physical meanings. From this model, the specific productivity of unit energy spilling-associated substrate consumption, and the maximum product yield coefficient, can be determined. Results show that the majority of energy spilling-associated substrate consumption was converted to carbon dioxide and less than 6% was fluxed into the metabolites, while it was found that the maximum product yield coefficients varied markedly under different nutrient limitations. The results from this research can be used to develop the optimized bioprocess for maximizing valuable product formation.     

The coupling between catabolism and anabolism of Methanobacterium thermoautotrophicum in H2- and iron-limited continuous cultures

The aim of the present work was to investigate whether uncoupling of catabolism from anabolism, which was often observed in heterotrophic microorganisms under energy-sufficient growth conditions, also occurs in the autotrophic bacterium Methanobacterium thermoautotrophicum. For this purpose, M. thermoautotrophicum was cultivated in continuous cultures that were limited by the trace element iron. The influences of both dilution rate and iron supply rate on the coupling between anabolism and catabolism were investigated. As compared to continuous cultures of M. thermoautotrophicum limited by the energy substrate H₂, a 5-fold decrease in the biomass concentration and a 3-fold decrease in H₂, CO₂, and CH₄ conversion rates were observed in iron-limited cultures. However, the specific substrate and product conversion rates increased as compared to the values determined in energy-limited cultures. Thus, iron limitation provoked an uncoupling of catabolism from anabolism. At a dilution rate of 0.096 h⁻¹ and at an iron concentration of 17 μM in the feed, the specific H₂ consumption rate was 100% higher than the rate determined under H₂-limiting conditions, whereas at a dilution rate of 0.168 h⁻¹, the values differed only by 5%. Uncoupling of catabolism from anabolism also increased dramatically when the iron supply rate was lowered but the dilution rate was kept constant. Thus, the extent of uncoupling is a function of both the dilution rate and the iron supply rate. It was found that the specific consumption rate of H₂ increased in parallel with the partial pressure of H₂ in the culture medium. This suggested that the catabolic activity of M. thermoautotrophicum was not stringently controlled at the enzymatic level and can be considerably stimulated by the excess of H₂ in the medium. Hypotheses as to the fate of the excess energy derived from uncoupled catabolism are discussed, but the physiological reason for the partial uncoupling between catabolism and anabolism remains yet to be clarified.     

A kinetic model for product formation of microbial and mammalian cells

Growth of microbial and mammalian cells can be classified into substrate-limited and substrate-sufficient growth according to the relative availability of the substrate (carbon and energy source) and other nutrients. It has been observed for a number of microbial and mammalian cells that the consumption rate of substrate and energy (ATP) is generally higher under substratesufficient conditions than under substrate limitation. Accordingly, the product formation under substrate excess often exhibits different patterns from those under substrate limitation. The extent of increase or decrease in product formation may depend not only on the nature of limitation and cell growth rate but also on the residual substrate concentration in a relatively wide range. The product formation kinetic models existing in literature cannot describe these effects. In this study, the Luedeking-Piret kinetic is extended to include a term describing the effect of residual substrate concentration. The extended model has a similar structure to the kinetic model for substrate and energy consumption rate recently proposed by Zeng and Deckwer. The applicability of the extended model is demonstrated with three microbial cultures for the production of primary metabolites and three hybridoma cell cultures for the production of ammonia and lactic acid over a wide range of substrate concentration. The model describes the product formation in all these cultures satisfactorily. Using this model, the range of residual substrate concentration, in which the product formation is affected, can be quantitatively assessed. (c) 1995 John Wiley & Sons, Inc.     

Kinetics of soluble microbial product formation in substrate-sufficient batch culture of activated sludge

The kinetics of soluble microbial product (SMP) formation under substrate-sufficient conditions appear to exhibit different patterns from substrate-limited cultures. However, energy spilling-associated SMP formation is not taken into account in the existing kinetic models and classification of SMP. Based on the concepts of growth yield and energy uncoupling, a kinetic model describing energy spilling-associated SMP formation in relation to the ratio of initial substrate concentration to initial biomass concentration (S ₀/X ₀) was developed for substrate-sufficient batch culture of activated sludge, and was verified by experimental data. The specific rate of energy spilling-associated SMP formation showed an increasing trend with the S ₀/X ₀ ratio up to its maximum value. The SMP productivity coefficient (α _p/e) was defined from the model on the basis of energy spilling-associated substrate consumption. Results revealed that less than 5% of energy spilling-associated substrate consumption was converted into SMP. Electronic Publication     

Dynamics of energy charge and adenine nucleotides during uncoupling of catabolism and anabolism in Penicillium ochrochloron

Filamentous fungi are able to spill energy when exposed to energy excess by uncoupling catabolism from anabolism, e.g. via overflow metabolism. In current study we tested the hypothesis that overflow metabolism is regulated via the energetic status of the hyphae (i.e. energy charge, ATP concentration). This hypothesis was studied in Penicillium ochrochloron during the steady state of glucose- or ammonium-limited chemostat cultures as well as during three transient states ((i) glucose pulse to a glucose-limited chemostat, (ii) shift from glucose-limited to ammonium-limited conditions in a chemostat, and (iii) ammonium exhaustion in batch culture). Organic acids were excreted under all conditions, even during exponential growth in batch culture as well as under glucose-limited conditions in a chemostat. Partial uncoupling of catabolism and anabolism via overflow metabolism was thus constitutively present. Under all tested conditions, overflow metabolism was independent of the energy charge or the ATP concentration of the hyphae. There was a reciprocal correlation between glucose uptake rate and intracellular adenine nucleotide content. During all transients states a rapid decrease in energy charge and the concentrations of nucleotides was observed shortly after a change in glycolytic flux (“ATP paradoxon”). A possible connection between the change in adenine nucleotide concentrations and the purine salvage pathway is discussed.     

Metabolic uncoupling of Shewanella oneidensis MR-1, under the influence of excess substrate and 3, 3', 4', 5-tetrachlorosalicylanilide (TCS)

The dissociation between catabolism and anabolism is generally termed as metabolic uncoupling. Experimentally, metabolic uncoupling is characterized by a reduction in the observed biomass yield. This condition can be brought about by: (a) excess-substrate (as measured by S(0)/X(0)), and (b) addition of chemical uncouplers such as 3, 3', 4', 5-Tetrachlorosalicylanilide (TCS). An empirical model is proposed to quantify the uncoupling effects of both excess-substrate and uncoupler addition on the microbial cultures. Metabolic uncoupling of Shewanella oneidensis MR-1, under the influence of excess pyruvate and TCS, has been modeled using the proposed expression. The degree of uncoupling was measured as a fractional reduction in theoretical maximum observed yield. Excess-substrate was observed to successively reduce biomass yield as substrate concentration was increased. In the presence of TCS, conflicting trends were obtained for number yield and protein yield. This could, in part, be attributed to the observed increase in cellular protein content upon addition of TCS. Excess-substrate conditions dominated uncoupling, as compared to uncoupler addition. However, these two approaches were found to have additive effects and could, in conjunction, be employed to control biomass growth during microbial processes such as subsurface bioremediation and activated sludge treatment.     

Unstructured models for suspension cultures of Taxus media cells in a bioreactor under substrate-sufficient conditions

For a better understanding of the simulation, optimization, and process control in cell cultures, good kinetic models are necessary for large scale plant cell culture. In this paper, the systematic kinetics of taxol production by Taxus media cell suspension cultures in a stirred 15-L bioreactor under substrate-sufficient conditions and the absence of inducer intervention were studied. A kinetic model of cell growth was established by logistic equation, and kinetic unstructured models of substrate consumption, product synthesis and rheological behavior were constituted, which incorporated energy spilling. These models were verified by comparing the simulation results with those obtained experimentally. These results showed that energy spilling was a key factor that must be considered in constructing unstructured kinetic models of Taxus media cell suspension cultures in a stirred bioreactor under substrate-sufficient conditions. Besides, an optimized operation measure of decreasing energy spilling was proposed. An increase of 17.64% in cell biomass and 14.88% in taxol concentration were obtained when the strategy of limiting added carbon several times was experimentally implemented in a 15-L bioreactor. Results demonstrated that these established models should be helpful in the process prediction and operation optimization to guide the production and amplification of Taxus media cell suspension cultures in a bioreactor.     

Mathematical modeling and analysis of glucose and glutamine utilization and regulation in cultures of continuous mammalian cells

A number of factors have been shown to affect the metabolism of glucose and glutamine in mammalian cells and their mechanisms have been partially elucidated. Despite these efforts, a quantitative knowledge of the significance of these factors, the regulation of glucose and glutamine utilization, and particularly the interactions of these two nutrients is still lacking. Controversies exist in the literature. To clarify some of these controversies, mathematical models are proposed in this work which enable to separate and identify the effects of individual factors. Experimental data from five cell lines obtained in batch, fed-batch, and continuous cultures, both under steady-state and transient conditions, were used to verify the model formulations. The resulting kinetic models successfully describe all these cultures. According to the models, the specific consumption rate of glucose (Q(Glc)) of continuous animal cells under normal culture conditions can be expressed as a sum of three parts: a part owing to cell growth; a part owing to glucose excess; and a part owing to glutamine regulation. The specific consumption rate of glutamine (q(Glc)7) can be expressed as a sum of only two parts: a part owing to cell growth; and a part owing to glutamine excess. Using the kinetic models the interaction and regulation of glucose and glutamine utilizations are quantitatively analyzed. The results indicate that, whereas q(Glc) is affected by glutamine, q(Gln) appears to be not or less significantly affected by glucose. It is also shown that the relative utilizations of glucose and glutamine by anabolism and catabolism are mainly affected by the residual concentrations of the respective compounds and are less sensitive to growth rate and the nature of growth limitation.(c) 1995 John Wiley & Sons, Inc.     

Interaction between catabolism and anabolism in the oxidative assimilation of dissolved organic carbon

Catabolism is tightly coupled to anabolism in substrate-limited cultures. However, the dissolved organic carbon (DOC) distribution between catabolism and anabolism has been hardly studied. Based on a balanced DOC reaction, the DOC distribution between catabolism and anabolism was defined using a ratio of the DOC channeled into CO₂ ( ) to that DOC converted to biomass (S _g). A /S _g-dependent growth yield model was proposed for substrate-limited cultures and was verified using the literature data obtained in the oxidative assimilation processes of different types of organic substrates. The model showed that the growth yield (Y _s) was proportional to anabolic activity, but was inversely related to catabolic activity. Results indicated that both Y _s and /S _g varied markedly with the free energy of oxidation of the organic substrate. Further, the observed phenomena were closely associated with maintenance metabolism under substrate-limited conditions.     

Simple generic model for dynamic experiments with Saccharomyces cerevisiae in continuous culture: decoupling between anabolism and catabolism

The dynamic behavior of a continuous culture of Saccharomyces cerevisiae subjected to a sudden increase in the dilution rate has been successfully modelled for anaerobic growth on glucose, and for aerobic growth on acetate, on ethanol, and on glucose. The catabolism responded by an immediate jump whereas biosynthesis did not. Thus catabolism was in excess to anabolism. The model considers the decoupling between biosynthesis and catabolism, both types of reactions being modelled by first-order kinetic expressions evolving towards maximal values. Yield parameters and maximal reaction rates were identified in steady state continuous cultures or during batch experiments. Only the time constant of biosynthesis regeneration, tauX, and the time constant of catabolic capacity regeneration, taucat, had to be identified during transient experiments. In most experiments tauX was around 3 h, and taucat varied between 2 and 2.5 h for the different metabolisms investigated.     

Metabolic aspects of the growth of a pink-pigmented facultative methylotroph in carbon-limited chemostat culture

Summary The regulation of carbon metabolism in a pink-pigmented facultative methylotroph has been studied. In methanol-limited chemostat culture a pH optimum at 7.0 with a narrow growth rate optimum with respect to growth yield and metabolic uncoupling was revealed. The average growth yield was 14±0.036 g·mol^–1 and the organism displayed a low maintenance energy and high maximum specific growth rate. When the carbon concentration in the feed remained constant and the dilution rate increased a deviation from linearity between substrate consumption and growth rate was found at higher growth rates. The addition of a pulse of methanol to a carbon-limited culture showed that anabolism could be dissociated from catabolism with the resulting accumulation of formaldehyde in concentrations which were not lethal. Offprint requests to: F. M. Girio     

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.     

A model for energy-sufficient culture growth

Pirt's maintenance model has been widely accepted for the effects of growth rate and maintenance on growth yield. However, the interpretation of parameters in Pirt's model as biological constants is difficult for energy-sufficient culture growth. In this study, a mechanistic model for the growth energetics of energy-sufficient chemostat cultures is proposed and verified with literature data. In the model, the overutilization of the energy substrate in energy-sufficient culture growth is attributed to the defective regulation of the energy substrate metabolism and energy uncoupling. The model also uses an "energy surplus" concept to collectively represent the effects of energy excessiveness. The proposed model provides a better quantitative understanding of the maximum growth yield and maintenance of energy-sufficient cultures. It also explains the glucose concentration effect reported in the literature.     

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.     

Inhibition kinetics of phenol degradation from unstable steady-state data

Multiplicity of steady states of a continuous culture with an inhibitory substrate was used to estimate kinetic parameters under steady-state conditions. A continuous culture of Pseudomonas cepacia G4, using phenol as the sole source of carbon and energy, was overloaded by increasing the dilution rate above the critical dilution rate. The culture was then stabilized in the inhibitory branch by a proportional controller using the carbon dioxide concentration in the reactor exhaust gas as the controlled variable and the dilution rate as the manipulated variable. By variation of the set point, several unstable steady states in the inhibitory branch were investigated and the specific phenol conversion rates calculated. In addition, phenol degradation was investigated under substrate limitation (chemostat operation).The results show that the phenol degradation by P. cepacia can be described by the same set of inhibition parameters under substrate limitation and under high substrate concentrations in the inhibitory branch. Biomass yield and maintenance coefficients were identical. Fitting of the data to various inhibition models resulted in the best fit for the Yano and Koga equation. The well-known Haldane model, which is most often used to describe substrate inhibition by phenol, gave the poorest fit. The described method allows a precise data estimation under steady-state conditions from the maximum of the biological reaction rate up to high substrate concentrations in the inhibitory branch. Inhibition parameter estimation by controlling unstable steady states may thus be useful in avoiding discrepancies between data generated by batch runs and their application to continuous cultures which have been often described in the literature. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 567-576, 1997.     

Development of linear irreversible thermodynamic model for oxidation reduction potential in environmental microbial system

Nernst equation has been directly used to formulate the oxidation reduction potential (ORP) of reversible thermodynamic conditions but applied to irreversible conditions after several assumptions and/or modifications. However, the assumptions are sometimes inappropriate in the quantification of ORP in nonequilibrium system. We propose a linear nonequilibrium thermodynamic model, called microbial related reduction and oxidation reaction (MIRROR Model No. 1) for the interpretation of ORP in biological process. The ORP was related to the affinities of catabolism and anabolism. The energy expenditure of catabolism and anabolism was directly proportional to overpotential (eta), straight coefficient of electrode (L(EE)), and degree of coupling between catabolism and ORP electrode, respectively. Finally, the limitations of MIRROR Model No. 1 were discussed for expanding the applicability of the model.     

Citrate efflux in glucose-limited and glucose-sufficient chemostat culture of Penicillium simplicissium

Citrate excretion by Penicillium simplicissimum was investigated in a chemostat. Carbon-limited grown P. simplicissimum did not excrete no citrate. Citrate was excreted, however, when growth was nitrogen-limited. Further effects of nitrogen-limitation were a slightly increased rate of glucose and oxygen consumption. This behaviour is typical for a so-called `overflow metabolism', i.e. the uncoupling of anabolism from catabolism under conditions of carbon excess. Still more citrate was excreted by nitrogen-limited P. simplicissimum when (i) the extracellular osmolarity was increased from 0.2 to 1.5 osm kg^–1 or (ii) when the pH was increased from 4 to 7; or (iii) when the extracellular potassium concentration was lowered from 6 to 0.5 mM. These results were interpreted in terms of a higher energy-consumption under these conditions.