Cybernetic models based on lumped elementary modes accurately predict strain‐specific metabolic function

In a recent article, Song and Ramkrishna (Song and Ramkrishna [2010]. Biotechnol Bioeng 106(2):271–284) proposed a lumped hybrid cybernetic model (L‐HCM) towards extracting maximum information about metabolic function from a minimum of data. This approach views the total uptake flux as distributed among lumped elementary modes (L‐EMs) so as to maximize a prescribed metabolic objective such as growth or uptake rate. L‐EM is computed as a weighted average of EMs where the weights are related to the yields of vital products (i.e., biomass and ATP). In this article, we further enhance the predictive power of L‐HCMs through modifications in lumping weights with additional parameters that can be tuned with data viewed to be critical. The resulting model is able to make predictions of diverse metabolic behaviors varying greatly with strain types as evidenced from case studies of anaerobic growth of various Escherichia coli strains. Incorporation of the new lumping formula into L‐HCM remarkably improves model predictions with a few critical data, thus presenting L‐HCM as a dynamic tool as being not only qualitatively correct but also quantitatively accurate. Biotechnol. Bioeng. 2011; 108:127–140. © 2010 Wiley Periodicals, Inc.     

Cybernetic modeling and regulation of metabolic pathways in multiple steady states of hybridoma cells

Hybridoma cells utilize a pair of complementary and partially substitutable substrates, glucose and glutamine, for growth. It has been shown that cellular metabolism shifts under different culture conditions. When those cultures at different metabolic states are switched to a continuous mode, they reach different steady states under the same operating conditions. A cybernetic model was constructed to describe the complementary and partial substitutable nature of substrate utilization. The model successfully predicted the metabolic shift and multiple steady-state behavior. The results are consistent with the experimental observation that the history of the culture affects the resulting steady state.     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Prediction of dynamic metabolic behavior of Pediococcus pentosaceus producing lactic acid from lignocellulosic sugars

A dynamic metabolic model is presented for Pediococcus pentosaceus producing lactic acid from lignocellulose-derived mixed sugars including glucose, mannose, galactose, arabinose, and xylose. Depending on the pairs of mixed sugars, P. pentosaceus exhibits diverse (i.e., sequential, simultaneous or mixed) consumption patterns. This regulatory behavior of P. pentosaceus is portrayed using the hybrid cybernetic model (HCM) framework which views elementary modes of the network as metabolic options dynamically modulated. Comprehensive data are collected for model identification and validation through fermentation experiments involving single substrates and various combinations of mixed sugars. Most sugars are metabolized rather sequentially while co-consumption of galactose and arabinose is observed. It is demonstrated that the developed HCM successfully predicts mixed sugar data based on the parameters identified mostly from single substrate data only. Further, we discuss the potential of HCMs as a tool for predicting intracellular flux distribution with comparison with flux balance analysis.     

Bonded Cumomer Analysis of Human Melanoma Metabolism Monitored by 13C NMR Spectroscopy of Perfused Tumor Cells

A network model for the determination of tumor metabolic fluxes from ¹³C NMR kinetic isotopomer data has been developed and validated with perfused human DB-1 melanoma cells carrying the BRAF V600E mutation, which promotes oxidative metabolism. The model generated in the bonded cumomer formalism describes key pathways of tumor intermediary metabolism and yields dynamic curves for positional isotopic enrichment and spin-spin multiplets. Cells attached to microcarrier beads were perfused with 26 mm [1,6-¹³C₂]glucose under normoxic conditions at 37 °C and monitored by ¹³C NMR spectroscopy. Excellent agreement between model-predicted and experimentally measured values of the rates of oxygen and glucose consumption, lactate production, and glutamate pool size validated the model. ATP production by glycolytic and oxidative metabolism were compared under hyperglycemic normoxic conditions; 51% of the energy came from oxidative phosphorylation and 49% came from glycolysis. Even though the rate of glutamine uptake was ∼50% of the tricarboxylic acid cycle flux, the rate of ATP production from glutamine was essentially zero (no glutaminolysis). De novo fatty acid production was ∼6% of the tricarboxylic acid cycle flux. The oxidative pentose phosphate pathway flux was 3.6% of glycolysis, and three non-oxidative pentose phosphate pathway exchange fluxes were calculated. Mass spectrometry was then used to compare fluxes through various pathways under hyperglycemic (26 mm) and euglycemic (5 mm) conditions. Under euglycemic conditions glutamine uptake doubled, but ATP production from glutamine did not significantly change. A new parameter measuring the Warburg effect (the ratio of lactate production flux to pyruvate influx through the mitochondrial pyruvate carrier) was calculated to be 21, close to upper limit of oxidative metabolism.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Analysis of optimal phenotypic space using elementary modes as applied to Corynebacterium glutamicum

Background  

Quantification of the metabolic network of an organism offers insights into possible ways of developing mutant strain for better productivity of an extracellular metabolite. The first step in this quantification is the enumeration of stoichiometries of all reactions occurring in a metabolic network. The structural details of the network in combination with experimentally observed accumulation rates of external metabolites can yield flux distribution at steady state. One such methodology for quantification is the use of elementary modes, which are minimal set of enzymes connecting external metabolites. Here, we have used a linear objective function subject to elementary modes as constraint to determine the fluxes in the metabolic network of Corynebacterium glutamicum. The feasible phenotypic space was evaluated at various combinations of oxygen and ammonia uptake rates.     

Optimization of 13C isotopic tracers for metabolic flux analysis in mammalian cells

Mammalian cells consume and metabolize various substrates from their surroundings for energy generation and biomass synthesis. Glucose and glutamine, in particular, are the primary carbon sources for proliferating cancer cells. While this combination of substrates generates static labeling patterns for use in (13)C metabolic flux analysis (MFA), the inability of single tracers to effectively label all pathways poses an obstacle for comprehensive flux determination within a given experiment. To address this issue we applied a genetic algorithm to optimize mixtures of (13)C-labeled glucose and glutamine for use in MFA. We identified tracer combinations that minimized confidence intervals in an experimentally determined flux network describing central carbon metabolism in tumor cells. Additional simulations were used to determine the robustness of the [1,2-(13)C(2)]glucose/[U-(13)C(5)]glutamine tracer combination with respect to perturbations in the network. Finally, we experimentally validated the improved performance of this tracer set relative to glucose tracers alone in a cancer cell line. This versatile method allows researchers to determine the optimal tracer combination to use for a specific metabolic network, and our findings applied to cancer cells significantly enhance the ability of MFA experiments to precisely quantify fluxes in higher organisms.     

Elementary mode analysis to study the preculturing effect on the metabolic state of Lactobacillus rhamnosus during growth on mixed substrates

Quantification of metabolism through elementary modes offers insights into the working of a metabolic network. We have determined the fluxes of elementary modes through linear optimization using the stoichiometry of the elementary modes as a constraint. We apply this methodology to obtain insights into the effect of preculturing on growth of Lactobacillus rhamnosus on medium containing mixed substrates. L. rhamnosus, a microaerophilic organism, produces flavor compounds such as diacetyl and acetoin during growth on glucose and citrate. The uptake of citrate has been shown to be sensitive to preculturing states of the cells. Elementary modes demonstrated that citrate was utilized by the organism as a sole carbon source. Further, both glucose and citrate was catabolized by this organism through aerobic and anaerobic routes. The flux analysis indicated that only 21 elementary modes were operational during growth of L. rhamnosus on glucose and citrate. Glucose specifically accounted for 6 elementary modes, while the remaining 15 involved citrate as substrate. The modes associated with glucose were mainly operational when cells were precultured on glucose. It was observed that all the 21 modes contributed to the fluxes when the cells were precultured on citrate. The NADH recycling through lactate formation and oxygen uptake were dependent on the preculturing state. The analysis also demonstrated that preculturing on citrate yielded better productivity of diacetyl and acetoin.     

A computer model of gluconeogenesis and lipid metabolism in the perfused liver

A mathematical model of the perfused rat liver was developed to predict intermediate metabolite concentrations and fluxes in response to changes in various substrate concentrations in the perfusion medium. The model simulates gluconeogenesis in the liver perfused separately with lactate and pyruvate and the combination of these substrates with fatty acids (oleate). The model consists of key reactions representing gluconeogenesis, glycolysis, fatty acid metabolism, tricarboxylic acid cycle, oxidative phosphorylation, and ketogenesis. Michaelis-Menten-type kinetic expressions, with control by ATP/ADP, are used for many of the reactions. For key regulated reactions (fructose-1,6-bisphosphatase, phosphofructokinase, pyruvate carboxylase, pyruvate dehydrogenase complex, and pyruvate kinase), rate expressions were developed that incorporate allosteric effectors, specific substrate relationships (e.g., cooperative binding), and/or phosphorylation/dephosphorylation using in vitro enzyme activity data and knowledge of the specific mechanisms. The model was independently validated by comparing model predictions with 10 sets of experimental data from 7 different published works, with no parameter adjustments. The simulations predict the same trends, in terms of stimulation of substrate uptake by fatty acid addition, as observed experimentally. In general, the major metabolic indicators calculated by the model are in good agreement with experimental results. For example, the simulated glucose/pyruvate mass yield is 43% compared with the average of 45% reported in the literature. The model accurately predicts the specific time constants of the glucose response (2.5-4 min) and the dynamic behavior of substrate and product fluxes. It is expected that this model will be a useful tool for analyzing the complex relationships between carbohydrate and fat metabolism.     

Continuous modeling of metabolic networks with gene regulation in yeast and in vivo determination of rate parameters

A continuous model of a metabolic network including gene regulation to simulate metabolic fluxes during batch cultivation of yeast Saccharomyces cerevisiae was developed. The metabolic network includes reactions of glycolysis, gluconeogenesis, glycerol and ethanol synthesis and consumption, the tricarboxylic acid cycle, and protein synthesis. Carbon sources considered were glucose and then ethanol synthesized during growth on glucose. The metabolic network has 39 fluxes, which represent the action of 50 enzymes and 64 genes and it is coupled with a gene regulation network which defines enzyme synthesis (activities) and incorporates regulation by glucose (enzyme induction and repression), modeled using ordinary differential equations. The model includes enzyme kinetics, equations that follow both mass-action law and transport as well as inducible, repressible, and constitutive enzymes of metabolism. The model was able to simulate a fermentation of S. cerevisiae during the exponential growth phase on glucose and the exponential growth phase on ethanol using only one set of kinetic parameters. All fluxes in the continuous model followed the behavior shown by the metabolic flux analysis (MFA) obtained from experimental results. The differences obtained between the fluxes given by the model and the fluxes determined by the MFA do not exceed 25% in 75% of the cases during exponential growth on glucose, and 20% in 90% of the cases during exponential growth on ethanol. Furthermore, the adjustment of the fermentation profiles of biomass, glucose, and ethanol were 95%, 95%, and 79%, respectively. With these results the simulation was considered successful. A comparison between the simulation of the continuous model and the experimental data of the diauxic yeast fermentation for glucose, biomass, and ethanol, shows an extremely good match using the parameters found. The small discrepancies between the fluxes obtained through MFA and those predicted by the differential equations, as well as the good match between the profiles of glucose, biomass, and ethanol, and our simulation, show that this simple model, that does not rely on complex kinetic expressions, is able to capture the global behavior of the experimental data. Also, the determination of parameters using a straightforward minimization technique using data at only two points in time was sufficient to produce a relatively accurate model. Thus, even with a small amount of experimental data (rates and not concentrations) it was possible to estimate the parameters minimizing a simple objective function. The method proposed allows the obtention of reasonable parameters and concentrations in a system with a much larger number of unknowns than equations. Hence a contribution of this study is to present a convenient way to find in vivo rate parameters to model metabolic and genetic networks under different conditions.     

Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

Fundamental Escherichia coli biochemical pathways for biomass and energy production: creation of overall flux states

We have previously shown that the metabolism for most efficient cell growth can be realized by a combination of two types of elementary modes. One mode produces biomass while the second mode generates only energy. The identity of the four most efficient biomass and energy pathway pairs changes, depending on the degree of oxygen limitation. The identification of such pathway pairs for different growth conditions offers a pathway-based explanation of maintenance energy generation. For a given growth rate, experimental aerobic glucose consumption rates can be used to estimate the contribution of each pathway type to the overall metabolic flux pattern. All metabolic fluxes are then completely determined by the stoichiometries of involved pathways defining all nutrient consumption and metabolite secretion rates. We present here equations that permit computation of network fluxes on the basis of unique pathways for the case of optimal, glucose-limited Escherichia coli growth under varying levels of oxygen stress. Predicted glucose and oxygen uptake rates and some metabolite secretion rates are in remarkable agreement with experimental observations supporting the validity of the presented approach. The entire most efficient, steady-state, metabolic rate structure is explicitly defined by the developed equations without need for additional computer simulations. The approach should be generally useful for analyzing and interpreting genomic data by predicting concise, pathway-based metabolic rate structures.     

Analysis of metabolic fluxes for hyaluronic acid (HA) production by Streptococcus zooepidemicus

Summary A detailed metabolic flux analysis (MFA) for hyaluronic acid (HA) production by Streptococcus zooepidemicus was carried out. A metabolic network was constructed for the metabolism of S. zooepidemicus. Fluxes through these reactions were estimated by MFA using accumulation rates of biomass and product, consumption rate of glucose in batch fermentation and dissolved oxygen-controlled fermentation. The changes of the fluxes were observed at different stages of batch fermentation and in different dissolved oxygen tension (DOT)-controlled fermentation processes. The effects of metabolic nodes on HA accumulation under various culture conditions were investigated. The results showed that high concentration of glucose in the medium did not affect metabolic flux distribution, but did influence the uptake rate of glucose. HA synthesis was influenced by DOT via flux redistribution in the principal node. Adenosine triphosphate (ATP) and reduced nicotinamide adenine dinucleotide (NADH) produced in the fermentation process are associated with cell growth and HA synthesis.     

Unveiling steady-state multiplicity in hybridoma cultures: the cybernetic approach

Mammalian cells grown in suspension produce waste metabolites such as lactate, alanine, and ammonia, which reduce the yield of cell mass and the desired product on the nutrients supplied. Previous studies (Cruz et al., 1999; Europa et al., 2000; Follstad et al., 1999) have shown that the cells can be made to alter their metabolism by starving them on their nutrients in continuous cultures at low dilution rates or starting the culture as a fed-batch. This leads to multiple steady states in continuous reactors, with some states being more favorable than others. Mathematical models that take into account the metabolic regulation that leads to these multiple steady states are invaluable tools for bioreactor control. In this article we present a cybernetic modeling strategy in which Metabolic Flux Analysis (MFA) is used to guide the cybernetic formulation. The hybridoma model presented as a result of this strategy considers the partially substitutable, partially complementary nature of glucose and glutamine. The choice of competitions within the network is guided by MFA and the model is successful in explaining the three multiple steady states observed. The cybernetic model though identified for the hybridoma experiments of Hu and others (Europa et al., 2000) seem generally applicable to mammalian systems as it captures the pathways that are common to mammalian cells grown in suspension. The model presented here could be used for start-up strategies for continuous reactors and model-based feedback control for maintaining high productivity of the reactor.     

Metabolic flux analysis gives an insight on verapamil induced changes in central metabolism of HL-1 cells

Verapamil has been shown to inhibit glucose transport in several cell types. However, the consequences of this inhibition on central metabolism are not well known. In this study we focused on verapamil induced changes in metabolic fluxes in a murine atrial cell line (HL-1 cells). These cells were adapted to serum free conditions and incubated with 4 μM verapamil and [U-¹³C₅] glutamine. Specific extracellular metabolite uptake/production rates together with mass isotopomer fractions in alanine and glutamate were implemented into a metabolic network model to calculate metabolic flux distributions in the central metabolism. Verapamil decreased specific glucose consumption rate and glycolytic activity by 60%. Although the HL-1 cells show Warburg effect with high lactate production, verapamil treated cells completely stopped lactate production after 24 h while maintaining growth comparable to the untreated cells. Calculated fluxes in TCA cycle reactions as well as NADH/FADH₂ production rates were similar in both treated and untreated cells. This was confirmed by measurement of cell respiration. Reduction of lactate production seems to be the consequence of decreased glucose uptake due to verapamil. In case of tumors, this may have two fold effects; firstly depriving cancer cells of substrate for anaerobic glycolysis on which their growth is dependent; secondly changing pH of the tumor environment, as lactate secretion keeps the pH acidic and facilitates tumor growth. The results shown in this study may partly explain recent observations in which verapamil has been proposed to be a potential anticancer agent. Moreover, in biotechnological production using cell lines, verapamil may be used to reduce glucose uptake and lactate secretion thereby increasing protein production without introduction of genetic modifications and application of more complicated fed-batch processes.     

Quantitative in vivo nuclear magnetic resonance studies of hybridoma metabolism

Carbon-13 nuclear magnetic resonance (NMR) spectroscopy was used to study the metabolism of a murine hybridoma cell line at two feed glutamine concentrations, 4.0 and 1.7 mM. Carbon-13 labeling patterns were used in conjunction with nutrient uptake rates to calculate the metabolic fluxes through the glycolytic pathway, the pentose shunt, the malate shunt, lipid biosynthesis, and the tricarboxylic acid (TCA) cycle. Decreasing the feed glutamine concentration significantly decreased glutamine uptake but had little effect on glucose metabolism. A significant incrase in antibody productivity occurred upon decreasing the feed glutamine level. The increased antibody productivity in concert with decreased glutamine uptake and no apparent change in glucolytic metabolism suggests that antibody production was not energy limited. Metabolic flux calculations indicate that (1) approximately 92% of the glucose consumed proceeds directly through glycolysis with 8% channeled through the pentose shunt; (2) lipid biosynthesis appears to be greater than malate shunt activity; and (3) considerable exchange occurs between TCA cycle intermediates and amino acid metabolic pools, leading to substantial loss of (13)C label from the TCA cycle. These results illustrate that (13)NMR spectroscopy is a powerfulf tool in the calculation of metabolic fluxes, particularly for exchange pathways where no net flux occurs. (c) 1994 John Wiley & Sons, Inc.     

Role of microvillar cell surfaces in the regulation of glucose uptake and organization of energy metabolism

Experimental evidencesuggesting a type of glucose uptake regulation prevailing inresting and differentiated cells was surveyed. This type of regulationis characterized by transport-limited glucose metabolism and depends onsegregation of glucose transporters on microvilli of differentiated orresting cells. Earlier studies on glucose transport regulation and arecently presented general concept of influx regulation for ions andmetabolic substrates via microvillar structures provide the basicframework for this theory. According to this concept, glucose uptakevia transporters on microvilli is regulated by changes in thestructural organization of the microfilament bundle, which is acting asa diffusion barrier between the microvillar tip compartment and thecytoplasm. Both microvilli formation and the switch of glucosemetabolism from "metabolic regulation" to "transportlimitation" occur during differentiation. The formation ofmicrovillar cell surfaces creates the essential preconditions toestablish the characteristic functions of specialized tissue cellsincluding the coordination between glycolysis and oxidativephosphorylation, regulation of cellular functions by external signals,and Ca²⁺ signaling. The proposed concept integrates variousaspects of glucose uptake regulation into a ubiquitous cellularmechanism involved in regulation of transmembrane ion and substrate fluxes.