Development and validation of a general purpose linearization program for rigid aircraft models

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft

Ensemble Modeling for Aromatic Production in Escherichia coli

Ensemble Modeling (EM) is a recently developed method for metabolic modeling, particularly for utilizing the effect of enzyme tuning data on the production of a specific compound to refine the model. This approach is used here to investigate the production of aromatic products in Escherichia coli. Instead of using dynamic metabolite data to fit a model, the EM approach uses phenotypic data (effects of enzyme overexpression or knockouts on the steady state production rate) to screen possible models. These data are routinely generated during strain design. An ensemble of models is constructed that all reach the same steady state and are based on the same mechanistic framework at the elementary reaction level. The behavior of the models spans the kinetics allowable by thermodynamics. Then by using existing data from the literature for the overexpression of genes coding for transketolase (Tkt), transaldolase (Tal), and phosphoenolpyruvate synthase (Pps) to screen the ensemble, we arrive at a set of models that properly describes the known enzyme overexpression phenotypes. This subset of models becomes more predictive as additional data are used to refine the models. The final ensemble of models demonstrates the characteristic of the cell that Tkt is the first rate controlling step, and correctly predicts that only after Tkt is overexpressed does an increase in Pps increase the production rate of aromatics. This work demonstrates that EM is able to capture the result of enzyme overexpression on aromatic producing bacteria by successfully utilizing routinely generated enzyme tuning data to guide model learning

An analytic and systematic framework for estimating metabolic flux ratios from 13C tracer experiments

<p>Abstract</p> <p>Background</p> <p>Metabolic fluxes provide invaluable insight on the integrated response of a cell to environmental stimuli or genetic modifications. Current computational methods for estimating the metabolic fluxes from ¹³<it>C </it>isotopomer measurement data rely either on manual derivation of analytic equations constraining the fluxes or on the numerical solution of a highly nonlinear system of isotopomer balance equations. In the first approach, analytic equations have to be tediously derived for each organism, substrate or labelling pattern, while in the second approach, the global nature of an optimum solution is difficult to prove and comprehensive measurements of external fluxes to augment the ¹³<it>C </it>isotopomer data are typically needed.</p> <p>Results</p> <p>We present a novel analytic framework for estimating metabolic flux ratios in the cell from ¹³<it>C </it>isotopomer measurement data. In the presented framework, equation systems constraining the fluxes are derived automatically from the model of the metabolism of an organism. The framework is designed to be applicable with all metabolic network topologies, ¹³<it>C </it>isotopomer measurement techniques, substrates and substrate labelling patterns.</p> <p>By analyzing nuclear magnetic resonance (NMR) and mass spectrometry (MS) measurement data obtained from the experiments on glucose with the model micro-organisms <it>Bacillus subtilis </it>and <it>Saccharomyces cerevisiae </it>we show that our framework is able to automatically produce the flux ratios discovered so far by the domain experts with tedious manual analysis. Furthermore, we show by <it>in silico </it>calculability analysis that our framework can rapidly produce flux ratio equations – as well as predict when the flux ratios are unobtainable by linear means – also for substrates not related to glucose.</p> <p>Conclusion</p> <p>The core of ¹³<it>C </it>metabolic flux analysis framework introduced in this article constitutes of flow and independence analysis of metabolic fragments and techniques for manipulating isotopomer measurements with vector space techniques. These methods facilitate efficient, analytic computation of the ratios between the fluxes of pathways that converge to a common junction metabolite. The framework can been seen as a generalization and formalization of existing tradition for computing metabolic flux ratios where equations constraining flux ratios are manually derived, usually without explicitly showing the formal proofs of the validity of the equations.</p

13C-assisted metabolic flux analysis to investigate heterotrophic and mixotrophic metabolism in Cupriavidus necator H16

Introduction. Cupriavidus necator H16 is a gram-negative bacterium, capable of lithoautotrophic growth by utilizing hydrogen as an energy source and fixing carbon dioxide (CO2) through Calvin-Benson-Bassham (CBB) cycle. The potential to utilize synthesis gas (Syngas) and the prospects of rerouting carbon from polyhydroxybutyrate synthesis to value-added compounds makes C. necator an excellent chassis for industrial application. Objectives. In the context of lack of sufficient quantitative information of the metabolic pathways and to advance in rational metabolic engineering for optimized product synthesis in C. necator H16, we carried out a metabolic flux analysis based on steady-state 13C-labelling. Methods. In this study, steady-state carbon labelling experiments, using either D-[1-13C]fructose or [1,2-13C]glycerol, were undertaken to investigate the carbon flux through the central carbon metabolism in C. necator H16 under heterotrophic and mixotrophic growth conditions, respectively. Results. We found that the CBB cycle is active even under heterotrophic condition, and growth is indeed mixotrophic. While Entner-Doudoroff (ED) pathway is shown to be the major route for sugar degradation, tricarboxylic acid (TCA) cycle is highly active in mixotrophic condition. Enhanced flux is observed in reductive pentose phosphate pathway (redPPP) under the mixotrophic condition to supplement the precursor requirement for CBB cycle. The flux distribution was compared to the mRNA abundance of genes encoding enzymes involved in key enzymatic reactions of the central carbon metabolism. Conclusion. This study leads the way to establishing 13C-based quantitative fluxomics for rational pathway engineering in C. necator H16

Integrating Flux Balance Analysis into Kinetic Models to Decipher the Dynamic Metabolism of Shewanella oneidensis MR-1

Shewanella oneidensis MR-1 sequentially utilizes lactate and its waste products (pyruvate and acetate) during batch culture. To decipher MR-1 metabolism, we integrated genome-scale flux balance analysis (FBA) into a multiple-substrate Monod model to perform the dynamic flux balance analysis (dFBA). The dFBA employed a static optimization approach (SOA) by dividing the batch time into small intervals (i.e., ∼400 mini-FBAs), then the Monod model provided time-dependent inflow/outflow fluxes to constrain the mini-FBAs to profile the pseudo-steady-state fluxes in each time interval. The mini-FBAs used a dual-objective function (a weighted combination of “maximizing growth rate” and “minimizing overall flux”) to capture trade-offs between optimal growth and minimal enzyme usage. By fitting the experimental data, a bi-level optimization of dFBA revealed that the optimal weight in the dual-objective function was time-dependent: the objective function was constant in the early growth stage, while the functional weight of minimal enzyme usage increased significantly when lactate became scarce. The dFBA profiled biologically meaningful dynamic MR-1 metabolisms: 1. the oxidative TCA cycle fluxes increased initially and then decreased in the late growth stage; 2. fluxes in the pentose phosphate pathway and gluconeogenesis were stable in the exponential growth period; and 3. the glyoxylate shunt was up-regulated when acetate became the main carbon source for MR-1 growth

Phosphoglycerate dehydrogenase diverts glycolytic flux and contributes to oncogenesis

Most tumors exhibit increased glucose metabolism to lactate, however, the extent to which glucose-derived metabolic fluxes are used for alternative processes is poorly understood [1, 2]. Using a metabolomics approach with isotope labeling, we found that in some cancer cells a relatively large amount of glycolytic carbon is diverted into serine and glycine metabolism through phosphoglycerate dehydrogenase (PHGDH). An analysis of human cancers showed that PHGDH is recurrently amplified in a genomic region of focal copy number gain most commonly found in melanoma. Decreasing PHGDH expression impaired proliferation in amplified cell lines. Increased expression was also associated with breast cancer subtypes, and ectopic expression of PHGDH in mammary epithelial cells disrupted acinar morphogenesis and induced other phenotypic alterations that may predispose cells to transformation. Our findings show that the diversion of glycolytic flux into a specific alternate pathway can be selected during tumor development and may contribute to the pathogenesis of human cancer.National Institutes of Health (U.S.)National Cancer Institute (U.S.)Smith Family FoundationDamon Runyon Cancer Research FoundationBurroughs Wellcome Fun

Oxygen dependence of metabolic fluxes and energy generation of Saccharomyces cerevisiae CEN.PK113-1A

<p>Abstract</p> <p>Background</p> <p>The yeast <it>Saccharomyces cerevisiae </it>is able to adjust to external oxygen availability by utilizing both respirative and fermentative metabolic modes. Adjusting the metabolic mode involves alteration of the intracellular metabolic fluxes that are determined by the cell's multilevel regulatory network. Oxygen is a major determinant of the physiology of <it>S. cerevisiae </it>but understanding of the oxygen dependence of intracellular flux distributions is still scarce.</p> <p>Results</p> <p>Metabolic flux distributions of <it>S. cerevisiae </it>CEN.PK113-1A growing in glucose-limited chemostat cultures at a dilution rate of 0.1 h^-1with 20.9%, 2.8%, 1.0%, 0.5% or 0.0% O₂in the inlet gas were quantified by ¹³C-MFA. Metabolic flux ratios from fractional [U-¹³C]glucose labelling experiments were used to solve the underdetermined MFA system of central carbon metabolism of <it>S. cerevisiae</it>.</p> <p>While ethanol production was observed already in 2.8% oxygen, only minor differences in the flux distribution were observed, compared to fully aerobic conditions. However, in 1.0% and 0.5% oxygen the respiratory rate was severely restricted, resulting in progressively reduced fluxes through the TCA cycle and the direction of major fluxes to the fermentative pathway. A redistribution of fluxes was observed in all branching points of central carbon metabolism. Yet only when oxygen provision was reduced to 0.5%, was the biomass yield exceeded by the yields of ethanol and CO₂. Respirative ATP generation provided 59% of the ATP demand in fully aerobic conditions and still a substantial 25% in 0.5% oxygenation. An extensive redistribution of fluxes was observed in anaerobic conditions compared to all the aerobic conditions. Positive correlation between the transcriptional levels of metabolic enzymes and the corresponding fluxes in the different oxygenation conditions was found only in the respirative pathway.</p> <p>Conclusion</p> <p>¹³C-constrained MFA enabled quantitative determination of intracellular fluxes in conditions of different redox challenges without including redox cofactors in metabolite mass balances. A redistribution of fluxes was observed not only for respirative, respiro-fermentative and fermentative metabolisms, but also for cells grown with 2.8%, 1.0% and 0.5% oxygen. Although the cellular metabolism was respiro-fermentative in each of these low oxygen conditions, the actual amount of oxygen available resulted in different contributions through respirative and fermentative pathways.</p

Influence of band width on the scattered ion yield spectra of a He + Ion by resonant or quasi-resonant charge exchange neutralization

The influence of the band structure, especially the bandwidth, on the scattered ion yield spectra of a He+ ion by the resonant or quasi-resonant neutralization was theoretically examined using quantum rate equations. When calculating the scattered ion yield spectra of He+ to simulate the experimental data, we observed that the band structure, especially the bandwidth, had a strong influence on the spectra at relatively low incident He+ ion energies of less than several hundred eV. Through many simulations, it was determined that theoretical calculations that include bandwidth calculation can simulate or reproduce the experimentally observed spectra of He+-In, He+-Ga, and He+-Sn systems. In contrast, simulations not including bandwidth simulation could neither reproduce nor account for such spectra. Furthermore, the calculated ion survival probability (ISP) at low incident ion energies tended to decrease with increasing bandwidth. This decrease in ISP probably corresponds to the relatively small scattered ion yield usually observed at low incident ion energies. Theoretically, such a decrease indicates that a He+ ion with a low incident energy can be easily neutralized on the surface when the bandwidth is large