Mathematical modeling of living cell metabolism using the method of steady-state stoichiometric flux balance

This approach uses a set of algebraic linear equations for reaction rates (the method of steady-state stoichiometric flux balance) to model the purposeful metabolism of the living self-reproducing biochemical system (i.e. cell), which persists in steady-state growth. Linear programming (SIMPLEX method) is used to derive the solution for the model equations set (determining reaction rates which provide flux balance at given conditions). Here, we demonstrate the approach through the mathematical modeling of steady-state metabolism in Saccharomyces cerevisiae mitochondria.     

Evaluation of central metabolism based on a genomic database of<Emphasis Type="Italic">Synechocystis</Emphasis> PCC6803

Cyanobacteria produce industrially important secondary metabolites such as lipopeptide, oligosaccharide, fatty acid (esp. sulfolipid),etc. Among them,Synechocystis PCC6803 is the first strain with a publicly available full genome sequence, as of 1996, and is one of the most extensively studied photosynthetic microorganisms. Using this genomic information, the central metabolism ofSynechocystis PCC6803 was reconstructed, including photosynthesis, oxidative phosphorylation, glycolysis, pyruvate metabolism, TCA cycle, carbon fixation, and transport system. Each biochemical reaction was carefully incorporated into the model, taking into consideration the metabolite formula, stoichiometry, charge balance, and thermodynamic properties using information from genomic and metabolic databases as well as biochemical literature. The metabolic flux of the model was calculated using flux balance analysis according to its cultivation with various carbon sources. The results of simulation were in accordance with experimental data, which suggests that the central metabolism model can properly estimate the behavior ofSynechocystis PCC6803. This model would aid in the understanding of the whole cell metabolism ofSynechocystis PCC6803, the first effort of its kind for photosynthetic bacteria.     

Stoichiometry of formation of Ruhemann's purple in the ninhydrin reaction

The course and mechanism of reaction of ninhydrin with amines has both bioanalytical and bioorganic significance since the reaction is widely used for analysis of amino groups and serves as a model for several biochemical reactions that occur in metabolism of phosphonic acid derivatives, deamination, transamination, and transpeptidation. In many cases, e.g., with lysine, cysteine, proteins, the yield of the ninhydrin product, Ruhemann's purple, does not correspond exactly to the expected 1 equiv. per amino group. Possible reasons for this apparent nonideal stoichiometry include slow formation, side reactions, hydrolytic, oxidative, and photolytic instability, and interfering color. The origin and contributions of each of these factors are examined.     

Molecular and biochemical analysis of the enzymes of cysteine biosynthesis in the plant <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis>

Summary. Among the amino acids produced by plants cysteine plays a special role as a mediator between assimilatory sulfate reduction and provision of reduced sulfur for cell metabolism. Part of this characteristic feature is the presence of cysteine synthesis in plastids, mitochondria and cytosol. Plants are the major source of reduced sulfur for human and animal nutrition. Cysteine biosynthesis deserves special attention, since reduced sulfur is channelled from cysteine into many sulfur-containing compounds in food and feed. Recent investigations are reviewed that focus on structure and regulation of cysteine synthesis in the model plant Arabidopsis thaliana. These data indicate that cysteine synthesis is not just an intermediate reaction step but that it is part of a regulatory network that mediates between inorganic sulfur supply and the demand for reduced sulfur during plant growth and in response to environmental changes. Received December 3, 2001 Accepted December 21, 2001     

Bayesian flux balance analysis applied to a skeletal muscle metabolic model

In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.     

A genome‐scale metabolic network reconstruction of tomato (Solanum lycopersicum L.) and its application to photorespiratory metabolism

Tomato (Solanum lycopersicum L.) has been studied extensively due to its high economic value in the market, and high content in health‐promoting antioxidant compounds. Tomato is also considered as an excellent model organism for studying the development and metabolism of fleshy fruits. However, the growth, yield and fruit quality of tomatoes can be affected by drought stress, a common abiotic stress for tomato. To investigate the potential metabolic response of tomato plants to drought, we reconstructed iHY3410, a genome‐scale metabolic model of tomato leaf, and used this metabolic network to simulate tomato leaf metabolism. The resulting model includes 3410 genes and 2143 biochemical and transport reactions distributed across five intracellular organelles including cytosol, plastid, mitochondrion, peroxisome and vacuole. The model successfully described the known metabolic behaviour of tomato leaf under heterotrophic and phototrophic conditions. The in silico investigation of the metabolic characteristics for photorespiration and other relevant metabolic processes under drought stress suggested that: (i) the flux distributions through the mevalonate (MVA) pathway under drought were distinct from that under normal conditions; and (ii) the changes in fluxes through core metabolic pathways with varying flux ratio of RubisCO carboxylase to oxygenase may contribute to the adaptive stress response of plants. In addition, we improved on previous studies of reaction essentiality analysis for leaf metabolism by including potential alternative routes for compensating reaction knockouts. Altogether, the genome‐scale model provides a sound framework for investigating tomato metabolism and gives valuable insights into the functional consequences of abiotic stresses.     

Effect of amino acid supplementation on titer and glycosylation distribution in hybridoma cell cultures—Systems biology‐based interpretation using genome‐scale metabolic flux balance model and multivariate data analysis

Genome‐scale flux balance analysis (FBA) is a powerful systems biology tool to characterize intracellular reaction fluxes during cell cultures. FBA estimates intracellular reaction rates by optimizing an objective function, subject to the constraints of a metabolic model and media uptake/excretion rates. A dynamic extension to FBA, dynamic flux balance analysis (DFBA), can calculate intracellular reaction fluxes as they change during cell cultures. In a previous study by Read et al. (2013), a series of informed amino acid supplementation experiments were performed on twelve parallel murine hybridoma cell cultures, and this data was leveraged for further analysis (Read et al., Biotechnol Prog. 2013;29:745–753). In order to understand the effects of media changes on the model murine hybridoma cell line, a systems biology approach is applied in the current study. Dynamic flux balance analysis was performed using a genome‐scale mouse metabolic model, and multivariate data analysis was used for interpretation. The calculated reaction fluxes were examined using partial least squares and partial least squares discriminant analysis. The results indicate media supplementation increases product yield because it raises nutrient levels extending the growth phase, and the increased cell density allows for greater culture performance. At the same time, the directed supplementation does not change the overall metabolism of the cells. This supports the conclusion that product quality, as measured by glycoform assays, remains unchanged because the metabolism remains in a similar state. Additionally, the DFBA shows that metabolic state varies more at the beginning of the culture but less by the middle of the growth phase, possibly due to stress on the cells during inoculation. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1163–1173, 2016     

Formate as the main branch point for methylotrophic metabolism in Methylobacterium extorquens AM1

In serine cycle methylotrophs, methylene tetrahydrofolate (H4F) is the entry point of reduced one-carbon compounds into the serine cycle for carbon assimilation during methylotrophic metabolism. In these bacteria, two routes are possible for generating methylene H4F from formaldehyde during methylotrophic growth: one involving the reaction of formaldehyde with H4F to generate methylene H4F and the other involving conversion of formaldehyde to formate via methylene tetrahydromethanopterin-dependent enzymes and conversion of formate to methylene H4F via H4F-dependent enzymes. Evidence has suggested that the direct condensation reaction is the main source of methylene H4F during methylotrophic metabolism. However, mutants lacking enzymes that interconvert methylene H4F and formate are unable to grow on methanol, suggesting that this route for methylene H4F synthesis should have a significant role in biomass production during methylotrophic metabolism. This problem was investigated in Methylobacterium extorquens AM1. Evidence was obtained suggesting that the existing deuterium assay might overestimate the flux through the direct condensation reaction. To test this possibility, it was shown that only minor assimilation into biomass occurred in mutants lacking the methylene H4F synthesis pathway through formate. These results suggested that the methylene H4F synthesis pathway through formate dominates assimilatory flux. A revised kinetic model was used to validate this possibility, showing that physiologically plausible parameters in this model can account for the metabolic fluxes observed in vivo. These results all support the suggestion that formate, not formaldehyde, is the main branch point for methylotrophic metabolism in M. extorquens AM1.     

Reaction–diffusion constraints in living tissue: Effectiveness factors in skeletal muscle design

A mathematical model was developed to analyze the effects of intracellular diffusion of O₂ and high‐energy phosphate metabolites on aerobic energy metabolism in skeletal muscle. We tested the hypotheses that in a range of muscle fibers from different species (1) aerobic metabolism was not diffusion limited and (2) that fibers had a combination of rate and fiber size that placed them at the brink of substantial diffusion limitation. A simplified chemical reaction rate law for mitochondrial oxidative phosphorylation was developed utilizing a published detailed model of isolated mitochondrial function. This rate law was then used as a boundary condition in a reaction–diffusion model that was further simplified using the volume averaging method and solved to determine the rates of oxidative phosphorylation as functions of the volume fraction of mitochondria, the size of the muscle cell, and the amount of oxygen delivered by the capillaries. The effectiveness factor, which is the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitations, defined the regions where intracellular diffusion of metabolites and O₂ may limit aerobic metabolism in both very small, highly oxidative fibers as well as in larger fibers with lower aerobic capacity. Comparison of model analysis with experimental data revealed that none of the fibers was strongly limited by diffusion, as expected. However, while some fibers were near substantial diffusion limitation, most were well within the domain of reaction control of aerobic metabolic rate. This may constitute a safety factor in muscle that provides a level of protection from diffusion constraints under conditions such as hypoxia. Biotechnol. Bioeng. 2011; 108:104–115. © 2010 Wiley Periodicals, Inc.     

Metabolic flux analysis as a tool for the elucidation of the metabolism of neurotransmitter glutamate

A flux analysis model for the metabolism of neurotransmitter glutamate is constructed, in order to study functional aspects of its metabolism. This work is based on the potassium [K(+)] evoked neurotransmitter glutamate released, as measured in a series of experiments of superfused rat or mouse brain preparations. These measurements are combined with data reported, concerning the metabolism of glutamate and its precursors, glutamine and glucose in rat cerebral cells in vivo. The proposed stoichiometry of the specific reaction network renders the model solvable. The classification procedure establishes that the measured fluxes are all balanceable and all non-measured fluxes can be calculated. The system is well posed with a condition number of 7.8536. The results emphasize the importance of phosphate activated glutaminase and aspartate aminotransferase in the metabolism of neurotransmitter glutamate. Reported data on the rate of the malate-aspartate shuttle, as well as the anaplerotic flux of the glial pyruvate carboxylase reaction are in agreement with the estimations calculated from the proposed model.     

Fehlermöglichkeiten der Gelöstsauerstoffmessung beim Betrieb von Bioreaktoren

A review of errors, which can influence the measured data of electrochemical oxygen sensors (OS) in fermentation technique is presented. The specifities of various sensor constructions are pointed out. References are given for selection of sensors to application in fermenters. Influences on the measured values can take place by fermentation conditions, arrangement of sensors in the fermenter and composition of the fermentation broth. The oxygen measurement in the multi-phase system of fermentation fluids can cause a remarkable deviation of the measured values to the real ones. Practical hints are given for use, calibration and sterilization of OS. Restricting conditions for measurements with this sensors are enumerated.     

Whole-genome metabolic model of <Emphasis Type="Italic">Trichoderma reesei</Emphasis> built by comparative reconstruction

Background

Trichoderma reesei is one of the main sources of biomass-hydrolyzing enzymes for the biotechnology industry. There is a need for improving its enzyme production efficiency. The use of metabolic modeling for the simulation and prediction of this organism’s metabolism is potentially a valuable tool for improving its capabilities. An accurate metabolic model is needed to perform metabolic modeling analysis.

Results

A whole-genome metabolic model of T. reesei has been reconstructed together with metabolic models of 55 related species using the metabolic model reconstruction algorithm CoReCo. The previously published CoReCo method has been improved to obtain better quality models. The main improvements are the creation of a unified database of reactions and compounds and the use of reaction directions as constraints in the gap-filling step of the algorithm. In addition, the biomass composition of T. reesei has been measured experimentally to build and include a specific biomass equation in the model.

Conclusions

The improvements presented in this work on the CoReCo pipeline for metabolic model reconstruction resulted in higher-quality metabolic models compared with previous versions. A metabolic model of T. reesei has been created and is publicly available in the BIOMODELS database. The model contains a biomass equation, reaction boundaries and uptake/export reactions which make it ready for simulation. To validate the model, we dem1onstrate that the model is able to predict biomass production accurately and no stoichiometrically infeasible yields are detected. The new T. reesei model is ready to be used for simulations of protein production processes.

     

Regularity in the pattern of the metabolic reaction network

A basically new approach to the presentation of information on metabolism based on the regularity in the pattern of metabolic reaction network is discussed. The existence of such regularity is theoretically substantiated. The metabolic charts of carbohydrates, carboxylic acids and nitrogen-containing compounds with a regular structure are given. The possibilities of exploiting the regularity of the metabolic reaction network in the systematization of information relevant to the metabolism and prognostication of new information are considered.     

Sekundärstoffe – die Geheimwaffen der Pflanzen

Secondary metabolites Already 400 million years ago when land plants evolved, they probably produced secondary metabolites as means of defence against herbivores, microbes and competing plants. Secondary metabolites usually are bioactive agents, which can interfere with molecular targets in animals and microbes. Therefore, many plants and substances isolated from them can serve as valuable drugs in medicine and pharmacy. Some secondary metabolites also serve as signal compounds to attract pollinating animals and seed‐dispersing animals, but also for UV protection, as antioxidants or mobile nitrogen stores. Biology and evolution but also physiological and genetic bases of secondary metabolism are discussed in this overview.     

An integrative dynamic model of brain energy metabolism using <Emphasis Type="Italic">in vivo</Emphasis> neurochemical measurements

An integrative, systems approach to the modelling of brain energy metabolism is presented. Mechanisms such as glutamate cycling between neurons and astrocytes and glycogen storage in astrocytes have been implemented. A unique feature of the model is its calibration using in vivo data of brain glucose and lactate from freely moving rats under various stimuli. The model has been used to perform simulated perturbation experiments that show that glycogen breakdown in astrocytes is significantly activated during sensory (tail pinch) stimulation. This mechanism provides an additional input of energy substrate during high consumption phases. By way of validation, data from the perfusion of 50 μM propranolol in the rat brain was compared with the model outputs. Propranolol affects the glucose dynamics during stimulation, and this was accurately reproduced in the model by a reduction in the glycogen breakdown in astrocytes. The model’s predictive capacity was verified by using data from a sensory stimulation (restraint) that was not used for model calibration. Finally, a sensitivity analysis was conducted on the model parameters, this showed that the control of energy metabolism and transport processes are critical in the metabolic behaviour of cerebral tissue.