Carbon metabolism and the sign of control coefficients in metabolic adaptations underlying K-ras transformation

Metabolic adaptations are associated with changes in enzyme activities. These adaptations are characterized by patterns of positive and negative changes in metabolic fluxes and concentrations of intermediate metabolites. Knowledge of the mechanism and parameters governing enzyme kinetics is rarely available. However, the signs-increases or decreases-of many of these changes can be predicted using the signs of metabolic control coefficients. These signs require the only knowledge of the structure of the metabolic network and a limited qualitative knowledge of the regulatory dependences, which is widely available for carbon metabolism. Here, as a case study, we identified control coefficients with fixed signs in order to predict the pattern of changes in key enzyme activities which can explain the observed changes in fluxes and concentrations underlying the metabolic adaptations in oncogenic K-ras transformation in NIH-3T3 cells. The fixed signs of control coefficients indicate that metabolic changes following the oncogenic transformation-increased glycolysis and oxidative branch of the pentose-phosphate pathway, and decreased concentration in sugar-phosphates-could be associated with increases in activity for glucose-6-phosphate dehydrogenase, pyruvate kinase and lactate dehydrogenase, and decrease for transketolase. These predictions were validated experimentally by measuring specific activities. We conclude that predictions based on fixed signs of control coefficients are a very robust tool for the identification of changes in enzyme activities that can explain observed metabolic adaptations in carbon metabolism.     

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.     

Model of Tryptophan Metabolism,Readily Scalable Using Tissue-specific Gene Expression Data

Tryptophan is utilized in various metabolic routes including protein synthesis, serotonin, and melatonin synthesis and the kynurenine pathway. Perturbations in these pathways have been associated with neurodegenerative diseases and cancer. Here we present a comprehensive kinetic model of the complex network of human tryptophan metabolism based upon existing kinetic data for all enzymatic conversions and transporters. By integrating tissue-specific expression data, modeling tryptophan metabolism in liver and brain returned intermediate metabolite concentrations in the physiological range. Sensitivity and metabolic control analyses identified expected key enzymes to govern fluxes in the branches of the network. Combining tissue-specific models revealed a considerable impact of the kynurenine pathway in liver on the concentrations of neuroactive derivatives in the brain. Moreover, using expression data from a cancer study predicted metabolite changes that resembled the experimental observations. We conclude that the combination of the kinetic model with expression data represents a powerful diagnostic tool to predict alterations in tryptophan metabolism. The model is readily scalable to include more tissues, thereby enabling assessment of organismal tryptophan metabolism in health and disease.     

A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments

While flux balance analysis (FBA) provides a framework for predicting steady-state leaf metabolic network fluxes, it does not readily capture the response to environmental variables without being coupled to other modelling formulations. To address this, we coupled an FBA model of 903 reactions of soybean (Glycine max) leaf metabolism with e-photosynthesis, a dynamic model that captures the kinetics of 126 reactions of photosynthesis and associated chloroplast carbon metabolism. Successful coupling was achieved in an iterative formulation in which fluxes from e-photosynthesis were used to constrain the FBA model and then, in turn, fluxes computed from the FBA model used to update parameters in e-photosynthesis. This process was repeated until common fluxes in the two models converged. Coupling did not hamper the ability of the kinetic module to accurately predict the carbon assimilation rate, photosystem II electron flux, and starch accumulation of field-grown soybean at two CO₂ concentrations. The coupled model also allowed accurate predictions of additional parameters such as nocturnal respiration, as well as analysis of the effect of light intensity and elevated CO₂ on leaf metabolism. Predictions included an unexpected decrease in the rate of export of sucrose from the leaf at high light, due to altered starch–sucrose partitioning, and altered daytime flux modes in the tricarboxylic acid cycle at elevated CO₂. Mitochondrial fluxes were notably different between growing and mature leaves, with greater anaplerotic, tricarboxylic acid cycle and mitochondrial ATP synthase fluxes predicted in the former, primarily to provide carbon skeletons and energy for protein synthesis.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies

The metabolism of a cell can be viewed as a weighted sum of elementary modes. Due to the multiplicity of modes the identification of the individual weights represents a non-trivial problem. To enable the determination of weighting factors we have identified and implemented two gene deletions in combination with defined growth conditions that limit the metabolism from 4374 original elementary modes to 24 elementary modes for a non-PHB synthesizing control and 40 modes for a PHB synthesizing strain. These remaining modes can be further grouped into five families that have the same overall stoichiometry. Thus, the complexity of the problem is significantly reduced, and weighting factors for each family of modes could be determined from the measurement of accumulation rates of metabolites. Moreover, it is shown that individual weights are inversely correlated with the entropy generated by the operation of the used pathways defined in elementary modes. This suggests that evolution developed cellular regulatory patterns that permit diversity of pathways while favoring efficient pathways with low entropy generation. Furthermore, such correlation provides a rational way of estimating metabolic fluxes based on the thermodynamic properties of elementary modes. This is demonstrated with an example in which experimentally determined, intracellular fluxes are shown to be highly correlated with fluxes computed based on elementary modes and reaction entropies. The analysis suggests that the set of elementary modes can be interpreted analogous to a metabolic ensemble of quantum states of a macroscopic system.     

Candidate metabolic network states in human mitochondria. Impact of diabetes, ischemia, and diet

The human mitochondrial metabolic network was recently reconstructed based on proteomic and biochemical data. Linear programming and uniform random sampling were applied herein to identify candidate steady states of the metabolic network that were consistent with the imposed physico-chemical constraints and available experimental data. The activity of the mitochondrion was studied under four metabolic conditions: normal physiologic, diabetic, ischemic, and dietetic. Pairwise correlations between steady-state reaction fluxes were calculated in each condition to evaluate the dependence among the reactions in the network. Applying constraints on exchange fluxes resulted in predictions for intracellular fluxes that agreed with experimental data. Analyses of the steady-state flux distributions showed that the experimentally observed reduced activity of pyruvate dehydrogenase in vivo could be a result of stoichiometric constraints and therefore would not necessarily require enzymatic inhibition. The observed changes in the energy metabolism of the mitochondrion under diabetic conditions were used to evaluate the impact of previously suggested treatments. The results showed that neither normalized glucose uptake nor decreased ketone body uptake have a positive effect on the mitochondrial energy metabolism or network flexibility. Taken together, this study showed that sampling of the steady-state flux space is a powerful method to investigate network properties under different conditions and provides a basis for in silico evaluations of effects of potential disease treatments.     

Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns

A dynamic model called hybrid cybernetic model (HCM) based on structured metabolic network is established for simulating mammalian cell metabolism featured with partially substitutable and partially complementary consumption patterns of two substrates, glucose and glutamine. Benefiting from the application of elementary mode analysis (EMA), the complicated metabolic network is decomposed into elementary modes (EMs) facilitating the employment of the hybrid cybernetic framework to investigate the external and internal flux distribution and the regulation mechanism among them. According to different substrate combination, two groups of EMs are obtained, i.e., EMs associated with glucose uptake and simultaneous uptake of glucose and glutamine. Uptake fluxes through various EMs are coupled together via cybernetic variables to maximize substrate uptake. External fluxes and internal fluxes could be calculated and estimated respectively, by the combination of the stoichiometrics of metabolic networks and fluxes through regulated EMs. The model performance is well validated via three sets of experimental data. Through parameter identification of limited number of experimental data, other external metabolites are precisely predicted. The obtained kinetic parameters of three experimental cultures have similar values, which indicates the robustness of the model. Furthermore, the prediction performance of the model is successfully validated based on identified parameters.     

Development of a mathematical model for evaluating the dynamics of normal and apoptotic Chinese hamster ovary cells

A metabolic flux based methodology was developed for modeling the metabolism of a Chinese hamster ovary cell line. The elimination of insignificant fluxes resulted in a simplified metabolic network which was the basis for modeling the significant metabolites. Employing kinetic rate expressions for growing and non-growing subpopulations, a logistic model was developed for cell growth and dynamic models were formulated to describe culture composition and monoclonal antibody (MAb) secretion. The model was validated for a range of nutrient concentrations. Good agreement was obtained between model predictions and experimental data. The ultimate goal of this study is to establish a comprehensive dynamic model which may be used for model-based optimization of the cell culture for MAb production in both batch and fed-batch systems.     

Metabolic flux analysis of hepatocyte function in hormone- and amino acid-supplemented plasma

Understanding the metabolic and regulatory pathways of hepatocytes is important for biotechnological applications involving liver cells. Previous attempts to culture hepatocytes in plasma yielded poor functional results. Recently we reported that hormone (insulin and hydrocortisone) and amino acid supplementation reduces intracellular lipid accumulation and restores liver-specific function in hepatocytes exposed to heparinized human plasma. In the current study, we performed metabolic flux analysis (MFA) using a simplified metabolic network model of cultured hepatocytes to quantitively estimate the changes in lipid metabolism and relevant intracellular pathways in response to hormone and amino acid supplementation. The model accounts for the majority of central carbon and nitrogen metabolism, and assumes pseudo-steady-state with no metabolic futile cycles. We found that beta-oxidation and tricarboxylic acid (TCA) cycle fluxes were upregulated by both hormone and amino acid supplementation, thus enhancing the rate of lipid oxidation. Concomitantly, hormone and amino acid supplementation increased gluconeogenic fluxes. This, together with an increased rate of glucose clearance, caused an increase in predicted glycogen synthesis. Urea synthesis was primarily derived from ammonia and aspartate generated through transamination reactions, while exogenous ammonia removal accounted for only 3-6% of the urea nitrogen. Amino acid supplementation increased the endogenous synthesis of oxaloacetate, and in turn that of aspartate, a necessary substrate for the urea cycle. These findings from MFA provide cues as to which genes/pathways relevant to fatty acid oxidation, urea production, and gluconeogenesis may be upregulated by plasma supplementation, and are consistent with current knowledge of hepatic amino acid metabolism, which provides further credence to this approach for evaluating the metabolic state of hepatocytes under various environmental conditions.     

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.     

Pathway analysis of liver metabolism under stressed condition

Pathway analysis is a useful tool which reveals important metabolic network properties. However, the big challenge is to propose an objective function for estimating active pathways, which represent the actual state of network. In order to provide weight values for all possible pathways within the metabolic network, this study presents different approaches, considering the structural and physiological properties of the metabolic network, aiming at a unique decomposition of the flux vector into pathways. These methods were used to analyze the hepatic metabolism considering available data sets obtained from the perfused livers of fasted rats receiving burn injury. Utilizing unique decomposition techniques and different fluxes revealed that higher weights were always attributed to short pathways. Specific pathways, including pyruvate, glutamate and oxaloacetate pools, and urea production from arginine, were found to be important or essential in all methods and experimental conditions. Moreover the pathways, including serine production from glycine and conversion between acetoacetate and B—OH-butyrate, were assigned higher weights. Pathway analysis was also used to identify the main sources for the production of certain products in the hepatic metabolic network to gain a better understanding of the effects of burn injury on liver metabolism.     

Physiology of microbial cells and metabolic engineering

This review is devoted to the problems of the physiology and cell biology of microorganisms in relation to metabolic engineering. The latter is considered as a branch of fundamental and applied biotechnology aimed at controlling microbial metabolism by methods of genetic engineering and classical genetics and based on intimate knowledge of cell metabolism. Attention is also given to the problems associated with the metabolic limitation of microbial biosyntheses, analysis and control of metabolic fluxes, rigidity of metabolic pathways, the role of pleiotropic (global) regulatory systems in the control of metabolic fluxes, and prospects of physiological and evolutionary approaches in metabolic engineering.     

Physiology of microbial cell and metabolic engineering

This review is devoted to the problems of the physiology and cell biology of microorganisms in relation to metabolic engineering. The latter is considered as a branch of fundamental and applied biotechnology aimed at controlling microbial metabolism by methods of genetic engineering and classical genetics and based on intimate knowledge of cell metabolism. Attention is also given to the problems associated with the metabolic limitation of microbial biosyntheses, analysis and control of metabolic fluxes, rigidity of metabolic pathways, the role of pleiotropic (global) regulatory systems in the control of metabolic fluxes, and prospects of physiological and evolutionary approaches in metabolic engineering.