Carbon Balance of a Mannitol Fermentation and the Biosynthetic Pathway

The carbon balance was determined for a fermentation in which mannitol is produced from glucose by an Aspergillus species. The products found were: cells (17% of carbon input), CO(2) (26%), mannitol (35%), glycerol (10%), erythritol (2.5%), glycogen (1%), and unidentified compounds (8%). Thus, 92% of the carbon input was accounted for. Cell-free enzyme studies showed that mannitol was synthesized via the reduction of fructose-6-phosphate and not by the direct reduction of fructose. If the cell yield from glucose was assumed to be 50% and the theoretical conversion efficiency from glucose to polyols was 90%, as calculated from the energy balance, then 34% of the glucose carbon was used for growth and 53% was used for polyol formation.     

Expanded thermodynamic true yield prediction model: adjustments and limitations

Bacterial yield prediction is critical for bioprocess optimization and modeling of natural biological systems. In previous work, an expanded thermodynamic true yield prediction model was developed through incorporating carbon balance and nitrogen balance along with electron balance and energy balance. In the present work, the application of the expanded model is demonstrated in multiple growth situations (aerobic heterotrophs, anoxic, anaerobic heterotrophs, and autolithotrophs). Two adjustments are presented that enable improved prediction when additional information regarding the environmental conditions (pH) or degradation pathway (requirement for oxygenase- or oxidase-catalyzed reactions) is known. A large data set of reported yields is presented and considered for suitability in model validation. Significant uncertainties of literature-reported yield values are described. Evaluation of the model with experimental yield values shows good predictive ability. However, the wide range in reported yields and the variability introduced into the prediction by uncertainty in model parameters, limits comprehensive validation. Our results suggest that the uncertainty of the experimental data used for validation limits further improvement of thermodynamic prediction models.     

The estimation of growth yield and maintenance parameters for photoautotrophic growth

Methods are presented for examining the consistency of experimental data for microbial growth where light energy is converted to chemical energy through photosynthesis. True growth yield and maintenance parameters are estimated for several sets of available experimental data. Methods of parameter estimation are presented which allow all of the measured variables to be used simultaneously for parameter estimation. The results show that a wide range of values have been found for the true growth yield and maintenance parameters. Values of the true growth yield range from 0.04 to values above those predicted by the Z-scheme model for photosynthesis.     

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.     

Acclimation in dynamic models based on structural relationships

1. A number of recent tree growth models have been based on the assumption that tree structure follows certain empirical rules and carbon allocation is performed so as to maintain these rules when growth and senescence occur simultaneously. This paper introduces a method of combining structural rules with adaptive regulation in a carbon balance model.
2. The method is based on regulating gross growth but situations are analysed where increased senescence of tissue functions as an alternative means of re-establishing the balance.
3. The model does not aim to be mechanistic but merely to describe the process of regulation, or acclimation to changing environments and situations, as constrained by the carbon balance. The method incorporates parameters that describe the rate of returning to the balance after disturbance or after a change in the goal, which can be determined empirically.
4. Two models are given as examples of the use of the method, and the requirements and limitations of control in a carbon balance framework are discussed.
5. The method is best applied as a technical tool to describe variations and disturbance in balanced growth models when the variations are present but not very large. In addition, it can be used as a theoretical framework for the analysis of regulation as constrained by the conservation of mass.     

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.     

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.     

Growth efficiency of thielavia terrestris mycelial structures

The growth energetic efficiency (η) of two mycelial forms of Thielavia terrestris (pellets and diffused form) was studied by different methods. η Values determined by the pulse method are similar for the two forms, but the values determined by C balance for pellets were lower than those for diffused mycelium. These balance data prove that pellets yield more extracellular products than the diffused mycelium form, which is also confirmed by experimental data for different amounts of carbon in the culture fluid. Growth efficiency can be determined by various methods based on the principles of mass and energy balance. The estimates most frequently used are the biomass and substrate balances. However, growth efficiency determination according to oxygen balance (particularly by the pulse method) is simpler and more accurate; as it makes possible the immediate fixation of changes in the physiological condition of microorganisms and the determination of complex substrate utilization efficiency [1]. Earlier the possible use of this method for evaluating the growth efficiency of heterotrophic bacteria [2], hyphalic and yeast forms of microscopic fungi [3] was shown. The aim of the present study is the comparative investigation of the growth efficiency of two mycelial structures (hyphalic and pellets) by different methods as well as by pulse additions.     

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.     

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.     

A combined mass and energy balance to provide bioindicators of soil microbiological quality

In this work, a method is proposed to quantify the efficiency of carbon utilization by soil microbes. Microcalorimetry was used to compute the heat yield (Y(Q/X)) of six soil samples collected in the Amazon. A combined mass and energy balance is developed to quantify the enthalpy of the glucose oxidation reaction (Delta(r)H(s)) and the biomass yield (Y(X/S)) from the experimental values of Y(Q/X). Results were compared by graphical analysis to establish the kinetics of the glucose oxidation and the microbial growth reactions in terms of energy dissipation. The correlations found suggest that the measured values for Y(Q/X) and Delta(r)H(s) are biomass yield dependent. The main environmental factors affecting the kinetics of the glucose oxidation and the microbial growth reactions in soils are the initial microbial population and the percentage of nitrogen of the samples. The comparative study among the samples showed that the deforestation of the Primary forests in the Amazon to establish arable lands, affected the efficiency of the carbon utilization by soil microorganisms.     

Thermodynamic electron equivalents model for bacterial yield prediction: modifications and comparative evaluations

Modifications are made to an earlier thermodynamic model (TEEM1) for prediction of maximum microbial yields from aerobic and anaerobic as well as heterotrophic and autotrophic growth. The revised model (TEEM2) corrects for lower yields found with aerobic oxidations of organic compounds where an oxygenase is involved and with growth on single-carbon (C1) compounds. TEEM1 and TEEM2 are based on energy release and consumption as determined from the reduction potential or Gibbs free energy of (1/2)-reaction reduction equations together with losses of energy during energy transfer. Energy transfer efficiency is a key parameter needed to make predictions with TEEM2, and was determined through evaluations with extensive data sets on aerobic heterotrophic yield available in the literature. For compounds following normal catabolic pathways, the best-fit value for energy transfer efficiency was 0.37, which permitted accurate predictions of growth with a precision of 15%-20% as determined by standard deviation. Using the same energy transfer efficiency, a similar precision, but somewhat less accuracy was found for organic compounds where oxidation involves an oxygenase (estimates 8% too high) and for C1 compounds (estimates 17% too high). In spite of the somewhat lower accuracy, the TEEM2 modifications resulted in improved predictions over TEEM1 and the comparison models.     

Assessment of macroenergetic parameters for an anaerobic upflow biomass bed and filter (UBF) reactor

This article reports the steady-state performance of two hybrid anaerobic digesters treating soluble synthetic sugar wastes of 1 and 0.5% strength and the assessment of the associated macroenergetic parameters (growth yield, so-called maintenance coefficient). A theoretical development shows a "nongrowth" parameter concept to be more appropriate than maintenance or decay. Combined energy and mass balances are used to develop a model for growth rate which compares well with experimental data. The COD removal efficiency had no significant effect on growth yield and the maintenance parameter, although a dual combined balance indicated the possibility of such an effect. Macroenergetic parameters did not vary significantly with the specific feeding rate of the system. We thus conclude that a single model may be used over a broad range of feeding and performance conditions.     

Kinetic and stoichiometric parameters estimation in a nitrifying bubble column through "in-situ" pulse respirometry

This article proposes a simple "in-situ" pulse respirometric method for the estimation of four important kinetic and stoichiometric parameters. The method is validated in a suspended biomass nitrifying reactor for the determination of (i) maximum oxygen uptake rate (OUR(ex)max), (ii) oxidation yield (f(E)), (iii) biomass growth yield (f(S)), and (iv) affinity constant (K(S)). OUR(ex)max and f(E) were directly obtained from respirograms. In the presented case study, a minimum substrate pulse of 10 mgNH(4) (+)-N L(-1) was necessary to determine OUR(ex)max which was 61.15 +/- 4.09 mgO(2) L(-1) h(-1) (5 repetitions). A linear correlation (r(2) = 0.93) obtained between OUR(ex)max and the biomass concentration in the reactor suggests that biomass concentration can be estimated from respirometric experiments. The substrate oxidation yield, f(E), was determined along 60 days of continuous operation with an average error of 5.6%. The biomass growth yield was indirectly estimated from the substrate oxidation yield f(E). The average obtained value (0.10 +/- 0.04 mgCOD mg(-1)COD) was in accordance with the f(S) estimation by the traditional COD mass balance method under steady-state conditions (0.09 +/- 0.01). The affinity constant K(S) was indirectly estimated after fitting the ascending part of the respirogram to a theoretical model. An average value of 0.48 +/- 0.08 mgNH(4) (+)-N L(-1) was obtained, which is in the range of affinity constants reported in the literature for the nitrification process (0.16-2 mgNH(4) (+)-N L(-1)).     

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.     

Modeling aerobic carbon oxidation and storage by integrating respirometric, titrimetric, and off-gas CO2 measurements

A method for detailed investigation of aerobic carbon degradation processes by microorganisms is presented. The method relies on an integrated use of the respirometric, titrimetric, and off-gas CO(2) measurements. The oxygen uptake rate (OUR), hydrogen ion production rate (HPR), and the carbon dioxide transfer rate (CTR) resulting from the biological as well as physicochemical processes, coupled with a metabolic model characterizing both the growth and carbon storage processes, enables the comprehensive study of the carbon degradation processes. The method allows the formation of carbon storage products and the biomass growth rates to be estimated without requiring any off-line biomass or liquid-phase measurements, although the practical identifiability of the system could be improved with additional measurements. Furthermore, the combined yield for biomass growth and carbon storage is identifiable, along with the affinity constant with respect to the carbon substrate. However, the individual yields for growth and carbon storage are not identifiable without further knowledge about the metabolic pathways employed by the microorganisms in the carbon conversion. This is true even when more process variables are measured. The method is applied to the aerobic carbon substrate degradation by a full-scale sludge using acetate as an example carbon source. The sludge was able to quickly take up the substrate and store it as poly-beta-hydroxybutyrate (PHB). The PHB formation rate was a few times faster than the biomass growth rate, which was confirmed by off-line liquid- and solid-phase analysis. The estimated combined yield for biomass growth and carbon storage compared closely to that determined from the theoretical yields reported in literature based on thermodynamics. This suggests that the theoretical yields may be used as default parameters for modeling purposes.