Application of mass and energy balance regularities in fermentation

Material and energy balances for fermentation processes are developed based on the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Mass–energy balance equations are developed which relate the biomass energetic yield coefficient to sets of variables which may be determined experimentally. Organic substrate consumption, biomass production, oxygen consumption, carbon dioxide production, heat evolution, and nitrogen consumption are considered as measured variables. Application of the balances using direct and indirect methods of yield coefficient estimation is illustrated using experimental results from the literature. Product formation is included in the balance equations and the effect of product formation on biomass yield estimates is examined. Application of mass–energy balances in the optimal operation of continuous single-cell protein production facilities is examined, and the variation of optimal operating conditions with changes in yield are illustrated for methanol as organic substrate.     

Application of mass and energy balance regularities in fermentation. Reprinted from Biotechnology and Bioengineering, Vol. XX, No. 10, Pages 1595-1621 (1978)

Material and energy balances for fermentation processes are developed based on the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Mass-energy balance equations are developed which relate the biomass energetic yield coefficient to sets of variables which may be determined experimentally. Organic substrate consumption, biomass production, oxygen consumption, carbon dioxide production, heat evolution, and nitrogen consumption are considered as measured variables. Application of the balances using direct and indirect methods of yield coefficient estimation is illustrated using experimental results from the literature. Product formation is included in the balance equations and the effect of product formation on biomass yield estimates is examined. Application of mass-energy balances in the optimal operation of continuous single-cell protein production facilities is examined, and the variation of optimal operating conditions with changes in yield are illustrated for methanol as organic substrate.     

Estimating the maintenance energy and biomass concentration of Saccharomyces cerevisiae by continuous calorimetry

Continuous calorimetry has been applied to monitoring the heat evolution of Saccharomyces cerevisiae grown on d-glucose. The heat evolution, together with the energy and carbon balances, was used to evaluate the energetic efficiency of biomass, by-product biosynthesis, fermentative heat evolution as well as the maintenance energy of S. cerevisiae in ‘aerobic fermentation’ and ‘aerobic respiration’. In aerobic fermentation, under catabolite repression, the fraction of substrate energy converted to heat evolution, maintenance requirement, and biomass decreased with the increase of d-glucose concentration. The fraction of substrate energy converted to ethanol is the highest value and it could contribute up to 70% of the total substrate energy. In aerobic respiration, 43% of the total substrate energy was evolved as heat. While 50% of the total substrate energy was converted into biomass, only 7% of the total substrate energy was used for maintenance functions. The maintenance energy coefficient of S. cerevisiae was determined to be 0.427 MJ kg^?1 cell h^?1 (0.102 kcal g^?1 cell h^?1). For the first time, heat evolution together with yield-maintenance energy was used to predict biomass concentration during the fed-batch cultivation of S. cerevisiae.     

Utilization of mass–energy balance regularities in the analysis of continuous-culture data

Material and energy balances for continuous-culture processes are described based on the facts that the heat of reaction per electron transferred to oxygen for a wide variety of organic molecules, the number of available electrons per carbon atom in biomass, and the weight fraction carbon in biomass are relatively constant. Energy requirements for growth and maintenance are investigated and related to the biomass energetic yield. The consistency of experimental data is examined using material and energy balances and the regularities identified above. When extracellular products are absent, the consistency of yield models containing separate terms for growth and maintenance may be investigated using organic substrate consumption, biomass production, oxygen consumption (or heat evolution), and carbon dioxide evolution rate data for a series of dilution rates. The consistency of continuous-culture data in the published literature is examined.     

Experimental bioenergetics ofSaccharomyces cerevisiae in respiration and fermentation

Aerobic growth of Saccharomyces cerevisiae on glucose was investigated, focusing on the heat evolution as it relates to biomass and ethanol synthesis. “Aerobic fermentation” and “aerobic respiration” were established respectively in the experimental system by performing batch and fed-batch experiments. “Balanced growth” batch cultivations were carried out with initial sugar concentrations ranging from 10 to 70 g/L, resulting in different degrees of catabolite repression. The fermentative heat generation was continuously monitored in addition to the key culture parameters such as ethanol production rate, CO₂ evolution rate, O₂ uptake rate, specific growth rate, and sugar consumption rate. The respective variations of the above quantities reflecting the variations in the catabolic activity of the culture were studied. This was done in order to evaluate the microbial regulatory system, the energetics of microbial growth including the rate of heat evolution and the distribution of organic substrate between respiration and fermentation. This study was supported by closing C, energy, and electron balances on the system. The comparison of the fractions of substrate energy evolved as heat (δ_h) with the fraction of available electrons transferred to oxygen (?_O2) indicated equal values of the two (0.46) in the aerobic respiration (fed-batch cultivation). However, the glucose effect in batch cultivations resulted in smaller ?_O2 than δ_h, while both values decreased in their absolute values. The evaluation of the heat energetic yield coefficients, together with the fraction of the available electrons transferred to O, contributed to the estimation of the extent of heat production through oxidative phosphorylation.     

Application of data consistency tests and new parameter estimation methods to microbial growth on corn dust in batch culture

The microorganism Candida utilis was grown on both filtered and unfiltered substrate obtained from enzymatic hydrolysis of starch in corn dust. For growth on filtered substrate, the average integrated biomass energetic yield value based on biomass-substrate data was η = 0.55 and for growth on unfiltered substrate an average yield value of η = 0.59 was obtained. Material and energy balances showed that the presence of unfiltered corn residue in the media had no significant effect on the yields. Statistical methods were developed and used to obtain best estimates of the growth parameters. Values of the biomass energetic yield corrected for maintenance (η_max = 0.619) and the maintenance coefficient (m_e = 0.043) were obtained for growth on filtered substrate. Values of η_max = 0.741 and m_e = 0.142 were obtained for the growth on unfiltered substrate. The consistency of data and parameter estimates was relatively good for filtered substrate; however, parameter estimates for unfiltered substrate were not consistent. Growth experiments without filtration of the products of starch hydrolysis resulted in protein-enriched products with about 39.73% protein.     

Application of material and energy balances in the interpretation of intermediate product build-up in batch growth of Pseudomonas aeruginosa on n-hexadecane

Summary This work is concerned with the application of material and energy balances in an attempt to understand the phenomenon of product build-up when Pseudomonas aeruginosa is grown on n-hexadecane in a batch fermentor. It is shown that the organism accumulates a polyactide, called poly-B-hydroxybutyrate (PHB) during early stages of growth and metabolizes it at later stages of growth. This explains the low carbon and available electron balances which have been observed.Nomenclature d Moles of carbon dioxide per quantity of organic substrate containing one g atom carbon, g mole/g atom carbon - m _e Rate of organic substrate consumption for maintenance, g equiv. of available electrons/g equiv. of available electrons in biomass (h) - Specific rate of evolution of carbon dioxide, g moles/g dry wt (h) - Specific rate of oxygen consumption, g mole/g dry wt (h) - s Organic substrate concentration, g/liter - t Time (h) - x Biomass concentration, g/liter - y _c Biomass carbon yield (fraction of organic substrate carbon in biomass), dimensionless - _b Reductance degree of biomass, equivalents of available electrons per g atom carbon - _s Reductance degree of substrate, equivalents of available electrons per g atom carbon - Fraction of energy in organic substrate which is evolved as heat, dimensionless - Fraction of energy in organic substrate which is coverted to biomass or biomass energetic yield, dimensionless - Specific growth rate, h^-1 - _b Weight fraction carbon in biomass, dimensionless - _s Weight fraction carbon in substrate, dimensionless     

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)     

Application of dynamic calorimetry for monitoring fermentation processes

The rate of heat evolution (kcal/liter-hr) in mycelial fermentations for novobiocin and cellulase production with media containing noncellular solids was measured by an in situ dynamic calorimetric procedure. Thermal data so obtained have proved significant both in monitoring cell concentration during the trophophase (growth phase) and in serving as a physiological variable in the fermentation process. The validity of this technique has been demonstrated by closing the overall material and energy balances. The maintenance energy in a batch fermentation can also be calculated by integrating heat evolution data. This integration method is applicable to a fermentation lacking a precise cell growth curve. The maintenance coefficient, obtained for the novobiocin fermentation by Streptomyces niveus, is equal to 0.028 g glucose equivalent/g cell-hr. The production of novobiocin in the idio-phase (production phase) also correlates well with the amount of energy catabolixed for maintenance and this results in an observed conversion yield of glucose to novobiocin of 11.8 mg of novobiocin produced per gram of glucose catabolized. A new physiological variable, kilocalories of heat evolved per millimole of oxygen consumed, has been proposed to monitor the state of cells during the fermentation. This method may provide a simple way to monitor on-line shifts in the efficiency of cell respiration and changes in growth yields during a microbial process.     

Growth of the yeast Saccharomyces cerevisiae on a non-fermentable substrate: control of energetic yield by the amount of mitochondria

The purpose of this study was to investigate the long-term control of ATP synthesis during the course of Saccharomyces cerevisiae batch grown on lactate, a purely respiratory substrate. For this, we used a respirometric and on-line calorimetric approach to analyse the energetic balances and the control of energetic metabolism during growth. Enthalpic growth yields assessed by enthalpy balance (taking account of substrate consumption, by-product accumulation, biomass formation and heat dissipation) remained constant during the entire exponential growth. Moreover, at the same time, a parallel decrease in basal respiratory rate and enthalpy flux occurred. It is shown that the decrease in respiration corresponds to a decrease in the amount of mitochondria per cell but not to a change of steady state of oxidative phosphorylation. Taking into account the part of energy used for maintenance, it can be concluded that mitochondria by themselves are the major heat dissipative system in a fully aerobic metabolism, and that the decrease in the amount of mitochondria when growth rate decreases leads to an enthalpic growth yield constant.     

Production of single cell protein from rice polishings using Candida utilis

Microbial protein was produced from defatted rice polishings using Candida utilis in shake-flasks and a 14-l fermentor to optimize fermentation conditions before producing biomass in a 50-l fermentor. The organism supported maximum values of 0.224 h⁻¹, 0.94, 1.35, 1.75, 2.12 g l⁻¹ h⁻¹, 0.62 g cells g⁻¹ substrate utilized and 0.38 g g⁻¹ for specific growth rate, true protein productivity, crude protein productivity, cell mass productivity, substrate consumption rate, cell yield, crude protein yield, respectively in 50-l fermentor studies using optimized cultural conditions. Maximum values compared favourably or were superior to published data in literature. The biomass protein in the 50-l fermentor contained 22.3, 27.8, 19.2, 9.5, 38.12, 8.5 and 0.27% true protein, crude protein, crude fibre, ash, carbon, cellulose and RNA content, respectively. The dried biomass showed a gross metabolizable energy value of 2678 kcal kg⁻¹ and contained all essential and non-essential amino acids. Yeast biomass as animal feed may replace expensive feed ingredients currently being used in poultry feed and may improve the economics of feed produced in countries like Pakistan. This revised version was published online in August 2006 with corrections to the Cover Date.     

Optimization of Phaffia rhodozyma continuous culture through response surface methodology

Response surface methodology was applied to optimize the growth of the yeast Phaffia rhodozyma in continuous fermentation using peat hydrolysates as substrate. A second-order, complete, factorial design of the experiments was used to develop empirical models providing a quantitative interpretation of the relationships between the two variables studied, dilution rate and pH. Maximum biomass concentration in the fermentor was obtained by employing the following predicted optimum fermentation conditions: a dilution rate of 0.017/h and a pH level of 7.19. A verification experiment, conducted at previously optimized conditions for maximum biomass volumetric productivity (a dilution rate of 0.022/h, and a pH level of 6.90), produced values for biomass concentration, residual substrate concentration, biomass yield, and biomass volumetric productivity that were very close to the predicted values, indicating the reliability of the empirical model. The concentration of the pigment astaxanthin produced by the yeast under the optimized growth conditions was found to be 544 mg astaxanthin/kg dry cell biomass.     

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.     

Application of macroscopic principles to microbial metabolism

General expressions for mass, elemental, energy, and entropy balances are derived and applied to microbial growth and product formation. The state of the art of the application of elemental balances to aerobic and heterotrophic growth is reviewed and extended somewhat to include the majority of the cases commonly encountered in biotechnology. The degree of reduction concept is extended to include nitrogen sources other than ammonia. The relationship between a number of accepted measures for the comparison of substrate yields is investigated. The theory is illustrated using a generalized correlation for oxygen yield data. The stoichiometry of anaerobic product formation is briefly treated, a limit to the maximum carbon conservation in product is derived, using the concept of elemental balance. In the treatment of growth energetics the correct statement of the second law of thermodynamics for growing organisms is emphasized. For aerobic heterotrophic growth the concept of thermodynamic efficiency is used to formulate a limit the substrate yield can never surpass. It is combined with a limit due to the fact that the maximum carbon conservation in biomass can obviously never surpass unity. It is shown that growth on substrates of a low degree of reduction is energy limited, for substrates of a high degree of reduction carbon limitation takes over. Based on a literature review concerning yield data some semiempirical notions useful for a preliminary evolution of aerobic heterotrophic growth are developed. The thermodynamic efficiency definition is completed by two other efficiency measures, which allow derivation of simple equations for oxygen consumption and heat production. The range of validity of the constancy of the rate of heat production to the rate of oxygen consumption is analyzed using these efficiency measures. The energetic of anaerobic growth are treated—it is shown that an approximate analysis in terms of an enthalpy balance is not valid for this case, the evaluation of the efficiency of growth has to be based on Gibbs free energy changes. A preliminary analysis shows the existence of regularities concerning the free energy conservation on anaerobic growth. The treatment is extended to include the effect of growth rate by the introduction of a linear relationship for substrate consumption. Aerobic and anaerobic growth are discussed using this relationship. A correlation useful in judging the potentialities for improvement in anaerobic product formation processes is derived. Finally the relevance of macroscopic principles to the modeling of bioengineering systems is discussed.     

Ethanol fermentation by flocculating yeast: Performance and stability dependence on a critical fermentation rate

Summary A system coupling fermentor and decantor permitted strong accumulation of yeast flocs that were homogeneously suspended in the reactional volume. At 100–190 g/l glucose feed practically total substrate conversion was attained. At 130 g/l glucose feed the highest productivity (18.4 g.l.h) and the highest ethanol yield (90.6%) were reached with biomass levels of 80–90 g/l. We observed that the stability of this system is limited when a critical fermentation rate (D.S_o) close to 39–40 g/l.h (with corresponding ethanol productivities of 19–20 g/l.h) is reached. Higher fermentation rates provoked de-flocculation and lost of biomass.Symbols D dilution rate (h^–1) - E ethanol (g/l) - S_r residual substrate (g/l) - S_o substrate in the feed (g/l) - X biomass (g/l) - ethanol yield (%) - DS_o fermentation rate (g/l.h) (for S_r0) - P_E ethanol productivity (g/l.h)     

Analysis of the respiro-fermentative growth of Saccharomyces cerevisiae on glucose in a fed-batch fermentation strategy for accurate parameter estimation

Analysis of the respiro-fermentive growth of a strain of Saccharomyces cerevisiae, DSM 2155 on glucose, in a simulated 5-phase feeding strategy of fedbatch cultures executed on the Universal BIoprocess CONtrol (UBICON) system, was carried out. There was a good agreement between the estimated and the simulated values of specific growth rates. In this study, which was designed to span 0.20–0.23 h^–1 growth rates before returning to lower growth rates, the critical dilution rate at which the switch between purely oxidative and respiro-fermentative growth takes was not observed. The biomass yield, specific substrate uptake and O₂ consumption rates as well as the consistency of the data using both carbon and available electron balances were examined. A high average value of true biomass energetic yield, _max = 0.707, and a low value of maintenance coefficient, m_e = 0.0114 h^–1, were obtained indicating that the organism was in no danger from the ethanol produced as a high-density fermentation with a yeast concentration above 54 g 1^–1 was possible within a period of 24 h. The yeast produced also had good dough-leavening characteristics. Thus it is possible to operate a yeast plant without resorting to using respiratory quotient, which may be problematic, as the controlling parameter.     

Data consistency,yield, maintenance,and hysteresis in batch cultures of Candida lipolytica cultured on n-hexadecane

Candida lipolytica was cultured batchwise using n-hexadecane as the main carbon source. Biomass production, n-hexadecane consumption, oxygen consumption, and carbon dioxide evolution were measured to follow the fermentation. The consistency of the measured data was examined using integrated and instantaneous available electron and carbon balances. Values of the “true” growth yield, η_max, and maintenance coefficient, m_e were estimated using three different sets of data (biomass and n-hexadecane, oxygen and biomass, and CO₂ and biomass), and the results were compared with estimates obtained from literature data. Hysteresis patterns were observed in plots of specific rates of oxygen consumption and carbon dioxide evolution versus specific growth rate.     

Stoichiometry of carbohydrate fermentation and microbial growth efficiency in a continous culture of mixed rumen bacteria

Summary A population of mixed rumen bacteria was maintained in a chemostat at four different dilution rates, with glocose as the growth limiting carbon and energy substrate. Increasing the dilution rate shifted the proportions of end products: methane decreased and propionate increased. Fermentation and hydrogen balances were calculated from the fermentation end products. Values were similar to earlier ones from batch incubations of rumen contents. This suggests that theoretical overall reaction schemes for carbohydrate fermentation in the rumen, proposed earlier, are also valid in continuous culture.A positive correlation between dilution rate and microbial growth efficiency (gN_inc./kg OM_f was observed, confirming earlier work.Apparently conflicting results of chemostat work and recent in vivo experiments are discussed.     

Computer-aided material balancing for prediction of fermentation parameters.

Despite the importance of biomass as a parameter in fermentation processes, there are no commercially available sensors suitable for its measurement. An indirect approach for the assessment of biomass concentration can be based on material balances and on the direct monitoring of fermentation parameters for which there are established sensors (e.g., gaseous oxygen and carbon dioxide). As a consequence, this method requires no assumption of cellular yield coefficients or rate constants. This approach is also readily adaptable to general use since it requires only some knowledge of the compositions of the substrate, cells, and noncellular products.     

On-line identification of parameters in a fermentation process

In a fermentation process, the establishment of gas mass balances provides valuable information and allows both measurements concerning the characteristics of the biomass itself and the monitoring of a cultivation process. If the quantity and oxidation level of substances excreted into the fermentation broth are known or constant, the yield factor and the dry cell-weight production are stoichiometrically related to the quantity of CO₂ evolved and to the quantity of O₂ consumed. Where frequent measurements of both yield factor and dry cell-weight production are desirable or where rapid adjustment of the parameters is necessary, on-line identification of these parameters is required, An algorithm allowing the identification of the specific growth rate is presented. Moreover, this technique allows one to estimate the percent protein in the biomass during continuous culture.