redLips: a comprehensive mechanistic model of the lipid metabolic network of yeast.

Over the last decades, yeast has become a key model organism for the study of lipid biochemistry. Because the regulation of lipids has been closely linked to various physiopathologies, the study of these biomolecules could lead to new diagnostics and treatments. Before the field can reach this point, however, sufficient tools for integrating and analyzing the ever-growing availability of lipidomics data will need to be developed. To this end, genome-scale models (GEMs) of metabolic networks are useful tools, though their large size and complexity introduces too much uncertainty in the accuracy of predicted outcomes. Ideally, therefore, a model for studying lipids would contain only the pathways required for the proper analysis of these biomolecules, but would not be an ad hoc reduction. We hereby present a metabolic model that focuses on lipid metabolism constructed through the integration of detailed lipid pathways into an already existing GEM of Saccharomyces cerevisiae. Our model was then systematically reduced around the subsystems defined by these pathways to provide a more manageable model size for complex studies. We show that this model is as consistent and inclusive as other yeast GEMs regarding the focus and detail on the lipid metabolism, and can be used as a scaffold for integrating lipidomics data to improve predictions in studies of lipid-related biological functions.

Thermodynamics-based Metabolite Sensitivity Analysis in metabolic networks.

The increasing availability of large metabolomics datasets enhances the need for computational methodologies that can organize the data in a way that can lead to the inference of meaningful relationships. Knowledge of the metabolic state of a cell and how it responds to various stimuli and extracellular conditions can offer significant insight in the regulatory functions and how to manipulate them. Constraint based methods, such as Flux Balance Analysis (FBA) and Thermodynamics-based flux analysis (TFA), are commonly used to estimate the flow of metabolites through genome-wide metabolic networks, making it possible to identify the ranges of flux values that are consistent with the studied physiological and thermodynamic conditions. However, unless key intracellular fluxes and metabolite concentrations are known, constraint-based models lead to underdetermined problem formulations. This lack of information propagates as uncertainty in the estimation of fluxes and basic reaction properties such as the determination of reaction directionalities. Therefore, knowledge of which metabolites, if measured, would contribute the most to reducing this uncertainty can significantly improve our ability to define the internal state of the cell. In the present work we combine constraint based modeling, Design of Experiments (DoE) and Global Sensitivity Analysis (GSA) into the Thermodynamics-based Metabolite Sensitivity Analysis (TMSA) method. TMSA ranks metabolites comprising a metabolic network based on their ability to constrain the gamut of possible solutions to a limited, thermodynamically consistent set of internal states. TMSA is modular and can be applied to a single reaction, a metabolic pathway or an entire metabolic network. This is, to our knowledge, the first attempt to use metabolic modeling in order to provide a significance ranking of metabolites to guide experimental measurements.

Molecular thermodynamics of metabolism: hydration quantities and the equation-of-state approach.

The present work is part of a series of papers aiming at a thorough understanding of the thermodynamics of metabolism over a broad range of external conditions. The focus here is on the systematic study of solvation/hydration of a variety of fluids via an equation-of-state approach. This approach permits the study not only of the overall free energy, enthalpy or entropy of hydration but also their key components from cavitation, charging, and solute conformations/solvent restructuring contributions. These latter components shed light into the mechanism of hydration and contribute to our understanding of solvation phenomena at remote conditions of temperature and pressure. Hydrogen bonding is of central importance in this respect and is handled via the partial solvation parameter (PSP) approach. The developed solvation model is used for the estimation of the hydration quantities of key metabolites. The challenges and perspectives of this equation-of-state approach are critically discussed.

Molecular thermodynamics of metabolism: quantum thermochemical calculations for key metabolites.

The present work is the first of a series of papers aiming at a coherent and unified development of the thermodynamics of metabolism and the rationalization of feasibility analysis of metabolic pathways. The focus in this part is on high-level quantum chemical calculations of the thermochemical quantities of relatively heavy metabolites such as amino acids/oligopeptides, nucleosides, saccharides and their derivatives in the ideal gas state. The results of this study will be combined with the corresponding hydration/solvation results in subsequent parts of this work in order to derive the desired thermochemical quantities in aqueous solutions. The above metabolites exist in a vast conformational/isomerization space including rotational conformers, tautomers or anomers exhibiting often multiple or cooperative intramolecular hydrogen bonding. We examine the challenges posed by these features for the reliable estimation of thermochemical quantities. We discuss conformer search, conformer distribution and averaging processes. We further consider neutral metabolites as well as protonated and deprotonated metabolites. In addition to the traditional presentation of gas-phase acidities, basicities and proton affinities, we also examine heats and free energies of ionic species. We obtain simple linear relations between the thermochemical quantities of ions and the formation quantities of their neutral counterparts. Furthermore, we compare our calculations with reliable experimental measurements and predictive calculations from the literature, when available. Finally, we discuss the next steps and perspectives for this work.

Exploration of trade-offs between steady-state and dynamic properties in signaling cycles.

In the intracellular signaling networks that regulate important cell processes, the base pattern comprises the cycle of reversible phosphorylation of a protein, catalyzed by kinases and opposing phosphatases. Mathematical modeling and analysis have been used for gaining a better understanding of their functions and to capture the rules governing system behavior. Since biochemical parameters in signaling pathways are not easily accessible experimentally, it is necessary to explore possibilities for both steady-state and dynamic responses in these systems. While a number of studies have focused on analyzing these properties separately, it is necessary to take into account both of these responses simultaneously in order to be able to interpret a broader range of phenotypes. This paper investigates the trade-offs between optimal characteristics of both steady-state and dynamic responses. Following an inverse sensitivity analysis approach, we use systematic optimization methods to find the biochemical and biophysical parameters that simultaneously achieve optimal steady-state and dynamic performance. Remarkably, we find that even a single covalent modification cycle can simultaneously and robustly achieve high ultrasensitivity, high amplification and rapid signal transduction. We also find that the response rise and decay times can be modulated independently by varying the activating- and deactivating-enzyme-to-interconvertible-protein ratios.

A mathematical description of regulation of the G1-S transition of the mammalian cell cycle.

A mathematical model of regulation of the G1-S transition of the mammalian cell cycle has been formulated to organize available experimental molecular-level information in a systematic quantitative framework and to evaluate the ability of this manifestation of current knowledge to calculate correctly experimentally observed phenotypes. This model includes nine components and includes cyclin-cdk complexes, a pocket protein (pRb), a transcription factor (E2F-1), and a cyclin-cdk complex inhibitor. Simulation of the model equations yields stable oscillatory solutions corresponding to cell proliferation and asymptotically stable solutions corresponding to cell cycle arrest (quiescence). Bifurcation analysis of the system suggests changes in the intracellular concentrations of either E2F or cyclin E can activate cell proliferation and that co-overexpression of these molecules can prevent cell proliferation. Further analysis suggests that the amount of inhibitor necessary to prevent cell proliferation is independent of the concentrations of cyclin E and E2F and depends only on the equilibrium ratio between the bound and unbound forms of the inhibitor to the complex.

Proteomics: theoretical and experimental considerations.

Cellular engineering relies on the ability to decipher the genetic basis of various phenotypes. Emerging technologies for analyzing the biological function of the information encoded in the genome of particular organisms and/or tissues focus on the monitoring of transcription (mRNA) and translation (protein) processes. Elementary theoretical considerations presented in this article strongly suggest that a combination of mRNA and protein expression patterns should be simultaneously considered to fully develop a conceptual understanding of the functional architecture of genomes and gene networks. We propose a framework of experimental and mathematical methods for acquiring and analyzing quantitative proteomic information and discuss recent developments in proteome analytical technology.

Nonlinear metabolic control analysis.

Mathematical description of metabolic systems allows the calculation of the expected responses of metabolism to genetic modifications and the identification of the most promising targets for metabolic engineering. Metabolic control analysis (MCA) provides such a description in the form of quantitative indices (elasticities and control coefficients). These indices are determined by perturbation experiments around a reference steady state and, therefore, the predictive power of MCA is limited to small changes in the metabolic parameters. The modeling framework introduced here allows accurate description of the metabolic responses over wide range of changes in the metabolic parameters. The framework requires information about the MCA indices at the reference state and the corresponding values of the metabolic reaction rates, and employs simplifying assumptions about the reaction mechanisms. It is shown that knowledge of the intracellular metabolite concentrations is not necessary for the application of the framework. The performance of the methodology is illustrated using three elementary metabolic systems that display highly nonlinear responses to the modification in their parameters: an unbranched pathway, an interconvertible enzyme system, and a branched pathway subject to feedback inhibition.

Dynamical analysis of gene networks requires both mRNA and protein expression information.

One of the important goals of biology is to understand the relationship between DNA sequence information and nonlinear cellular responses. This relationship is central to the ability to effectively engineer cellular phenotypes, pathways, and characteristics. Expression arrays for monitoring total gene expression based on mRNA can provide quantitative insight into which gene or genes are on or off; but this information is insufficient to fully predict dynamic biological phenomena. Using nonlinear stability analysis we show that a combination of gene expression information at the message level and at the protein level is required to describe even simple models of gene networks. To help illustrate the need for such information we consider a mechanistic model for circadian rhythmicity which shows agreement with experimental observations when protein and mRNA information are included and we propose a framework for acquiring and analyzing experimental and mathematically derived information about gene networks.

Application of mathematical tools for metabolic design of microbial ethanol production.

Many attempts to engineer cellular metabolism have failed due to the complexity of cellular functions. Mathematical and computational methods are needed that can organize the available experimental information, and provide insight and guidance for successful metabolic engineering. Two such methods are reviewed here. Both methods employ a (log)linear kinetic model of metabolism that is constructed based on enzyme kinetics characteristics. The first method allows the description of the dynamic responses of metabolic systems subject to spatiotemporal variations in their parameters. The second method considers the product-oriented, constrained optimization of metabolic reaction networks using mixed-integer linear programming methods. The optimization framework is used in order to identify the combinations of the metabolic characteristics of the glycolytic enzymes from yeast and bacteria that will maximize ethanol production. The methods are also applied to the design of microbial ethanol production metabolism. The results of the calculations are in qualitative agreement with experimental data presented here. Experiments and calculations suggest that, in resting Escherichia coli cells, ethanol production and glucose uptake rates can be increased by 30% and 20%, respectively, by overexpression of a deregulated pyruvate kinase, while increase in phosphofructokinase expression levels has no effect on ethanol production and glucose uptake rates.

Metabolic consequences of phosphotransferase (PTS) mutation in a phenylalanine-producing recombinant Escherichia coli.

E. coli strain PPA305, which has a wild-type PTS system, and PPA316, which utilizes a proton-galactose symport system for glucose uptake, were used as host strains to harbor a phenylalanine overproduction plasmid pSY130-14 and to study the effects of using different glucose uptake systems on phenylalanine production. The non-PTS strain (PPA316/pSY130-14) produced much less phenylalanine, ranging from 0 to 67% of that produced by the PTS strain (PPA305/pSY130-14) depending on cultivation conditions used. The non-PTS strain PPA316/pSY130-14 had an intracellular PEP concentration only one-sixth that of the PTS strain, PPA305/pSY130-14. Additionally, PPA316/pSY130-14 had a substantially lower energy state in terms of the size of the pool of high-energy phosphate compounds and the magnitude of the pH difference across the cytoplasmic membrane. The non-PTS strain consumed oxygen at a higher rate, attained lower biomass concentration, and produced no acetate and phenylalanine during fermentation, suggesting more carbon was oxidized to CO2, most likely through the TCA cycle. Analysis of intracellular fluxes through the central carbon pathways was performed for each strain utilizing exponential phase data on extracellular components and assuming quasi-steady state for intermediate metabolites. The non-PTS strain had a higher flux through pyruvate kinase (PYK) and TCA cycle which, in agreement with the observed higher oxygen uptake rate, suggests that more carbon was oxidized to CO2 through the TCA cycle. Further analysis using rate expression data for PYK and NMR data for the intracellular metabolites identified the regulatory properties of PYK as the probable cause for lower intracellular PEP levels in PPA316/pSY130-14.

Metabolic fluxes in riboflavin-producing Bacillus subtilis.

The pentose phosphate pathway and the pyruvate shunt were identified as major pathways of glucose catabolism in a recombinant, riboflavin-producing Bacillus subtilis strain. Reactions connecting the tricarboxylic acid cycle and glycolysis, catalyzed by the malic enzyme and phosphoenolpyruvate carboxykinase, consume up to 23% of the metabolized glucose. These are examples of important fluxes that can be accessed explicitly using a novel analysis based on synergistic application of flux balancing and recently introduced techniques of fractional 13C-labeling and two-dimensional nuclear magnetic resonance spectroscopy. The overall flux distribution also suggests that B. subtilis metabolism has an unusually high capacity for the reoxidation of NADPH. Under the conditions investigated, riboflavin formation in B. subtilis is limited by the fluxes through the biosynthetic rather than the central carbon pathways, which suggests a focus for future metabolic engineering of this system.

Effects of spatiotemporal variations on metabolic control: approximate analysis using (log)linear kinetic models.

For many metabolic systems, available experimental data allow description of the system by elasticities and control coefficients. The availability of information of this kind motivated the development of a (log)linear kinetic model of metabolic systems that is completely and explicitly determined by this information. It is shown here that this model can accurately describe the dynamic responses of metabolic systems that exhibit strong nonlinearities. Based on the excellent approximation provided by the (log)linear model, a method is developed for the estimation of the performance of metabolic systems subject to spatiotemporal variations of the system parameters and the process operating conditions. The method suggests experiments that can quantify the effect of these variations. Study of a model glycolytic pathway illustrates the applicability and the usefulness of this framework. Time-average flux control coefficients are shown to vary strongly and not monotonically as the period of the external variations changes.

The AlkB monooxygenase of Pseudomonas oleovorans--synthesis, stability and level in recombinant Escherichia coli and the native host.

We have studied the synthesis and stability of the monooxygenase AlkB of Pseudomonas oleovorans in its natural host and in recombinant Escherichia coli. Three strains were investigated: the prototype strain P. oleovorans and the E. coli alk+ recombinants HB101 (pGEc47) and W3110 (pGEc47). Plasmid pGEc47 allows regulated expression of alkB and synthesis of active AlkB in E. coli. The E. coli strains were selected because E. coli HB101 (pGEc47) produces similar amounts of AlkB as P. oleovorans (1.5-2% of total cell protein), whereas E. coli W3110 (pGEc47) is able to make substantially (about fivefold) more AlkB. The AlkB synthesis and degradation rates in batch cultures of the three strains were determined by means of isotopic-labeling and immunological techniques. The mean specific AlkB synthesis rates in P. oleovorans, E. coli HB101 (pGEc47) and E. coli W3110 (pGEc47) were approximately 7, 12.5 and 45 microg x mg protein(-1) x h(-1), respectively. The half-lives of AlkB were estimated to be 80, 3 and 15 for P. oleovorans, E. coli HB101 (pGEc47) and E. coli W3110 (pGEc47), respectively. Thus, the intracellular AlkB level in each of the three strains was the result of their AlkB synthesis and degradation rates. The AlkB level during batch growth was modelled by means of experimentally derived parameters for AlkB synthesis and degradation, and showed good agreement with AlkB levels determined by means of immunoblotting in all strains investigated.

Optimization of regulatory architectures in metabolic reaction networks.

Successful biotechnological applications, such as amino acid production, have demonstrated significant improvement in bioprocess performance by genetic modifications of metabolic control architectures and enzyme expression levels. However, the stoichiometric complexity of metabolic pathways, along with their strongly nonlinear nature and regulatory coupling, necessitates the use of structured kinetic models to direct experimental applications and aid in quantitative understanding of cellular bioprocesses. A novel optimization problem is introduced here, the objective of which is to identify changes in the regulatory characteristics of pertinent enzymes and in their cellular content which should be implemented to optimize a particular metabolic process. The mathematical representation of the metabolic reaction networks used is the S-system representation, which at steady state is characterized by linear equations. Exploiting the linearity of the representation, we formulated the optimization problem as a mixed-integer linear programming (MILP) problem. This formulation allows the consideration of a regulatory superstructure that contains all alternative regulatory structures that can be considered for a given pathway. The proposed approach is developed and illustrated using a simple linear pathway. Application of the framework on a complicated pathway-namely, the xanthine monophosphate (XMP) and guanosine monophosphate (GMP) synthesis pathway-identified the modification of the regulatory architecture that, along with changes in enzyme expression levels, can increase the XMP and GMP concentration by over 114 times the reference value, which is 50 times more than could be achieved by changes in enzyme expression levels only. (c) 1996 John Wiley & Sons, Inc.

MCA has more to say.

The recent development of two mathematical frameworks for the analysis and design of metabolic systems is reviewed here. Both frameworks employ a (log)linear kinetic metabolic model that is constructed making direct, explicit use of the individual enzyme kinetic parameters which are a foundation of Metabolic Control Analysis (MCA) information. The first framework allows the description of the dynamic responses of metabolic systems subject to fluctuations in their parameters. The second framework considers the problem of optimizing the regulatory structure of metabolic networks. Both frameworks are powerful in enabling greater insights into metabolism based on MCA quantities.

Physiology and metabolic fluxes of wild-type and riboflavin-producing Bacillus subtilis.

Continuous cultivation in a glucose-limited chemostat was used to determine the growth parameters of wild-type Bacillus subtilis and of a recombinant, riboflavin-producing strain. Maintenance coefficients of 0.45 and 0.66 mmol of glucose g-1 h-1 were determined for the wild-type and recombinant strains, respectively. However, the maximum molar growth yield of 82 to 85 g (cell dry weight)/mol of glucose was found to be almost identical in both strains. A nonlinear relationship between the specific riboflavin production rate and the dilution rate was observed, revealing a coupling of product formation and growth under strict substrate-limited conditions. Most prominently, riboflavin formation completely ceased at specific growth rates below 0.15 h-1. For molecular characterization of B. subtilis, the total amino acid composition of the wild type was experimentally determined and the complete building block requirements for biomass formation were derived. In particular, the murein sacculus was found to constitute approximately 9% of B. subtilis biomass, three- to fivefold more than in Escherichia coli. Estimation of intracellular metabolic fluxes by a refined mass balance approach revealed a substantial, growth rate-dependent flux through the oxidative branch of the pentose phosphate pathway. Furthermore, this flux is indicated to be increased in the strain engineered for riboflavin formation. Glucose catabolism at low growth rates with reduced biomass yields was supported mainly by the tricarboxylic acid cycle.

Inverse metabolic engineering: A strategy for directed genetic engineering of useful phenotypes.

The classical method of metabolic engineering, identifying a rate-determining step in a pathway and alleviating the bottleneck by enzyme overexpression, has motivated much research but has enjoyed only limited practical success. Intervention of other limiting steps, of counterbalancing regulation, and of unknown coupled pathways often confounds this direct approach. Here the concept of inverse metabolic engineering is codified and its application is illustrated with several examples. Inverse metabolic engineering means the elucidation of a metabolic engineering strategy by: first, identifying, constructing, or calculating a desired phenotype; second, determining the genetic or the particular environmental factors conferring that phenotype; and third, endowing that phenotype on another strain or organism by directed genetic or environmental manipulation. This paradigm has been successfully applied in several contexts, including elimination of growth factor requirements in mammalian cell culture and increasing the energetic efficiency of microaerobic bacterial respiration. (c) 1996 John Wiley & Sons, Inc.

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.

Effect of Vitreoscilla hemoglobin dosage on microaerobic Escherichia coli carbon and energy metabolism.

The amount of Vitreoscilla hemoglobin (VHb) expression was modulated over a broad range with an isopropyl-beta-D-thiogalactopyranoside- (IPTG-) inducible plasmid, and the consequences on microaerobic Escherichia coli physiology were examined in glucose fed-batch cultivations. The effect of IPTG induction on growth under oxygen-limited conditions was most visible during late fed-batch phase where the final cell density increased initially linearly with increasing VHb concentrations, ultimately saturating at a 2.7-fold increase over the VHb-negative (Vhb(-)) control. During the same growth phase, the specific excretions of fermentation by-products, acetate, ethanol, formate, lactate, and succinate from the culture expressing the highest amount of VHb were reduced by 25%, 49%, 68%, 72%, and 50%, respectively, relative to the VHb(-) control. During the exponential growth phase, VHb exerted a positive but smaller control on growth rate, growth yield, and respiration. Varying the amount of VHb from 0 to 3.8 mumol/g dry cell weight (DCW) increased the specific growth rate, the growth yield, and the oxygen consumption rate by 33%, 35%, and 60%, respectively. Increasing VHb concentration to 3.8 mumol/g DCW suppressed the rate of carbon dioxide evolution in the exponential phase by 30%. A metabolic flux distribution analysis incorporating data from these cultivations discloses that VHb(+) cells direct a larger fraction of glucose toward the pentose phosphate pathway and a smaller fraction of carbon through the tricarboxylic acid cycle from acetyl coenzyme A. The overall nicotinamide adenine dinucleotide [NAD(P)H] flux balance indicates that VHb-expressing cells generate a net NADH flux by the NADH/NADPH transhydrogenase while the VHb(-) cells yield a net NADPH flux under the same growth conditions. Flux distribution analysis also reveals that VHb(+) cells have a smaller adenosine triphosphate (ATP) synthesis rate from substrate-level phosphorylation but a larger overall ATP production rate under microaerobic conditions. The thermodynamic efficiency of growth, based on reducing equivalents generated per unit of biomass produced, is greater for VHb(+) cells. (c) 1996 John Wiley & Sons, Inc.