Yield and maintenance relations of yeast growth in the chemostat at superoptimal temperatures

A model is proposed that accounts for the decreases in yield which occur in chemostat cultures of mesophilic yeasts at superoptimal growth temperatures. Two yield depressing effects were identified, one due to increased maintenance requirements by the viable fraction of the population, the other due to energy substrate dissipation by the nonviable fraction. The two effects are functions of the dilution rate, as is the fraction of nonviable cells. Experimental results were obtained on the yield, maintenance, and dissipation of energy substrate in a glucose-limited chemostat culture of a respiration-deficient mutant of Saccharomyces cerevisiae at 39°C. The rates of glucose utilization for maintenance and for dissipation constituted, respectively, 33–28% and 15–9% of the total glucose utilization rate over the range of dilution rates tested (0.038–0.064 hr^?1), while the yield varied over this range from 0.066–0.085 g of biomass (dry wt) per gram of glucose.     

Utilization of statistics and experimental design in data collection and analysis

Application of experimental design techniques to Pirt's yield model shows that it is important to collect data at the lowest and highest specific growth rates. In the fed-batch fermentation process, values of specific growth rate can be varied from the maximum value at the start of the process to very low values near the end of the experiment. Candida utilis was cultivated using batch followed by fed-batch culture with glucose as the main source of carbon and energy. Values of substrate concentration, oxygen consumption, carbon dioxide evolution, liquid volume, flow rate cell concentration, and nitrogen concentration, which was an indirect measure of biomass, were measured. Least-squares estimates of the true biomass energetic yield and maintenance coefficient were obtained using a multivariate statistical analysis procedure referred to as the covariate adjustment procedure. Methods of selecting the best estimates using covariate adjustment are illustrated. The results show that useful parameter estimates with relatively short confidence intervals can be obtained using these statistical methods.     

Cybernetic modeling of bacteriol cultures at low growth rates: single-substrate systems

The cybernetic framework developed by Ramkrishna and co-workers has been expanded to include the effects of cellular maintenance energy requirements on biomass levels in slow-growing, carbon-substrate-limited cultures. A simple structured model, based on the existence of distinct key enzymes for growth and maintenance functions, is presented. Comparisons of the model with experimental data for the growth of Klebsiella oxytoca in constant fed-batch culture on glucose, fructose, arabinose, and xylose show good agreement. In addition, perturbed fed-batch culture experiments indicate that slow-growing cultures respond less rapidly to a removal of the growth limitation than do faster-growing ones. The possibility of a growth-rate dependent "critical resource" is discussed.     

The energetics of microbes at slow growth rates: Maintenance energies and dormant organisms

In continuous cultures at slow growth rates (less than about 10% maximum) bacterial growth yields from the carbon and energy source are higher than those expected. To account for this deviation it is proposed that dormant or non-viable cells with zero maintenance energy are generated at slow growth rates. From the growth yield variation, it is shown, the dormant fraction of the culture can be calculated. The few quantitative data available on the viability of bacteria in chemostat steady states at very slow growth rates are in agreement with the hypothesis. It is suggested that enzymic, chemical and morphological characters also may be used to distinguish between the growing and dormant fractions of a culture.The model provides a unifying theory for studies of microbial function at slow growth rates, which is a field of great practical importance.     

Relationship between substrate inhibition and maintenance energy ofChlamydomonas reinhardtii in heterotrophic culture

The relationship between substrate inhibition and maintenance energy ofChlamydomonas reinhardtii grown heterotrophically on acetate was investigated. At low acetate concentrations (<0.4 g l^–1), where no inhibition of cell growth was observed, the cell growth yield and specific growth rate could be represented by the Pirt model, 1/Y=1/Y _g +m/ with a constant value of maintenance energy coefficient m. However, at high acetate concentrations (>0.4 g l^–1), inhibition of cell growth occurred, in which m became variable and dependent on the acetate concentration. A simple mathematical model was proposed to predict the actual maintenance energy coefficient m in the inhibited cultures and experimentally validated.Author for correspondence     

Modelling of continuous microbial cultivation taking into account the memory effects

The problem of chemostat dynamics modelling for the purpose of control is considered. The "memory" of the culture is explicitly taken into account. Two possibilities for improving the quality of the proposed modelling approaches are discussed. A general model that accounts for the culture `memory' by means of different `memory' functions in the expressions of the specific growth rate and of the specific consumption rate and a polynomial function of the substrate concentration for the yield factor is proposed. The case where the maintenance energy is taken into account is also discussed. Two modifications of the general model (w-type and S-type) are presented. A zero-order `memory' function and a i-function with delay are applied in order to describe the `memory' effects. Continuous growth of the strain Saccharomyces cerevisiae on a glucose limited medium is considered as a case study. Detailed investigations of the variety of models, derived from the general model by applying different `memory' functions and different assumptions are carried out. The results are compared with those previously reported for the same process. It is shown that a significant improvement in predicting the substrate dynamics (not accompanied by any decrease in the quality of the model with respect to the biomass concentration) could be achieved, involving a first- or second-order polynomial function for the yield factor. It is also shown that the quality of the model mainly depends on the way that `memory' function is incorporated. The detailed investigations give priority to the w-type models. In this case past values of both biomass and substrate variables are considered. The time delay models with pure (constant) delay and those which account for the culture `memory' by zero-order `memory' function (adaptability parameter) are compared with respect to their utilization for the purpose of model-based control.     

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.     

Model of energy uncoupling for substrate-sufficient culture

The growth yields (Y(obs)) 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, which leads to energy spilling. Although the uncoupling between anabolism and catabolism has already been recognized in the microbiology literature, how to quantitatively describe such uncoupling remains unclear. Based on a balance on substrate reaction, a growth yield model was developed in relation to residual substrate concentration for substrate-sufficient continuous cultures. On the basis of that yield model, the concept of an uncoupling coefficient between anabolism and catabolism is defined in this work. A model describing the effect of the residual substrate concentration on the uncoupling coefficient of anabolism to catabolism is proposed. This model agrees very well with literature data. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 571-576, 1997.     

Ralstonia eutropha as a biocatalyst for desulfurization of dibenzothiophene

The potential of Ralstonia eutropha as a biocatalyst for desulfurization of dibenzothiophene (DBT) was studied in growing and resting cell conditions. The results of both conditions showed that sulfur was removed from DBT which accompanied by the formation of 2-hydroxybiphenyl (2-HBP). In growing cell experiments, glucose was used as an energy supplying substrate in initial concentrations of 55 mM (energy-limited) and 111 mM (energy-sufficient). The growing cell behaviors were quantitatively described using the logistic equation and maintenance concept. The results indicated that 2-HBP production was higher for the energy-sufficient cultures, while the values of the specific growth rate and the maintenance coefficient for these media were lower than those of the energy-limited cultures. Additionally, the kinetic studies showed that the half-saturation constant for the energy-limited cultures was 2 times higher than the energy-sufficient ones where the inhibition constant (0.08 mM) and the maximum specific DBT desulfurization rate (0.002 mmol g_cell ⁻¹ h⁻¹) were almost constant. By defining desulfurizing capacity (D _DBT) including both the biomass concentration and time to reach a particular percentage of DBT conversion, the best condition for desulfurizing cell was determined at 23% g_cell L⁻¹ h⁻¹ which corresponded with the resting cells that were harvested at the mid-exponential growth phase.

     

Comparison of maximum cell yield and maintenance coefficients in axenic cultures and activated sludge communities

Comparison of the equations that describe the relationship between the maximum cell yield coefficient, the maintenance coefficient, and the specific growth rate at steady-state conditions revealed that the equations used for axenic cultures are congruent with those commonly used for mixed-culture system such as activated sludge. A unified basis was proposed. The expression of the yield and maintenance coefficients in carbon units according to the unified basis permitted one to evaluate literature data on both axenic and mixed-culture systems. From this it appears that the maximum cell yield ranges from 0.50–0.80 (mg biomass carbon formed/mg substrate carbon used) for both axenic and mixed systems. However, the maintenance coefficient (mg substrate C/mg biomass C·hr) for the axenic cultures was between 0.010 and 0.100, but for activated sludge communities it was between 0.001 and 0.010. Microorganisms were isolated from sludge communities with these apparently low maintenance requirements and grown axenilly. Their maintenance coefficients but not their maximum yield coefficients decreased with decreasing specific growth rates. The consequences of this finding with regard to species selection in mixed-culture systems and the concept of cellular maintenance requirement are discussed.     

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.     

A calorimetric determination of maintenance energy requirements during the aerobic growth of Klebsiella aerogenes in batch culture

Theoretical values for the maximum yield, heat output, conversion of substrate energy and number of generations possible for carbon-limited growth of K. aerogenes in batch culture are reported. Values for the maintenance energy and maintenance coefficients are reported for growth in glucose- and -methylglucoside - limited media.     

Cybernetic modeling of bacterial cultures at low growth rates: Mixed-substrate systems

A cybernetic model to predict the low-growth-rate behavior of bacteria in mixed-substrate environment is presented. Using only growth and maintenance parameters from single-substrate experiments, the model accurately predicts the simultaneous substrate utilization and maintenance energy effects in constant fed-batch cultures of Klebsiella oxytoca. The robustness of the model was examined more rigorously by perturbing glucose-limited fed-batch cultures with additions of arabinose, xylose, and fructose. In all cases, reasonable agreement of the model prediction with the experimental data was observed.     

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.     

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 method for the determination of confidence limits for the P/2e − ratio for chosen values of Y ATP max from the results of continuous culture experiments

A model is described, which allows the determination of 95% confidence limits for the maintenance coefficient and the efficiency of oxidative phosphorylation for chosen values of the growth yield for ATP corrected for energy maintenance (Y _ATP ^max ). As experimental data the specific rates of substrate consumption, product formation and oxygen uptake in chemostat cultures at various growth rates are used.     

Data consistency,yield and maintenance coefficient for the growth of Candida lypoytica and Pseudomonas aeruginosa on n-hexadecane

Summary When more than the minimum number of variables are measured, and measurement error is taken into account, the results of parameter estimation depend on which of the measured variables are selected for this purpose. The reparameterization of Pirt's models for growth produces multiresponse models with common parameters. By using the covariate adjustment technique, a unit variate linear model with covariates is obtained. This allows a combined point and interval estimates of biomass energetic yield and maintenance coefficient to be obtained using standard multiple regression programmes. When this method was applied using form I and form II of the Pirt's models, good combined estimates were obtained and compared. Using data from the literature for Candida lipolytica produced reliable results. However, for Pseudomonas aeruginosa, which has been known to produce intermediate products, a modified Pirt's model is required for a good estimate of the biomass energetic yield.Nomenclature a Mole of ammonia per quantity of organic substrate containing 1 g atom carbon, g mole/g atom carbon - b Moles of oxygen per quantity of organic substrate containing 1 g atom carbon, g mole/g atom carbon - c Moles of water per quantity of organic substrate containing 1 g atom carbon, g mole/g atom carbon; no of covariates included in model - d Moles of carbon dioxide per quantity of organic substrate containing 1 g atom carbon, g mole/g atom carbon - e _i Error terms in Eqs. (6–8) - l Atomic ratio of oxygen to carbon in organic substrate, dimensionless - m Atomic ratio of hydrogen to carbon in organic substrate, dimensionless - m _e Rate of organic substrate consumption for maintenance, g equiv. of available electrons in biomass (h) or kcal/Kcal of biomass(h) - n Atomic ratio of oxygen to carbon in biomass, dimensionless - p Atomic ratio of hydrogen to carbon in biomass, dimensionless - Q _{CO 2} Rate of evolution of carbon dioxide, g moles/g dry wt (h) - Q _{O 2} Rate of oxygen consumption, g moles/g dry wt (h) - Q _s Rate of organic substrate consumption g/g dry wt (h) - q Atomic ratio of nitrogen to carbon in biomass, dimensionless - r Atom ratio of hydrogen to carbon in products, dimensionless; the number of parameters of interest - s Atomic ratio of oxygen to carbon in products, dimensionless - t Atomic ratio of nitrogen to carbon in products, dimensionless - r Mean of k responses in Eq. (10) - x _ki Kth response in the ith observation - y _c Biomass carbon yield (fraction of organic substrate carbon in biomass), dimensionless - z _i Covariate matrix - z Fraction of organic substrate carbon in products, dimensionless - a _i Parameters associated with covariates - _s Reductance degree of biomass, equivalents of available electrons per gram atom carbon - Reductance degree of organic substrate, equivalents of available electrons per gram atom carbon - Fraction of energy in organic substrate which is evolved as heat, dimensionless - Fraction of available electrons transferred to biomass; biomass energetic yield - True growth yield - Specific growth rate, h^-1 - _p Fraction of available electrons incorporated into products; product energetic yield - Correlation coefficient - Mass fraction carbon - ² Mean square error of model (10)     

A macroscopic model describing yield and maintenance relationships in aerobic fermentation processes

The present paper presents a generalized treatment of the principles of elemental and enthalpy balances which are applied to aerobic fermentation processes. It is shown that strict relations do exist between the various yield factors of biomass or product on substrate, oxygen, carbon dioxide, and between the various maintenance coefficients. These relations are confirmed from the existing body of literature data on yield and maintenance coefficients. Another consequences of the application of elemental balances is the existence of limits for the maximum biomass yield on substrate and oxygen, which depend on the degree of reduction of the substrates with different degree of reduction. It appears from this model that substrates with a high degree of reduction are C limited and substrates with a low degree of reduction are energy limited. Finally the effects of temperature on yield and maintenance coefficients are analyzed from the existing body of literature data. It can be concluded that the maintenance coefficients follow an Arrhenius type of relationship and that yield is temperature independent. The literature data seem to indicate that a degree of reduction of about 4 is optimal for the carbon and energy needs for biomass formation.