Energy transformation and entropy production in living systems I. Applications to embryonic growth

Generalized material and energy balances are presented for biological systems that experience negligible kinetic, elastic, and potential energy changes. The balances are used to characterize the mass changes and energy transformations that occur in the developing avian embryo, using as an example a consistent set of data for the chicken egg. It is shown that the rate of total chemical energy turnover by the embryo is a quantity of interest and that this rate is not necessarily equivalent to the metabolic rate that is predicted from heat transfer measurements or oxygen consumption rates. The energy required for evaporative water loss is accounted for in the overall energy balance. Using the results of the energy calculations and a generalized expression for the rates of internal and total entropy production, the Prigogine-Wiame hypothesis is examined for the developing embryo with two different assumptions regarding the efficiency of biomass conversion. An order of magnitude analysis of the internal heat-conduction term is performed to show that the chemical reaction term dominates the entropy production relation. The constant efficiency case is shown to be in agreement with the Prigogine-Wiame hypothesis for the data used in the analysis.     

Dynamic metabolic flux analysis (DMFA): a framework for determining fluxes at metabolic non-steady state

Metabolic flux analysis (MFA) is a key tool for measuring in vivo metabolic fluxes in systems at metabolic steady state. Here, we present a new method for dynamic metabolic flux analysis (DMFA) of systems that are not at metabolic steady state. The advantages of our DMFA method are: (1) time-series of metabolite concentration data can be applied directly for estimating dynamic fluxes, making data smoothing and estimation of average extracellular rates unnecessary; (2) flux estimation is achieved without integration of ODEs, or iterations; (3) characteristic metabolic phases in the fermentation data are identified automatically by the algorithm, rather than selected manually/arbitrarily. We demonstrate the application of the new DMFA framework in three example systems. First, we evaluated the performance of DMFA in a simple three-reaction model in terms of accuracy, precision and flux observability. Next, we analyzed a commercial glucose-limited fed-batch process for 1,3-propanediol production. The DMFA method accurately captured the dynamic behavior of the fed-batch fermentation and identified characteristic metabolic phases. Lastly, we demonstrate that DMFA can be used without any assumed metabolic network model for data reconciliation and detection of gross measurement errors using carbon and electron balances as constraints.     

Error propagation in constraint-based modeling of Chinese hamster ovary cells

Chinese hamster ovary (CHO) cells are the most popular mammalian cell factories for the production of glycosylated biopharmaceuticals. To further increase titer and productivity and ensure product quality, rational system-level engineering strategies based on constraint-based metabolic modeling, such as flux balance analysis (FBA), have gained strong interest. However, the quality of FBA predictions depends on the accuracy of the experimental input data, especially on the exchange rates of extracellular metabolites. Yet, it is not standard practice to devote sufficient attention to the accurate determination of these rates. In this work, we investigated to what degree the sampling frequency during a batch culture and the measurement errors of metabolite concentrations influence the accuracy of the calculated exchange rates and further, how this error then propagates into FBA predictions of growth rates. We determined that accurate measurements of essential amino acids with low uptake rates are crucial for the accuracy of FBA predictions, followed by a sufficient number of analyzed time points. We observed that the measured difference in growth rates of two cell lines can only be reliably predicted when both high measurement accuracy and sampling frequency are ensured.     

Metabolic flux analysis of hybridoma cells in different culture media using mass balances

The estimation of the intracellular fluxes of mammalian cells using only the mass balances of the relevant metabolites is not possible because the set of linear equations defined by these mass balances is underdetermined. Either additional experimental flux data or additional theoretical constraints are required to find one unique flux distribution out of the solution space that is bound by the mass balances. Here, a method is developed using the latter approach. The uptake and production rates of amino acids, glucose, lactate, O(2), CO(2), NH(4), MAB, and the intracellular amino acid pools have been determined for two different steady-states. The cellular composition {total protein and protein composition, total lipids and fatty acid distribution, total carbohydrates, DNA and RNA} has been measured to calculate the requirements for biosynthesis. It is shown to be essential to determine the uptake/production rates of ammonia and either carbon dioxide or oxygen. In mammalian cells these are cometabolites of cyclic metabolic pathways. The flux distribution that is found using the Euclidean minimum norm as the additional theoretical constraint and taking either the CO(2) or the NAD(P)H mass balance into account is shown to be in agreement with the measured O(2) and CO(2) metabolic rates.The metabolic fluxes in hybridoma cells in continuous culture at a specific growth rate of 0.83 day(-1) are estimated for a medium with (optimal medium) and without (suboptimal medium) Primatone RL, an enzymatic hydrolysate of animal tissue that causes a more than twofold increase in cell density. It is concluded that (i)The majority of the consumed glucose (>90%) is channeled through the pentose-phosphate pathway in rapidly proliferating cells.(ii)Pyruvate oxidation and tricarboxylic acid (TCA) cycle activity are relatively low, i.e., 8% of the glucose uptake in suboptimal and 14% in optimal medium, respectively. Under both conditions, only a small fraction of pyruvate is further oxidized to CO(2).(iii)The flux from glutamate to alpha-ketoglutarate (catalyzed by glutamate dehydrogenase) is almost zero in medium with and even slightly reversed in medium without Primatone RL. Almost all glutamate enters the TCA cycle due to the action of transaminases.(iv)Transhydrogenation plays a significant role in hybridoma cells under our experimental conditions. NADPH is produced at relatively high rates (11 x 10(-12) to 13 x 10(-12) mol . cell(-1) . day(-1)) compared to other fluxes in both culture media. (c) 1996 John Wiley & Sons, Inc.     

Metabolic flux and metabolic network analysis of Penicillium chrysogenum using 2D [13C, 1H] COSY NMR measurements and cumulative bondomer simulation

At present two alternative methods are available for analyzing the fluxes in a metabolic network: (1) combining measurements of net conversion rates with a set of metabolite balances including the cofactor balances, or (2) leaving out the cofactor balances and fitting the resulting free fluxes to measured (13)C-labeling data. In this study these two approaches are applied to the fluxes in the glycolysis and pentose phosphate pathway of Penicillium chrysogenum growing on either ammonia or nitrate as the nitrogen source, which is expected to give different pentose phosphate pathway fluxes. The presented flux analyses are based on extensive sets of 2D [(13)C, (1)H] COSY data. A new concept is applied for simulation of this type of (13)C-labeling data: cumulative bondomer modeling. The outcomes of the (13)C-labeling based flux analysis substantially differ from those of the pure metabolite balancing approach. The fluxes that are determined using (13)C-labeling data are shown to be highly dependent on the chosen metabolic network. Extending the traditional nonoxidative pentose phosphate pathway with additional transketolase and transaldolase reactions, extending the glycolysis with a fructose 6-phosphate aldolase/dihydroxyacetone kinase reaction sequence or adding a phosphoenolpyruvate carboxykinase reaction to the model considerably improves the fit of the measured and the simulated NMR data. The results obtained using the extended version of the nonoxidative pentose phosphate pathway model show that the transketolase and transaldolase reactions need not be assumed reversible to get a good fit of the (13)C-labeling data. Strict statistical testing of the outcomes of (13)C-labeling based flux analysis using realistic measurement errors is demonstrated to be of prime importance for verifying the assumed metabolic model.     

Fermentation data analysis and state estimation in the presence of incomplete mass balance

A method is developed for identifying measurement errors and estimating fermentation states in the presence of unidentified reactant or product. Unlike conventional approaches using elemental balances, this method employs an empirically determined basis, which can tolerate unidentified reaction species. The essence of this approach is derived from the concept of reaction subspace and the technique of singular value decomposition. It is shown that the subspace determined via singular value decomposition of multiple experimental data provides an empirical basis for identifying measurement errors. The same approach is applied to fermentation state estimation. Via the formulation of the reaction subspace, the sensitivity of state estimates to measurement errors is quantified in terms of a dimensionless quantity, maximum error gain (MEG). It is shown that using the empirically determined subspace, one can circumvent the problem of unidentified reaction species, meanwhile reducing the sensitivity of the estimates.     

Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems

The last few years have brought tremendous progress in experimental methods for metabolic flux determination by carbon-labeling experiments. A significant enlargement of the available measurement data set has been achieved, especially when isotopomer fractions within intracellular metabolite pools are quantitated. This information can be used to improve the statistical quality of flux estimates. Furthermore, several assumptions on bidirectional intracellular reaction steps that were hitherto indispensable may now become obsolete. To make full use of the complete measurement information a general mathematical model for isotopomer systems is established in this contribution. Then, by introducing the important new concept of cumomers and cumomer fractions, it is shown that the arising nonlinear isotopomer balance equations can be solved analytically in all cases. In particular, the solution of the metabolite flux balances and the positional carbon-labeling balances presented in part I of this series turn out to be just the first two steps of the general solution procedure for isotopomer balances. A detailed analysis of the isotopomer network structure then opens up new insights into the intrinsic structure of isotopomer systems. In particular, it turns out that isotopomer systems are not as complex as they appear at first glance. This enables some far-reaching conclusions to be drawn on the information potential of isotopomer experiments with respect to flux identification. Finally, some illustrative examples are examined to show that an information increase is not guaranteed when isotopomer measurements are used in addition to positional enrichment data.     

Possible pitfalls of flux calculations based on (13)C-labeling

Metabolic engineers have enthusiastically adopted the (13)C-labeling technique as a powerful tool for elucidating fluxes in metabolic networks. This tracer technique makes it possible to determine fluxes that are unobservable using only metabolite balances and allows the elimination of doubtful cofactor balances that are indispensable in flux analysis based on metabolite balancing alone. The (13)C-labeling technique, however, relies on a number of assumptions that are not free from uncertainties. Two possible errors in the models that are needed to determine the metabolic fluxes from labeling data are omitted reactions and ignored occurrence of channeling. By means of two representative examples it is shown that these modeling errors may lead to serious errors in the calculated flux distributions despite the use of labeling data. A complicating fact is that the model errors are not always easily detected as poor models may still yield good fits of experimental data. Results of (13)C-labeling experiments should therefore be interpreted with appropriate caution.     

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.     

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.     

Modeling threshold phenomena, metabolic pathways switches and signals in chemostat-cultivated cells: the Crabtree effect in Saccharomyces cerevisiae

The long-term Crabtree effect in Saccharomyces cerevisiae cultivated in aerobic chemostat at steady state has been studied for three different substrate concentrations in the feed of the bioreactor (data: J. Gen. Microbiol., 129 (1983) 653). We have shown that a model using two ways of transport/metabolization (T/M) of hyperbolic form, with high and low affinity for the substrate, allowed to represent correctly the main characteristics of the phenomenon. The model is based on an explicit form of the T/M kinetics when the bioreactor is considered as a polyphasic dispersed system (PDS). Mass balances analysis also allows to quantify the critical dilution rate value (threshold), Dc, of the transition between respiratory and respirofermentative mode, for which ethanol is produced. A good approximation for the threshold is Dc = V(S)0 Y(Xc, S) where Y(Xc,S) is the average yield coefficient before transition and V(S)0, the maximum specific rate of high affinity T/M pathway. The theoretical value is 0.3 h(-1), and is equal to the experimental value. We thus show in a quantitative way that the transition depends both on culture conditions (global characteristic of the system) and on strain properties (intrinsic characteristic of the microorganism as well). Using two different methods to calculate the residual substrate has carried out the comparison between the simulations end the experimental data. This allowed showing that the latter is not well represented by Monod's model and has confirmed that the affinity for the substrate varies according to the biomass. We have then shown how to calculate the most important specific rates (or metabolic flux) related to biomass, ethanol, oxygen, hydrogen, respiratory and fermentative CO(2) and H(2)O within the cellular phase. It has appeared that the oxygen uptake rate directly depends on high-affinity T/M pathway. This let us think that the regulation of the Crabtree effect in S. cerevisiae depends on the saturation of some glucose metabolization and transport pathways rather than on saturation of the respiratory chains. The specific rates analysis has also allowed us to show, at least in this case, that the metabolization rate (biosynthesis+fueling) had its maximum value on the whole dilution rates interval; metabolites excretion (ethanol and fermentative CO(2)) only intervenes to drain a "surplus" glucose flux. As a consequence, the transport capacity must be higher than the one of metabolization. Maximization of the metabolization specific rate could then be used as an optimization criterion in the stoichiometric calculation of metabolic flux (and not the specific growth rate maximization because growth is limited in a chemostat (mu = D)). We have also shown that the mass balances based on the T/M processes are in agreement with molar and elementary balances of the general stoichiometric equation for glucose respiration and fermentation under aerobic conditions. Thanks to the specific rates calculating the stoichiometric coefficients has done this. The total mass balance difference does not exceed 4%, which is compatible with the experimental carbon balance. Finally, we have emphasized that the ratio of biosynthesis flux and metabolization flux is constant before and after transition. This observation could be applied as soon as the free substrate concentration in the cellular phase is low. The paper succinctly describes the former theoretical results on which the model is built and sufficiently explains the algorithm for straightforward implementation.     

Optimal co-allocation of carbon and nitrogen in a forest stand at steady state

Nitrogen (N) is essential for plant production, but N uptake imposes carbon (C) costs through maintenance respiration and fine-root construction, suggesting that an optimal C:N balance can be found. Previous studies have elaborated this optimum under exponential growth; work on closed canopies has focused on foliage only. Here, the optimal co-allocation of C and N to foliage, fine roots and live wood is examined in a closed forest stand. Optimal co-allocation maximizes net primary productivity (NPP) as constrained by stand-level C and N balances and the pipe model. Photosynthesis and maintenance respiration increase with foliar nitrogen concentration ([N]), and stand-level photosynthesis and N uptake saturate at high foliage and fine-root density. Optimal NPP increases almost linearly from low to moderate N availability, saturating at high N. Where N availability is very low or very high, the system resembles a functional balance with a steady foliage [N]; in between, [N] increases with N availability. Carbon allocation to fine roots decreases, allocation to wood increases, and allocation to foliage remains stable with increasing N availability. The predicted relationships between biomass density and foliage [N] are in reasonable agreement with data from coniferous stands across Finland. All predictions agree with our qualitative understanding of N effects on growth.     

On describing microbial growth kinetics from continuous culture data: Some general considerations,observations, and concepts

Analysis of continuous culture methodology suggests that this potentially powerful tool for kinetic analysis can be improved by minimizing several inherent shortcomings. Medium background substrates — organic carbon, phosphate, and manganese — were shown to dominate kinetic observations at concentrations below chemical detection methods. Reactor wall growth, culture size distribution changes, sample removal-induced steady state perturbations, and limiting substrate leakage from organisms are treated in terms of kinetic measurement errors. Large variations in maximal growth rates and substrate uptake rates found are attributed to experimental protocol-induced transient states. Relationships are presented for correcting limiting substrate concentrations for lability during sampling, contamination with unreacted medium, and background substrate effects. Analytical procedures are discussed for improved measurement of limiting substrate kinetics involving enzymes, isotopes, and material balance manipulation. Relaxation methods as applied to continuous culture are introduced as a means for isolating separate rate constants describing net substrate transport and for evaluating cellular metabolite leakage. Low velocity growth, multiple substrate metabolism, and endogenous metabolism are discussed along with measurements showing that 1-month generation times for aquatic microorganisms can be quite normal and that the kinetics are compatible withμg/liter limiting substrate concentrations. The concept of regarding growth kinetics as the sum of several net accumulation processes is suggested.     

Metabolic Profiling and Flux Analysis of MEL-2 Human Embryonic Stem Cells during Exponential Growth at Physiological and Atmospheric Oxygen Concentrations

As human embryonic stem cells (hESCs) steadily progress towards regenerative medicine applications there is an increasing emphasis on the development of bioreactor platforms that enable expansion of these cells to clinically relevant numbers. Surprisingly little is known about the metabolic requirements of hESCs, precluding the rational design and optimisation of such platforms. In this study, we undertook an in-depth characterisation of MEL-2 hESC metabolic behaviour during the exponential growth phase, combining metabolic profiling and flux analysis tools at physiological (hypoxic) and atmospheric (normoxic) oxygen concentrations. To overcome variability in growth profiles and the problem of closing mass balances in a complex environment, we developed protocols to accurately measure uptake and production rates of metabolites, cell density, growth rate and biomass composition, and designed a metabolic flux analysis model for estimating internal rates. hESCs are commonly considered to be highly glycolytic with inactive or immature mitochondria, however, whilst the results of this study confirmed that glycolysis is indeed highly active, we show that at least in MEL-2 hESC, it is supported by the use of oxidative phosphorylation within the mitochondria utilising carbon sources, such as glutamine to maximise ATP production. Under both conditions, glycolysis was disconnected from the mitochondria with all of the glucose being converted to lactate. No difference in the growth rates of cells cultured under physiological or atmospheric oxygen concentrations was observed nor did this cause differences in fluxes through the majority of the internal metabolic pathways associated with biogenesis. These results suggest that hESCs display the conventional Warburg effect, with high aerobic activity despite high lactate production, challenging the idea of an anaerobic metabolism with low mitochondrial activity. The results of this study provide new insight that can be used in rational bioreactor design and in the development of novel culture media for hESC maintenance and expansion.     

Analysis of CHO cells metabolic redistribution in a glutamate-based defined medium in continuous culture.

The effect of glutamine replacement by glutamate and the balance between glutamate and glucose metabolism on the redistribution of t-PA-producing recombinant CHO cells metabolism is studied in a series of glucose shift down and shift up experiments in continuous culture. These experiments reveal the existence of multiple steady states, and experimental data are used to perform metabolic flux analysis to gain a better insight into cellular metabolism and its redistribution. Regulation of glucose feed rate promotes a higher efficiency of glucose and nitrogen source utilization, with lower production of metabolic byproducts, but this reduces t-PA specific production rate. This reduction under glucose limitation can be attributed to the fact that the cells are forced to efficiently utilize the carbon and energy source for growth, impairing the production of dispensable metabolites. It is, therefore, the combination of growth rate and carbon and energy source availability that determines the level of t-PA production in continuous culture.     

L-缬氨酸生物合成中的代谢流量分析

应用流量平衡模型 ,通过物料衡算和MATLAB线性规划方法得到了发酵中后期L 缬氨酸合成过程的代谢流量分步。代谢流分析结果表明 ,在分批培养生成L 缬氨酸的过程中 ,有62 8%的葡萄糖进入糖酵解途径生成L 缬氨酸 ,38 2 %进入HMP途径 ,仅 9 2 %的碳架进入TCA循环。实验条件下的代谢流 (58)与理想代谢流 (92 31 )相比 ,仍应从遗传改造和发酵控制方面降低TCA循环的代谢流 ,减少副产氨基酸的生成来进一步提高缬氨酸的产率。     

Application of dynamic metabolic flux analysis for process modeling: Robust flux estimation with regularization,confidence bounds,and selection of elementary modes

In macroscopic dynamic models of fermentation processes, elementary modes (EM) derived from metabolic networks are often used to describe the reaction stoichiometry in a simplified manner and to build predictive models by parameterizing kinetic rate equations for the EM. In this procedure, the selection of a set of EM is a key step which is followed by an estimation of their reaction rates and of the associated confidence bounds. In this paper, we present a method for the computation of reaction rates of cellular reactions and EM as well as an algorithm for the selection of EM for process modeling. The method is based on the dynamic metabolic flux analysis (DMFA) proposed by Leighty and Antoniewicz (2011, Metab Eng, 13(6), 745–755) with additional constraints, regularization and analysis of uncertainty. Instead of using estimated uptake or secretion rates, concentration measurements are used directly to avoid an amplification of measurement errors by numerical differentiation. It is shown that the regularized DMFA for EM method is significantly more robust against measurement noise than methods using estimated rates. The confidence intervals for the estimated reaction rates are obtained by bootstrapping. For the selection of a set of EM for a given st oichiometric model, the DMFA for EM method is combined with a multiobjective genetic algorithm. The method is applied to real data from a CHO fed-batch process. From measurements of six fed-batch experiments, 10 EM were identified as the smallest subset of EM based upon which the data can be described sufficiently accurately by a dynamic model. The estimated EM reaction rates and their confidence intervals at different process conditions provide useful information for the kinetic modeling and subsequent process optimization.     

METABOLISM AS RELATED TO CHROMOSOME STRUCTURE AND THE DURATION OF LIFE

This paper presents the rates of CO₂ production for four groups of Drosophila which differ in their chromosome constitutions. The four groups have metabolic rates which correlate with the balance of their chromosomes, the balanced chromosome groups of flies producing less CO₂ than the unbalanced chromosome groups. It is concluded therefore that genic balance plays a prominent part in metabolic control. The carbon dioxide rates are related to the duration of life within these groups. The results show that qualitatively the larger the production of CO₂ per day the shorter the time which the flies are capable of living. The agreement is not exact quantitatively. Rubner''s theory postulating a limit for the energy an organism is capable of metabolizing does not hold for the six classes of flies. The data show that the theory can be at most not more than a partial truth. Cell size is found to show no direct correlation with the metabolic rates of the different fly cohorts.