Modeling of microbial substrate conversion,growth and product formation in a recycling fermentor

Paracoccus denitrificans and Bacillus licheniformis were grown in a carbon- and energy source-limited recycling fermentor with 100% biomass feedback. Experimental data for biomass accumulation and product formation as well as rates of carbon dioxide evolution and oxygen consumption were used in a parameter optimization procedure. This procedure was applied on a model which describes biomass growth as a linear function of the substrate consumption rate and the rate of product formation as a linear function of the biomass growth rate. The fitting procedure yielded two growth domains for P. denitrificans. In the first domain the values for the maximal growth yield and the maintenance coefficient were identical to those found in a series of chemostat experiments. The second domain could be described best with linear biomass increase, which is equal to a constant growth yield. Experimental data of a protease producing B. licheniformis also yielded two growth domains via the fitting procedure. Again, in the first domain, maximal growth yield and maintenance requirements were not significantly different from those derived from a series of chemostat experiments. Domain 2 behaviour was different from that observed with P. denitrificans. Product formation halts and more glucose becomes available for biomass formation, and consequently the specific growth rate increases in the shift from domain 1 to 2. It is concluded that for many industrial production processes, it is important to select organisms on the basis of a low maintenance coefficient and a high basic production of the desired product. It seems less important that the maximal production becomes optimized, which is the basis of most selection procedures.     

Studies on quantitative physiology of Trichoderma reesei with two-stage continuous culture for cellulose production

By employing a two-stage continuous-culture system, some of the more important physiological parameters involved in cellulose biosynthesis have been evaluated with an ultimate objective of designing an optimally controlled cellulose process. The two-stage continuous-culture system was run for a period of 1350 hr with Trichoderma reesei strain MCG-77. The temperature and pH were controlled at 32°C and pH 4.5 for the first stage (growth) and 28°C and pH 3.5 for the second stage (enzyme production). Lactose was the only carbon source for the both stages. The ratio of specific uptake rate of carbon to that of nitrogen, Q(C)/Q(N), that supported good cell growth ranged from 11 to 15, and the ratio for maximum specific enzyme productivity ranged from 5 to 13. The maintenance coefficients determined for oxygen, M_O, and for carbon source, M_C, are 0.85 mmol O₂/g biomass/hr and 0.14 mmol hexose/g biomass/hr, respectively. The yield constants determined are: Y_X/O = 32.3 g biomass/mol O₂, Y_X/C = 1.1 g biomass/g C or Y_X/C = 0.44 g biomass/g hexose, Y_X/N = 12.5 g biomass/g nitrogen for the cell growth stage, and Y_X/N = 16.6 g biomass/g nitrogen for the enzyme production stage. Enzyme was produced only in the second stage. Volumetric and specific enzyme productivities obtained were 90 IU/liter/hr and 8 IU/g biomass/hr, respectively. The maximum specific enzyme productivity observed was 14.8 IU/g biomass/hr. The optimal dilution rate in the second stage that corresponded to the maximum enzyme productivity was 0.026 ～ 0.028 hr^?1, and the specific growth rate in the second stage that supported maximum specific enzyme productivity was equal to or slightly less than zero.     

Effect of malic acid on the growth kinetics of<Emphasis Type="Italic"> Lactobacillus plantarum</Emphasis>

The fermentation kinetics of Lactobacillus plantarum were studied in a specially designed broth formulated from commercially available, dehydrated components (yeast extract, trypticase, ammonium sulfate) in batch and continuous culture. During batch growth in the absence of malic acid, the specific growth rate was 0.20 h^–1. Malic acid in the medium, at 2 mM or 10 mM, increased the specific growth rate of L. plantarum to 0.34 h^–1. An increase in the maximum cell yield due to malic acid also was observed. Malic acid in the medium (12 mM) reduced the non-growth-associated (maintenance energy) coefficient and increased the biomass yield in continuous culture, based on calculations from the Luedeking and Piret model. The biomass yield coefficient was estimated as 27.4 mg or 34.3 mg cells mmol^–1 hexose in the absence or presence of malic acid, respectively. The maintenance coefficient was estimated as 3.5 mmol or 1.5 mmol hexose mg^–1 cell h^–1 in the absence or presence of malic acid. These results clearly demonstrate the energy-sparing effect of malic acid on the growth- and non-growth-associated energy requirements for L. plantarum. The quantitative energy-sparing effect of malic acid on L. plantarum has heretofore not been reported, to our knowledge.     

The effect of temperature on bacterial degradation of EDTA in pH-auxostat

The effect of temperature on the maximum specific growth rate and the cell yield was studied during cultivation of two bacterial strains (LPM-4 and Pseudomonas sp. LPM-410) on EDTA under unlimited cell growth conditions in a pH-auxostat. Both strains displayed linear dependence of reciprocal biomass yield against reciprocal specific growth rate, from which the values of rate of substrate expenditure for cell maintenance and the “maximum” yield (i.e., hypothetical yield without cell maintenance processes) were estimated. Analysis of the maximum yield values based on mass–energy balance theory suggested that oxidation of the carboxylic acid side chains of EDTA by a monooxygenase had zero or low energetic efficiency. An Arrhenius equation with different values of Arrhenius parameters within different temperature ranges gave a good fit with the temperature dependence of both growth rate and biomass yield. Specific growth rates of both strains showed a more pronounced temperature dependence than did the cell yields. A possible kinetic mechanism was suggested which might be responsible for the modes of the temperature dependences of specific growth rate and yield that were found. The mechanism is based on a hypothetical key substance governing the metabolic flows, which is formed in a zero-order reaction and destroyed in a first-order reaction, both rate constants depending on temperature according to the Arrhenius law.     

Stoichiometric and kinetic characterisation of Nitrosomonas sp. in mixed culture by decoupling the growth and energy generation processes

A novel method that relies on the decoupling of the energy production and biosynthesis processes was used to characterise the maintenance, cell lysis and growth processes of Nitrosomonas sp. A Nitrosomonas culture was enriched in a sequencing batch reactor (SBR) with ammonium as the sole energy source. Fluorescent in situ hybridization (FISH) showed that Nitrosomonas bound to the NEU probe constituted 82% of the bacterial population, while no other known ammonium or nitrite oxidizing bacteria were detected. Batch tests were carried out under conditions that both ammonium and CO2 were in excess, and in the absence of one of these two substrates. The oxygen uptake rate and nitrite production rate were measured during these batch tests. The results obtained from these batch tests, along with the SBR performance data, allowed the determination of the maintenance coefficient and the in situ cell lysis rate, as well as the maximum specific growth rate of the Nitrosomonas culture. It is shown that, during normal growth, the Nitrosomonas culture spends approximately 65% of the energy generated for maintenance. The maintenance coefficient was determined to be 0.14-0.16 mgN mgCOD(biomass)(-1)h(-1), and was shown to be independent of the specific growth rate. The in situ lysis rate and the maximum specific growth rate of the Nitrosomonas culture were determined to be 0.26 and 1.0 day(-1) (0.043 h(-1)), respectively, under aerobic conditions at 30 degrees C and pH 7.     

Software sensors for fermentation processes

Four software sensors based on standard on-line data from fermentation processes and simple mathematical models were used to monitor a number of state variables in Escherichia coli fed-batch processes: the biomass concentration, the specific growth rate, the oxygen transfer capacity of the bioreactor, and the new R _O/S sensor which is the ratio between oxygen and energy substrate consumption. The R _O/S variable grows continuously in a fed-batch culture with constant glucose feed, which reflects the increasing maintenance demand at declining specific growth rate. The R _O/S sensor also responded to rapid pH shift-downs reflecting the increasing demand for maintenance energy. It is suggested that this sensor may be used to monitor the extent of physiological stress that demands energy for survival.     

A screening model to predict microalgae biomass growth in photobioreactors and raceway ponds

A microalgae biomass growth model was developed for screening novel strains for their potential to exhibit high biomass productivities under nutrient‐replete conditions in photobioreactors or outdoor ponds. Growth is modeled by first estimating the light attenuation by biomass according to Beer‐Lambert's Law, and then calculating the specific growth rate in discretized culture volume slices that receive declining light intensities due to attenuation. The model uses only two physical and two species‐specific biological input parameters, all of which are relatively easy to determine: incident light intensity, culture depth, as well as the biomass light absorption coefficient and the specific growth rate as a function of light intensity. Roux bottle culture experiments were performed with Nannochloropsis salina at constant temperature (23°C) at six different incident light intensities (10, 25, 50, 100, 250, and 850 µmol/m² s) to determine both the specific growth rate under non‐shading conditions and the biomass light absorption coefficient as a function of light intensity. The model was successful in predicting the biomass growth rate in these Roux bottle batch cultures during the light‐limited linear phase at different incident light intensities. Model predictions were moderately sensitive to minor variations in the values of input parameters. The model was also successful in predicting the growth performance of Chlorella sp. cultured in LED‐lighted 800 L raceway ponds operated in batch mode at constant temperature (30°C) and constant light intensity (1,650 µmol/m² s). Measurements of oxygen concentrations as a function of time demonstrated that following exposure to darkness, it takes at least 5 s for cells to initiate dark respiration. As a result, biomass loss due to dark respiration in the aphotic zone of a culture is unlikely to occur in highly mixed small‐scale photobioreactors where cells move rapidly in and out of the light. By contrast, as supported also by the growth model, biomass loss due to dark respiration occurs in the dark zones of the relatively less well‐mixed pond cultures. In addition to screening novel microalgae strains for high biomass productivities, the model can also be used for optimizing the pond design and operation. Additional research is needed to validate the biomass growth model for other microalgae species and for the more realistic case of fluctuating temperatures and light intensities observed in outdoor pond cultures. Biotechnol. Bioeng. 2013; 110: 1583–1594. © 2012 Wiley Periodicals, Inc.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

Stoichiometric and kinetic characterisation of Nitrobacter in mixed culture by decoupling the growth and energy generation processes

The growth, maintenance and lysis processes of Nitrobacter were characterised. A Nitrobacter culture was enriched in a sequencing batch reactor (SBR). Fluorescent in situ hybridisation showed that Nitrobacter constituted 73% of the bacterial population. Batch tests were carried out to measure the oxygen uptake rate and/or nitrite consumption rate when both nitrite and CO2 were in excess, and in the absence of either of these two substrates. The results obtained, along with the SBR performance data, allowed the determination of the maintenance coefficient and in situ cell lysis rate of Nitrobacter. Nitrobacter spends a significant amount of energy for maintenance, which varies considerably with the specific growth rate. At maximum growth, Nitrobacter consume nitrite at a rate of 0.042 mgN/mgCOD(biomass) . h for maintenance purposes, which increases more than threefold to 0.143 mgN/mgCOD(biomass) . h in the absence of growth. In the SBR, where Nitrobacter grew at 40% of its maximum growth rate, a maintenance coefficient of 0.113 mgN/mgCOD . h was found, resulting in 42% of the total amount of nitrite being consumed for maintenance. The above three maintenance coefficient values obtained at different growth rates appear to support the maintenance model proposed in Pirt (1982). The in situ lysis rate of Nitrobacter was determined to be 0.07/day under aerobic conditions at 22 degrees C and pH 7.3. Further, the maximum specific growth rate of Nitrobacter was estimated to be 0.02/h (0.48/day). The affinity constant of Nitrobacter with respect to nitrite was determined to be 1.50 mgNO2(-)-N/L, independent of the presence or absence of CO2.     

Respiratory energy costs for the maintenance of biomass, for growth and for ion uptake in roots of Carex diandra and Carex acudformis

van der Werf, A., Kooijman, A., Welschen, R. and Lambers, H. 1988. Respiratory energy costs for the maintenance of biomass, for growth and for ion uptake in roots of Carex diandra and Carex acutiformis. - Physiol. Plant. 72: 483–491. The respiratory characteristics of the roots of Carex diandra Schrank and Carex acutiformis Ehrh. were investigated. The aims were, firstly to determine the respiratory energy costs for the maintenance of root biomass, for root growth and for ion uptake, and secondly to explain the higher rate of root respiration and ATP production in C. diandra. The three respiratory energy components were derived from a multiple regression analysis, using the relative growth rate and the net rate of nitrate uptake as independent variables and the rate of ATP production as a dependent variable. Although the rate of root respiration and ATP production was significantly higher in C. diandra than in C. acutiformis, the two species showed no significant difference in their rate of ATP production for the maintenance of biomass, in the respiratory energy coefficient for growth (the amount of ATP production per unit of biomass produced) and the respiratory energy coefficient for ion uptake (amount of ATP production per unit of ions absorbed). It is concluded that the higher rate of root respiration of C. diandra is caused by a higher rate of nitrate uptake. At relatively high rates of growth and nitrate uptake, the contribution of the rate of ATP production for ion uptake to the total rate of ATP production amounted to 38 and 25% for C. diandra and C. acutiformis, respectively. At this growth rate, the respiratory energy production for growth contributed 37 and 50%, respectively, to the total rate of ATP production. The relative contribution of the rate of ATP production for the maintenance of biomass increased from 25 to 70% with increasing plant age for both species. The results suggest that ion uptake is one of the major sinks for respiratory energy in roots. These experimentally derived values for the rate of ATP production for the maintenance of biomass, the respiratory energy coefficient for growth and the respiratory energy coefficient for ion uptake are discussed in relation to other experimentally and theoretically derived values.     

Selection and evaluation of astaxanthin-overproducing mutants of Phaffia rhodozyma

Mutagenesis of Phaffia rhodozyma with NTG yielded a mutant with an astaxanthin content of 1688 g (g dry biomass)^-1, a cell yield coefficient of 0.47 on glucose and a maximum specific growth rate of 0.12 h^-1. Re-mutation of the mutant decreased the cell yield and maximum specific growth rate but increased the astaxanthin content. The use of mannitol or succinate as carbon sources enhanced pigmentation, yielding astaxanthin contents of 1973 g g^-1 and 1926 g g^-1, respectively. The use of valine as sole nitrogen source also increased astaxanthin production, but severely decreased the maximum specific growth rate and cell yield coefficient. The optimum pH for growth of P. rhodozyma was between pH 4.5 and 5.5, whereas the astaxanthin content remained constant above pH 3.     

A theoretical reassessment of microbial maintenance and implications for microbial ecology modeling

We attempted to reconcile three microbial maintenance models (Herbert, Pirt, and Compromise) through a theoretical reassessment. We provided a rigorous proof that the true growth yield coefficient (Y(G) ) is the ratio of the specific maintenance rate (a in Herbert) to the maintenance coefficient (m in Pirt). Other findings from this study include: (1) the Compromise model is identical to the Herbert for computing microbial growth and substrate consumption, but it expresses the dependence of maintenance on both microbial biomass and substrate; (2) the maximum specific growth rate in the Herbert (μ(max,H) ) is higher than those in the other two models (μ(max,P) and μ(max,C) ), and the difference is the physiological maintenance factor (m(q) =?a); and (3) the overall maintenance coefficient (m(T) ) is more sensitive to m(q) than to the specific growth rate (μ(G) ) and Y(G) . Our critical reassessment of microbial maintenance provides a new approach for quantifying some important components in soil microbial ecology models.     

Effect of Growth Rate and Nutrient Limitation on the Composition and Biomass Yield of Acinetobacter calcoaceticus

Acinetobacter calcoaceticus was grown on ethanol in a chemostat as a model system for single-cell protein production. The substrate yield coefficient (Y(s), grams of biomass/gram of ethanol), protein yield coefficient (Y(p), grams of protein/gram of ethanol), and biomass composition were measured as a function of the specific growth rate. Nucleic acid, protein, Y(p), and Y(s) all increased at higher growth rates. Although protein content increased only 14% (from 53 to 67%), Y(p) almost doubled over the same range of growth rates. The increase in Y(p) was due to the higher protein content of the biomass and to higher values of Y(s). The higher values of Y(s) were attributed to maintenance metabolism, and the value of the maintenance coefficient was found to be 0.11 g of ethanol per g of cell per h. When A. calcoaceticus was cultivated under a phosphorus limitation protein content, Y(p) and Y(s) were lower than in carbon-limited cultures. It was concluded that a single-cell protein fermentation using A. calcoaceticus should be operated at a high growth rate under ethanol-limiting conditions in order to maximize both the protein content of the biomass and the amount of biomass and/or protein made from the substrate.     

Effect of bioreactor configuration on substrate uptake by cell suspension cultures of the plant Eschscholtzia californica

Summary The uptake of carbohydrates and oxygen by cell suspension cultures of the plant Eschscholtzia californica (California poppy) was studied in relation to biomass production in shake flasks, a 1-1 stirred-tank bioreactor and a 1-1 pneumatically agitated bioreactor. The sequence of carbohydrate uptake was similar in all cases, with sucrose hydrolysis occurring followed by the preferential uptake of glucose. The uptake of fructose was found to be affected by the oxygen supply rate. Carbohydrate utilization occurred at a slower rate in the bioreactors. Apparent biomass yields, Y _X/S, ranged from 0.42 to 0.50 g biomass/g carbohydrate, while true biomass yields, Y _X/S, were about 0.69 g/g. The maintenance coefficient for carbohydrate, m _S, ranged between 0.002 and 0.008 g/dry weight (DW) per hour. The maximum measured specific oxygen uptake rate was 0.56 mmol O₂/g DW per hour and occurred early in the growth stage. The decline in specific uptake rate coincided with a decline in cell viability. The oxygen uptake rate was faster in shake flasks, corresponding to the higher growth rate obtained. The true growth yield on oxygen, YX/O₂, was calculated to range from 0.83 to 1.23 g biomass/g O₂, while the maintenance coefficient, mO₂, ranged from 0.15 to 0.25 mmol O₂/g DW per hour. The growth yields for oxygen determined from the stoichiometry of an elemental balance were within 10% of those calculated from experimental data. Offprint requests to: Raymond L. Legge     

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.     

Misconceptions About the Relation Between Plant Growth and Respiration

Abstract: The relation between plant growth rate and respiration rate is readily derived from the overall chemical reaction for aerobic metabolism. The derived relation can be used to show that separation of respiration into growth (g) and maintenance (m) components is not a useful concept. g and m cannot be unambiguously measured or defined in terms of biochemical processes. Moreover, because growth yield calculations from biochemical pathway analysis, from biomass molecular composition, from biomass heat of combustion, and from biomass elemental composition have not included all of the energy costs for biosynthesis, they are not accurate measures of the carbon cost for plant growth. Improper definitions of growth-respiration relations are impeding the use of physiological properties for prediction of plant growth as a function of environmental variables.     

Influence of substrate concentration on the macroenergetic parameters of anaerobic digestion of black-olive wastewater

Summary The macroenergetic parameters of the anaerobic digestion of black-olive wastewater, i.e. the yield coefficient for the biomass (Y. g VSS/g COD) and the specific rate of substrate uptake for cell maintenance (m, g COD/g VSS-day) decreased 6 limes and increased 5 times. respectively, when the influent substrate concentration increased from 1.1 to 4.4 g COD/l. This was significant at 95% confidence level. The use of the Guiot kinetic model allows a more accurate prediction of growth yield to be made as it relates substrate utilization to product formation.     

Growth of thiobacillus ferrooxidans under electrochemical reduction of inorganic energy source used

An electrolytic cell was designed and constructed for the formentation of T. ferroxidans using Fe²⁺ as the energy-supplying substrate. The Fe³⁺ produced by T. ferrooxidans by fermentation is continuously reduced to Fe ₂₊ in the electrolytic cell. A suitable version of the electrolytic cell permitted the elimination of most inorganic solid matter (precipitate) from the fermentation process. The fermentation of T. ferrooxidans was carried out with and without the electrolytic cell. Fermentation with the cell yielded significant rises both in the maximum obtainable growth rate and the biomass concentration. The experimental of data are discussed and the theoretical substrate consumption coefficient was calculated for Fe²⁺ as a function of the pH and the coefficient was compared with the experimental results.     

2,3-Butanediol production by Enterobacter aerogenes in continuous culture: role of oxygen supply

Summary The influence of oxygen on growth and production of 2,3-butanediol and acetoin by Enterobacter aerogenes was studied in continuous culture. At all dilution rates (D) studied cell mass increased steadily with increasing oxygen uptake rate (OUR), hence the micro-aerobic cultivation was energy-limited. The biomass yield on oxygen increased with D which suggests that cells need more energy for maintenance functions at lower D. At each D an optimal OUR giving highest volumetric productivity for the sum of butanediol and acetoin was found. The optimal OUR increased with D. The occurrence of optimal OURs results from the various effects of O₂ on growth and specific productivity. The latter was found to be a linear function of the specific OUR irrespective of D. At optimal OUR the cells proved to have equal specific OURs and equal specific productivities representing a fixed relationship between fermentative and respiratory metabolism. The product yield based on glucose and corrected for biomass formation was 80%. A product concentration as high as 43 g/l was obtained at D =0.1 h^–1 while the volumetric productivity was the highest at D =0.28 h^–1 (5.6 g/l and hour). The findings further indicate that growth and product generation are obviously non-associated phenomena. Hence, high productivities may be achievable by cell recycling and cell immobilisation systems. Offprint requests to: W.-D. Deckwer     

A comparison between aerobic growth of Bacillus licheniformis in continuous culture and partial-recycling fermentor,with contributions to the discussion on maintenance energy demand

Energy costs of biomass synthesis are relatively higher at low than at high specific growth rates () because of an increased protein content of the cell and increased costs of protein synthesis as such at low values. A comparison of aerobic, glucose limited cultures of Bacillus licheniformis in a chemostat and in a partial-recycling fermentor indicated that pulse-wise nutrient addition increased the maintenance energy demand (m). In the chemostat experiments, we also found a striking deviation from linearity between substrate consumption and , with large implications for the maintenance coefficient. The deviation is mainly due to a large shift in metabolic carbon flows at specific growth rates between 50 and 100% of _max. At those growth rates, uncoupled growth occurs, presumably as a necessary condition for faster growth, since uncoupling results in a faster energysupply for biosynthetic purposes.The maintenance coefficient as determined by chemostat studies should be regarded as a compounds parameter, constituted of maintenance energy demands like ppGpp accumulation, variable costs of mRNA and protein accumulation, kinetic proofreading etc. and influenced by fermentor operation parameters like the substrate addition rate; moreover, both constancy of m and a linear relation between m and appear quite unlikely.