Metabolite-balancing techniques vs. 13C tracer experiments to determine metabolic fluxes in hybridoma cells

The estimation of intracellular fluxes of mammalian cells using only mass balances of the relevant metabolites is not possible because the set of linear equations defined by these mass balances is underdetermined. In order to quantify fluxes in cyclic pathways the mass balance equations can be complemented with several constraints: (1) the mass balances of co-metabolites, such as ATP or NAD(P)H, (2) linear objective functions, (3) flux data obtained by isotopic-tracer experiments. Here, these three methods are compared for the analysis of fluxes in the primary metabolism of continuously cultured hybridoma cells. The significance of different theoretical constraints and different objective functions is discussed after comparing their resulting flux distributions to the fluxes determined using 13CO2 and 13C-lactate measurements of 1 - 13C-glucose-fed hybridoma cells. Metabolic fluxes estimated using the objective functions "maximize ATP" and "maximize NADH" are relatively similar to the experimentally determined fluxes. This is consistent with the observation that cancer cells, such as hybridomas, are metabolically hyperactive, and produce ATP and NADH regardless of the need for these cofactors.     

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.     

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 a metabolic balancing technique to the analysis of microbial fermentation data

A general method for the development of fermentation models, based on elemental and metabolic balances, is illustrated with three examples from the literature. Physiological parameters such as the (maximal) yield on ATP, the energetic maintenance coefficient, the P/O ratio and others are estimated by fitting model equations to experimental data. Further, phenomenological relations concerning kinetics of product formation and limiting enzyme activities are assessed. The results are compared with the conclusions of the original articles, and differences due to the application of improved models are discussed.     

Simple model for the energetics of growth on substrates with different degrees of reduction

A simple model is developed for the energy transformation in growing microbial systems. The model is based on a linear equation for ATP consumption in the processes of growth and maintenance. A combination of this equation with macroscopic balances for the various components, the systems exchanges with the environment, and application of the concepts of the elementary balance allow the derivation of linear equations for the exchange of substrate, oxygen, and carbon dioxide with the environment. For growth on one sole carbon and energy source the model allows the definition of a critical substrate yield are expected and below which is decreasing substrate yield and energy supply growth limitation are expected. This restriction can be interpreted in a variety of other ways. It supplies a rationale for non-energy-production-coupled transfer of hydrogen to oxygen or wasteful expenditure of ATP in growth on highly reduced substrates. It also allows the formulation of a limit to the maximum yield on oxygen that can never be exceeded in growth on highly reduced substrates.     

Estimating cell and product yields

The balance equations for carbon, reduction potential, and energy during cell growth and product formation are rederived in a general form. Cells are treated simply as a very complex product, and the Y(ATP) concept is extended to products. Limitations on the theoretical yield are discussed for different product types. Simple aerobic products cannot be energy limited unless the maintenance requirement is large, while complex products cannot be reduction limited. A maximum yield is defined for products much more oxidized than their substrate (carbon limited) because the theoretical yield conditions may violate the energy balance. For reduced complex products the yield on available electrons is related to Y(ATP), the P/O ratio, and the product composition. Narrow bounds are established on the actual yields in simple anaerobic fermentations, and the significance of the yields in the linear growth equation is discussed.     

Studies on on-line bioreactor identification. III. Sensitivity problems with respiratory and heat evolution measurements

The applicability of the respiratory quotient measurement, a heat evolution measurement, and a commonly observed correlation between the respiratory quotient and product yield to on-line bioreactor identification and control were inspected. It was found that singularities can exist in macroscopic balances used in connection with these measurements or the correlation, rendering them inappropriate for process parameter identification. By the formulation of generalized metabolic pathways together with NADH(2) and ATP balances, general rules were derived for identifying conditions causing singularities. Thus it was found that, in addition to other less probable situations, the RQ measurement becomes impractical when the degree of reductance of the substrate is identical to that of the product, if any, and close to that of biomass. The correlation always presents sensitivity problems because it is nearly a linear combination of the elemental balances and the balance arising from the definition of the respiratory quotient. The heat evolution measurement nearly always presents sensitivity problems because of a linear dependence between the enthalpy balance and the degree of reductance, or NADH(2), balance due to the regularity that the degrees of reductance of most biological compounds are proportional to their heats of combustion. Problems are considered and suggestions made for replacing the measurements, when inapplicable, or the correlation with an ATP balance. Experimental results and numerical studies on the fermentations of yeast and E. coli support the theoretically derived rules.     

Analytical solution for a hybrid Logistic-Monod cell growth model in batch and continuous stirred tank reactor culture

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth-inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic-Monod growth model, which accounts for multiple growth-dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic-Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Y_x/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic-Monod equation represents the cell growth transition from substrate-limiting condition to growth-inhibiting condition, which could be adopted to accurately describe the multi-phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale-up in industrial biotechnology.     

Yield regulation of lysine biosynthesis in Brevibacterium flavum

A scheme for lysine biosynthesis using variants of the Brevibacterium flavum intermediary metabolite synthesis is discussed. The main precursor of lysine that we are concerned with here is oxalacetate, which can be synthesized through the TCA or glyoxylate cycles or by carboxylation of PEP. Material energy balances for the main pathways of lysine biosynthesis from glucose and acetate have been formulated. Energy consumption, in the from of ATP – P_ATP (number of mol ATP consumed/1 mol lysine synthesized), was calculated for the main pathways of lysine biosynthesis. Theoretical conversion yields Y_p^max (g product/g substrate) were estimated. Experimental data were presented concerning the increase of Y_p by means of metabolism regulation: (a) by TCA-and glyoxylate-cycle enzyme induction; (b) by maintaining PEP carboxylase activity; (c) by eliminating by-product synthesis.     

Macrokinetic model for methylotrophic Pichia pastoris based on stoichiometric balance

A macrokinetic model for Pichia pastoris expressing recombinant human serum albumin is proposed. The model describes the balances of some key metabolites, ATP and NADH, during glycerol and methanol metabolism. In the glycerol growth phase, the metabolic pathways mainly include phosphorylation, glycolysis, tricarboxylic acid cycle, and respiratory chain. In the methanol growth phase, methanol is oxidized to formaldehyde at first. Then, while a part of formaldehyde is oxidized to formate, the rest is condensed with xylulose-5-monophosphate to form glyceraldehyde-3-phosphate, and further assimilated to form cell constituents. The metabolic pathways following glyceraldehyde-3-phosphate were assumed to be similar to those in the glycerol growth phase. Based on the model, the macrokinetic bioreaction rates such as the specific substrate consumption rate, the specific growth rate, the specific acetyl-CoA formation rate as well as the specific oxygen uptake rate are obtained. The specific substrate consumption rate and the specific growth rate are then coupled into a bioreactor model such that the relationship between substrate feeding rates and the main state variables, i.e., the medium volume, the concentrations of the biomass, the substrate, and the product, is set up. Experimental results demonstrate that the model can describe the cell growth and the protein production with reasonable accuracy.     

Xylitol production from sugarcane bagasse hydrolyzate in fluidized bed reactor. Effect of air flowrate

Cells of Candida guilliermondii immobilized onto porous glass spheres were cultured batchwise in a fluidized bed bioreactor for xylitol production from sugarcane bagasse hemicellulose hydrolyzate. An aeration rate of only 25 mL/min ensured minimum yields of xylose consumption (0.60) and biomass production (0.14 g(DM)/g(Xyl)), as well as maximum xylitol yield (0.54 g(Xyt)/g(Xyl)) and ratio of immobilized to total cells (0.83). These results suggest that cell metabolism, although slow because of oxygen limitation, was mainly addressed to xylitol production. A progressive increase in the aeration rate up to 140 mL/min accelerated both xylose consumption (from 0.36 to 0.78 g(Xyl)/L.h) and xylitol formation (from 0.19 to 0.28 g(Xyt)/L.h) but caused the fraction of immobilized to total cells and the xylitol yield to decrease up to 0.22 and 0.36 g(Xyt)/g(Xyl), respectively. The highest xylitol concentration (17.0 g(Xyt)/L) was obtained at 70 mL/min, but the specific xylitol productivity and the xylitol yield were 43% and 22% lower than the corresponding values obtained at the lowest air flowrate, respectively. The concentrations of consumed substrates and formed products were used in material balances to evaluate the xylose fractions consumed by C. guilliermondii for xylitol production, complete oxidation through the hexose monophosphate shunt, and cell growth. The experimental data collected at variable oxygen level allowed estimating a P/O ratio of 1.35 mol(ATP)/mol(O) and overall ATP requirements for biomass growth and maintenance of 3.4 mol(ATP)/C-mol(DM).     

Modelling Xanthomonas campestris batch fermentations in a bubble column

Rate and yield expressions relating to biomass and xanthan formation and to nitrogen, glucose, and oxygen consumption were established for Xanthomonas campestris batch fermentations in a bubble column. Microbial growth was described by the logistic rate equation, characterized by a maximum specific growth rate mu(M) = 0.5 h(-1) and a maximum attainable cell concentration provided by nitrogenous compounds. With regard to carbon metabolism, the decrease with time in experimental yields and in the experimental specific rates of xanthan production and glucose assimilation demonstrated the inadequacy of the Luedeking-Piret model. These decreases were connected to the simultaneous drop in dissolved-oxygen tension observed during xanthan synthesis. The knowledge of metabolic pathways and energetic balance were used to establish the relationships between substrate utilization, ATP generation, and xanthan production. The model was structured by assuming the oxygen limitation of both the respiration rate and the efficiency of the oxidative phosphorylation mechanism (P/O ratio). Consequently, the specific rates and yield expressions became dependent on the dissolved-oxygen tension, i.e., of the volumetric oxygen transfer in the fermentor.     

On-line stoichiometry and identification of metabolic state under dynamic process conditions

A method for the on-line calculation of conversion rates and yield coefficients under dynamic process conditions was developed. The method is based on cumulated mass balances using a moving average method. Elemental balances were used to test the measured cumulated quantities for gross errors and inappropriate stoichiometry definition followed by data reconciliation and estimation of non-measured conversion rates, using a bioprocess set-up including multiple on-line analysis techniques. The quantitative potential of the proposed method is demonstrated by executing transient experiments in aerobic cultures of Saccharomyces cerevisiae on glucose. Rates and yield coefficients could be consistently quantified in shift-up, shift-down, and accelerostat experiments. The method shows the capability to describe quantitatively transient changes in metabolism including uncoupling of catabolism and anabolism, also for the case when multiple components of metabolism are not measured. The validity of the experiment can be evaluated on-line. Additionally, the method detects with high sensitivity inappropriate stoichiometry definition, such as a change in state of metabolism. It was shown that concentration values can be misleading for the identification of the metabolic state. In contrast, the proposed method provides a clear picture of the metabolic state and new physiological regulations could be revealed. Hence, the novelty of the proposed method is the on-line availability of consistent stoichiometric coefficients allowing a significant speed up in strain characterization and bioprocess development using minimal knowledge of the metabolism. Additionally, it opens up the use of transient experiments for physiological studies.     

Modeling growth and succinoglucan production by Agrobacterium radiobacter NCIB 9042 in batch cultures

Wild-type Agrobacterium radiobacter NCIB 9042 has been cultivated in batch cultures on a synthetic medium which was adapted for growth and succinoglucan production. Experiments were carried out in a 4-L stirred-tank aerated reactor. Glucose, biomass, polysaccharide, protein, and inorganic- and organic-nitrogen concentrations were measured, and oxygen consumption and CO(2) production rates were obtained by a gas-balance technique. Nitrogen balance shows that inorganic nitrogen is entirely recovered into proteins. The carbon balance is satisfied with in +/-5%. Stoichiometric equations for biomass growth and succinoglucan synthesis were established. The biosyntheticpolymer pathways including ATP and cofactor consumption were investigated. From previous studies, a (P/O) value of 1.66 is selected for oxygen sufficient cultures. The actual ATP requirements of 25.4 mmol ATP/g succinoglucan (38.5 mol ATP/mol succinoglucan), determined by a metabolic analysis, is 2.39 times the stoichiometric value. Experimental results were modeled by a system of differential equations. The exponential growth phase was described by a nitrogen-limited Monod equation. Subsequent succinoglucan synthesis followed a slightly modified Luedeking-Piret relation partitioning internal and external polysaccharide. Experimentally determined coefficients are compared with published results for continuous culture of A. radiobacter NCIB 11883.     

Effect of oxygen on steady-state product distribution in Bacillus polymyxa fermentations

Bacillus polymyxa ferments glucose to 1-2,3 butanediol, acetoin, ethanol, acetic acid, lactic acid, and formic acid. This research investigates product formation as a function of oxygen availability. A predictive model that simulates product distribution at known oxygen transfer rates is developed on the hypothesis that, in an energy-limited environment, B. polymyxa utilizes glucose and oxygen in the most efficient manner. The efficiency of utilization of glucose and oxygen is measured in terms of the ATP yields of each oxidative pathway. The identity of the products constituting the profile at the given oxygen transfer rate is determined by comparing the ATP production and consumption rates. While the ATP generated is calculated from a knowledge of the oxygen transfer rate and ATP yields of the oxidative pathways, the ATP consumption is estimated by the Pirt expression in terms of growth- and nongrowth-associated components. The product formation rates are obtained by solving ATP and NAD balance equations. They equate the production and consumption rates of these intermediates and are derived from the pseudo-steady-state hypothesis. The model is applied to continuous culture systems that are both open and closed with respect to biomass. At a given oxygen transfer rate, dilution rate, and inlet glucose concentration, the model predicts steady-state concentrations of two dominant fermentation endproducts with the help of four parameters that can be determined from independent experiments. In contrast with earlier approaches, the experimental studies are carried out in continuous culture. Product profiles are obtained at various oxygen transfer rates, fer rates, inlet glucose concentrations, and dilution rates. The effect of pH on the relative distribution of products is also demonstrated. Results indicate that the model is fairly successful in predicting product profiles as a function of oxygen availability. (c) 1992 John Wiley & Sons, Inc.     

Energy coupling in Saccharomyces cerevisiae: selected opportunities for metabolic engineering

Free-energy (ATP) conservation during product formation is crucial for the maximum product yield that can be obtained, but often overlooked in metabolic engineering strategies. Product pathways that do not yield ATP or even demand input of free energy (ATP) require an additional pathway to supply the ATP needed for product formation, cellular maintenance, and/or growth. On the other hand, product pathways with a high ATP yield may result in excess biomass formation at the expense of the product yield. This mini-review discusses the importance of the ATP yield for product formation and presents several opportunities for engineering free-energy (ATP) conservation, with a focus on sugar-based product formation by Saccharomyces cerevisiae. These engineering opportunities are not limited to the metabolic flexibility within S.?cerevisiae itself, but also expression of heterologous reactions will be taken into account. As such, the diversity in microbial sugar uptake and phosphorylation mechanisms, carboxylation reactions, product export, and the flexibility of oxidative phosphorylation via the respiratory chain and H(+) -ATP synthase can be used to increase or decrease free-energy (ATP) conservation. For product pathways with a negative, zero or too high ATP yield, analysis and metabolic engineering of the ATP yield of product formation will provide a promising strategy to increase the product yield and simplify process conditions.     

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.     

Dynamic in vivo metabolome response of Saccharomyces cerevisiae to a stepwise perturbation of the ATP requirement for benzoate export

Although much information is available on in vitro role of ATP in regulation, the in vivo kinetics of reactions in which ATP plays a role are only partly known. In order to study such reactions, it is therefore necessary to study the role of ATP in vivo. This study presents an in vivo, targeted perturbation of the ATP flux in aerobic glucose-limited chemostat cultures of Saccharomyces cerevisiae, which was accomplished by transiently (20 min) changing the extracellular undissociated benzoic acid concentration via the pH of the culture. The performed pH shifts resulted in, within about 20 s, a 40% decrease (pH upshift) or a 23% increase (pH downshift) of the calculated ATP consumption rate while the specific glucose uptake rate did not change because of the glucose-limited condition. The pH upshift resulted in a strong decrease in the glycolytic and TCA cycle fluxes; carbon and energy balances indicated an increased flux toward storage carbohydrates. As expected, the pH downshift leads to the opposite effects. Overall, consistent responses were observed in the metabolic fluxes, the off gas concentrations of O(2) and CO(2) and intracellular metabolite concentrations, except for the concentrations of adenosine nucleotides which unexpectedly only showed minor dynamics. This demonstrates that our knowledge of the regulation of the ATP level, the storage metabolism, and central carbon metabolism of yeast is still incomplete. The new dynamic metabolite datasets obtained in this study will prove of great value in developing kinetic models.     

Availability, not respiratory capacity governs oxygen consumption of solid tumors

Contrary to conventional belief, the mitochondria of most cancer cells usually function normally, i.e., their respiratory capacity is not fundamentally impaired as compared to normal cells. Strong evidence against the misconception of mitochondrial dysfunction is provided by in vivo data clearly showing that O(2) availability is the major determinant of the O(2) consumption rate of cancer cells, independent of the means for increasing availability (e.g., by increasing blood flow or by elevating arterial O(2) content, the latter being accomplished either by an increase in the hemoglobin level and/or arterial hyperoxia). Additional support against the Warburg effect in its original concept comes from normal temperature coefficients (Q(10)) for O(2) consumption rates of malignant cells. Thus, the Warburg hypothesis postulating that mitochondrial dysfunction in cancer cells forces them to generate energy with a poor ATP yield through glycolysis appears to be elusive. Instead, due to a "reprogrammed" cancer cell metabolism, glycolysis is used to produce intermediates as building blocks for various biosynthetic pathways of cancer cells.     

Direct activation of purified protein kinase C by unsaturated fatty acids (oleate and arachidonate) in the absence of phospholipids and Ca2+

31P saturation transfer techniques have been used to measure phosphate kinetics in the yeast Saccharomyces cerevisiae. The phosphate consumption rate observed in acetate grown mid-log cells was combined with measurements of O2 consumption to yield P/O ratios of 2.2 and 2.9, for cells respiring on glucose and ethanol, respectively. However, no phosphate consumption activity was observed in saturation transfer experiments on anaerobic glucose fed cells. The phosphate consumption rates measured by saturation transfer in cells respiring on glucose and ethanol was attributed to the unidirectional rates of mitochondrial ATP synthesis.